Reproducible kernel Nat.powMod tuning for lean4 PR 15167

README.md

Retuning kernel Nat.powMod

An optional experiment for leanprover/lean4#15167. Nothing here is registered with Lean's tests or CI. The implementation PR contains only the arithmetic change and its ordinary regression tests/benchmark.

Run

Build the PR checkout using its normal build instructions, then download this gist's files into a separate directory:

make -j$(nproc) -C /path/to/lean4/build/release
python3 tune.py --repo /path/to/lean4 --out sweep

Optional extended validation and cutoff diagnostics:

python3 tune.py --repo /path/to/lean4 --suite heldout --blocks 2 --out heldout
python3 tune.py --repo /path/to/lean4 --suite boundaries --out boundaries

The main sweep takes about two minutes on the recorded host. The optional validation took 7½ minutes; the boundary diagnostic took about 12 minutes with four blocks. See EVIDENCE.md for measured run times.

The published evidence.json also contains complete recorded runs (including source snapshots and the exploratory inputs). To inspect or rescore them:

python3 tune.py --restore evidence.json --run calibration --out recorded
python3 tune.py --summarize --out recorded
python3 alternatives.py recorded

Use a new output directory for each run. Python's standard library is the only additional dependency. --suite smoke --blocks 2 checks the setup quickly. --summarize --out sweep regenerates a summary without repeating measurements.

Current Lean comparison

To reproduce the first PR table, including the original upstream implementation:

python3 current.py --repo /path/to/lean4 --ref 95f4f3c3fd6754b2d909ffc3c14bdd912c701e5f --out current

The git revision must be available in that checkout. The driver extracts its Nat.powMod definition verbatim into namespace Upstream, then measures all three implementations on the same kernel and deterministic base-2 inputs. Elaboration is outside the timer. It preserves the tuning harness's independent references, rejection controls, uniform preparation, fresh kernel checks and four adjacent comparisons per candidate. Both candidates are paired with binary. It takes about 36 seconds on the recorded host, with a 180-second process limit. The complete run is archived as current. Its summary uses per-case medians, then geometric means across the four exponent classes. Every sample is retained.

Larger operands

The optional bounded comparison uses dense full-length exponents at 8,192, 16,384, and 32,768 bits, for base 2 and coprime full-size bases; a second run adds 24,576 bits:

python3 tune.py --restore evidence.json --run exploration-large-interrupted --out large-inputs
python3 large.py --repo /path/to/lean4 --cases large-inputs/cases.json --out large
python3 tune.py --restore evidence.json --run large-mid --out mid-inputs
python3 large.py --repo /path/to/lean4 --cases mid-inputs/cases.json --out mid

large.py uses the same proof construction and candidate loops as Tune.lean. It runs two adjacent AB/BA blocks, with a fresh Lean process and kernel checker per arm. Successful samples time only the kernel check. Each process has a 30-second limit (editable with --seconds); a timeout includes imports and reference setup and is not an exact kernel timing. This diagnostic has no warmup or incorrect-result controls; the separate tuning harness retains those controls. The imported implementation still has to pass Kernel.check against the independently computed result. All successes and timeouts are recorded in samples.jsonl. The dense-only results are separate from the four-exponent-class averages in the main sweep. --cases accepts other recorded inputs; the driver selects their dense exponent cases.

The original four-block large sweep stalled before its first 32,768-bit timed pair and was interrupted. Its 24 completed checks, source snapshots, inputs, exit status, and short profile remain in exploration-large-interrupted. They are not pooled into the bounded comparison. The bounded results are in large and large-mid; a separate one-case diagnosis is in diagnostic-large-policy.

Read the evidence

The width columns compare the same verified window loop at different widths. The reference is this PR’s Nat.powMod.go, the binary accumulator adapted from PrimeCert, not the pre-PR well-founded-recursion implementation. policy checks the actual imported Nat.powMod, including its dispatch. Each call creates a fresh kernel checker and checks a modular-power equality; Python supplies the expected result and GMP independently cross-checks it before the timer. Incorrect-result controls must fail. Imports, JSON parsing, expression construction and controls are outside timing. These are modular-power checks, not whole primality certificates or native timings.

Every candidate is paired immediately with binary, alternating AB/BA order across four blocks by default (two for the validation command above). One untimed policy check prepares each case in every block uniformly; each timed check still has fresh kernel caches. All completed samples are retained. Linux runs automatically reserve and pin a CPU among copies of this runner; they do not wait for an idle host. Host load is recorded and never used to reject a sample.

summary.md shows ratios relative to binary (lower is better), aggregated with equal weight for dense, mixed, sparse and short exponents. It also lists the largest individual losses in separate ratio and absolute-millisecond rankings: a mean alone can hide an unacceptable regression. Close widths should be treated as a plateau, not evidence for an exact threshold. Dispatch adds noticeable overhead to submillisecond checks, so the imported policy can cost more than its selected loop. The “best fixed gm ms” column is a geometric mean across the row’s exponent classes, not a prediction for any one exponent. Results are specific to a kernel/toolchain and host; there is no promise of a universally optimal policy.

Choose again

The sweep uses SHAKE256-generated odd moduli and mixed exponents, plus dense, sparse and short exponent classes. Bases are tiny, near one word, half-size and full-size; they are adjusted to be coprime. Numeric inputs are always recorded, including any adjustment across a word boundary. The held-out suite uses different sizes, irregular moduli, and structured exponents. The boundary suite tests exact bases around the small-base cutoff (including non-coprime inputs), plus short and long exponents at large moduli. Run it after making a choice from the sweep rather than selecting only workloads that favor that choice.

Edit choose() and run --summarize to score a different policy from the same samples, without running Lean again. Its predicted cost excludes dispatch; rebuild Lean to measure the complete implementation. Edit the short configuration at the top of tune.py to change sizes, exponent patterns or candidate widths. --cases custom.json accepts an editable copy of cases.json, including exact numeric inputs and each case's candidate widths. For example, add bases on both sides of a proposed cutoff, try exponents around a proposed length cutoff, or give sparse exponents more weight in your analysis.

The default candidate cap is 65,536 intermediate bits, using the conservative bound modulus_bits * 2^width + reduced_base_bits * (2^width - 1). Excluded candidates are visible as dashes; raise the cap to investigate them. The default sweep is not exhaustive and its tables do not justify all exact cutoffs uniquely. Pick a simple policy near the measured minima, check its individual losses, then rebuild Lean with that policy and repeat the held-out comparison. The policy column will measure your implementation directly.

The small alternatives.py script generates the concise single-change table in EVIDENCE.md; edit its counterfactuals to test different compromises.

The output streams every completed sample to disk, including if interrupted, and includes all inputs and samples, runner snapshots, source hashes, Lean version, git revision and diff, CPU, host load and process exit status.

The archive preserves the exact runner and harness for every recorded run; some exploratory runs predate the final reporting and uniform-preparation features. Their source hashes intentionally differ. The final records are named calibration, validation, and large; exploratory data is never pooled with them.

Isolating dispatch-bound notation

python3 bounds.py --repo /path/to/lean4 --out /tmp/powmod-bounds-new compares the same dispatch tree with shifts, powers, and literal bounds. It uses four adjacent alternating-order blocks and direct kernel checking, independently of Meta's exponentiation threshold. Restore the recorded run with python3 tune.py --restore evidence.json --run bounds --out /tmp/powmod-bounds-recorded.

The binary accumulator comes from Bhavik Mehta's powModK in PrimeCert, developed with help from Joachim Breitner.

alternatives.py

#!/usr/bin/env python3
"""Compare editable, single-change policies on an archived run; no Lean execution.
Copyright (c) 2026 Lean FRO, LLC. Apache-2.0 (Lean repository LICENSE).
Usage: python3 alternatives.py recorded-directory
"""
import collections
import csv
import json
from pathlib import Path
import statistics
import sys
from tune import choose, gm

root = Path(sys.argv[1])
cases = json.loads((root / "cases.json").read_text())
rows = list(csv.DictReader((root / "samples.csv").open()))
meta = json.loads((root / "metadata.json").read_text())
expected = meta["blocks"] * 2 * sum(1+len(c["widths"]) for c in cases)
if meta["returncode"] != 0 or len(rows) != expected:
    raise SystemExit("Incomplete run: use tune.py --summarize to inspect it")
pairs = collections.defaultdict(dict)
for row in rows:
    key = (row["block"], row["case"], row["candidate"])
    pairs[key][row["arm"]] = int(row["kernel_ns"])
ratios = collections.defaultdict(list)
for (_, case, width), arms in pairs.items():
    ratios[case, width].append(arms[width] / arms["binary"])
medians = {key: statistics.median(xs) for key, xs in ratios.items()}

def cost(c, width):
    return 1.0 if width == 0 else medians[c["id"], f"w{width}"]

# The proposal is choose() in tune.py. Edit these counterfactuals freely.
variants = {
    "Small width 4": lambda c: 4 if c["m"] <= 2**64 else choose(c),
    "Small width 5": lambda c: 5 if c["m"] <= 2**64 else choose(c),
    "Small width 7": lambda c: 7 if c["m"] <= 2**64 else choose(c),
    "Width 6 through 128 bits": lambda c: 6 if c["m"] <= 2**128 else choose(c),
    "Width 3 in the 65–512 band": lambda c: 3 if 2**64 < c["m"] <= 2**512 else choose(c),
    "Width 4 in the 513–1024 band": lambda c: 4 if 2**512 < c["m"] <= 2**1024 else choose(c),
    "Width 2 in the 513–1024 band": lambda c: 2 if 2**512 < c["m"] <= 2**1024 else choose(c),
    "Binary for large bases through 2048": lambda c: 0 if 2**1024 < c["m"] <= 2**2048 and c["b"] >= 2**64 else choose(c),
    "Width 2 through 8192 for small bases": lambda c: 2 if 2**4096 < c["m"] <= 2**8192 and c["b"] < 2**64 else choose(c),
    "Small-base cutoff 128 bits": lambda c: (2 if c["m"] <= 2**4096 else 1) if c["m"] > 2**2048 and c["b"] < 2**128 else choose(c),
}
print("| Alternative | Affected cases | Mean cost / selected | Worst cost / selected |")
print("|---|---:|---:|---:|")
for name, select in variants.items():
    subset = [c for c in cases if select(c) != choose(c)]
    values = [cost(c, select(c)) / cost(c, choose(c)) for c in subset]
    if values:
        print(f"| {name} | {len(values)} | {gm(values):.3f} | {max(values):.3f} |")

bounds.py

from pathlib import Path
import json,re,subprocess,os,sys,platform,time,statistics,argparse
from tune import pin
parser=argparse.ArgumentParser(description='Compare shift, power and literal powMod dispatch bounds in the kernel.')
parser.add_argument('--repo',type=Path,required=True)
parser.add_argument('--out',type=Path,required=True)
args=parser.parse_args()
root=args.repo.resolve()
src=(root/'src/Init/Data/Nat/PowMod.lean').read_text()
a=src.index('def powMod (b e m : @& Nat)'); b=src.index('\nprivate theorem powMod.go_eq',a)
body=src[a:b].replace('def powMod (b e m : @& Nat)', '@[expose] noncomputable def boundsShift (b e m : Nat)').replace('powMod.go','Nat.powMod.go').replace('powMod.window','Nat.powMod.window')
pat=r'\(\(1 : Nat\)\.shiftLeft (\d+)\)'
power=re.sub(pat,lambda m:'((2 : Nat).pow '+m[1]+')',body.replace('boundsShift','boundsPower'))
literal=re.sub(pat,lambda m:str(1<<int(m[1])),body.replace('boundsShift','boundsLiteral'))
cases=[]
for bits in [255,2048,8192]:
 for base in ['small','full']:
  for exp in ['dense','short']:
   m=(1<<bits)-19; bv=2 if base=='small' else m//3; e=m-1 if exp=='dense' else 65537
   cases.append(dict(id=f'{bits}-{base}-{exp}',b=bv,e=e,m=m,expected=pow(bv,e,m),widths=[]))
prefix=(Path(__file__).with_name('Tune.lean').read_text())
a=prefix.index('def power'); b=prefix.index('-- Checking',a)
prefix=prefix[:a]+body+'\n'+power+'\n'+literal+'''\ndef power (c : Case) (width : Option Nat) : Expr :=
  mkApp3 (mkConst (match width with
    | none => ``boundsShift
    | some 0 => ``boundsShift
    | some 1 => ``boundsPower
    | some _ => ``boundsLiteral)) (mkRawNatLit c.b) (mkRawNatLit c.e) (mkRawNatLit c.m)

'''+prefix[b:]
prefix=prefix.replace('("policy", none) :: c.widths.map (fun w => (s!"w{w}", some w))','[("power", some 1), ("literal", some 2)]').replace('("binary", some 0)','("shift", some 0)')
out=args.out.resolve();out.mkdir(parents=True,exist_ok=False)
(out/'cases.json').write_text(json.dumps(cases))
p=root/'tests/elab_bench/powmod_bounds_work.lean';p.write_text(prefix)
cpu,lock=pin(); env=dict(os.environ,POWMOD_CASES=str(out/'cases.json'),POWMOD_SAMPLES=str(out/'samples.csv'),POWMOD_BLOCKS='4')
rec=dict(cpu=cpu,host=platform.node(),source=prefix,inputs=cases,load_before=os.getloadavg(),command=['tests/with_stage1_test_env.sh','tests/elab_bench/run_bench.sh',p.name])
t=time.time();r=subprocess.run(rec['command'],cwd=root,env=env,capture_output=True,text=True)
rec.update(stdout=r.stdout,stderr=r.stderr,returncode=r.returncode,elapsed=time.time()-t,load_after=os.getloadavg(),samples=(out/'samples.csv').read_text() if (out/'samples.csv').exists() else '')
(out/'record.json').write_text(json.dumps(rec,indent=2)+'\n');print(r.stdout,r.stderr)
if r.returncode:sys.exit(r.returncode)
data={}
for line in rec['samples'].splitlines():
 _,block,case,candidate,arm,ns=line.split(','); data.setdefault((case,candidate,arm),[]).append(int(ns)/1e6)
for key,vals in data.items():print(*key,round(statistics.median(vals),6))

current.py

#!/usr/bin/env python3
"""Compare the upstream definition, PrimeCert-style binary, and this PR.
Copyright (c) 2026 Lean FRO, LLC. Apache-2.0 (Lean repository LICENSE).
"""
import argparse, collections, csv, hashlib, json, os, pathlib, platform, statistics, subprocess, time
import tune

p = argparse.ArgumentParser(description=__doc__)
p.add_argument('--repo', type=pathlib.Path, required=True)
p.add_argument('--ref', required=True, help='upstream git revision providing Nat.powMod')
p.add_argument('--out', type=pathlib.Path, required=True)
a = p.parse_args(); repo = a.repo.resolve(); out = a.out.resolve()
out.mkdir(parents=True, exist_ok=False)
source = pathlib.Path(__file__).resolve().parent

def git(*args): return subprocess.check_output(['git','-C',str(repo),*args],text=True).strip()
upstream = git('show',a.ref+':src/Init/Data/Nat/PowMod.lean')+'\n'
start = upstream.index('@[expose, semireducible, extern "lean_nat_powmod"]')
stop = upstream.index('decreasing_by omega',start)+len('decreasing_by omega')
definition = '\nnamespace Upstream\n'+upstream[start:stop]+'\nend Upstream\n\n'
harness = (source/'Tune.lean').read_text().replace('open Lean\n','open Lean\n'+definition)
harness = harness.replace('  | some 0 =>','  | some 8 => return mkApp3 (mkConst ``Upstream.powMod) b e m\n  | some 0 =>')
harness = harness.replace('let candidates := ("policy", none) :: c.widths.map (fun w => (s!"w{w}", some w))',
                          'let candidates := [("current", some 8), ("policy", none)]')
harness = harness.replace('          let _ ← ofExceptKernelException checked\n          samples.putStrLn s!"SAMPLE,{block},{c.id},{name},{arm},{stop - start}"', '''          match checked with
          | .ok _ => samples.putStrLn s!"SAMPLE,{block},{c.id},{name},{arm},{stop - start}"
          | .error ex =>
            let message ← (ex.toMessageData {}).toString
            samples.putStrLn s!"FAIL,{block},{c.id},{name},{arm},{stop - start},{(Json.str message).compress}"''')
(out/'Current.lean').write_text(harness)
(out/'Upstream.lean').write_text(upstream)
for name in ['current.py','tune.py','Tune.lean']: (out/name).write_bytes((source/name).read_bytes())
inputs = tune.cases([32,64,256,512,1024,2048,4096,8192],'random',['small'])
for c in inputs: c.update(widths=[], expected=pow(c['b'],c['e'],c['m']))
(out/'cases.json').write_text(json.dumps(inputs,indent=2)+'\n')
cpu, lock = tune.pin(); lean = repo/'build/release/stage1/bin/lean'
meta = dict(cpu=cpu, blocks=4, host=platform.platform(), machine=platform.node(),
            upstream_commit=git('rev-parse',a.ref), commit=git('rev-parse','HEAD'), diff=git('diff','HEAD'),
            load_before=os.getloadavg(), command=os.sys.argv,
            lean=subprocess.check_output([str(lean),'--version'],text=True).strip(),
            source_sha256=hashlib.sha256((repo/'src/Init/Data/Nat/PowMod.lean').read_bytes()).hexdigest(),
            hashes={f.name:hashlib.sha256(f.read_bytes()).hexdigest() for f in out.iterdir() if f.is_file()})
(out/'metadata.json').write_text(json.dumps(meta,indent=2)+'\n')
env=dict(os.environ,POWMOD_CASES=str(out/'cases.json'),POWMOD_BLOCKS='4',POWMOD_SAMPLES=str(out/'raw.csv'))
env.pop('LEAN_PATH',None); began=time.monotonic()
with (out/'stdout.txt').open('w') as stdout,(out/'stderr.txt').open('w') as stderr:
    try:
        r=subprocess.run([str(lean),str(out/'Current.lean')],cwd=repo,env=env,stdout=stdout,stderr=stderr,timeout=180)
    except subprocess.TimeoutExpired:
        meta.update(returncode=None, timeout=True, elapsed_seconds=time.monotonic()-began, load_after=os.getloadavg())
        (out/'metadata.json').write_text(json.dumps(meta,indent=2)+'\n')
        raise SystemExit(f'180-second process limit; every completed sample is retained in {out}')
meta.update(returncode=r.returncode,elapsed_seconds=time.monotonic()-began,load_after=os.getloadavg())
(out/'metadata.json').write_text(json.dumps(meta,indent=2)+'\n')
assert r.returncode==0 and 'COMPLETE' in (out/'stdout.txt').read_text(), (out/'stdout.txt').read_text()+(out/'stderr.txt').read_text()
rows=list(csv.reader((out/'raw.csv').open()))
assert len(rows)==512 and len({tuple(r[1:5]) for r in rows})==512
values=collections.defaultdict(list); failed=set()
for row in rows:
    status,block,case,candidate,arm,ns,*error=row
    if status=='FAIL': failed.add((case,arm))
    else: values[case,arm].append(int(ns)/1e6)
lines=['# Current upstream definition versus both alternatives','',
       'Same inputs/kernel; four adjacent pairs per candidate, alternating order. Each pair uses the binary reference.',
       'Upstream source is copied verbatim into namespace Upstream; definition elaboration is outside the timer.',
       'Geometric means across dense, mixed, sparse and short exponents, using per-case medians. All failures are retained.', '',
       '| Bits | Current Lean ms | PrimeCert-style binary ms | This PR ms |','|---:|---:|---:|---:|']
for bits in [32,64,256,512,1024,2048,4096,8192]:
    cs=[c for c in inputs if c['bits']==bits]; cells=[]
    for arm in ['current','binary','policy']:
        cells.append('kernel error' if any((c['id'],arm) in failed for c in cs) else
                     f"{tune.gm(statistics.median(values[c['id'],arm]) for c in cs):.3f}")
    lines.append(f"| {bits} | {' | '.join(cells)} |")
(out/'summary.md').write_text('\n'.join(lines)+'\n')
print(out/'summary.md')

EVIDENCE.md

Evidence for the window policy

The implementation uses windows of 6, 4, 3, and 2 bits through moduli 2^64, 2^512, 2^1024, and 2^2048. Above that, reduced bases below 2^64 use two bits through 2^4096, then one bit. Other bases use binary. There is no exponent-length cutoff.

Quick assessment

• The final calibration has 144 inputs and 7,296 timed kernel checks, with four adjacent AB/BA blocks. It took 122 seconds on an AMD EPYC 9455.
• Against the fastest measured loop for each individual input, the selected loops cost 1.032× on average; the complete imported dispatch costs 1.067×. These are equal-case-weight geometric means, not worst-case bounds.
• The independent final validation uses different operand sizes, modulus seeds, and exponent patterns, with two adjacent AB/BA blocks. It took 450 seconds; selected loops cost 1.046× the per-input best, and complete dispatch 1.103×. Its full loss tables are in the archived summary.md.
• The complete matrices and both relative and absolute loss tables are regenerated by tune.py --summarize; every timed sample is retained.

Can a nearby choice do better?

This table is generated by python3 alternatives.py recorded after restoring and summarizing the calibration run. It compares loop choices on the affected inputs only. Less than 1 favors the alternative. Dispatch costs are excluded from these counterfactuals and measured separately by the harness.

Alternative	Affected cases	Mean cost / selected	Worst cost / selected
Small width 4	32	1.175	1.296
Small width 5	32	1.055	1.125
Small width 7	32	1.108	1.469
Width 6 through 128 bits	16	1.153	1.506
Width 3 in the 65–512 band	48	1.093	1.285
Width 4 in the 513–1024 band	16	1.319	1.629
Width 2 in the 513–1024 band	16	1.023	1.127
Binary for large bases through 2048	8	1.282	1.456
Width 2 through 8192 for small bases	8	1.102	1.195
Small-base cutoff 128 bits	4	0.789	0.938

This supports the window-width sequence as a compact compromise. It does not identify uniquely optimal numerical cutoffs. In particular, widths 2 and 3 are close around 1024 bits; the best 3/4-bit transition depends on base size. The exact small-base cutoff is conservative: widening it improves the four calibration inputs shown above. The cutoff suite lets reviewers examine that choice separately; there is insufficient evidence here to call 2^64 optimal.

The two-bit range includes all bases through 2048 bits because binary loses there across the calibration and earlier validation suites. One-bit windows above 4096 bits trade some sparse-exponent speed for faster dense/mixed powers. The absolute-loss table keeps that trade-off visible even when its ratio is modest.

Comparison with the current Lean definition

The pinned upstream definition at 95f4f3c3fd6754b2d909ffc3c14bdd912c701e5f uses well-founded recursion. current.py copies it verbatim into a separate namespace and compares it with the PrimeCert-style loop and this PR on the same kernel. All columns below come from one run, with the same base-2 inputs and four exponent classes as the first PR table.

Bits	Current Lean ms	PrimeCert-style binary ms	This PR ms
32	1.065	0.200	0.069
64	1.724	0.352	0.099
256	4.898	1.037	0.320
512	8.331	1.794	0.682
1024	15.099	3.259	1.543
2048	29.180	6.796	4.043
4096	61.621	16.917	12.855
8192	239.362	55.753	44.511

The run took 36 seconds. All 512 timed checks passed; negative-result controls also passed. Each candidate is paired with the binary reference in four alternating-order blocks. There are four samples per candidate and eight for the shared binary reference per input. The cells are geometric means of per-input medians across dense, mixed, sparse and short exponents. Definition elaboration, imports, references, controls and preparation are outside timing. The complete raw data, upstream source, generated harness and provenance are archived as current; the earlier calibration records remain unchanged.

Larger operands

The bounded large comparison measures the actual dispatch against binary at 8,192, 16,384, 24,576, and 32,768 bits, with dense full-length exponents, base 2 and coprime full-size bases. It uses the deterministic random input generator from calibration. There are no short exponents in these results.

Bits	Base 2: PrimeCert-style binary	Base 2: this PR	Full-size base: PrimeCert-style binary	Full-size base: this PR
8,192	269.6	177.6	284.6	268.3
16,384	1447.3	762.5	3124.8	3134.8
24,576	timeout	1935.7	timeout	timeout
32,768	timeout	3654.6	timeout	timeout

Successful cells report median kernel milliseconds from two adjacent AB/BA blocks. Each arm gets a fresh process and kernel checker, without warmup or incorrect-result controls in this diagnostic. Python-precomputed answers are cross-checked with GMP outside the timer, and the kernel must check each equality. Every timeout shown occurred in both blocks. The 30-second limit covers the whole process, including imports and reference setup; it is not an exact kernel duration. All 32 completed or timed-out invocations are retained across large and large-mid. The latter adds the intermediate 24,576-bit point after the 32,768-bit full-size-base processes timed out. These runs are not pooled with the main four-exponent-class calibration.

An initial four-block sweep was interrupted after 446 seconds of Lean execution, before its first 32,768-bit timed pair. All 24 completed timings, inputs, source snapshots and its interrupted status remain in exploration-large-interrupted. A one-second 49 Hz profile at the stall sampled 56.85% of cycles in expression equality's apply and 21.95% in its check_cache; this is a brief observation, not a diagnosis of the underlying cause. It occurred before a timed pair; no completed sample was removed. The profile and raw perf capture are archived. A separate policy-only diagnosis checked the 32,768-bit base-2 case in 3.562 s; it is archived separately and not pooled into the table.

This is finite scaling evidence, not a proof of kernel runtime complexity. For positive large moduli, the full-size-base branch is the same binary loop. The small-base branch uses one exponent bit per iteration and intermediates below m^2 * 2^64: at most twice the modulus bit length plus 64 bits. Neither the window width nor the ratio of intermediate bit length to modulus bit length grows without bound. Kernel expression handling can still dominate, as the larger cases show. The timeouts are part of the evidence, not numeric speedup estimates or grounds for claiming uniform dominance.

Reproduction and scope

Read README.md, run the default sweep, edit choose() or alternatives.py, and rescore the same samples. Rebuild Lean to measure a changed dispatch. The candidate loops come directly from the PR's exposed definitions. Python modular powering and the compiled GMP implementation cross-check each reference; fresh kernel checkers validate the actual equalities. Every arm also has an incorrect-result rejection control. Timing excludes those controls, input generation, imports, and expression construction.

The binary reference is the accumulator adapted from PrimeCert on this same kernel. The measurements cover modular powers; the pre-PR implementation and complete primality certificates are outside this comparison.

evidence.json contains complete inputs, raw samples, exact source snapshots, source hashes, toolchain versions, git revisions/diffs, CPU/load context and return status. calibration and validation are the final tuning records; large and large-mid hold the bounded scaling comparison. Other records preserve exploratory inputs and protocol development; they are not pooled with the final results. The structured exploratory run used a non-coprime m/3 base; final random full-size bases are coprime. All exclusions from the candidate matrix come from the declared intermediate-size cap, never timing.

The extended diagnostics include very slow binary reductions for some inputs. They are retained without exclusions; this experiment does not diagnose their cause or use their extreme ratios as typical speedups. On the recorded host, the four-block cutoff diagnostic took 728 seconds. The default sweep is the short entry point; the extended suites are optional and never run in CI.

Dispatch bounds: shifts versus powers and literals

All tuning above times kernel checks. Meta's exponentiation.threshold (256) is not a kernel limit; ordinary decide also reduces through Meta, whereas decide +kernel checks the decision proof in the kernel directly.

A separate four-block adjacent AB/BA comparison replaces only the dispatch bounds with Nat.pow 2 k or precomputed numerals. All 192 timed kernel checks passed, with wrong-result controls and every sample retained under bounds. Inputs cover 255, 2048 and 8192 bits, small/full-size bases, and dense/short exponents. The following are medians in milliseconds; shifts have their own adjacent baseline for each candidate.

Input	Shifts	Powers	Shifts	Literals
255 bits, base 2, dense	0.432	0.444	0.422	0.429
2048 bits, full base, dense	16.431	16.374	16.364	16.343
8192 bits, base 2, dense	164.863	168.705	168.661	167.902
8192 bits, base 2, exponent 65537	0.114	0.141	0.106	0.124
8192 bits, full base, dense	264.662	265.186	264.409	268.920

These measurements provide no reason to replace shifts for kernel performance. The larger dense computations are close; shifts are faster on the short-exponent cases. Supporting ordinary decide is incidental to this kernel choice. Run python3 bounds.py --repo /path/to/lean4 --out /tmp/powmod-bounds-new to repeat the comparison. This experiment does not change window widths.

Validation

The full Lean build and all 4,215 tests pass. The existing powMod benchmark also passes its full manual mode with coprime large bases. The artifact is outside the repository; no workflow or test target runs the tuning sweep.

Tune.lean

/-
Copyright (c) 2026 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the Lean repository LICENSE.
Authors: Kim Morrison
-/
module
import Lean
meta import Lean

/-! Standalone kernel powMod tuning. No declarations are added to the library.
The JSON cases and every timed sample are retained by tune.py. -/

open Lean

structure Case where
  id : String
  b : Nat
  e : Nat
  m : Nat
  widths : List Nat
  expected : Nat
  deriving FromJson

def power (c : Case) (width : Option Nat) : Expr := Id.run do
  let b := mkRawNatLit c.b
  let e := mkRawNatLit c.e
  let m := mkRawNatLit c.m
  let base := mkApp2 (mkConst ``Nat.mod) b m
  let fuel := mkApp (mkConst ``Nat.succ) e
  match width with
  | none => return mkApp3 (mkConst ``Nat.powMod) b e m
  | some 0 => return mkApp5 (mkConst ``Nat.powMod.go) m fuel base e (mkRawNatLit 1)
  | some w => return mkApp5 (mkConst ``Nat.powMod.window) base m (mkRawNatLit (2^w)) fuel e

-- Checking the identity application forces the supplied equality's endpoints
-- to agree; merely checking Eq.refl's inferred type would not test the power.
def proof (lhs : Expr) (value : Nat) : Expr :=
  let n := mkConst ``Nat
  let rhs := mkRawNatLit value
  let type := mkApp3 (mkConst ``Eq [.succ .zero]) n lhs rhs
  mkApp (mkLambda `h .default type (mkBVar 0))
    (mkApp2 (mkConst ``Eq.refl [.succ .zero]) n rhs)

run_cmd do
  let path ← IO.getEnv "POWMOD_CASES"
  let some path := path | throwError "set POWMOD_CASES to the generated JSON file"
  let cases : List Case ← ofExcept <| (Json.parse (← IO.FS.readFile path)).bind fromJson?
  let some output ← IO.getEnv "POWMOD_SAMPLES" | throwError "set POWMOD_SAMPLES"
  let samples ← IO.FS.Handle.mk output .write
  let blocks := ((← IO.getEnv "POWMOD_BLOCKS").getD "4").toNat!
  -- Drain asynchronous checking before creating the reusable import environment.
  let ready ← IO.mkRef (← getEnv).toKernelEnv
  let env := Environment.ofKernelEnv (← ready.get)
  for block in [:blocks] do
    for c in cases do
      -- The compiled GMP implementation supplies an untrusted reference outside
      -- the timer. Each fresh kernel checker must establish the equality itself.
      let value := Nat.powMod c.b c.e c.m
      if value != c.expected then throwError "GMP disagrees with Python reference"
      let candidates := ("policy", none) :: c.widths.map (fun w => (s!"w{w}", some w))
      if block == 0 then
        for width in some 0 :: candidates.map Prod.snd do
          let bad ← IO.mkRef (Kernel.check env {} (proof (power c width) (value + 1)))
          if (← bad.get).isOk then throwError "incorrect-result control was accepted"
      -- Equal preparation in every block; kernel caches are still fresh per call.
      let warm ← IO.mkRef (Kernel.check env {} (proof (power c none) value))
      let _ ← ofExceptKernelException (← warm.get)
      for (name, width) in candidates do
        let arms := [("binary", some 0), (name, width)]
        let arms := if block % 2 == 0 then arms else arms.reverse
        for (arm, width) in arms do
          -- References prevent the pure check from moving across the IO timer.
          let input ← IO.mkRef (env, proof (power c width) value)
          let (env, term) ← input.get
          let start ← IO.monoNanosNow
          let checked ← IO.mkRef (Kernel.check env {} term)
          let checked ← checked.get
          let stop ← IO.monoNanosNow
          let _ ← ofExceptKernelException checked
          samples.putStrLn s!"SAMPLE,{block},{c.id},{name},{arm},{stop - start}"
          samples.flush
  IO.println "COMPLETE"

evidence.json

{
  "calibration": {
    "Tune.lean": "/-\nCopyright (c) 2026 Lean FRO, LLC. All rights reserved.\nReleased under Apache 2.0 license as described in the Lean repository LICENSE.\nAuthors: Kim Morrison\n-/\nmodule\nimport Lean\nmeta import Lean\n\n/-! Standalone kernel powMod tuning. No declarations are added to the library.\nThe JSON cases and every timed sample are retained by tune.py. -/\n\nopen Lean\n\nstructure Case where\n  id : String\n  b : Nat\n  e : Nat\n  m : Nat\n  widths : List Nat\n  expected : Nat\n  deriving FromJson\n\ndef power (c : Case) (width : Option Nat) : Expr := Id.run do\n  let b := mkRawNatLit c.b\n  let e := mkRawNatLit c.e\n  let m := mkRawNatLit c.m\n  let base := mkApp2 (mkConst ``Nat.mod) b m\n  let fuel := mkApp (mkConst ``Nat.succ) e\n  match width with\n  | none => return mkApp3 (mkConst ``Nat.powMod) b e m\n  | some 0 => return mkApp5 (mkConst ``Nat.powMod.go) m fuel base e (mkRawNatLit 1)\n  | some w => return mkApp5 (mkConst ``Nat.powMod.window) base m (mkRawNatLit (2^w)) fuel e\n\n-- Checking the identity application forces the supplied equality's endpoints\n-- to agree; merely checking Eq.refl's inferred type would not test the power.\ndef proof (lhs : Expr) (value : Nat) : Expr :=\n  let n := mkConst ``Nat\n  let rhs := mkRawNatLit value\n  let type := mkApp3 (mkConst ``Eq [.succ .zero]) n lhs rhs\n  mkApp (mkLambda `h .default type (mkBVar 0))\n    (mkApp2 (mkConst ``Eq.refl [.succ .zero]) n rhs)\n\nrun_cmd do\n  let path \u2190 IO.getEnv \"POWMOD_CASES\"\n  let some path := path | throwError \"set POWMOD_CASES to the generated JSON file\"\n  let cases : List Case \u2190 ofExcept <| (Json.parse (\u2190 IO.FS.readFile path)).bind fromJson?\n  let some output \u2190 IO.getEnv \"POWMOD_SAMPLES\" | throwError \"set POWMOD_SAMPLES\"\n  let samples \u2190 IO.FS.Handle.mk output .write\n  let blocks := ((\u2190 IO.getEnv \"POWMOD_BLOCKS\").getD \"4\").toNat!\n  -- Drain asynchronous checking before creating the reusable import environment.\n  let ready \u2190 IO.mkRef (\u2190 getEnv).toKernelEnv\n  let env := Environment.ofKernelEnv (\u2190 ready.get)\n  for block in [:blocks] do\n    for c in cases do\n      -- The compiled GMP implementation supplies an untrusted reference outside\n      -- the timer. Each fresh kernel checker must establish the equality itself.\n      let value := Nat.powMod c.b c.e c.m\n      if value != c.expected then throwError \"GMP disagrees with Python reference\"\n      let candidates := (\"policy\", none) :: c.widths.map (fun w => (s!\"w{w}\", some w))\n      if block == 0 then\n        for width in some 0 :: candidates.map Prod.snd do\n          let bad \u2190 IO.mkRef (Kernel.check env {} (proof (power c width) (value + 1)))\n          if (\u2190 bad.get).isOk then throwError \"incorrect-result control was accepted\"\n      -- Equal preparation in every block; kernel caches are still fresh per call.\n      let warm \u2190 IO.mkRef (Kernel.check env {} (proof (power c none) value))\n      let _ \u2190 ofExceptKernelException (\u2190 warm.get)\n      for (name, width) in candidates do\n        let arms := [(\"binary\", some 0), (name, width)]\n        let arms := if block % 2 == 0 then arms else arms.reverse\n        for (arm, width) in arms do\n          -- References prevent the pure check from moving across the IO timer.\n          let input \u2190 IO.mkRef (env, proof (power c width) value)\n          let (env, term) \u2190 input.get\n          let start \u2190 IO.monoNanosNow\n          let checked \u2190 IO.mkRef (Kernel.check env {} term)\n          let checked \u2190 checked.get\n          let stop \u2190 IO.monoNanosNow\n          let _ \u2190 ofExceptKernelException checked\n          samples.putStrLn s!\"SAMPLE,{block},{c.id},{name},{arm},{stop - start}\"\n          samples.flush\n  IO.println \"COMPLETE\"\n",
    "tune.py": "#!/usr/bin/env python3\n\"\"\"Standalone powMod kernel tuning; Python standard library, no CI integration.\nCopyright (c) 2026 Lean FRO, LLC. Apache-2.0 (Lean repository LICENSE).\n\"\"\"\nimport argparse\nimport collections\nimport csv\nimport hashlib\nimport json\nimport math\nimport os\nfrom pathlib import Path\nimport platform\nimport statistics as stats\nimport subprocess\nimport sys\nimport tempfile\nimport time\n\n# These are the experiment, not the policy. Edit them or supply --cases JSON.\nBITS = [32, 64, 128, 256, 512, 1024, 2048, 4096, 8192]\nPATTERNS = [\"dense\", \"mixed\", \"sparse\", \"short\"]\nBASES = [\"small\", \"word\", \"half\", \"large\"]\nWIDTHS = list(range(1, 8))\nMAX_INTERMEDIATE_BITS = 65536  # excludes costly cells, explicitly recorded\n\n\ndef random_bits(n, label):\n    data = hashlib.shake_256(label.encode()).digest((n+7)//8)\n    return (int.from_bytes(data, \"little\") & ((1 << n)-1)) | (1 << (n-1))\n\n\ndef choose(c):\n    \"\"\"Editable policy: returns 0 for binary, otherwise the window width.\n    --summarize scores edits from existing samples; rebuild Lean to time dispatch.\n    \"\"\"\n    m, b = c[\"m\"], c[\"b\"] % c[\"m\"]\n    if m <= 1 << 64: return 6\n    if m <= 1 << 512: return 4\n    if m <= 1 << 1024: return 3\n    if m <= 1 << 2048: return 2\n    if b >= 1 << 64: return 0\n    if m <= 1 << 4096: return 2\n    return 1\n\n\ndef cases(bits, family, bases=BASES):\n    out = []\n    for n in bits:\n        seed = f\"powmod-{family}-{n}\"\n        if family == \"irregular\": m = ((1 << (n-1))*8//7 + 147) | 1\n        else: m = random_bits(n, seed+\"m\") | 1\n        used = set()\n        for base in bases:\n            b = (2 if base == \"small\" else (1 << 64)-1 if base == \"word\" else\n                 random_bits(n//2, seed+\"half\") if base == \"half\" else\n                 random_bits(n, seed+\"full\") if base == \"large\" else (1 << int(base))-1)\n            b %= m\n            while math.gcd(b, m) != 1:\n                b = (b+1) % m\n            if b in used: continue\n            used.add(b)\n            for pattern in PATTERNS:\n                e = {\"dense\": (1 << n)-1,\n                     \"mixed\": random_bits(n, seed+\"e\") if family == \"random\" else ((1 << n)-1)//3,\n                     \"sparse\": (1 << (n-1))+1,\n                     \"short\": random_bits(62, seed+\"short\") if family == \"random\" else 65537}[pattern]\n                widths = [w for w in WIDTHS\n                          if n*(1 << w) + b.bit_length()*((1 << w)-1) <= MAX_INTERMEDIATE_BITS]\n                out.append(dict(id=f\"{family}-{n}-{base}-{pattern}\", bits=n, family=family,\n                                base=base, pattern=pattern, b=b, e=e, m=m, widths=widths))\n    return out\n\n\ndef gm(xs):\n    return math.exp(stats.mean(math.log(x) for x in xs))\n\n\ndef summarize(out):\n    meta = json.loads((out / \"metadata.json\").read_text())\n    inputs = json.loads((out / \"cases.json\").read_text())\n    samples = []\n    raw = out / \"raw.csv\"\n    if not raw.exists(): raw = out / \"stdout.txt\"  # retained exploratory records\n    for line in raw.read_text().splitlines():\n        if line.startswith(\"SAMPLE,\"):\n            _, block, case, candidate, arm, ns = line.split(\",\")\n            samples.append((int(block), case, candidate, arm, int(ns)))\n    with (out / \"samples.csv\").open(\"w\") as f:\n        writer = csv.writer(f)\n        writer.writerow([\"block\", \"case\", \"candidate\", \"arm\", \"kernel_ns\"])\n        writer.writerows(samples)\n    expected = meta[\"blocks\"] * 2 * sum(1+len(c[\"widths\"]) for c in inputs)\n    if len(samples) != expected or meta[\"returncode\"] != 0 or \"COMPLETE\" not in (out/\"stdout.txt\").read_text():\n        raise SystemExit(f\"Incomplete run: retained {len(samples)}/{expected} samples in {out}\")\n    pairs = collections.defaultdict(dict)\n    for block, case, candidate, arm, ns in samples:\n        key = (block, case, candidate)\n        if arm in pairs[key]:\n            raise SystemExit(f\"duplicate sample: {key} {arm}\")\n        pairs[key][arm] = ns\n    ratios = collections.defaultdict(list)\n    absolute = collections.defaultdict(list)\n    for (block, case, candidate), arms in pairs.items():\n        ratios[case, candidate].append(arms[candidate] / arms[\"binary\"])\n        absolute[case, candidate].append(arms[candidate] / 1e6)\n        absolute[case, \"binary\"].append(arms[\"binary\"] / 1e6)\n    med = {key: stats.median(values) for key, values in ratios.items()}\n    lines = [\"# Kernel powMod tuning\", \"\", f\"{len(inputs)} cases; {len(samples)} retained checks; {meta['blocks']} adjacent AB/BA blocks.\",\n             \"\", \"Each cell is the geometric mean of per-case median paired ratios to the binary loop (lower is better).\",\n             \"Dense, mixed, sparse and short exponents receive equal weight. `policy` includes dispatch; width columns time the loops directly.\",\n             \"A dash means the intermediate-size cap excluded that width. No statistical equivalence or universal optimum is claimed.\", \"\",\n             \"| Modulus family/bits | Base (reduced bits) | best fixed gm ms | policy | \" + \" | \".join(f\"w{w}\" for w in WIDTHS) + \" | best fixed width |\",\n             \"|---|---|---:|---:|\" + \"---:|\"*len(WIDTHS) + \"---:|\"]\n    groups = collections.defaultdict(list)\n    for c in inputs:\n        groups[c[\"family\"], c[\"bits\"], c[\"base\"]].append(c)\n    for (family, bits, base), cs in groups.items():\n        values = {}\n        for name in [\"policy\"]+[f\"w{w}\" for w in WIDTHS]:\n            if all((c[\"id\"], name) in med for c in cs):\n                values[name] = gm(med[c[\"id\"], name] for c in cs)\n        best = min((k for k in values if k != \"policy\"), key=values.get)\n        lines.append(f\"| {family}/{bits} | {base} ({cs[0]['b'].bit_length()}) | {gm(stats.median(absolute[c['id'], best]) for c in cs):.3f} | \" + \" | \".join(f\"{values[k]:.3f}\" if k in values else \"\u2014\" for k in [\"policy\"]+[f\"w{w}\" for w in WIDTHS]) + f\" | {best} |\")\n    lines += [\"\", \"## Largest policy costs relative to the best measured loop\", \"\",\n              \"Per-case ratios retain exponent-specific losses that a mean can hide; the baseline is also eligible.\", \"\",\n              \"| Case | Policy ms | Policy/binary | Best loop | Policy/best |\", \"|---|---:|---:|---|---:|\"]\n    regrets = []\n    for c in inputs:\n        scores = {\"binary\": 1.0, **{f\"w{w}\": med[c[\"id\"], f\"w{w}\"] for w in c[\"widths\"]}}\n        best = min(scores, key=scores.get)\n        policy = med[c[\"id\"], \"policy\"]\n        regrets.append((policy/scores[best], c[\"id\"], best, policy))\n    for regret, case, best, policy in sorted(regrets, reverse=True)[:12]:\n        lines.append(f\"| {case} | {stats.median(absolute[case, 'policy']):.3f} | {policy:.3f} | {best} | {regret:.3f} |\")\n    lines += [\"\", \"## Largest absolute losses\", \"\",\n              \"Absolute differences use per-case medians; the baseline is eligible. All cases remain in the score.\", \"\",\n              \"| Case | Policy ms | Best ms | Extra ms |\", \"|---|---:|---:|---:|\"]\n    losses = []\n    for c in inputs:\n        policy_ms = stats.median(absolute[c[\"id\"], \"policy\"])\n        best_ms = min(stats.median(absolute[c[\"id\"], name]) for name in\n                      [\"binary\"]+[f\"w{w}\" for w in c[\"widths\"]])\n        losses.append((policy_ms-best_ms, c[\"id\"], policy_ms, best_ms))\n    for loss, case, current, best in sorted(losses, reverse=True)[:8]:\n        lines.append(f\"| {case} | {current:.3f} | {best:.3f} | {loss:.3f} |\")\n    predicted = []\n    actual = []\n    for c in inputs:\n        costs = [1.0]+[med[c[\"id\"], f\"w{w}\"] for w in c[\"widths\"]]\n        w = choose(c)\n        chosen = 1.0 if w == 0 else med.get((c[\"id\"], f\"w{w}\"))\n        if chosen is None: raise SystemExit(f\"policy selects unmeasured w{w} at {c['id']}\")\n        predicted.append(chosen/min(costs))\n        actual.append(med[c[\"id\"], \"policy\"]/min(costs))\n    lines += [\"\", f\"Geometric mean cost relative to the best measured loop: imported policy {gm(actual):.3f}; editable choose() prediction {gm(predicted):.3f}.\",\n              \"The prediction excludes dispatch. Every case has equal weight; minima are a hindsight comparison, not a statistical lower bound.\"]\n    lines += [\"\", f\"Elapsed wall time: {meta['elapsed_seconds']:.1f} s. CPU: {meta['cpu']} ({meta.get('cpu_model', 'model absent in this archived run')}). Host: {meta['host']}.\",\n              \"\", \"All samples, inputs, source snapshots, return status and toolchain metadata accompany this summary.\"]\n    (out / \"summary.md\").write_text(\"\\n\".join(lines)+\"\\n\")\n    print(out / \"summary.md\")\n\n\ndef pin():\n    \"\"\"Reserve an available affinity CPU among simultaneous copies of this runner.\"\"\"\n    if not hasattr(os, \"sched_getaffinity\"):\n        return None, None\n    import fcntl\n    allowed = sorted(os.sched_getaffinity(0))\n    start = os.getpid() % len(allowed)\n    for cpu in allowed[start:]+allowed[:start]:\n        lock = open(Path(tempfile.gettempdir()) / f\"powmod-tuning-{cpu}.lock\", \"a\")\n        try:\n            fcntl.flock(lock, fcntl.LOCK_EX | fcntl.LOCK_NB)\n        except BlockingIOError:\n            lock.close()\n            continue\n        os.sched_setaffinity(0, {cpu})\n        return cpu, lock\n    raise SystemExit(\"All affinity CPUs reserved by other tuning runners\")\n\n\ndef main():\n    parser = argparse.ArgumentParser(description=__doc__)\n    parser.add_argument(\"--restore\", type=Path, help=\"unpack one run from evidence.json\")\n    parser.add_argument(\"--run\", default=\"calibration\", help=\"archived run to restore\")\n    parser.add_argument(\"--repo\", type=Path, default=Path.cwd())\n    parser.add_argument(\"--out\", type=Path, required=True)\n    parser.add_argument(\"--blocks\", type=int, default=4)\n    parser.add_argument(\"--bits\", help=\"comma-separated sweep sizes\")\n    parser.add_argument(\"--cases\", type=Path, help=\"replace the generated corpus with this JSON\")\n    parser.add_argument(\"--suite\", choices=[\"sweep\", \"heldout\", \"boundaries\", \"smoke\"], default=\"sweep\")\n    parser.add_argument(\"--summarize\", action=\"store_true\")\n    args = parser.parse_args()\n    out = args.out.resolve()\n    if args.restore:\n        files = json.loads(args.restore.read_text())[args.run]\n        if any(Path(name).name != name for name in files): parser.error(\"invalid archive filename\")\n        out.mkdir(parents=True, exist_ok=False)\n        for name, content in files.items(): (out/name).write_text(content)\n        return\n    if args.summarize:\n        summarize(out)\n        return\n    if args.blocks < 2 or args.blocks % 2:\n        parser.error(\"--blocks must be positive and even (AB/BA)\")\n    repo = args.repo.resolve()\n    lean = repo / \"build/release/stage1/bin/lean\"\n    if not lean.is_file():\n        parser.error(\"build Lean first: make -j$(nproc) -C build/release\")\n    if args.cases:\n        inputs = json.loads(args.cases.read_text())\n    elif args.suite == \"smoke\":\n        inputs = cases([32], \"random\")[:1]\n    elif args.suite == \"heldout\":\n        inputs = cases([48, 80, 160, 320, 640, 1280, 2560, 5120, 10240], \"validation\")\n    elif args.suite == \"boundaries\":\n        inputs = cases([2048, 8192], \"irregular\", [\"32\", \"63\", \"64\", \"65\", \"96\", \"128\"])\n        for c in inputs:\n            c[\"b\"] = (1 << int(c[\"base\"]))-1  # exact bases, even when non-coprime\n        extra = []\n        for c in inputs:\n            if c[\"base\"] == \"64\":\n                for delta in [0, 1]:\n                    extra.append(dict(c, id=c[\"id\"]+f\"-plus{delta}\", base=f\"2^64+{delta}\", b=(1 << 64)+delta))\n        inputs += extra\n        for c in cases([4096, 8192], \"irregular\", [\"small\", \"large\"]):\n            if c[\"pattern\"] != \"dense\": continue\n            for bits, delta in [(32, -1), (63, -1), (64, -1), (64, 0), (64, 1), (65, -1), (96, -1)]:\n                extra_id = f\"{bits}{delta:+}\"\n                inputs.append(dict(c, id=c[\"id\"]+\"-e\"+extra_id, family=\"exponent-cutoff\",\n                                   pattern=\"e\"+extra_id, e=(1 << bits)+delta))\n    else:\n        inputs = cases([int(n) for n in args.bits.split(\",\")] if args.bits else BITS, \"random\")\n    if len({c[\"id\"] for c in inputs}) != len(inputs): parser.error(\"duplicate case IDs\")\n    for c in inputs:\n        if min(c[\"m\"], c[\"b\"]+1, c[\"e\"]+1) <= 0: parser.error(\"positive modulus and natural inputs required\")\n        c[\"expected\"] = pow(c[\"b\"], c[\"e\"], c[\"m\"])\n    out.mkdir(parents=True, exist_ok=False)\n    cpu, lock = pin()\n    source = Path(__file__).resolve().parent\n    for name in [\"tune.py\", \"Tune.lean\"]:\n        (out/name).write_bytes((source/name).read_bytes())\n    (out / \"cases.json\").write_text(json.dumps(inputs, indent=2)+\"\\n\")\n    def git(*xs):\n        return subprocess.check_output([\"git\", \"-C\", str(repo), *xs], text=True).strip()\n    meta = dict(host=platform.platform(), machine=platform.node(), cpu=cpu, returncode=None, blocks=args.blocks, suite=args.suite,\n                commit=git(\"rev-parse\", \"HEAD\"), diff=git(\"diff\", \"HEAD\"),\n                lean=subprocess.check_output([str(lean), \"--version\"], text=True).strip(),\n                load_before=os.getloadavg(), command=sys.argv,\n                hashes={n: hashlib.sha256((out/n).read_bytes()).hexdigest() for n in [\"tune.py\", \"Tune.lean\", \"cases.json\"]})\n    info = Path(\"/proc/cpuinfo\")\n    meta[\"cpu_model\"] = next((line.split(\":\", 1)[1].strip() for line in info.read_text().splitlines()\n                              if line.startswith(\"model name\")), \"unknown\") if info.exists() else platform.processor()\n    meta[\"source_sha256\"] = hashlib.sha256((repo/\"src/Init/Data/Nat/PowMod.lean\").read_bytes()).hexdigest()\n    (out/\"metadata.json\").write_text(json.dumps(meta, indent=2)+\"\\n\")\n    start = time.monotonic()\n    env = dict(os.environ, POWMOD_CASES=str(out/\"cases.json\"), POWMOD_BLOCKS=str(args.blocks), POWMOD_SAMPLES=str(out/\"raw.csv\"))\n    env.pop(\"LEAN_PATH\", None)\n    with (out/\"stdout.txt\").open(\"w\") as stdout, (out/\"stderr.txt\").open(\"w\") as stderr:\n        try:\n            result = subprocess.run([str(lean), str(out/\"Tune.lean\")], cwd=repo, env=env, stdout=stdout, stderr=stderr)\n            meta[\"returncode\"] = result.returncode\n        finally:\n            meta.update(elapsed_seconds=time.monotonic()-start, load_after=os.getloadavg())\n            (out/\"metadata.json\").write_text(json.dumps(meta, indent=2)+\"\\n\")\n    summarize(out)\n\n\nif __name__ == \"__main__\":\n    main()\n",
    "cases.json": "[\n  {\n    \"id\": \"random-32-small-dense\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"dense\",\n    \"b\": 2,\n    \"e\": 4294967295,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 298210271\n  },\n  {\n    \"id\": \"random-32-small-mixed\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"mixed\",\n    \"b\": 2,\n    \"e\": 3388031857,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 1469604554\n  },\n  {\n    \"id\": \"random-32-small-sparse\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"sparse\",\n    \"b\": 2,\n    \"e\": 2147483649,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 113785118\n  },\n  {\n    \"id\": \"random-32-small-short\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"short\",\n    \"b\": 2,\n    \"e\": 3453335119351565177,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 611462858\n  },\n  {\n    \"id\": \"random-32-word-dense\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"word\",\n    \"pattern\": \"dense\",\n    \"b\": 1833317047,\n    \"e\": 4294967295,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 682962307\n  },\n  {\n    \"id\": \"random-32-word-mixed\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"word\",\n    \"pattern\": \"mixed\",\n    \"b\": 1833317047,\n    \"e\": 3388031857,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 86608135\n  },\n  {\n    \"id\": \"random-32-word-sparse\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"word\",\n    \"pattern\": \"sparse\",\n    \"b\": 1833317047,\n    \"e\": 2147483649,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 3068587354\n  },\n  {\n    \"id\": \"random-32-word-short\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"word\",\n    \"pattern\": \"short\",\n    \"b\": 1833317047,\n    \"e\": 3453335119351565177,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 2199814249\n  },\n  {\n    \"id\": \"random-32-half-dense\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"half\",\n    \"pattern\": \"dense\",\n    \"b\": 51158,\n    \"e\": 4294967295,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 1924701494\n  },\n  {\n    \"id\": \"random-32-half-mixed\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"half\",\n    \"pattern\": \"mixed\",\n    \"b\": 51158,\n    \"e\": 3388031857,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 2326547369\n  },\n  {\n    \"id\": \"random-32-half-sparse\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"half\",\n    \"pattern\": \"sparse\",\n    \"b\": 51158,\n    \"e\": 2147483649,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 2232049769\n  },\n  {\n    \"id\": \"random-32-half-short\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"half\",\n    \"pattern\": \"short\",\n    \"b\": 51158,\n    \"e\": 3453335119351565177,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 177629825\n  },\n  {\n    \"id\": \"random-32-large-dense\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"large\",\n    \"pattern\": \"dense\",\n    \"b\": 2270674847,\n    \"e\": 4294967295,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 2057363099\n  },\n  {\n    \"id\": \"random-32-large-mixed\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"large\",\n    \"pattern\": \"mixed\",\n    \"b\": 2270674847,\n    \"e\": 3388031857,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 1845088166\n  },\n  {\n    \"id\": \"random-32-large-sparse\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"large\",\n    \"pattern\": \"sparse\",\n    \"b\": 2270674847,\n    \"e\": 2147483649,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 1805386049\n  },\n  {\n    \"id\": \"random-32-large-short\",\n    \"bits\": 32,\n    \"family\": \"random\",\n    \"base\": \"large\",\n    \"pattern\": \"short\",\n    \"b\": 2270674847,\n    \"e\": 3453335119351565177,\n    \"m\": 3185968773,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 3053598677\n  },\n  {\n    \"id\": \"random-64-small-dense\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"dense\",\n    \"b\": 2,\n    \"e\": 18446744073709551615,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 7787741074159324354\n  },\n  {\n    \"id\": \"random-64-small-mixed\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"mixed\",\n    \"b\": 2,\n    \"e\": 17195635114255293696,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 9346540696102477030\n  },\n  {\n    \"id\": \"random-64-small-sparse\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"sparse\",\n    \"b\": 2,\n    \"e\": 9223372036854775809,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 4150313204867199453\n  },\n  {\n    \"id\": \"random-64-small-short\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"short\",\n    \"b\": 2,\n    \"e\": 3489623376361201436,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 7620963171961664116\n  },\n  {\n    \"id\": \"random-64-word-dense\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"word\",\n    \"pattern\": \"dense\",\n    \"b\": 3888305213787659746,\n    \"e\": 18446744073709551615,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 7365893805957742155\n  },\n  {\n    \"id\": \"random-64-word-mixed\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"word\",\n    \"pattern\": \"mixed\",\n    \"b\": 3888305213787659746,\n    \"e\": 17195635114255293696,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 399528285442842252\n  },\n  {\n    \"id\": \"random-64-word-sparse\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"word\",\n    \"pattern\": \"sparse\",\n    \"b\": 3888305213787659746,\n    \"e\": 9223372036854775809,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 8638217953877917496\n  },\n  {\n    \"id\": \"random-64-word-short\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"word\",\n    \"pattern\": \"short\",\n    \"b\": 3888305213787659746,\n    \"e\": 3489623376361201436,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 10824604857133712143\n  },\n  {\n    \"id\": \"random-64-half-dense\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"half\",\n    \"pattern\": \"dense\",\n    \"b\": 2719777675,\n    \"e\": 18446744073709551615,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 10679639559225187121\n  },\n  {\n    \"id\": \"random-64-half-mixed\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"half\",\n    \"pattern\": \"mixed\",\n    \"b\": 2719777675,\n    \"e\": 17195635114255293696,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 9409318786288019138\n  },\n  {\n    \"id\": \"random-64-half-sparse\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"half\",\n    \"pattern\": \"sparse\",\n    \"b\": 2719777675,\n    \"e\": 9223372036854775809,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 1123000473237744782\n  },\n  {\n    \"id\": \"random-64-half-short\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"half\",\n    \"pattern\": \"short\",\n    \"b\": 2719777675,\n    \"e\": 3489623376361201436,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 4716623903004763531\n  },\n  {\n    \"id\": \"random-64-large-dense\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"large\",\n    \"pattern\": \"dense\",\n    \"b\": 13391429473496130783,\n    \"e\": 18446744073709551615,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 2058485278229109984\n  },\n  {\n    \"id\": \"random-64-large-mixed\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"large\",\n    \"pattern\": \"mixed\",\n    \"b\": 13391429473496130783,\n    \"e\": 17195635114255293696,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 11187420414301933000\n  },\n  {\n    \"id\": \"random-64-large-sparse\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"large\",\n    \"pattern\": \"sparse\",\n    \"b\": 13391429473496130783,\n    \"e\": 9223372036854775809,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 14251858132519309435\n  },\n  {\n    \"id\": \"random-64-large-short\",\n    \"bits\": 64,\n    \"family\": \"random\",\n    \"base\": \"large\",\n    \"pattern\": \"short\",\n    \"b\": 13391429473496130783,\n    \"e\": 3489623376361201436,\n    \"m\": 14558438859921891869,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 14400499563734803663\n  },\n  {\n    \"id\": \"random-128-small-dense\",\n    \"bits\": 128,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"dense\",\n    \"b\": 2,\n    \"e\": 340282366920938463463374607431768211455,\n    \"m\": 247311872516617791989976926280759660855,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 233540987375185750814440962793252395848\n  },\n  {\n    \"id\": \"random-128-small-mixed\",\n    \"bits\": 128,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"mixed\",\n    \"b\": 2,\n    \"e\": 334778882557094638869010816148266706842,\n    \"m\": 247311872516617791989976926280759660855,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 149620219472018859351763708281376909339\n  },\n  {\n    \"id\": \"random-128-small-sparse\",\n    \"bits\": 128,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"sparse\",\n    \"b\": 2,\n    \"e\": 170141183460469231731687303715884105729,\n    \"m\": 247311872516617791989976926280759660855,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 21717972613226025776876380036277547947\n  },\n  {\n    \"id\": \"random-128-small-short\",\n    \"bits\": 128,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"short\",\n    \"b\": 2,\n    \"e\": 3315693553117589487,\n    \"m\": 247311872516617791989976926280759660855,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 187460080568682128756404705037479879373\n  },\n  {\n    \"id\": \"random-128-word-dense\",\n    \"bits\": 128,\n    \"family\": \"random\",\n    \"base\": \"word\",\n    \"pattern\": \"dense\",\n    \"b\": 18446744073709551616,\n    \"e\": 340282366920938463463374607431768211455,\n    \"m\": 247311872516617791989976926280759660855,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 101867376625828173065459724167490955171\n  },\n  {\n    \"id\": \"random-128-word-mixed\",\n    \"bits\": 128,\n    \"family\": \"random\",\n    \"base\": \"word\",\n    \"pattern\": \"mixed\",\n    \"b\": 18446744073709551616,\n    \"e\": 334778882557094638869010816148266706842,\n    \"m\": 247311872516617791989976926280759660855,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 127528334518903959102886839253732968166\n  },\n  {\n    \"id\": \"random-128-word-sparse\",\n    \"bits\": 128,\n    \"family\": \"random\",\n    \"base\": \"word\",\n    \"pattern\": \"sparse\",\n    \"b\": 18446744073709551616,\n    \"e\": 170141183460469231731687303715884105729,\n    \"m\": 247311872516617791989976926280759660855,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 185620640354433801850415839325388180016\n  },\n  {\n    \"id\": \"random-128-word-short\",\n    \"bits\": 128,\n    \"family\": \"random\",\n    \"base\": \"word\",\n    \"pattern\": \"short\",\n    \"b\": 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\"b\": 18446744073709551615,\n    \"e\": 3119704998585386632,\n    \"m\": 65657640153235423722852188543580222634239642025450189244472322965922716957913,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 13706150259598774566909815672315858115482799992338982880485101630275630515819\n  },\n  {\n    \"id\": \"random-256-half-dense\",\n    \"bits\": 256,\n    \"family\": \"random\",\n    \"base\": \"half\",\n    \"pattern\": \"dense\",\n    \"b\": 187836005941688007263193831781892312159,\n    \"e\": 115792089237316195423570985008687907853269984665640564039457584007913129639935,\n    \"m\": 65657640153235423722852188543580222634239642025450189244472322965922716957913,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 57596866843698968370952085917075772470046875322911514986104610212897722750046\n  },\n  {\n    \"id\": \"random-256-half-mixed\",\n    \"bits\": 256,\n    \"family\": \"random\",\n    \"base\": \"half\",\n    \"pattern\": \"mixed\",\n    \"b\": 187836005941688007263193831781892312159,\n    \"e\": 107422134850879579002721418663346431452515123582491399067513743324480870385854,\n    \"m\": 65657640153235423722852188543580222634239642025450189244472322965922716957913,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 32370800034747524354997507360137619906074375510686313309142275964339036516719\n  },\n  {\n    \"id\": \"random-256-half-sparse\",\n    \"bits\": 256,\n    \"family\": \"random\",\n    \"base\": \"half\",\n    \"pattern\": \"sparse\",\n    \"b\": 187836005941688007263193831781892312159,\n    \"e\": 57896044618658097711785492504343953926634992332820282019728792003956564819969,\n    \"m\": 65657640153235423722852188543580222634239642025450189244472322965922716957913,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 8080506305329081866292612438639376744614017949149881981389214982649272871183\n  },\n  {\n    \"id\": \"random-256-half-short\",\n    \"bits\": 256,\n    \"family\": \"random\",\n    \"base\": \"half\",\n    \"pattern\": \"short\",\n    \"b\": 187836005941688007263193831781892312159,\n    \"e\": 3119704998585386632,\n    \"m\": 65657640153235423722852188543580222634239642025450189244472322965922716957913,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 29587096873561820305532931772318482372880973540147284965235990632889451395303\n  },\n  {\n    \"id\": \"random-256-large-dense\",\n    \"bits\": 256,\n    \"family\": \"random\",\n    \"base\": \"large\",\n    \"pattern\": \"dense\",\n    \"b\": 23994276031686177996831289809572292673800997799994985205807818945415500493002,\n    \"e\": 115792089237316195423570985008687907853269984665640564039457584007913129639935,\n    \"m\": 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\"expected\": 8398955794866536734535643830461130100721681650033722558210548976079534276225\n  },\n  {\n    \"id\": \"random-512-small-dense\",\n    \"bits\": 512,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"dense\",\n    \"b\": 2,\n    \"e\": 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084095,\n    \"m\": 9208776270225429168966145280213478009252787683019260012468157858011473551566126749777526691779521859705617281469849054019217838847350318934439905361171367,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6\n    ],\n    \"expected\": 1423527114460999686611895441299788128190189251847334010457011052124684371026602153987859330044091296453110293409782488175413904162438156964927086667526556\n  },\n  {\n    \"id\": \"random-512-small-mixed\",\n    \"bits\": 512,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"mixed\",\n    \"b\": 2,\n    \"e\": 13004802730578244346487693256819084818850732433044890913887573921435606053121930898007710263524964299898511235013984546044437964623388747456290491263738976,\n    \"m\": 9208776270225429168966145280213478009252787683019260012468157858011473551566126749777526691779521859705617281469849054019217838847350318934439905361171367,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6\n    ],\n    \"expected\": 6916916991245405526654384523365436081688879292318088578781233164785741668339768759445860770335390495560391862022459197623805043469829416607511742966696365\n  },\n  {\n    \"id\": \"random-512-small-sparse\",\n    \"bits\": 512,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"sparse\",\n    \"b\": 2,\n    \"e\": 6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243025426876941405973284973216824503042049,\n    \"m\": 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\"bits\": 512,\n    \"family\": \"random\",\n    \"base\": \"word\",\n    \"pattern\": \"mixed\",\n    \"b\": 18446744073709551615,\n    \"e\": 13004802730578244346487693256819084818850732433044890913887573921435606053121930898007710263524964299898511235013984546044437964623388747456290491263738976,\n    \"m\": 9208776270225429168966145280213478009252787683019260012468157858011473551566126749777526691779521859705617281469849054019217838847350318934439905361171367,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6\n    ],\n    \"expected\": 9184460452616122166880416380171804798606628665711569788732260221694590158508715912309457752173058794543292600725431078592815770804284897554084368450428415\n  },\n  {\n    \"id\": \"random-512-word-sparse\",\n    \"bits\": 512,\n    \"family\": \"random\",\n    \"base\": \"word\",\n    \"pattern\": \"sparse\",\n    \"b\": 18446744073709551615,\n    \"e\": 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},\n  {\n    \"id\": \"random-512-half-sparse\",\n    \"bits\": 512,\n    \"family\": \"random\",\n    \"base\": \"half\",\n    \"pattern\": \"sparse\",\n    \"b\": 78472400957395238816742342663555159377348963648149934648547460489475847593725,\n    \"e\": 6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243025426876941405973284973216824503042049,\n    \"m\": 9208776270225429168966145280213478009252787683019260012468157858011473551566126749777526691779521859705617281469849054019217838847350318934439905361171367,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6\n    ],\n    \"expected\": 7948008204253182023561144971836020677474005647439774027091215088758747055358865399157408899844523529177067817677802312038668800170551745057238729593885615\n  },\n  {\n    \"id\": \"random-512-half-short\",\n    \"bits\": 512,\n    \"family\": \"random\",\n    \"base\": \"half\",\n    \"pattern\": \"short\",\n    \"b\": 78472400957395238816742342663555159377348963648149934648547460489475847593725,\n    \"e\": 3640692154049845674,\n    \"m\": 9208776270225429168966145280213478009252787683019260012468157858011473551566126749777526691779521859705617281469849054019217838847350318934439905361171367,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6\n    ],\n    \"expected\": 6692115059900687851204698904205459379721884631243506954017976241308135853315493917244527352822879245331307040681817782142122855021052994077566592128738768\n  },\n  {\n    \"id\": \"random-512-large-dense\",\n    \"bits\": 512,\n    \"family\": \"random\",\n    \"base\": \"large\",\n    \"pattern\": \"dense\",\n    \"b\": 2522469174210676919266341033421788503162967190361797757543574956093062938395153195208233245627232873238651958068107626298649273576411908641457353305942125,\n    \"e\": 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13004802730578244346487693256819084818850732433044890913887573921435606053121930898007710263524964299898511235013984546044437964623388747456290491263738976,\n    \"m\": 9208776270225429168966145280213478009252787683019260012468157858011473551566126749777526691779521859705617281469849054019217838847350318934439905361171367,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6\n    ],\n    \"expected\": 6713730519797047112544043611731695548649846626149545401358085546112972484379977860909019120188277584809465858923679848921836121590002252542127465177973186\n  },\n  {\n    \"id\": \"random-512-large-sparse\",\n    \"bits\": 512,\n    \"family\": \"random\",\n    \"base\": \"large\",\n    \"pattern\": \"sparse\",\n    \"b\": 2522469174210676919266341033421788503162967190361797757543574956093062938395153195208233245627232873238651958068107626298649273576411908641457353305942125,\n    \"e\": 6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243025426876941405973284973216824503042049,\n    \"m\": 9208776270225429168966145280213478009252787683019260012468157858011473551566126749777526691779521859705617281469849054019217838847350318934439905361171367,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6\n    ],\n    \"expected\": 9199514072361261253841592277664711093955353762823913353961866269158607020518082591163293262459129084500740087127056049808430264845552558094484452802823526\n  },\n  {\n    \"id\": \"random-512-large-short\",\n    \"bits\": 512,\n    \"family\": \"random\",\n    \"base\": \"large\",\n    \"pattern\": \"short\",\n    \"b\": 2522469174210676919266341033421788503162967190361797757543574956093062938395153195208233245627232873238651958068107626298649273576411908641457353305942125,\n    \"e\": 3640692154049845674,\n    \"m\": 9208776270225429168966145280213478009252787683019260012468157858011473551566126749777526691779521859705617281469849054019217838847350318934439905361171367,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6\n    ],\n    \"expected\": 2696028868874051556533602156023413996511211938370534668117255941288254915957213988813901503455109361159620409308680785525604733203406133307487183491782985\n  },\n  {\n    \"id\": \"random-1024-small-dense\",\n    \"bits\": 1024,\n    \"family\": \"random\",\n    \"base\": \"small\",\n    \"pattern\": \"dense\",\n    \"b\": 2,\n    \"e\": 179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137215,\n    \"m\": 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 },\n  {\n    \"id\": \"random-8192-large-short\",\n    \"bits\": 8192,\n    \"family\": \"random\",\n    \"base\": \"large\",\n    \"pattern\": \"short\",\n    \"b\": 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   \"e\": 2556820411317466951,\n    \"m\": 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   \"widths\": [\n      1,\n      2\n    ],\n    \"expected\": 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 }\n]\n",
    "metadata.json": "{\n  \"host\": \"Linux-6.12.100-x86_64-with-glibc2.42\",\n  \"machine\": \"chungus2\",\n  \"cpu\": 83,\n  \"returncode\": 0,\n  \"blocks\": 4,\n  \"suite\": \"sweep\",\n  \"commit\": \"07d1fb7fe5788b8638559f84282df25f534dc972\",\n  \"diff\": \"diff --git a/tests/elab/lean_nat_powmod_module.lean b/tests/elab/lean_nat_powmod_module.lean\\nindex 4304d04ecf..320b3b280b 100644\\n--- a/tests/elab/lean_nat_powmod_module.lean\\n+++ b/tests/elab/lean_nat_powmod_module.lean\\n@@ -24,6 +24,6 @@ example : Nat.powMod 2 (Nat.shiftLeft 1 64 - 1) (Nat.shiftLeft 1 4096 + 1) =\\n     Nat.shiftLeft 1 4095 + 1 := by decide +kernel\\n example : Nat.powMod 2 (Nat.shiftLeft 1 64) (Nat.shiftLeft 1 4096 + 1) = 1 := by\\n   decide +kernel\\n--- A full-size exponent also reduces with the default kernel recursion limit.\\n+-- A full-size exponent also reduces without raising `maxRecDepth`.\\n example : Nat.powMod 2 (Nat.shiftLeft 1 5000) (Nat.shiftLeft 1 4096 + 1) = 1 := by\\n   decide +kernel\\ndiff --git a/tests/elab_bench/nat_powmod.lean b/tests/elab_bench/nat_powmod.lean\\nindex 4d0401c915..12b0b67e23 100644\\n--- a/tests/elab_bench/nat_powmod.lean\\n+++ b/tests/elab_bench/nat_powmod.lean\\n@@ -16,7 +16,9 @@ run_cmd do\\n     let m := 2 ^ bits - 19\\n     for largeBase in (if bench && bits \\u2265 2048 then [false, true] else [false]) do\\n       let e := m - 1\\n-      let base := if largeBase then m / 3 else 2\\n+      let mut base := if largeBase then m / 3 else 2\\n+      while Nat.gcd base m != 1 do\\n+        base := base + 1\\n       let result := Nat.powMod base e m\\n       let value := mkRawNatLit result\\n       let lhs := mkApp3 (mkConst ``Nat.powMod) (mkRawNatLit base) (mkRawNatLit e) (mkRawNatLit m)\",\n  \"lean\": \"Lean (version 4.35.0-pre, x86_64-unknown-linux-gnu, commit d8fba8cf2d8f6c02a32b99c3697c41ed49741929, Release)\",\n  \"load_before\": [\n    4.7265625,\n    11.26611328125,\n    11.86376953125\n  ],\n  \"command\": [\n    \"/tmp/lean-powmod-tuning-artifact/tune.py\",\n    \"--repo\",\n    \"/home/kim/worktrees/lean4/lean4-powmod-kernel\",\n    \"--out\",\n    \"/tmp/lean-powmod-tuning-reviewed-calibration\"\n  ],\n  \"hashes\": {\n    \"tune.py\": \"edb47a79d91d661496eeabb4328c8983d6a63ec207f4633178d8845b0460b73e\",\n    \"Tune.lean\": \"cc7d031fbc8cff1cb9e299c7f18b04e9a4a983eafc9159890b714cbe499e9dbc\",\n    \"cases.json\": \"10595ffd172351ce4c2f5badf822910051301e41ddc164248784ef29bb64cba7\"\n  },\n  \"cpu_model\": \"AMD EPYC 9455 48-Core Processor\",\n  \"source_sha256\": \"5c5811d01e69eef8769c2562b9edc4e82a8ff9822d5137b5b30f4e794383bc39\",\n  \"elapsed_seconds\": 122.29195254098158,\n  \"load_after\": [\n    5.0732421875,\n    9.2177734375,\n    11.0361328125\n  ]\n}\n",
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mall-dense,w4,binary,169511\nSAMPLE,2,random-32-small-dense,w4,w4,49534\nSAMPLE,2,random-32-small-dense,w5,binary,166677\nSAMPLE,2,random-32-small-dense,w5,w5,47510\nSAMPLE,2,random-32-small-dense,w6,binary,166607\nSAMPLE,2,random-32-small-dense,w6,w6,42052\nSAMPLE,2,random-32-small-dense,w7,binary,167649\nSAMPLE,2,random-32-small-dense,w7,w7,41782\nSAMPLE,2,random-32-small-mixed,policy,binary,164263\nSAMPLE,2,random-32-small-mixed,policy,policy,50876\nSAMPLE,2,random-32-small-mixed,w1,binary,161679\nSAMPLE,2,random-32-small-mixed,w1,w1,143523\nSAMPLE,2,random-32-small-mixed,w2,binary,161008\nSAMPLE,2,random-32-small-mixed,w2,w2,83053\nSAMPLE,2,random-32-small-mixed,w3,binary,163602\nSAMPLE,2,random-32-small-mixed,w3,w3,61691\nSAMPLE,2,random-32-small-mixed,w4,binary,161380\nSAMPLE,2,random-32-small-mixed,w4,w4,49704\nSAMPLE,2,random-32-small-mixed,w5,binary,158876\nSAMPLE,2,random-32-small-mixed,w5,w5,45347\nSAMPLE,2,random-32-small-mixed,w6,binary,159216\nSAMPLE,2,random-32-small-mixed,w6,w6,41722\nSAMPLE,2,random-32-small-mixed,w7,binary,160068\nSAMPLE,2,random-32-small-mixed,w7,w7,38367\nSAMPLE,2,random-32-small-sparse,policy,binary,161009\nSAMPLE,2,random-32-small-sparse,policy,policy,51056\nSAMPLE,2,random-32-small-sparse,w1,binary,156152\nSAMPLE,2,random-32-small-sparse,w1,w1,141019\nSAMPLE,2,random-32-small-sparse,w2,binary,154689\nSAMPLE,2,random-32-small-sparse,w2,w2,82583\nSAMPLE,2,random-32-small-sparse,w3,binary,154509\nSAMPLE,2,random-32-small-sparse,w3,w3,61201\nSAMPLE,2,random-32-small-sparse,w4,binary,157604\nSAMPLE,2,random-32-small-sparse,w4,w4,50986\nSAMPLE,2,random-32-small-sparse,w5,binary,152175\nSAMPLE,2,random-32-small-sparse,w5,w5,44776\nSAMPLE,2,random-32-small-sparse,w6,binary,153918\nSAMPLE,2,random-32-small-sparse,w6,w6,41171\nSAMPLE,2,random-32-small-sparse,w7,binary,154029\nSAMPLE,2,random-32-small-sparse,w7,w7,38988\nSAMPLE,2,random-32-small-short,policy,binary,313184\nSAMPLE,2,random-32-small-short,policy,policy,75613\nSAMPLE,2,random-32-small-short,w1,binary,304101\nSAMPLE,2,random-32-small-short,w1,w1,269730\nSAMPLE,2,random-32-small-short,w2,binary,318612\nSAMPLE,2,random-32-small-short,w2,w2,156111\nSAMPLE,2,random-32-small-short,w3,binary,305814\nSAMPLE,2,random-32-small-short,w3,w3,106398\nSAMPLE,2,random-32-small-short,w4,binary,306514\nSAMPLE,2,random-32-small-short,w4,w4,85126\nSAMPLE,2,random-32-small-short,w5,binary,304322\nSAMPLE,2,random-32-small-short,w5,w5,75882\nSAMPLE,2,random-32-small-short,w6,binary,302328\nSAMPLE,2,random-32-small-short,w6,w6,66779\nSAMPLE,2,random-32-small-short,w7,binary,306574\nSAMPLE,2,random-32-small-short,w7,w7,62883\nSAMPLE,2,random-32-word-dense,policy,binary,170282\nSAMPLE,2,random-32-word-dense,policy,policy,54781\nSAMPLE,2,random-32-word-dense,w1,binary,167018\nSAMPLE,2,random-32-word-dense,w1,w1,151335\nSAMPLE,2,random-32-word-dense,w2,binary,169191\nSAMPLE,2,random-32-word-dense,w2,w2,84205\nSAMPLE,2,random-32-word-dense,w3,binary,165235\nSAMPLE,2,random-32-word-dense,w3,w3,62623\nSAMPLE,2,random-32-word-dense,w4,binary,165365\nSAMPLE,2,random-32-word-dense,w4,w4,50866\nSAMPLE,2,random-32-word-dense,w5,binary,163432\nSAMPLE,2,random-32-word-dense,w5,w5,46659\nSAMPLE,2,random-32-word-dense,w6,binary,165486\nSAMPLE,2,random-32-word-dense,w6,w6,44626\nSAMPLE,2,random-32-word-dense,w7,binary,163553\nSAMPLE,2,random-32-word-dense,w7,w7,48833\nSAMPLE,2,random-32-word-mixed,policy,binary,161449\nSAMPLE,2,random-32-word-mixed,policy,policy,52478\nSAMPLE,2,random-32-word-mixed,w1,binary,159397\nSAMPLE,2,random-32-word-mixed,w1,w1,146237\nSAMPLE,2,random-32-word-mixed,w2,binary,161911\nSAMPLE,2,random-32-word-mixed,w2,w2,83464\nSAMPLE,2,random-32-word-mixed,w3,binary,158185\nSAMPLE,2,random-32-word-mixed,w3,w3,63043\nSAMPLE,2,random-32-word-mixed,w4,binary,157594\nSAMPLE,2,random-32-word-mixed,w4,w4,50014\nSAMPLE,2,random-32-word-mixed,w5,binary,157924\nSAMPLE,2,random-32-word-mixed,w5,w5,46769\nSAMPLE,2,random-32-word-mixed,w6,binary,157855\nSAMPLE,2,random-32-word-mixed,w6,w6,43324\nSAMPLE,2,random-32-word-mixed,w7,binary,161379\nSAMPLE,2,random-32-word-mixed,w7,w7,46639\nSAMPLE,2,random-32-word-sparse,policy,binary,156271\nSAMPLE,2,random-32-word-sparse,policy,policy,50174\nSAMPLE,2,random-32-word-sparse,w1,binary,154099\nSAMPLE,2,random-32-word-sparse,w1,w1,140588\nSAMPLE,2,random-32-word-sparse,w2,binary,152226\nSAMPLE,2,random-32-word-sparse,w2,w2,85427\nSAMPLE,2,random-32-word-sparse,w3,binary,151424\nSAMPLE,2,random-32-word-sparse,w3,w3,61672\nSAMPLE,2,random-32-word-sparse,w4,binary,152096\nSAMPLE,2,random-32-word-sparse,w4,w4,49484\nSAMPLE,2,random-32-word-sparse,w5,binary,152767\nSAMPLE,2,random-32-word-sparse,w5,w5,45298\nSAMPLE,2,random-32-word-sparse,w6,binary,150924\nSAMPLE,2,random-32-word-sparse,w6,w6,40921\nSAMPLE,2,random-32-word-sparse,w7,binary,150023\nSAMPLE,2,random-32-word-sparse,w7,w7,40180\nSAMPLE,2,random-32-word-short,policy,binary,310060\nSAMPLE,2,random-32-word-short,policy,policy,83083\nSAMPLE,2,random-32-word-short,w1,binary,305112\nSAMPLE,2,random-32-word-short,w1,w1,277331\nSAMPLE,2,random-32-word-short,w2,binary,303179\nSAMPLE,2,random-32-word-short,w2,w2,152316\nSAMPLE,2,random-32-word-short,w3,binary,301317\nSAMPLE,2,random-32-word-short,w3,w3,108621\nSAMPLE,2,random-32-word-short,w4,binary,304932\nSAMPLE,2,random-32-word-short,w4,w4,88301\nSAMPLE,2,random-32-word-short,w5,binary,301867\nSAMPLE,2,random-32-word-short,w5,w5,75201\nSAMPLE,2,random-32-word-short,w6,binary,305623\nSAMPLE,2,random-32-word-short,w6,w6,69924\nSAMPLE,2,random-32-word-short,w7,binary,300997\nSAMPLE,2,random-32-word-short,w7,w7,75552\nSAMPLE,2,random-32-half-dense,policy,binary,172395\nSAMPLE,2,random-32-half-dense,policy,policy,52498\nSAMPLE,2,random-32-half-dense,w1,binary,173227\nSAMPLE,2,random-32-half-dense,w1,w1,149582\nSAMPLE,2,random-32-half-dense,w2,binary,168030\nSAMPLE,2,random-32-half-dense,w2,w2,82353\nSAMPLE,2,random-32-half-dense,w3,binary,165806\nSAMPLE,2,random-32-half-dense,w3,w3,62022\nSAMPLE,2,random-32-half-dense,w4,binary,166046\nSAMPLE,2,random-32-half-dense,w4,w4,49844\nSAMPLE,2,random-32-half-dense,w5,binary,173087\nSAMPLE,2,random-32-half-dense,w5,w5,45317\nSAMPLE,2,random-32-half-dense,w6,binary,165876\nSAMPLE,2,random-32-half-dense,w6,w6,42553\nSAMPLE,2,random-32-half-dense,w7,binary,166887\nSAMPLE,2,random-32-half-dense,w7,w7,43655\nSAMPLE,2,random-32-half-mixed,policy,binary,164724\nSAMPLE,2,random-32-half-mixed,policy,policy,51437\nSAMPLE,2,random-32-half-mixed,w1,binary,161469\nSAMPLE,2,random-32-half-mixed,w1,w1,148100\nSAMPLE,2,random-32-half-mixed,w2,binary,160528\nSAMPLE,2,random-32-half-mixed,w2,w2,83004\nSAMPLE,2,random-32-half-mixed,w3,binary,159316\nSAMPLE,2,random-32-half-mixed,w3,w3,62332\nSAMPLE,2,random-32-half-mixed,w4,binary,158215\nSAMPLE,2,random-32-half-mixed,w4,w4,50996\nSAMPLE,2,random-32-half-mixed,w5,binary,157293\nSAMPLE,2,random-32-half-mixed,w5,w5,48251\nSAMPLE,2,random-32-half-mixed,w6,binary,157344\nSAMPLE,2,random-32-half-mixed,w6,w6,42343\nSAMPLE,2,random-32-half-mixed,w7,binary,159576\nSAMPLE,2,random-32-half-mixed,w7,w7,43755\nSAMPLE,2,random-32-half-sparse,policy,binary,158224\nSAMPLE,2,random-32-half-sparse,policy,policy,49994\nSAMPLE,2,random-32-half-sparse,w1,binary,155110\nSAMPLE,2,random-32-half-sparse,w1,w1,145666\nSAMPLE,2,random-32-half-sparse,w2,binary,156061\nSAMPLE,2,random-32-half-sparse,w2,w2,81881\nSAMPLE,2,random-32-half-sparse,w3,binary,154219\nSAMPLE,2,random-32-half-sparse,w3,w3,60780\nSAMPLE,2,random-32-half-sparse,w4,binary,154910\nSAMPLE,2,random-32-half-sparse,w4,w4,48923\nSAMPLE,2,random-32-half-sparse,w5,binary,154409\nSAMPLE,2,random-32-half-sparse,w5,w5,44056\nSAMPLE,2,random-32-half-sparse,w6,binary,157774\nSAMPLE,2,random-32-half-sparse,w6,w6,40630\nSAMPLE,2,random-32-half-sparse,w7,binary,153858\nSAMPLE,2,random-32-half-sparse,w7,w7,39469\nSAMPLE,2,random-32-half-short,policy,binary,308267\nSAMPLE,2,random-32-half-short,policy,policy,76153\nSAMPLE,2,random-32-half-short,w1,binary,307766\nSAMPLE,2,random-32-half-short,w1,w1,276139\nSAMPLE,2,random-32-half-short,w2,binary,303861\nSAMPLE,2,random-32-half-short,w2,w2,150583\nSAMPLE,2,random-32-half-short,w3,binary,305884\nSAMPLE,2,random-32-half-short,w3,w3,109031\nSAMPLE,2,random-32-half-short,w4,binary,303560\nSAMPLE,2,random-32-half-short,w4,w4,87389\nSAMPLE,2,random-32-half-short,w5,binary,300675\nSAMPLE,2,random-32-half-short,w5,w5,78656\nSAMPLE,2,random-32-half-short,w6,binary,302799\nSAMPLE,2,random-32-half-short,w6,w6,67951\nSAMPLE,2,random-32-half-short,w7,binary,301377\nSAMPLE,2,random-32-half-short,w7,w7,68441\nSAMPLE,2,random-32-large-dense,policy,binary,172806\nSAMPLE,2,random-32-large-dense,policy,policy,54872\nSAMPLE,2,random-32-large-dense,w1,binary,166847\nSAMPLE,2,random-32-large-dense,w1,w1,150093\nSAMPLE,2,random-32-large-dense,w2,binary,166226\nSAMPLE,2,random-32-large-dense,w2,w2,83835\nSAMPLE,2,random-32-large-dense,w3,binary,163863\nSAMPLE,2,random-32-large-dense,w3,w3,62022\nSAMPLE,2,random-32-large-dense,w4,binary,167779\nSAMPLE,2,random-32-large-dense,w4,w4,50335\nSAMPLE,2,random-32-large-dense,w5,binary,163252\nSAMPLE,2,random-32-large-dense,w5,w5,46529\nSAMPLE,2,random-32-large-dense,w6,binary,163002\nSAMPLE,2,random-32-large-dense,w6,w6,43895\nSAMPLE,2,random-32-large-dense,w7,binary,163783\nSAMPLE,2,random-32-large-dense,w7,w7,47681\nSAMPLE,2,random-32-large-mixed,policy,binary,162421\nSAMPLE,2,random-32-large-mixed,policy,policy,55392\nSAMPLE,2,random-32-large-mixed,w1,binary,159006\nSAMPLE,2,random-32-large-mixed,w1,w1,145195\nSAMPLE,2,random-32-large-mixed,w2,binary,158976\nSAMPLE,2,random-32-large-mixed,w2,w2,82452\nSAMPLE,2,random-32-large-mixed,w3,binary,158445\nSAMPLE,2,random-32-large-mixed,w3,w3,62192\nSAMPLE,2,random-32-large-mixed,w4,binary,157724\nSAMPLE,2,random-32-large-mixed,w4,w4,53419\nSAMPLE,2,random-32-large-mixed,w5,binary,157404\nSAMPLE,2,random-32-large-mixed,w5,w5,46830\nSAMPLE,2,random-32-large-mixed,w6,binary,157323\nSAMPLE,2,random-32-large-mixed,w6,w6,42463\nSAMPLE,2,random-32-large-mixed,w7,binary,157403\nSAMPLE,2,random-32-large-mixed,w7,w7,44356\nSAMPLE,2,random-32-large-sparse,policy,binary,156372\nSAMPLE,2,random-32-large-sparse,policy,policy,50355\nSAMPLE,2,random-32-large-sparse,w1,binary,156592\nSAMPLE,2,random-32-large-sparse,w1,w1,141029\nSAMPLE,2,random-32-large-sparse,w2,binary,152476\nSAMPLE,2,random-32-large-sparse,w2,w2,82973\nSAMPLE,2,random-32-large-sparse,w3,binary,152266\nSAMPLE,2,random-32-large-sparse,w3,w3,61251\nSAMPLE,2,random-32-large-sparse,w4,binary,151685\nSAMPLE,2,random-32-large-sparse,w4,w4,49273\nSAMPLE,2,random-32-large-sparse,w5,binary,155500\nSAMPLE,2,random-32-large-sparse,w5,w5,45468\nSAMPLE,2,random-32-large-sparse,w6,binary,151786\nSAMPLE,2,random-32-large-sparse,w6,w6,41181\nSAMPLE,2,random-32-large-sparse,w7,binary,150894\nSAMPLE,2,random-32-large-sparse,w7,w7,38497\nSAMPLE,2,random-32-large-short,policy,binary,308237\nSAMPLE,2,random-32-large-short,policy,policy,82272\nSAMPLE,2,random-32-large-short,w1,binary,307236\nSAMPLE,2,random-32-large-short,w1,w1,271913\nSAMPLE,2,random-32-large-short,w2,binary,303029\nSAMPLE,2,random-32-large-short,w2,w2,153768\nSAMPLE,2,random-32-large-short,w3,binary,304802\nSAMPLE,2,random-32-large-short,w3,w3,109653\nSAMPLE,2,random-32-large-short,w4,binary,300766\nSAMPLE,2,random-32-large-short,w4,w4,87039\nSAMPLE,2,random-32-large-short,w5,binary,304301\nSAMPLE,2,random-32-large-short,w5,w5,77314\nSAMPLE,2,random-32-large-short,w6,binary,303551\nSAMPLE,2,random-32-large-short,w6,w6,70625\nSAMPLE,2,random-32-large-short,w7,binary,301407\nSAMPLE,2,random-32-large-short,w7,w7,73819\nSAMPLE,2,random-64-small-dense,policy,binary,373204\nSAMPLE,2,random-64-small-dense,policy,policy,84876\nSAMPLE,2,random-64-small-dense,w1,binary,368206\nSAMPLE,2,random-64-small-dense,w1,w1,311612\nSAMPLE,2,random-64-small-dense,w2,binary,364360\nSAMPLE,2,random-64-small-dense,w2,w2,163653\nSAMPLE,2,random-64-small-dense,w3,binary,365101\nSAMPLE,2,random-64-small-dense,w3,w3,118276\nSAMPLE,2,random-64-small-dense,w4,binary,359323\nSAMPLE,2,random-64-small-dense,w4,w4,92437\nSAMPLE,2,random-64-small-dense,w5,binary,361686\nSAMPLE,2,random-64-small-dense,w5,w5,82993\nSAMPLE,2,random-64-small-dense,w6,binary,366263\nSAMPLE,2,random-64-small-dense,w6,w6,75022\nSAMPLE,2,random-64-small-dense,w7,binary,357490\nSAMPLE,2,random-64-small-dense,w7,w7,90644\nSAMPLE,2,random-64-small-mixed,policy,binary,352182\nSAMPLE,2,random-64-small-mixed,policy,policy,87009\nSAMPLE,2,random-64-small-mixed,w1,binary,347576\nSAMPLE,2,random-64-small-mixed,w1,w1,310761\nSAMPLE,2,random-64-small-mixed,w2,binary,344631\nSAMPLE,2,random-64-small-mixed,w2,w2,162611\nSAMPLE,2,random-64-small-mixed,w3,binary,344151\nSAMPLE,2,random-64-small-mixed,w3,w3,117765\nSAMPLE,2,random-64-small-mixed,w4,binary,341556\nSAMPLE,2,random-64-small-mixed,w4,w4,91696\nSAMPLE,2,random-64-small-mixed,w5,binary,344091\nSAMPLE,2,random-64-small-mixed,w5,w5,82843\nSAMPLE,2,random-64-small-mixed,w6,binary,347265\nSAMPLE,2,random-64-small-mixed,w6,w6,73910\nSAMPLE,2,random-64-small-mixed,w7,binary,344050\nSAMPLE,2,random-64-small-mixed,w7,w7,85647\nSAMPLE,2,random-64-small-sparse,policy,binary,318752\nSAMPLE,2,random-64-small-sparse,policy,policy,80800\nSAMPLE,2,random-64-small-sparse,w1,binary,313014\nSAMPLE,2,random-64-small-sparse,w1,w1,294887\nSAMPLE,2,random-64-small-sparse,w2,binary,312674\nSAMPLE,2,random-64-small-sparse,w2,w2,154810\nSAMPLE,2,random-64-small-sparse,w3,binary,310260\nSAMPLE,2,random-64-small-sparse,w3,w3,115441\nSAMPLE,2,random-64-small-sparse,w4,binary,309579\nSAMPLE,2,random-64-small-sparse,w4,w4,89122\nSAMPLE,2,random-64-small-sparse,w5,binary,309790\nSAMPLE,2,random-64-small-sparse,w5,w5,78126\nSAMPLE,2,random-64-small-sparse,w6,binary,313315\nSAMPLE,2,random-64-small-sparse,w6,w6,71256\nSAMPLE,2,random-64-small-sparse,w7,binary,311302\nSAMPLE,2,random-64-small-sparse,w7,w7,82733\nSAMPLE,2,random-64-small-short,policy,binary,332192\nSAMPLE,2,random-64-small-short,policy,policy,81931\nSAMPLE,2,random-64-small-short,w1,binary,321216\nSAMPLE,2,random-64-small-short,w1,w1,284261\nSAMPLE,2,random-64-small-short,w2,binary,321457\nSAMPLE,2,random-64-small-short,w2,w2,150503\nSAMPLE,2,random-64-small-short,w3,binary,318413\nSAMPLE,2,random-64-small-short,w3,w3,108552\nSAMPLE,2,random-64-small-short,w4,binary,317241\nSAMPLE,2,random-64-small-short,w4,w4,90414\nSAMPLE,2,random-64-small-short,w5,binary,316610\nSAMPLE,2,random-64-small-short,w5,w5,79117\nSAMPLE,2,random-64-small-short,w6,binary,318702\nSAMPLE,2,random-64-small-short,w6,w6,71146\nSAMPLE,2,random-64-small-short,w7,binary,319985\nSAMPLE,2,random-64-small-short,w7,w7,73609\nSAMPLE,2,random-64-word-dense,policy,binary,374085\nSAMPLE,2,random-64-word-dense,policy,policy,106508\nSAMPLE,2,random-64-word-dense,w1,binary,372643\nSAMPLE,2,random-64-word-dense,w1,w1,310641\nSAMPLE,2,random-64-word-dense,w2,binary,364601\nSAMPLE,2,random-64-word-dense,w2,w2,170123\nSAMPLE,2,random-64-word-dense,w3,binary,364871\nSAMPLE,2,random-64-word-dense,w3,w3,121510\nSAMPLE,2,random-64-word-dense,w4,binary,362848\nSAMPLE,2,random-64-word-dense,w4,w4,101390\nSAMPLE,2,random-64-word-dense,w5,binary,364420\nSAMPLE,2,random-64-word-dense,w5,w5,88361\nSAMPLE,2,random-64-word-dense,w6,binary,361125\nSAMPLE,2,random-64-word-dense,w6,w6,95471\nSAMPLE,2,random-64-word-dense,w7,binary,364430\nSAMPLE,2,random-64-word-dense,w7,w7,140429\nSAMPLE,2,random-64-word-mixed,policy,binary,354075\nSAMPLE,2,random-64-word-mixed,policy,policy,101530\nSAMPLE,2,random-64-word-mixed,w1,binary,344210\nSAMPLE,2,random-64-word-mixed,w1,w1,311121\nSAMPLE,2,random-64-word-mixed,w2,binary,346984\nSAMPLE,2,random-64-word-mixed,w2,w2,166517\nSAMPLE,2,random-64-word-mixed,w3,binary,341687\nSAMPLE,2,random-64-word-mixed,w3,w3,121450\nSAMPLE,2,random-64-word-mixed,w4,binary,343319\nSAMPLE,2,random-64-word-mixed,w4,w4,95802\nSAMPLE,2,random-64-word-mixed,w5,binary,339513\nSAMPLE,2,random-64-word-mixed,w5,w5,86839\nSAMPLE,2,random-64-word-mixed,w6,binary,342558\nSAMPLE,2,random-64-word-mixed,w6,w6,91706\nSAMPLE,2,random-64-word-mixed,w7,binary,343269\nSAMPLE,2,random-64-word-mixed,w7,w7,118787\nSAMPLE,2,random-64-word-sparse,policy,binary,320525\nSAMPLE,2,random-64-word-sparse,policy,policy,84445\nSAMPLE,2,random-64-word-sparse,w1,binary,313545\nSAMPLE,2,random-64-word-sparse,w1,w1,291622\nSAMPLE,2,random-64-word-sparse,w2,binary,311952\nSAMPLE,2,random-64-word-sparse,w2,w2,160879\nSAMPLE,2,random-64-word-sparse,w3,binary,312394\nSAMPLE,2,random-64-word-sparse,w3,w3,113548\nSAMPLE,2,random-64-word-sparse,w4,binary,311592\nSAMPLE,2,random-64-word-sparse,w4,w4,88591\nSAMPLE,2,random-64-word-sparse,w5,binary,314296\nSAMPLE,2,random-64-word-sparse,w5,w5,77325\nSAMPLE,2,random-64-word-sparse,w6,binary,312233\nSAMPLE,2,random-64-word-sparse,w6,w6,71567\nSAMPLE,2,random-64-word-sparse,w7,binary,313415\nSAMPLE,2,random-64-word-sparse,w7,w7,83564\nSAMPLE,2,random-64-word-short,policy,binary,326855\nSAMPLE,2,random-64-word-short,policy,policy,93209\nSAMPLE,2,random-64-word-short,w1,binary,318953\nSAMPLE,2,random-64-word-short,w1,w1,286375\nSAMPLE,2,random-64-word-short,w2,binary,318432\nSAMPLE,2,random-64-word-short,w2,w2,152877\nSAMPLE,2,random-64-word-short,w3,binary,322558\nSAMPLE,2,random-64-word-short,w3,w3,111765\nSAMPLE,2,random-64-word-short,w4,binary,317330\nSAMPLE,2,random-64-word-short,w4,w4,91206\nSAMPLE,2,random-64-word-short,w5,binary,319444\nSAMPLE,2,random-64-word-short,w5,w5,86708\nSAMPLE,2,random-64-word-short,w6,binary,316780\nSAMPLE,2,random-64-word-short,w6,w6,83464\nSAMPLE,2,random-64-word-short,w7,binary,317201\nSAMPLE,2,random-64-word-short,w7,w7,102953\nSAMPLE,2,random-64-half-dense,policy,binary,375346\nSAMPLE,2,random-64-half-dense,policy,policy,96383\nSAMPLE,2,random-64-half-dense,w1,binary,366344\nSAMPLE,2,random-64-half-dense,w1,w1,311732\nSAMPLE,2,random-64-half-dense,w2,binary,363590\nSAMPLE,2,random-64-half-dense,w2,w2,167930\nSAMPLE,2,random-64-half-dense,w3,binary,366504\nSAMPLE,2,random-64-half-dense,w3,w3,119547\nSAMPLE,2,random-64-half-dense,w4,binary,363799\nSAMPLE,2,random-64-half-dense,w4,w4,97514\nSAMPLE,2,random-64-half-dense,w5,binary,367165\nSAMPLE,2,random-64-half-dense,w5,w5,88611\nSAMPLE,2,random-64-half-dense,w6,binary,366744\nSAMPLE,2,random-64-half-dense,w6,w6,86969\nSAMPLE,2,random-64-half-dense,w7,binary,364230\nSAMPLE,2,random-64-half-dense,w7,w7,117024\nSAMPLE,2,random-64-half-mixed,policy,binary,354586\nSAMPLE,2,random-64-half-mixed,policy,policy,92156\nSAMPLE,2,random-64-half-mixed,w1,binary,345913\nSAMPLE,2,random-64-half-mixed,w1,w1,312514\nSAMPLE,2,random-64-half-mixed,w2,binary,347044\nSAMPLE,2,random-64-half-mixed,w2,w2,164083\nSAMPLE,2,random-64-half-mixed,w3,binary,347796\nSAMPLE,2,random-64-half-mixed,w3,w3,121300\nSAMPLE,2,random-64-half-mixed,w4,binary,345782\nSAMPLE,2,random-64-half-mixed,w4,w4,96643\nSAMPLE,2,random-64-half-mixed,w5,binary,350650\nSAMPLE,2,random-64-half-mixed,w5,w5,83705\nSAMPLE,2,random-64-half-mixed,w6,binary,344551\nSAMPLE,2,random-64-half-mixed,w6,w6,83434\nSAMPLE,2,random-64-half-mixed,w7,binary,344431\nSAMPLE,2,random-64-half-mixed,w7,w7,109231\nSAMPLE,2,random-64-half-sparse,policy,binary,320345\nSAMPLE,2,random-64-half-sparse,policy,policy,82913\nSAMPLE,2,random-64-half-sparse,w1,binary,315238\nSAMPLE,2,random-64-half-sparse,w1,w1,297822\nSAMPLE,2,random-64-half-sparse,w2,binary,313876\nSAMPLE,2,random-64-half-sparse,w2,w2,155741\nSAMPLE,2,random-64-half-sparse,w3,binary,314787\nSAMPLE,2,random-64-half-sparse,w3,w3,116252\nSAMPLE,2,random-64-half-sparse,w4,binary,311332\nSAMPLE,2,random-64-half-sparse,w4,w4,88151\nSAMPLE,2,random-64-half-sparse,w5,binary,311312\nSAMPLE,2,random-64-half-sparse,w5,w5,78006\nSAMPLE,2,random-64-half-sparse,w6,binary,314016\nSAMPLE,2,random-64-half-sparse,w6,w6,72848\nSAMPLE,2,random-64-half-sparse,w7,binary,311773\nSAMPLE,2,random-64-half-sparse,w7,w7,79588\nSAMPLE,2,random-64-half-short,policy,binary,331341\nSAMPLE,2,random-64-half-short,policy,policy,86859\nSAMPLE,2,random-64-half-short,w1,binary,324301\nSAMPLE,2,random-64-half-short,w1,w1,283450\nSAMPLE,2,random-64-half-short,w2,binary,324582\nSAMPLE,2,random-64-half-short,w2,w2,152877\nSAMPLE,2,random-64-half-short,w3,binary,320435\nSAMPLE,2,random-64-half-short,w3,w3,109903\nSAMPLE,2,random-64-half-short,w4,binary,322999\nSAMPLE,2,random-64-half-short,w4,w4,90314\nSAMPLE,2,random-64-half-short,w5,binary,319504\nSAMPLE,2,random-64-half-short,w5,w5,82022\nSAMPLE,2,random-64-half-short,w6,binary,324562\nSAMPLE,2,random-64-half-short,w6,w6,78767\nSAMPLE,2,random-64-half-short,w7,binary,324852\nSAMPLE,2,random-64-half-short,w7,w7,90184\nSAMPLE,2,random-64-large-dense,policy,binary,372052\nSAMPLE,2,random-64-large-dense,policy,policy,105086\nSAMPLE,2,random-64-large-dense,w1,binary,367465\nSAMPLE,2,random-64-large-dense,w1,w1,309710\nSAMPLE,2,random-64-large-dense,w2,binary,368086\nSAMPLE,2,random-64-large-dense,w2,w2,165075\nSAMPLE,2,random-64-large-dense,w3,binary,366483\nSAMPLE,2,random-64-large-dense,w3,w3,120939\nSAMPLE,2,random-64-large-dense,w4,binary,365422\nSAMPLE,2,random-64-large-dense,w4,w4,97054\nSAMPLE,2,random-64-large-dense,w5,binary,361036\nSAMPLE,2,random-64-large-dense,w5,w5,89373\nSAMPLE,2,random-64-large-dense,w6,binary,362047\nSAMPLE,2,random-64-large-dense,w6,w6,98136\nSAMPLE,2,random-64-large-dense,w7,binary,362427\nSAMPLE,2,random-64-large-dense,w7,w7,146267\nSAMPLE,2,random-64-large-mixed,policy,binary,356378\nSAMPLE,2,random-64-large-mixed,policy,policy,99027\nSAMPLE,2,random-64-large-mixed,w1,binary,349047\nSAMPLE,2,random-64-large-mixed,w1,w1,311812\nSAMPLE,2,random-64-large-mixed,w2,binary,347635\nSAMPLE,2,random-64-large-mixed,w2,w2,166507\nSAMPLE,2,random-64-large-mixed,w3,binary,344411\nSAMPLE,2,random-64-large-mixed,w3,w3,122863\nSAMPLE,2,random-64-large-mixed,w4,binary,345963\nSAMPLE,2,random-64-large-mixed,w4,w4,96013\nSAMPLE,2,random-64-large-mixed,w5,binary,341626\nSAMPLE,2,random-64-large-mixed,w5,w5,86788\nSAMPLE,2,random-64-large-mixed,w6,binary,344190\nSAMPLE,2,random-64-large-mixed,w6,w6,89362\nSAMPLE,2,random-64-large-mixed,w7,binary,345582\nSAMPLE,2,random-64-large-mixed,w7,w7,122361\nSAMPLE,2,random-64-large-sparse,policy,binary,322649\nSAMPLE,2,random-64-large-sparse,policy,policy,84415\nSAMPLE,2,random-64-large-sparse,w1,binary,319924\nSAMPLE,2,random-64-large-sparse,w1,w1,294807\nSAMPLE,2,random-64-large-sparse,w2,binary,320175\nSAMPLE,2,random-64-large-sparse,w2,w2,156142\nSAMPLE,2,random-64-large-sparse,w3,binary,313635\nSAMPLE,2,random-64-large-sparse,w3,w3,113008\nSAMPLE,2,random-64-large-sparse,w4,binary,311161\nSAMPLE,2,random-64-large-sparse,w4,w4,90935\nSAMPLE,2,random-64-large-sparse,w5,binary,311782\nSAMPLE,2,random-64-large-sparse,w5,w5,77765\nSAMPLE,2,random-64-large-sparse,w6,binary,313165\nSAMPLE,2,random-64-large-sparse,w6,w6,72878\nSAMPLE,2,random-64-large-sparse,w7,binary,314757\nSAMPLE,2,random-64-large-sparse,w7,w7,82593\nSAMPLE,2,random-64-large-short,policy,binary,331602\nSAMPLE,2,random-64-large-short,policy,policy,93339\nSAMPLE,2,random-64-large-short,w1,binary,325193\nSAMPLE,2,random-64-large-short,w1,w1,288398\nSAMPLE,2,random-64-large-short,w2,binary,321036\nSAMPLE,2,random-64-large-short,w2,w2,153988\nSAMPLE,2,random-64-large-short,w3,binary,320906\nSAMPLE,2,random-64-large-short,w3,w3,110604\nSAMPLE,2,random-64-large-short,w4,binary,318202\nSAMPLE,2,random-64-large-short,w4,w4,90784\nSAMPLE,2,random-64-large-short,w5,binary,321407\nSAMPLE,2,random-64-large-short,w5,w5,83164\nSAMPLE,2,random-64-large-short,w6,binary,318502\nSAMPLE,2,random-64-large-short,w6,w6,83323\nSAMPLE,2,random-64-large-short,w7,binary,316219\nSAMPLE,2,random-64-large-short,w7,w7,107930\nSAMPLE,2,random-128-small-dense,policy,binary,804863\nSAMPLE,2,random-128-small-dense,policy,policy,218925\nSAMPLE,2,random-128-small-dense,w1,binary,792225\nSAMPLE,2,random-128-small-dense,w1,w1,626339\nSAMPLE,2,random-128-small-dense,w2,binary,759937\nSAMPLE,2,random-128-small-dense,w2,w2,329549\nSAMPLE,2,random-128-small-dense,w3,binary,753678\nSAMPLE,2,random-128-small-dense,w3,w3,233726\nSAMPLE,2,random-128-small-dense,w4,binary,752826\nSAMPLE,2,random-128-small-dense,w4,w4,191244\nSAMPLE,2,random-128-small-dense,w5,binary,762701\nSAMPLE,2,random-128-small-dense,w5,w5,168971\nSAMPLE,2,random-128-small-dense,w6,binary,751535\nSAMPLE,2,random-128-small-dense,w6,w6,186817\nSAMPLE,2,random-128-small-dense,w7,binary,756011\nSAMPLE,2,random-128-small-dense,w7,w7,240867\nSAMPLE,2,random-128-small-mixed,policy,binary,729282\nSAMPLE,2,random-128-small-mixed,policy,policy,197663\nSAMPLE,2,random-128-small-mixed,w1,binary,719807\nSAMPLE,2,random-128-small-mixed,w1,w1,632428\nSAMPLE,2,random-128-small-mixed,w2,binary,716352\nSAMPLE,2,random-128-small-mixed,w2,w2,334536\nSAMPLE,2,random-128-small-mixed,w3,binary,712697\nSAMPLE,2,random-128-small-mixed,w3,w3,239495\nSAMPLE,2,random-128-small-mixed,w4,binary,715912\nSAMPLE,2,random-128-small-mixed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AMPLE,2,random-128-half-dense,policy,policy,212274\nSAMPLE,2,random-128-half-dense,w1,binary,759586\nSAMPLE,2,random-128-half-dense,w1,w1,629954\nSAMPLE,2,random-128-half-dense,w2,binary,757103\nSAMPLE,2,random-128-half-dense,w2,w2,332854\nSAMPLE,2,random-128-half-dense,w3,binary,755921\nSAMPLE,2,random-128-half-dense,w3,w3,239315\nSAMPLE,2,random-128-half-dense,w4,binary,758344\nSAMPLE,2,random-128-half-dense,w4,w4,197644\nSAMPLE,2,random-128-half-dense,w5,binary,750072\nSAMPLE,2,random-128-half-dense,w5,w5,209801\nSAMPLE,2,random-128-half-dense,w6,binary,756211\nSAMPLE,2,random-128-half-dense,w6,w6,258304\nSAMPLE,2,random-128-half-dense,w7,binary,764413\nSAMPLE,2,random-128-half-dense,w7,w7,411601\nSAMPLE,2,random-128-half-mixed,policy,binary,735220\nSAMPLE,2,random-128-half-mixed,policy,policy,204253\nSAMPLE,2,random-128-half-mixed,w1,binary,720048\nSAMPLE,2,random-128-half-mixed,w1,w1,629874\nSAMPLE,2,random-128-half-mixed,w2,binary,725165\nSAMPLE,2,random-128-half-mixed,w2,w2,337240\nSAMPLE,2,random-128-half-mixed,w3,binary,715390\nSAMPLE,2,random-128-half-mixed,w3,w3,247326\nSAMPLE,2,random-128-half-mixed,w4,binary,722842\nSAMPLE,2,random-128-half-mixed,w4,w4,196732\nSAMPLE,2,random-128-half-mixed,w5,binary,719087\nSAMPLE,2,random-128-half-mixed,w5,w5,191664\nSAMPLE,2,random-128-half-mixed,w6,binary,718426\nSAMPLE,2,random-128-half-mixed,w6,w6,233086\nSAMPLE,2,random-128-half-mixed,w7,binary,727950\nSAMPLE,2,random-128-half-mixed,w7,w7,348287\nSAMPLE,2,random-128-half-sparse,policy,binary,689553\nSAMPLE,2,random-128-half-sparse,policy,policy,200828\nSAMPLE,2,random-128-half-sparse,w1,binary,680990\nSAMPLE,2,random-128-half-sparse,w1,w1,628823\nSAMPLE,2,random-128-half-sparse,w2,binary,676794\nSAMPLE,2,random-128-half-sparse,w2,w2,326374\nSAMPLE,2,random-128-half-sparse,w3,binary,675582\nSAMPLE,2,random-128-half-sparse,w3,w3,233166\nSAMPLE,2,random-128-half-sparse,w4,binary,675842\nSAMPLE,2,random-128-half-sparse,w4,w4,186587\nSAMPLE,2,random-128-half-sparse,w5,binary,675552\nSAMPLE,2,random-128-half-sparse,w5,w5,166416\nSAMPLE,2,random-128-half-sparse,w6,binary,675773\nSAMPLE,2,random-128-half-sparse,w6,w6,185645\nSAMPLE,2,random-128-half-sparse,w7,binary,677966\nSAMPLE,2,random-128-half-sparse,w7,w7,240016\nSAMPLE,2,random-128-half-short,policy,binary,335999\nSAMPLE,2,random-128-half-short,policy,policy,107279\nSAMPLE,2,random-128-half-short,w1,binary,325302\nSAMPLE,2,random-128-half-short,w1,w1,286494\nSAMPLE,2,random-128-half-short,w2,binary,322779\nSAMPLE,2,random-128-half-short,w2,w2,155481\nSAMPLE,2,random-128-half-short,w3,binary,321256\nSAMPLE,2,random-128-half-short,w3,w3,114811\nSAMPLE,2,random-128-half-short,w4,binary,320996\nSAMPLE,2,random-128-half-short,w4,w4,95401\nSAMPLE,2,random-128-half-short,w5,binary,318712\nSAMPLE,2,random-128-half-short,w5,w5,96052\nSAMPLE,2,random-128-half-short,w6,binary,322388\nSAMPLE,2,random-128-half-short,w6,w6,121770\nSAMPLE,2,random-128-half-short,w7,binary,323740\nSAMPLE,2,random-128-half-short,w7,w7,153107\nSAMPLE,2,random-128-large-dense,policy,binary,768199\nSAMPLE,2,random-128-large-dense,policy,policy,220607\nSAMPLE,2,random-128-large-dense,w1,binary,760968\nSAMPLE,2,random-128-large-dense,w1,w1,634832\nSAMPLE,2,random-128-large-dense,w2,binary,758665\nSAMPLE,2,random-128-large-dense,w2,w2,337270\nSAMPLE,2,random-128-large-dense,w3,binary,750453\nSAMPLE,2,random-128-large-dense,w3,w3,242139\nSAMPLE,2,random-128-large-dense,w4,binary,750644\nSAMPLE,2,random-128-large-dense,w4,w4,209160\nSAMPLE,2,random-128-large-dense,w5,binary,766056\nSAMPLE,2,random-128-large-dense,w5,w5,221088\nSAMPLE,2,random-128-large-dense,w6,binary,757634\nSAMPLE,2,random-128-large-dense,w6,w6,318582\nSAMPLE,2,random-128-large-dense,w7,binary,761439\nSAMPLE,2,random-128-large-dense,w7,w7,557477\nSAMPLE,2,random-128-large-mixed,policy,binary,731515\nSAMPLE,2,random-128-large-mixed,policy,policy,211704\nSAMPLE,2,random-128-large-mixed,w1,binary,722021\nSAMPLE,2,random-128-large-mixed,w1,w1,633670\nSAMPLE,2,random-128-large-mixed,w2,binary,1919036\nSAMPLE,2,random-128-large-mixed,w2,w2,346254\nSAMPLE,2,random-128-large-mixed,w3,binary,734509\nSAMPLE,2,random-128-large-mixed,w3,w3,248549\nSAMPLE,2,random-128-large-mixed,w4,binary,748130\nSAMPLE,2,random-128-large-mixed,w4,w4,201689\nSAMPLE,2,random-128-large-mixed,w5,binary,716793\nSAMPLE,2,random-128-large-mixed,w5,w5,210031\nSAMPLE,2,random-128-large-mixed,w6,binary,720238\nSAMPLE,2,random-128-large-mixed,w6,w6,263611\nSAMPLE,2,random-128-large-mixed,w7,binary,723724\nSAMPLE,2,random-128-large-mixed,w7,w7,423789\nSAMPLE,2,random-128-large-sparse,policy,binary,955026\nSAMPLE,2,random-128-large-sparse,policy,policy,202199\nSAMPLE,2,random-128-large-sparse,w1,binary,683263\nSAMPLE,2,random-128-large-sparse,w1,w1,632498\nSAMPLE,2,random-128-large-sparse,w2,binary,684325\nSAMPLE,2,random-128-large-sparse,w2,w2,329418\nSAMPLE,2,random-128-large-sparse,w3,binary,684375\nSAMPLE,2,random-128-large-sparse,w3,w3,231693\nSAMPLE,2,random-128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,random-1024-half-dense,w4,binary,7198436\nSAMPLE,2,random-1024-half-dense,w4,w4,6298101\nSAMPLE,2,random-1024-half-dense,w5,binary,7178426\nSAMPLE,2,random-1024-half-dense,w5,w5,11261481\nSAMPLE,2,random-1024-half-mixed,policy,binary,6604024\nSAMPLE,2,random-1024-half-mixed,policy,policy,3753927\nSAMPLE,2,random-1024-half-mixed,w1,binary,6643793\nSAMPLE,2,random-1024-half-mixed,w1,w1,5995922\nSAMPLE,2,random-1024-half-mixed,w2,binary,6632917\nSAMPLE,2,random-1024-half-mixed,w2,w2,3705315\nSAMPLE,2,random-1024-half-mixed,w3,binary,6628781\nSAMPLE,2,random-1024-half-mixed,w3,w3,3739125\nSAMPLE,2,random-1024-half-mixed,w4,binary,6648610\nSAMPLE,2,random-1024-half-mixed,w4,w4,5176997\nSAMPLE,2,random-1024-half-mixed,w5,binary,6630864\nSAMPLE,2,random-1024-half-mixed,w5,w5,8799299\nSAMPLE,2,random-1024-half-sparse,policy,binary,6136961\nSAMPLE,2,random-1024-half-sparse,policy,policy,3036113\nSAMPLE,2,random-1024-half-sparse,w1,binary,6111093\nSAMPLE,2,random-1024-half-sparse,w1,w1,5796116\nSAMPLE,2,random-1024-half-sparse,w2,binary,6122239\nSAMPLE,2,random-1024-half-sparse,w2,w2,3357268\nSAMPLE,2,random-1024-half-sparse,w3,binary,6091033\nSAMPLE,2,random-1024-half-sparse,w3,w3,3035762\nSAMPLE,2,random-1024-half-sparse,w4,binary,6104243\nSAMPLE,2,random-1024-half-sparse,w4,w4,3694068\nSAMPLE,2,random-1024-half-sparse,w5,binary,6110162\nSAMPLE,2,random-1024-half-sparse,w5,w5,5570381\nSAMPLE,2,random-1024-half-short,policy,binary,377981\nSAMPLE,2,random-1024-half-short,policy,policy,238814\nSAMPLE,2,random-1024-half-short,w1,binary,363349\nSAMPLE,2,random-1024-half-short,w1,w1,331772\nSAMPLE,2,random-1024-half-short,w2,binary,358252\nSAMPLE,2,random-1024-half-short,w2,w2,213637\nSAMPLE,2,random-1024-half-short,w3,binary,362157\nSAMPLE,2,random-1024-half-short,w3,w3,224343\nSAMPLE,2,random-1024-half-short,w4,binary,355978\nSAMPLE,2,random-1024-half-short,w4,w4,323389\nSAMPLE,2,random-1024-half-short,w5,binary,358000\nSAMPLE,2,random-1024-half-short,w5,w5,579820\nSAMPLE,2,random-1024-large-dense,policy,binary,7177575\nSAMPLE,2,random-1024-large-dense,policy,policy,5455781\nSAMPLE,2,random-1024-large-dense,w1,binary,7168591\nSAMPLE,2,random-1024-large-dense,w1,w1,6309097\nSAMPLE,2,random-1024-large-dense,w2,binary,7187670\nSAMPLE,2,random-1024-large-dense,w2,w2,4421197\nSAMPLE,2,random-1024-large-dense,w3,binary,7192808\nSAMPLE,2,random-1024-large-dense,w3,w3,5436753\nSAMPLE,2,random-1024-large-dense,w4,binary,7179358\nSAMPLE,2,random-1024-large-dense,w4,w4,8940289\nSAMPLE,2,random-1024-large-dense,w5,binary,7176533\nSAMPLE,2,random-1024-large-dense,w5,w5,16313223\nSAMPLE,2,random-1024-large-mixed,policy,binary,6601029\nSAMPLE,2,random-1024-large-mixed,policy,policy,4254960\nSAMPLE,2,random-1024-large-mixed,w1,binary,6607449\nSAMPLE,2,random-1024-large-mixed,w1,w1,6080758\nSAMPLE,2,random-1024-large-mixed,w2,binary,6612576\nSAMPLE,2,random-1024-large-mixed,w2,w2,3886795\nSAMPLE,2,random-1024-large-mixed,w3,binary,6601910\nSAMPLE,2,random-1024-large-mixed,w3,w3,4207020\nSAMPLE,2,random-1024-large-mixed,w4,binary,6599748\nSAMPLE,2,random-1024-large-mixed,w4,w4,6238281\nSAMPLE,2,random-1024-large-mixed,w5,binary,6641320\nSAMPLE,2,random-1024-large-mixed,w5,w5,10937550\nSAMPLE,2,random-1024-large-sparse,policy,binary,6100848\nSAMPLE,2,random-1024-large-sparse,policy,policy,3045417\nSAMPLE,2,random-1024-large-sparse,w1,binary,6117422\nSAMPLE,2,random-1024-large-sparse,w1,w1,5784378\nSAMPLE,2,random-1024-large-sparse,w2,binary,6092956\nSAMPLE,2,random-1024-large-sparse,w2,w2,3365872\nSAMPLE,2,random-1024-large-sparse,w3,binary,6125244\nSAMPLE,2,random-1024-large-sparse,w3,w3,3037274\nSAMPLE,2,random-1024-large-sparse,w4,binary,6128118\nSAMPLE,2,random-1024-large-sparse,w4,w4,3710192\nSAMPLE,2,random-1024-large-sparse,w5,binary,6108099\nSAMPLE,2,random-1024-large-sparse,w5,w5,5608527\nSAMPLE,2,random-1024-large-short,policy,binary,377150\nSAMPLE,2,random-1024-large-short,policy,policy,269570\nSAMPLE,2,random-1024-large-short,w1,binary,363009\nSAMPLE,2,random-1024-large-short,w1,w1,337330\nSAMPLE,2,random-1024-large-short,w2,binary,357900\nSAMPLE,2,random-1024-large-short,w2,w2,226215\nSAMPLE,2,random-1024-large-short,w3,binary,357189\nSAMPLE,2,random-1024-large-short,w3,w3,257813\nSAMPLE,2,random-1024-large-short,w4,binary,358792\nSAMPLE,2,random-1024-large-short,w4,w4,380274\nSAMPLE,2,random-1024-large-short,w5,binary,360514\nSAMPLE,2,random-1024-large-short,w5,w5,741480\nSAMPLE,2,random-2048-small-dense,policy,binary,18755405\nSAMPLE,2,random-2048-small-dense,policy,policy,9732744\nSAMPLE,2,random-2048-small-dense,w1,binary,17801410\nSAMPLE,2,random-2048-small-dense,w1,w1,13907656\nSAMPLE,2,random-2048-small-dense,w2,binary,17769964\nSAMPLE,2,random-2048-small-dense,w2,w2,9728297\nSAMPLE,2,random-2048-small-dense,w3,binary,18032814\nSAMPLE,2,random-2048-small-dense,w3,w3,11108064\nSAMPLE,2,random-2048-small-dense,w4,binary,17785547\nSAMPLE,2,random-2048-small-dense,w4,w4,15987701\nSAMPLE,2,random-2048-small-mixed,policy,b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ndom-2048-half-sparse,w4,binary,14679110\nSAMPLE,2,random-2048-half-sparse,w4,w4,15977064\nSAMPLE,2,random-2048-half-short,policy,binary,456798\nSAMPLE,2,random-2048-half-short,policy,policy,366213\nSAMPLE,2,random-2048-half-short,w1,binary,449146\nSAMPLE,2,random-2048-half-short,w1,w1,405792\nSAMPLE,2,random-2048-half-short,w2,binary,444739\nSAMPLE,2,random-2048-half-short,w2,w2,349008\nSAMPLE,2,random-2048-half-short,w3,binary,447313\nSAMPLE,2,random-2048-half-short,w3,w3,476647\nSAMPLE,2,random-2048-half-short,w4,binary,448195\nSAMPLE,2,random-2048-half-short,w4,w4,803892\nSAMPLE,2,random-2048-large-dense,policy,binary,17835140\nSAMPLE,2,random-2048-large-dense,policy,policy,16284771\nSAMPLE,2,random-2048-large-dense,w1,binary,17802813\nSAMPLE,2,random-2048-large-dense,w1,w1,16825283\nSAMPLE,2,random-2048-large-dense,w2,binary,17823082\nSAMPLE,2,random-2048-large-dense,w2,w2,16303959\nSAMPLE,2,random-2048-large-dense,w3,binary,17884634\nSAMPLE,2,random-2048-large-dense,w3,w3,25294392\nSAMPLE,2,random-2048-large-dense,w4,binary,18070219\nSAMPLE,2,random-2048-large-dense,w4,w4,43884723\nSAMPLE,2,random-2048-large-mixed,policy,binary,16023434\nSAMPLE,2,random-2048-large-mixed,policy,policy,13130132\nSAMPLE,2,random-2048-large-mixed,w1,binary,15985086\nSAMPLE,2,random-2048-large-mixed,w1,w1,15281042\nSAMPLE,2,random-2048-large-mixed,w2,binary,15949855\nSAMPLE,2,random-2048-large-mixed,w2,w2,13063604\nSAMPLE,2,random-2048-large-mixed,w3,binary,15957195\nSAMPLE,2,random-2048-large-mixed,w3,w3,18274061\nSAMPLE,2,random-2048-large-mixed,w4,binary,15964786\nSAMPLE,2,random-2048-large-mixed,w4,w4,30985954\nSAMPLE,2,random-2048-large-sparse,policy,binary,14133420\nSAMPLE,2,random-2048-large-sparse,policy,policy,9723671\nSAMPLE,2,random-2048-large-sparse,w1,binary,14132679\nSAMPLE,2,random-2048-large-sparse,w1,w1,13729271\nSAMPLE,2,random-2048-large-sparse,w2,binary,14094583\nSAMPLE,2,random-2048-large-sparse,w2,w2,9702099\nSAMPLE,2,random-2048-large-sparse,w3,binary,14114673\nSAMPLE,2,random-2048-large-sparse,w3,w3,11090468\nSAMPLE,2,random-2048-large-sparse,w4,binary,14145469\nSAMPLE,2,random-2048-large-sparse,w4,w4,16076132\nSAMPLE,2,random-2048-large-short,policy,binary,463818\nSAMPLE,2,random-2048-large-short,policy,policy,414996\nSAMPLE,2,random-2048-large-short,w1,binary,453963\nSAMPLE,2,random-2048-large-short,w1,w1,426232\nSAMPLE,2,random-2048-large-short,w2,binary,444820\nSAMPLE,2,random-2048-large-short,w2,w2,403138\nSAMPLE,2,random-2048-large-short,w3,binary,442726\nSAMPLE,2,random-2048-large-short,w3,w3,596946\nSAMPLE,2,random-2048-large-short,w4,binary,446582\nSAMPLE,2,random-2048-large-short,w4,w4,1033994\nSAMPLE,2,random-4096-small-dense,policy,binary,60212428\nSAMPLE,2,random-4096-small-dense,policy,policy,37966426\nSAMPLE,2,random-4096-small-dense,w1,binary,58158522\nSAMPLE,2,random-4096-small-dense,w1,w1,40866076\nSAMPLE,2,random-4096-small-dense,w2,binary,57978716\nSAMPLE,2,random-4096-small-dense,w2,w2,37435809\nSAMPLE,2,random-4096-small-dense,w3,binary,57880920\nSAMPLE,2,random-4096-small-dense,w3,w3,51095717\nSAMPLE,2,random-4096-small-mixed,policy,binary,50665879\nSAMPLE,2,random-4096-small-mixed,policy,policy,37407948\nSAMPLE,2,random-4096-small-mixed,w1,binary,49372892\nSAMPLE,2,random-4096-small-mixed,w1,w1,40829432\nSAMPLE,2,random-4096-small-mixed,w2,binary,49259935\nSAMPLE,2,random-4096-small-mixed,w2,w2,37385664\nSAMPLE,2,random-4096-small-mixed,w3,binary,48949884\nSAMPLE,2,random-4096-small-mixed,w3,w3,49815649\nSAMPLE,2,random-4096-small-sparse,policy,binary,40206198\nSAMPLE,2,random-4096-small-sparse,policy,policy,37791627\nSAMPLE,2,random-4096-small-sparse,w1,binary,40697156\nSAMPLE,2,random-4096-small-sparse,w1,w1,40675193\nSAMPLE,2,random-4096-small-sparse,w2,binary,39744803\nSAMPLE,2,random-4096-small-sparse,w2,w2,37382550\nSAMPLE,2,random-4096-small-sparse,w3,binary,39680788\nSAMPLE,2,random-4096-small-sparse,w3,w3,49898171\nSAMPLE,2,random-4096-small-short,policy,binary,624646\nSAMPLE,2,random-4096-small-short,policy,policy,486892\nSAMPLE,2,random-4096-small-short,w1,binary,605989\nSAMPLE,2,random-4096-small-short,w1,w1,489756\nSAMPLE,2,random-4096-small-short,w2,binary,602894\nSAMPLE,2,random-4096-small-short,w2,w2,461003\nSAMPLE,2,random-4096-small-short,w3,binary,600631\nSAMPLE,2,random-4096-small-short,w3,w3,614492\nSAMPLE,2,random-4096-word-dense,policy,binary,57691579\nSAMPLE,2,random-4096-word-dense,policy,policy,58374953\nSAMPLE,2,random-4096-word-dense,w1,binary,58291899\nSAMPLE,2,random-4096-word-dense,w1,w1,41850306\nSAMPLE,2,random-4096-word-dense,w2,binary,59059839\nSAMPLE,2,random-4096-word-dense,w2,w2,38574848\nSAMPLE,2,random-4096-word-dense,w3,binary,58299381\nSAMPLE,2,random-4096-word-dense,w3,w3,52873113\nSAMPLE,2,random-4096-word-mixed,policy,binary,49260455\nSAMPLE,2,random-4096-word-mixed,policy,policy,49105936\nSAMPLE,2,random-4096-word-mixed,w1,binary,48821324\nSAMPLE,2,random-4096-word-mixed,w1,w1,42919221\nSAMPLE,2,random-4096-word-mixed,w2,binary,50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,2,random-8192-small-sparse,policy,policy,162498892\nSAMPLE,2,random-8192-small-sparse,w1,binary,150459407\nSAMPLE,2,random-8192-small-sparse,w1,w1,162191255\nSAMPLE,2,random-8192-small-sparse,w2,binary,150188245\nSAMPLE,2,random-8192-small-sparse,w2,w2,174236800\nSAMPLE,2,random-8192-small-short,policy,binary,1170255\nSAMPLE,2,random-8192-small-short,policy,policy,863551\nSAMPLE,2,random-8192-small-short,w1,binary,1131988\nSAMPLE,2,random-8192-small-short,w1,w1,840736\nSAMPLE,2,random-8192-small-short,w2,binary,1126420\nSAMPLE,2,random-8192-small-short,w2,w2,991570\nSAMPLE,2,random-8192-word-dense,policy,binary,252622548\nSAMPLE,2,random-8192-word-dense,policy,policy,163649518\nSAMPLE,2,random-8192-word-dense,w1,binary,252159051\nSAMPLE,2,random-8192-word-dense,w1,w1,164166544\nSAMPLE,2,random-8192-word-dense,w2,binary,252343975\nSAMPLE,2,random-8192-word-dense,w2,w2,177396736\nSAMPLE,2,random-8192-word-mixed,policy,binary,201323079\nSAMPLE,2,random-8192-word-mixed,policy,policy,163052172\nSAMPLE,2,random-8192-word-mixed,w1,binary,202351384\nSAMPLE,2,random-8192-word-mixed,w1,w1,161335976\nSAMPLE,2,random-8192-word-mixed,w2,binary,201920545\nSAMPLE,2,random-8192-word-mixed,w2,w2,175281919\nSAMPLE,2,random-8192-word-sparse,policy,binary,151163591\nSAMPLE,2,random-8192-word-sparse,policy,policy,162155512\nSAMPLE,2,random-8192-word-sparse,w1,binary,150097840\nSAMPLE,2,random-8192-word-sparse,w1,w1,162444691\nSAMPLE,2,random-8192-word-sparse,w2,binary,151648370\nSAMPLE,2,random-8192-word-sparse,w2,w2,172598569\nSAMPLE,2,random-8192-word-short,policy,binary,1274681\nSAMPLE,2,random-8192-word-short,policy,policy,948496\nSAMPLE,2,random-8192-word-short,w1,binary,1237515\nSAMPLE,2,random-8192-word-short,w1,w1,920014\nSAMPLE,2,random-8192-word-short,w2,binary,1236043\nSAMPLE,2,random-8192-word-short,w2,w2,1114843\nSAMPLE,2,random-8192-half-dense,policy,binary,252504343\nSAMPLE,2,random-8192-half-dense,policy,policy,251923882\nSAMPLE,2,random-8192-half-dense,w1,binary,254309028\nSAMPLE,2,random-8192-half-dense,w1,w1,230122028\nSAMPLE,2,random-8192-half-dense,w2,binary,251927647\nSAMPLE,2,random-8192-half-dense,w2,w2,300603724\nSAMPLE,2,random-8192-half-mixed,policy,binary,202729504\nSAMPLE,2,random-8192-half-mixed,policy,policy,202235922\nSAMPLE,2,random-8192-half-mixed,w1,binary,202034823\nSAMPLE,2,random-8192-half-mixed,w1,w1,196585352\nSAMPLE,2,random-8192-half-mixed,w2,binary,202066120\nSAMPLE,2,random-8192-half-mixed,w2,w2,242256894\nSAMPLE,2,random-8192-half-sparse,policy,binary,150680103\nSAMPLE,2,random-8192-half-sparse,policy,policy,150876444\nSAMPLE,2,random-8192-half-sparse,w1,binary,151332441\nSAMPLE,2,random-8192-half-sparse,w1,w1,161395244\nSAMPLE,2,random-8192-half-sparse,w2,binary,151025836\nSAMPLE,2,random-8192-half-sparse,w2,w2,172308077\nSAMPLE,2,random-8192-half-short,policy,binary,1333788\nSAMPLE,2,random-8192-half-short,policy,policy,1340358\nSAMPLE,2,random-8192-half-short,w1,binary,1321209\nSAMPLE,2,random-8192-half-short,w1,w1,1247520\nSAMPLE,2,random-8192-half-short,w2,binary,1326657\nSAMPLE,2,random-8192-half-short,w2,w2,1741894\nSAMPLE,2,random-8192-large-dense,policy,binary,252284145\nSAMPLE,2,random-8192-large-dense,policy,policy,252945485\nSAMPLE,2,random-8192-large-dense,w1,binary,251717634\nSAMPLE,2,random-8192-large-dense,w1,w1,273437475\nSAMPLE,2,random-8192-large-dense,w2,binary,254505188\nSAMPLE,2,random-8192-large-dense,w2,w2,399636732\nSAMPLE,2,random-8192-large-mixed,policy,binary,202674222\nSAMPLE,2,random-8192-large-mixed,policy,policy,202471791\nSAMPLE,2,random-8192-large-mixed,w1,binary,202810513\nSAMPLE,2,random-8192-large-mixed,w1,w1,220366179\nSAMPLE,2,random-8192-large-mixed,w2,binary,203949412\nSAMPLE,2,random-8192-large-mixed,w2,w2,288962850\nSAMPLE,2,random-8192-large-sparse,policy,binary,150339908\nSAMPLE,2,random-8192-large-sparse,policy,policy,150684979\nSAMPLE,2,random-8192-large-sparse,w1,binary,150218508\nSAMPLE,2,random-8192-large-sparse,w1,w1,161912270\nSAMPLE,2,random-8192-large-sparse,w2,binary,151360631\nSAMPLE,2,random-8192-large-sparse,w2,w2,174326530\nSAMPLE,2,random-8192-large-short,policy,binary,1350503\nSAMPLE,2,random-8192-large-short,policy,policy,1363122\nSAMPLE,2,random-8192-large-short,w1,binary,1331695\nSAMPLE,2,random-8192-large-short,w1,w1,1437792\nSAMPLE,2,random-8192-large-short,w2,binary,1338465\nSAMPLE,2,random-8192-large-short,w2,w2,2146804\nSAMPLE,3,random-32-small-dense,policy,policy,53810\nSAMPLE,3,random-32-small-dense,policy,binary,177303\nSAMPLE,3,random-32-small-dense,w1,w1,149382\nSAMPLE,3,random-32-small-dense,w1,binary,172285\nSAMPLE,3,random-32-small-dense,w2,w2,88561\nSAMPLE,3,random-32-small-dense,w2,binary,169952\nSAMPLE,3,random-32-small-dense,w3,w3,62352\nSAMPLE,3,random-32-small-dense,w3,binary,167899\nSAMPLE,3,random-32-small-dense,w4,w4,50124\nSAMPLE,3,random-32-small-dense,w4,binary,168650\nSAMPLE,3,random-32-small-dense,w5,w5,45918\nSAMPLE,3,random-32-small-dense,w5,binary,165626\nSAMPLE,3,random-32-small-dense,w6,w6,42653\nSAMPLE,3,random-32-small-dense,w6,binary,165815\nSAMPLE,3,random-32-small-dense,w7,w7,38627\nSAMPLE,3,random-32-small-dense,w7,binary,165405\nSAMPLE,3,random-32-small-mixed,policy,policy,50215\nSAMPLE,3,random-32-small-mixed,policy,binary,163092\nSAMPLE,3,random-32-small-mixed,w1,w1,146598\nSAMPLE,3,random-32-small-mixed,w1,binary,161620\nSAMPLE,3,random-32-small-mixed,w2,w2,83313\nSAMPLE,3,random-32-small-mixed,w2,binary,158455\nSAMPLE,3,random-32-small-mixed,w3,w3,61571\nSAMPLE,3,random-32-small-mixed,w3,binary,159616\nSAMPLE,3,random-32-small-mixed,w4,w4,49453\nSAMPLE,3,random-32-small-mixed,w4,binary,159346\nSAMPLE,3,random-32-small-mixed,w5,w5,44896\nSAMPLE,3,random-32-small-mixed,w5,binary,161380\nSAMPLE,3,random-32-small-mixed,w6,w6,40991\nSAMPLE,3,random-32-small-mixed,w6,binary,158445\nSAMPLE,3,random-32-small-mixed,w7,w7,39028\nSAMPLE,3,random-32-small-mixed,w7,binary,158134\nSAMPLE,3,random-32-small-sparse,policy,policy,49033\nSAMPLE,3,random-32-small-sparse,policy,binary,156302\nSAMPLE,3,random-32-small-sparse,w1,w1,141249\nSAMPLE,3,random-32-small-sparse,w1,binary,156933\nSAMPLE,3,random-32-small-sparse,w2,w2,82091\nSAMPLE,3,random-32-small-sparse,w2,binary,152997\nSAMPLE,3,random-32-small-sparse,w3,w3,60690\nSAMPLE,3,random-32-small-sparse,w3,binary,152265\nSAMPLE,3,random-32-small-sparse,w4,w4,49664\nSAMPLE,3,random-32-small-sparse,w4,binary,152987\nSAMPLE,3,random-32-small-sparse,w5,w5,44155\nSAMPLE,3,random-32-small-sparse,w5,binary,154559\nSAMPLE,3,random-32-small-sparse,w6,w6,40921\nSAMPLE,3,random-32-small-sparse,w6,binary,152166\nSAMPLE,3,random-32-small-sparse,w7,w7,39388\nSAMPLE,3,random-32-small-sparse,w7,binary,152205\nSAMPLE,3,random-32-small-short,policy,policy,72878\nSAMPLE,3,random-32-small-short,policy,binary,308518\nSAMPLE,3,random-32-small-short,w1,w1,267426\nSAMPLE,3,random-32-small-short,w1,binary,302920\nSAMPLE,3,random-32-small-short,w2,w2,150373\nSAMPLE,3,random-32-small-short,w2,binary,302379\nSAMPLE,3,random-32-small-short,w3,w3,107660\nSAMPLE,3,random-32-small-short,w3,binary,300877\nSAMPLE,3,random-32-small-short,w4,w4,84455\nSAMPLE,3,random-32-small-short,w4,binary,301998\nSAMPLE,3,random-32-small-short,w5,w5,74721\nSAMPLE,3,random-32-small-short,w5,binary,304432\nSAMPLE,3,random-32-small-short,w6,w6,68492\nSAMPLE,3,random-32-small-short,w6,binary,301176\nSAMPLE,3,random-32-small-short,w7,w7,63044\nSAMPLE,3,random-32-small-short,w7,binary,298703\nSAMPLE,3,random-32-word-dense,policy,policy,54000\nSAMPLE,3,random-32-word-dense,policy,binary,170703\nSAMPLE,3,random-32-word-dense,w1,w1,150383\nSAMPLE,3,random-32-word-dense,w1,binary,165956\nSAMPLE,3,random-32-word-dense,w2,w2,83714\nSAMPLE,3,random-32-word-dense,w2,binary,162341\nSAMPLE,3,random-32-word-dense,w3,w3,62964\nSAMPLE,3,random-32-word-dense,w3,binary,162121\nSAMPLE,3,random-32-word-dense,w4,w4,53179\nSAMPLE,3,random-32-word-dense,w4,binary,164154\nSAMPLE,3,random-32-word-dense,w5,w5,46619\nSAMPLE,3,random-32-word-dense,w5,binary,161800\nSAMPLE,3,random-32-word-dense,w6,w6,43895\nSAMPLE,3,random-32-word-dense,w6,binary,162280\nSAMPLE,3,random-32-word-dense,w7,w7,49173\nSAMPLE,3,random-32-word-dense,w7,binary,163082\nSAMPLE,3,random-32-word-mixed,policy,policy,51516\nSAMPLE,3,random-32-word-mixed,policy,binary,163422\nSAMPLE,3,random-32-word-mixed,w1,w1,144745\nSAMPLE,3,random-32-word-mixed,w1,binary,160297\nSAMPLE,3,random-32-word-mixed,w2,w2,83233\nSAMPLE,3,random-32-word-mixed,w2,binary,168099\nSAMPLE,3,random-32-word-mixed,w3,w3,69232\nSAMPLE,3,random-32-word-mixed,w3,binary,158575\nSAMPLE,3,random-32-word-mixed,w4,w4,50675\nSAMPLE,3,random-32-word-mixed,w4,binary,159356\nSAMPLE,3,random-32-word-mixed,w5,w5,46208\nSAMPLE,3,random-32-word-mixed,w5,binary,156212\nSAMPLE,3,random-32-word-mixed,w6,w6,43525\nSAMPLE,3,random-32-word-mixed,w6,binary,157344\nSAMPLE,3,random-32-word-mixed,w7,w7,46689\nSAMPLE,3,random-32-word-mixed,w7,binary,157403\nSAMPLE,3,random-32-word-sparse,policy,policy,48863\nSAMPLE,3,random-32-word-sparse,policy,binary,157043\nSAMPLE,3,random-32-word-sparse,w1,w1,140419\nSAMPLE,3,random-32-word-sparse,w1,binary,151645\nSAMPLE,3,random-32-word-sparse,w2,w2,81722\nSAMPLE,3,random-32-word-sparse,w2,binary,152286\nSAMPLE,3,random-32-word-sparse,w3,w3,61051\nSAMPLE,3,random-32-word-sparse,w3,binary,152045\nSAMPLE,3,random-32-word-sparse,w4,w4,48722\nSAMPLE,3,random-32-word-sparse,w4,binary,152276\nSAMPLE,3,random-32-word-sparse,w5,w5,48562\nSAMPLE,3,random-32-word-sparse,w5,binary,153248\nSAMPLE,3,random-32-word-sparse,w6,w6,41381\nSAMPLE,3,random-32-word-sparse,w6,binary,150082\nSAMPLE,3,random-32-word-sparse,w7,w7,38557\nSAMPLE,3,random-32-word-sparse,w7,binary,151255\nSAMPLE,3,random-32-word-short,policy,policy,77265\nSAMPLE,3,random-32-word-short,policy,binary,312583\nSAMPLE,3,random-32-word-short,w1,w1,271653\nSAMPLE,3,random-32-word-short,w1,binary,303930\nSAMPLE,3,random-32-word-short,w2,w2,152917\nSAMPLE,3,random-32-word-short,w2,binary,305013\nSAMPLE,3,random-32-word-short,w3,w3,109862\nSAMPLE,3,random-32-word-short,w3,binary,303410\nSAMPLE,3,random-32-word-short,w4,w4,88992\nSAMPLE,3,random-32-word-short,w4,binary,299955\nSAMPLE,3,random-32-word-short,w5,w5,78086\nSAMPLE,3,random-32-word-short,w5,binary,304341\nSAMPLE,3,random-32-word-short,w6,w6,71025\nSAMPLE,3,random-32-word-short,w6,binary,301357\nSAMPLE,3,random-32-word-short,w7,w7,75232\nSAMPLE,3,random-32-word-short,w7,binary,304692\nSAMPLE,3,random-32-half-dense,policy,policy,50895\nSAMPLE,3,random-32-half-dense,policy,binary,171193\nSAMPLE,3,random-32-half-dense,w1,w1,150954\nSAMPLE,3,random-32-half-dense,w1,binary,168940\nSAMPLE,3,random-32-half-dense,w2,w2,82212\nSAMPLE,3,random-32-half-dense,w2,binary,164584\nSAMPLE,3,random-32-half-dense,w3,w3,64996\nSAMPLE,3,random-32-half-dense,w3,binary,164133\nSAMPLE,3,random-32-half-dense,w4,w4,49994\nSAMPLE,3,random-32-half-dense,w4,binary,164925\nSAMPLE,3,random-32-half-dense,w5,w5,45277\nSAMPLE,3,random-32-half-dense,w5,binary,163432\nSAMPLE,3,random-32-half-dense,w6,w6,43054\nSAMPLE,3,random-32-half-dense,w6,binary,163582\nSAMPLE,3,random-32-half-dense,w7,w7,43444\nSAMPLE,3,random-32-half-dense,w7,binary,166597\nSAMPLE,3,random-32-half-mixed,policy,policy,50726\nSAMPLE,3,random-32-half-mixed,policy,binary,160017\nSAMPLE,3,random-32-half-mixed,w1,w1,144955\nSAMPLE,3,random-32-half-mixed,w1,binary,158325\nSAMPLE,3,random-32-half-mixed,w2,w2,83464\nSAMPLE,3,random-32-half-mixed,w2,binary,157854\nSAMPLE,3,random-32-half-mixed,w3,w3,61902\nSAMPLE,3,random-32-half-mixed,w3,binary,159767\nSAMPLE,3,random-32-half-mixed,w4,w4,50835\nSAMPLE,3,random-32-half-mixed,w4,binary,157704\nSAMPLE,3,random-32-half-mixed,w5,w5,47030\nSAMPLE,3,random-32-half-mixed,w5,binary,156002\nSAMPLE,3,random-32-half-mixed,w6,w6,41401\nSAMPLE,3,random-32-half-mixed,w6,binary,156121\nSAMPLE,3,random-32-half-mixed,w7,w7,42994\nSAMPLE,3,random-32-half-mixed,w7,binary,156892\nSAMPLE,3,random-32-half-sparse,policy,policy,49794\nSAMPLE,3,random-32-half-sparse,policy,binary,155661\nSAMPLE,3,random-32-half-sparse,w1,w1,142281\nSAMPLE,3,random-32-half-sparse,w1,binary,154650\nSAMPLE,3,random-32-half-sparse,w2,w2,81621\nSAMPLE,3,random-32-half-sparse,w2,binary,152837\nSAMPLE,3,random-32-half-sparse,w3,w3,60720\nSAMPLE,3,random-32-half-sparse,w3,binary,151434\nSAMPLE,3,random-32-half-sparse,w4,w4,51496\nSAMPLE,3,random-32-half-sparse,w4,binary,153799\nSAMPLE,3,random-32-half-sparse,w5,w5,44806\nSAMPLE,3,random-32-half-sparse,w5,binary,151885\nSAMPLE,3,random-32-half-sparse,w6,w6,40560\nSAMPLE,3,random-32-half-sparse,w6,binary,151644\nSAMPLE,3,random-32-half-sparse,w7,w7,39168\nSAMPLE,3,random-32-half-sparse,w7,binary,151074\nSAMPLE,3,random-32-half-short,policy,policy,74701\nSAMPLE,3,random-32-half-short,policy,binary,311211\nSAMPLE,3,random-32-half-short,w1,w1,274117\nSAMPLE,3,random-32-half-short,w1,binary,304182\nSAMPLE,3,random-32-half-short,w2,w2,150584\nSAMPLE,3,random-32-half-short,w2,binary,306555\nSAMPLE,3,random-32-half-short,w3,w3,109322\nSAMPLE,3,random-32-half-short,w3,binary,302799\nSAMPLE,3,random-32-half-short,w4,w4,88060\nSAMPLE,3,random-32-half-short,w4,binary,303651\nSAMPLE,3,random-32-half-short,w5,w5,75792\nSAMPLE,3,random-32-half-short,w5,binary,303470\nSAMPLE,3,random-32-half-short,w6,w6,67560\nSAMPLE,3,random-32-half-short,w6,binary,303139\nSAMPLE,3,random-32-half-short,w7,w7,68722\nSAMPLE,3,random-32-half-short,w7,binary,303461\nSAMPLE,3,random-32-large-dense,policy,policy,53370\nSAMPLE,3,random-32-large-dense,policy,binary,169391\nSAMPLE,3,random-32-large-dense,w1,w1,150413\nSAMPLE,3,random-32-large-dense,w1,binary,166737\nSAMPLE,3,random-32-large-dense,w2,w2,83734\nSAMPLE,3,random-32-large-dense,w2,binary,166507\nSAMPLE,3,random-32-large-dense,w3,w3,62262\nSAMPLE,3,random-32-large-dense,w3,binary,162721\nSAMPLE,3,random-32-large-dense,w4,w4,49974\nSAMPLE,3,random-32-large-dense,w4,binary,163472\nSAMPLE,3,random-32-large-dense,w5,w5,46208\nSAMPLE,3,random-32-large-dense,w5,binary,163062\nSAMPLE,3,random-32-large-dense,w6,w6,44015\nSAMPLE,3,random-32-large-dense,w6,binary,164985\nSAMPLE,3,random-32-large-dense,w7,w7,47471\nSAMPLE,3,random-32-large-dense,w7,binary,164254\nSAMPLE,3,random-32-large-mixed,policy,policy,51757\nSAMPLE,3,random-32-large-mixed,policy,binary,162030\nSAMPLE,3,random-32-large-mixed,w1,w1,146077\nSAMPLE,3,random-32-large-mixed,w1,binary,160427\nSAMPLE,3,random-32-large-mixed,w2,w2,83794\nSAMPLE,3,random-32-large-mixed,w2,binary,159917\nSAMPLE,3,random-32-large-mixed,w3,w3,62343\nSAMPLE,3,random-32-large-mixed,w3,binary,157884\nSAMPLE,3,random-32-large-mixed,w4,w4,50104\nSAMPLE,3,random-32-large-mixed,w4,binary,156321\nSAMPLE,3,random-32-large-mixed,w5,w5,45377\nSAMPLE,3,random-32-large-mixed,w5,binary,156742\nSAMPLE,3,random-32-large-mixed,w6,w6,42753\nSAMPLE,3,random-32-large-mixed,w6,binary,156261\nSAMPLE,3,random-32-large-mixed,w7,w7,44746\nSAMPLE,3,random-32-large-mixed,w7,binary,161148\nSAMPLE,3,random-32-large-sparse,policy,policy,49143\nSAMPLE,3,random-32-large-sparse,policy,binary,154920\nSAMPLE,3,random-32-large-sparse,w1,w1,141089\nSAMPLE,3,random-32-large-sparse,w1,binary,152507\nSAMPLE,3,random-32-large-sparse,w2,w2,82562\nSAMPLE,3,random-32-large-sparse,w2,binary,153037\nSAMPLE,3,random-32-large-sparse,w3,w3,65287\nSAMPLE,3,random-32-large-sparse,w3,binary,150944\nSAMPLE,3,random-32-large-sparse,w4,w4,49413\nSAMPLE,3,random-32-large-sparse,w4,binary,151605\nSAMPLE,3,random-32-large-sparse,w5,w5,44576\nSAMPLE,3,random-32-large-sparse,w5,binary,151084\nSAMPLE,3,random-32-large-sparse,w6,w6,40380\nSAMPLE,3,random-32-large-sparse,w6,binary,150073\nSAMPLE,3,random-32-large-sparse,w7,w7,38727\nSAMPLE,3,random-32-large-sparse,w7,binary,149872\nSAMPLE,3,random-32-large-short,policy,policy,76914\nSAMPLE,3,random-32-large-short,policy,binary,309929\nSAMPLE,3,random-32-large-short,w1,w1,274517\nSAMPLE,3,random-32-large-short,w1,binary,305994\nSAMPLE,3,random-32-large-short,w2,w2,151625\nSAMPLE,3,random-32-large-short,w2,binary,301707\nSAMPLE,3,random-32-large-short,w3,w3,108772\nSAMPLE,3,random-32-large-short,w3,binary,300957\nSAMPLE,3,random-32-large-short,w4,w4,87159\nSAMPLE,3,random-32-large-short,w4,binary,303610\nSAMPLE,3,random-32-large-short,w5,w5,76003\nSAMPLE,3,random-32-large-short,w5,binary,300866\nSAMPLE,3,random-32-large-short,w6,w6,70084\nSAMPLE,3,random-32-large-short,w6,binary,303150\nSAMPLE,3,random-32-large-short,w7,w7,73720\nSAMPLE,3,random-32-large-short,w7,binary,301887\nSAMPLE,3,random-64-small-dense,policy,policy,83264\nSAMPLE,3,random-64-small-dense,policy,binary,372192\nSAMPLE,3,random-64-small-dense,w1,w1,306564\nSAMPLE,3,random-64-small-dense,w1,binary,365942\nSAMPLE,3,random-64-small-dense,w2,w2,163652\nSAMPLE,3,random-64-small-dense,w2,binary,366214\nSAMPLE,3,random-64-small-dense,w3,w3,119056\nSAMPLE,3,random-64-small-dense,w3,binary,360655\nSAMPLE,3,random-64-small-dense,w4,w4,92337\nSAMPLE,3,random-64-small-dense,w4,binary,363149\nSAMPLE,3,random-64-small-dense,w5,w5,83534\nSAMPLE,3,random-64-small-dense,w5,binary,363139\nSAMPLE,3,random-64-small-dense,w6,w6,73629\nSAMPLE,3,random-64-small-dense,w6,binary,360455\nSAMPLE,3,random-64-small-dense,w7,w7,86879\nSAMPLE,3,random-64-small-dense,w7,binary,360905\nSAMPLE,3,random-64-small-mixed,policy,policy,82062\nSAMPLE,3,random-64-small-mixed,policy,binary,356658\nSAMPLE,3,random-64-small-mixed,w1,w1,308267\nSAMPLE,3,random-64-small-mixed,w1,binary,345693\nSAMPLE,3,random-64-small-mixed,w2,w2,164073\nSAMPLE,3,random-64-small-mixed,w2,binary,346353\nSAMPLE,3,random-64-small-mixed,w3,w3,119488\nSAMPLE,3,random-64-small-mixed,w3,binary,344450\nSAMPLE,3,random-64-small-mixed,w4,w4,92066\nSAMPLE,3,random-64-small-mixed,w4,binary,347055\nSAMPLE,3,random-64-small-mixed,w5,w5,82773\nSAMPLE,3,random-64-small-mixed,w5,binary,341626\nSAMPLE,3,random-64-small-mixed,w6,w6,74741\nSAMPLE,3,random-64-small-mixed,w6,binary,348958\nSAMPLE,3,random-64-small-mixed,w7,w7,83344\nSAMPLE,3,random-64-small-mixed,w7,binary,342248\nSAMPLE,3,random-64-small-sparse,policy,policy,78887\nSAMPLE,3,random-64-small-sparse,policy,binary,320445\nSAMPLE,3,random-64-small-sparse,w1,w1,296390\nSAMPLE,3,random-64-small-sparse,w1,binary,311762\nSAMPLE,3,random-64-small-sparse,w2,w2,155280\nSAMPLE,3,random-64-small-sparse,w2,binary,311992\nSAMPLE,3,random-64-small-sparse,w3,w3,113599\nSAMPLE,3,random-64-small-sparse,w3,binary,309179\nSAMPLE,3,random-64-small-sparse,w4,w4,88341\nSAMPLE,3,random-64-small-sparse,w4,binary,308508\nSAMPLE,3,random-64-small-sparse,w5,w5,77245\nSAMPLE,3,random-64-small-sparse,w5,binary,312133\nSAMPLE,3,random-64-small-sparse,w6,w6,70544\nSAMPLE,3,random-64-small-sparse,w6,binary,308277\nSAMPLE,3,random-64-small-sparse,w7,w7,81351\nSAMPLE,3,random-64-small-sparse,w7,binary,314696\nSAMPLE,3,random-64-small-short,policy,policy,78386\nSAMPLE,3,random-64-small-short,policy,binary,327166\nSAMPLE,3,random-64-small-short,w1,w1,282178\nSAMPLE,3,random-64-small-short,w1,binary,320916\nSAMPLE,3,random-64-small-short,w2,w2,149532\nSAMPLE,3,random-64-small-short,w2,binary,316579\nSAMPLE,3,random-64-small-short,w3,w3,108080\nSAMPLE,3,random-64-small-short,w3,binary,318783\nSAMPLE,3,random-64-small-short,w4,w4,89172\nSAMPLE,3,random-64-small-short,w4,binary,318853\nSAMPLE,3,random-64-small-short,w5,w5,75873\nSAMPLE,3,random-64-small-short,w5,binary,315228\nSAMPLE,3,random-64-small-short,w6,w6,71155\nSAMPLE,3,random-64-small-short,w6,binary,320415\nSAMPLE,3,random-64-small-short,w7,w7,73138\nSAMPLE,3,random-64-small-short,w7,binary,317391\nSAMPLE,3,random-64-word-dense,policy,policy,101781\nSAMPLE,3,random-64-word-dense,policy,binary,375397\nSAMPLE,3,random-64-word-dense,w1,w1,311222\nSAMPLE,3,random-64-word-dense,w1,binary,365322\nSAMPLE,3,random-64-word-dense,w2,w2,169722\nSAMPLE,3,random-64-word-dense,w2,binary,362888\nSAMPLE,3,random-64-word-dense,w3,w3,121811\nSAMPLE,3,random-64-word-dense,w3,binary,362318\nSAMPLE,3,random-64-word-dense,w4,w4,99668\nSAMPLE,3,random-64-word-dense,w4,binary,361867\nSAMPLE,3,random-64-word-dense,w5,w5,88511\nSAMPLE,3,random-64-word-dense,w5,binary,361326\nSAMPLE,3,random-64-word-dense,w6,w6,97565\nSAMPLE,3,random-64-word-dense,w6,binary,361687\nSAMPLE,3,random-64-word-dense,w7,w7,140388\nSAMPLE,3,random-64-word-dense,w7,binary,365662\nSAMPLE,3,random-64-word-mixed,policy,policy,95382\nSAMPLE,3,random-64-word-mixed,policy,binary,347165\nSAMPLE,3,random-64-word-mixed,w1,w1,310460\nSAMPLE,3,random-64-word-mixed,w1,binary,346704\nSAMPLE,3,random-64-word-mixed,w2,w2,166517\nSAMPLE,3,random-64-word-mixed,w2,binary,340495\nSAMPLE,3,random-64-word-mixed,w3,w3,121180\nSAMPLE,3,random-64-word-mixed,w3,binary,343919\nSAMPLE,3,random-64-word-mixed,w4,w4,98436\nSAMPLE,3,random-64-word-mixed,w4,binary,344781\nSAMPLE,3,random-64-word-mixed,w5,w5,87410\nSAMPLE,3,random-64-word-mixed,w5,binary,344060\nSAMPLE,3,random-64-word-mixed,w6,w6,90865\nSAMPLE,3,random-64-word-mixed,w6,binary,340926\nSAMPLE,3,random-64-word-mixed,w7,w7,117204\nSAMPLE,3,random-64-word-mixed,w7,binary,344080\nSAMPLE,3,random-64-word-sparse,policy,policy,83323\nSAMPLE,3,random-64-word-sparse,policy,binary,316970\nSAMPLE,3,random-64-word-sparse,w1,w1,293095\nSAMPLE,3,random-64-word-sparse,w1,binary,317210\nSAMPLE,3,random-64-word-sparse,w2,w2,156712\nSAMPLE,3,random-64-word-sparse,w2,binary,310190\nSAMPLE,3,random-64-word-sparse,w3,w3,113839\nSAMPLE,3,random-64-word-sparse,w3,binary,308338\nSAMPLE,3,random-64-word-sparse,w4,w4,90815\nSAMPLE,3,random-64-word-sparse,w4,binary,309348\nSAMPLE,3,random-64-word-sparse,w5,w5,77325\nSAMPLE,3,random-64-word-sparse,w5,binary,312053\nSAMPLE,3,random-64-word-sparse,w6,w6,71466\nSAMPLE,3,random-64-word-sparse,w6,binary,312914\nSAMPLE,3,random-64-word-sparse,w7,w7,83754\nSAMPLE,3,random-64-word-sparse,w7,binary,311272\nSAMPLE,3,random-64-word-short,policy,policy,90955\nSAMPLE,3,random-64-word-short,policy,binary,328588\nSAMPLE,3,random-64-word-short,w1,w1,283531\nSAMPLE,3,random-64-word-short,w1,binary,320796\nSAMPLE,3,random-64-word-short,w2,w2,152677\nSAMPLE,3,random-64-word-short,w2,binary,320735\nSAMPLE,3,random-64-word-short,w3,w3,112157\nSAMPLE,3,random-64-word-short,w3,binary,318121\nSAMPLE,3,random-64-word-short,w4,w4,92617\nSAMPLE,3,random-64-word-short,w4,binary,317200\nSAMPLE,3,random-64-word-short,w5,w5,86048\nSAMPLE,3,random-64-word-short,w5,binary,317190\nSAMPLE,3,random-64-word-short,w6,w6,83794\nSAMPLE,3,random-64-word-short,w6,binary,315358\nSAMPLE,3,random-64-word-short,w7,w7,103333\nSAMPLE,3,random-64-word-short,w7,binary,322869\nSAMPLE,3,random-64-half-dense,policy,policy,94400\nSAMPLE,3,random-64-half-dense,policy,binary,369187\nSAMPLE,3,random-64-half-dense,w1,w1,315397\nSAMPLE,3,random-64-half-dense,w1,binary,368746\nSAMPLE,3,random-64-half-dense,w2,w2,167789\nSAMPLE,3,random-64-half-dense,w2,binary,369107\nSAMPLE,3,random-64-half-dense,w3,w3,120288\nSAMPLE,3,random-64-half-dense,w3,binary,362597\nSAMPLE,3,random-64-half-dense,w4,w4,95111\nSAMPLE,3,random-64-half-dense,w4,binary,362748\nSAMPLE,3,random-64-half-dense,w5,w5,88762\nSAMPLE,3,random-64-half-dense,w5,binary,365552\nSAMPLE,3,random-64-half-dense,w6,w6,87520\nSAMPLE,3,random-64-half-dense,w6,binary,361536\nSAMPLE,3,random-64-half-dense,w7,w7,118636\nSAMPLE,3,random-64-half-dense,w7,binary,365342\nSAMPLE,3,random-64-half-mixed,policy,policy,89602\nSAMPLE,3,random-64-half-mixed,policy,binary,347886\nSAMPLE,3,random-64-half-mixed,w1,w1,311533\nSAMPLE,3,random-64-half-mixed,w1,binary,346483\nSAMPLE,3,random-64-half-mixed,w2,w2,164985\nSAMPLE,3,random-64-half-mixed,w2,binary,346144\nSAMPLE,3,random-64-half-mixed,w3,w3,121770\nSAMPLE,3,random-64-half-mixed,w3,binary,340455\nSAMPLE,3,random-64-half-mixed,w4,w4,94080\nSAMPLE,3,random-64-half-mixed,w4,binary,344752\nSAMPLE,3,random-64-half-mixed,w5,w5,82953\nSAMPLE,3,random-64-half-mixed,w5,binary,340094\nSAMPLE,3,random-64-half-mixed,w6,w6,83284\nSAMPLE,3,random-64-half-mixed,w6,binary,341347\nSAMPLE,3,random-64-half-mixed,w7,w7,112467\nSAMPLE,3,random-64-half-mixed,w7,binary,346233\nSAMPLE,3,random-64-half-sparse,policy,policy,79968\nSAMPLE,3,random-64-half-sparse,policy,binary,316579\nSAMPLE,3,random-64-half-sparse,w1,w1,294227\nSAMPLE,3,random-64-half-sparse,w1,binary,311272\nSAMPLE,3,random-64-half-sparse,w2,w2,153698\nSAMPLE,3,random-64-half-sparse,w2,binary,309058\nSAMPLE,3,random-64-half-sparse,w3,w3,116202\nSAMPLE,3,random-64-half-sparse,w3,binary,309459\nSAMPLE,3,random-64-half-sparse,w4,w4,87339\nSAMPLE,3,random-64-half-sparse,w4,binary,308778\nSAMPLE,3,random-64-half-sparse,w5,w5,77215\nSAMPLE,3,random-64-half-sparse,w5,binary,312343\nSAMPLE,3,random-64-half-sparse,w6,w6,72377\nSAMPLE,3,random-64-half-sparse,w6,binary,308808\nSAMPLE,3,random-64-half-sparse,w7,w7,79889\nSAMPLE,3,random-64-half-sparse,w7,binary,310200\nSAMPLE,3,random-64-half-short,policy,policy,84806\nSAMPLE,3,random-64-half-short,policy,binary,326164\nSAMPLE,3,random-64-half-short,w1,w1,284121\nSAMPLE,3,random-64-half-short,w1,binary,326605\nSAMPLE,3,random-64-half-short,w2,w2,152466\nSAMPLE,3,random-64-half-short,w2,binary,318432\nSAMPLE,3,random-64-half-short,w3,w3,110744\nSAMPLE,3,random-64-half-short,w3,binary,322839\nSAMPLE,3,random-64-half-short,w4,w4,90684\nSAMPLE,3,random-64-half-short,w4,binary,317561\nSAMPLE,3,random-64-half-short,w5,w5,79207\nSAMPLE,3,random-64-half-short,w5,binary,319464\nSAMPLE,3,random-64-half-short,w6,w6,78527\nSAMPLE,3,random-64-half-short,w6,binary,322738\nSAMPLE,3,random-64-half-short,w7,w7,91446\nSAMPLE,3,random-64-half-short,w7,binary,320175\nSAMPLE,3,random-64-large-dense,policy,policy,103204\nSAMPLE,3,random-64-large-dense,policy,binary,376468\nSAMPLE,3,random-64-large-dense,w1,w1,311351\nSAMPLE,3,random-64-large-dense,w1,binary,364110\nSAMPLE,3,random-64-large-dense,w2,w2,169651\nSAMPLE,3,random-64-large-dense,w2,binary,362898\nSAMPLE,3,random-64-large-dense,w3,w3,120899\nSAMPLE,3,random-64-large-dense,w3,binary,360125\nSAMPLE,3,random-64-large-dense,w4,w4,100118\nSAMPLE,3,random-64-large-dense,w4,binary,360825\nSAMPLE,3,random-64-large-dense,w5,w5,87650\nSAMPLE,3,random-64-large-dense,w5,binary,360595\nSAMPLE,3,random-64-large-dense,w6,w6,98987\nSAMPLE,3,random-64-large-dense,w6,binary,360564\nSAMPLE,3,random-64-large-dense,w7,w7,144684\nSAMPLE,3,random-64-large-dense,w7,binary,361166\nSAMPLE,3,random-64-large-mixed,policy,policy,96403\nSAMPLE,3,random-64-large-mixed,policy,binary,353554\nSAMPLE,3,random-64-large-mixed,w1,w1,312453\nSAMPLE,3,random-64-large-mixed,w1,binary,349839\nSAMPLE,3,random-64-large-mixed,w2,w2,165465\nSAMPLE,3,random-64-large-mixed,w2,binary,344501\nSAMPLE,3,random-64-large-mixed,w3,w3,121601\nSAMPLE,3,random-64-large-mixed,w3,binary,345412\nSAMPLE,3,random-64-large-mixed,w4,w4,95342\nSAMPLE,3,random-64-large-mixed,w4,binary,341076\nSAMPLE,3,random-64-large-mixed,w5,w5,85587\nSAMPLE,3,random-64-large-mixed,w5,binary,343920\nSAMPLE,3,random-64-large-mixed,w6,w6,88992\nSAMPLE,3,random-64-large-mixed,w6,binary,339003\nSAMPLE,3,random-64-large-mixed,w7,w7,122552\nSAMPLE,3,random-64-large-mixed,w7,binary,346213\nSAMPLE,3,random-64-large-sparse,policy,policy,81421\nSAMPLE,3,random-64-large-sparse,policy,binary,319314\nSAMPLE,3,random-64-large-sparse,w1,w1,293516\nSAMPLE,3,random-64-large-sparse,w1,binary,318492\nSAMPLE,3,random-64-large-sparse,w2,w2,155321\nSAMPLE,3,random-64-large-sparse,w2,binary,313375\nSAMPLE,3,random-64-large-sparse,w3,w3,113749\nSAMPLE,3,random-64-large-sparse,w3,binary,312233\nSAMPLE,3,random-64-large-sparse,w4,w4,91656\nSAMPLE,3,random-64-large-sparse,w4,binary,311983\nSAMPLE,3,random-64-large-sparse,w5,w5,80489\nSAMPLE,3,random-64-large-sparse,w5,binary,315118\nSAMPLE,3,random-64-large-sparse,w6,w6,73379\nSAMPLE,3,random-64-large-sparse,w6,binary,314867\nSAMPLE,3,random-64-large-sparse,w7,w7,80700\nSAMPLE,3,random-64-large-sparse,w7,binary,311021\nSAMPLE,3,random-64-large-short,policy,policy,90585\nSAMPLE,3,random-64-large-short,policy,binary,331061\nSAMPLE,3,random-64-large-short,w1,w1,284141\nSAMPLE,3,random-64-large-short,w1,binary,321136\nSAMPLE,3,random-64-large-short,w2,w2,153278\nSAMPLE,3,random-64-large-short,w2,binary,324431\nSAMPLE,3,random-64-large-short,w3,w3,111005\nSAMPLE,3,random-64-large-short,w3,binary,316809\nSAMPLE,3,random-64-large-short,w4,w4,90714\nSAMPLE,3,random-64-large-short,w4,binary,320355\nSAMPLE,3,random-64-large-short,w5,w5,81981\nSAMPLE,3,random-64-large-short,w5,binary,317942\nSAMPLE,3,random-64-large-short,w6,w6,83374\nSAMPLE,3,random-64-large-short,w6,binary,317591\nSAMPLE,3,random-64-large-short,w7,w7,103574\nSAMPLE,3,random-64-large-short,w7,binary,326965\nSAMPLE,3,random-128-small-dense,policy,policy,194889\nSAMPLE,3,random-128-small-dense,policy,binary,786657\nSAMPLE,3,random-128-small-dense,w1,w1,637014\nSAMPLE,3,random-128-small-dense,w1,binary,752686\nSAMPLE,3,random-128-small-dense,w2,w2,334386\nSAMPLE,3,random-128-small-dense,w2,binary,750082\nSAMPLE,3,random-128-small-dense,w3,w3,236541\nSAMPLE,3,random-128-small-dense,w3,binary,752135\nSAMPLE,3,random-128-small-dense,w4,w4,187268\nSAMPLE,3,random-128-small-dense,w4,binary,744474\nSAMPLE,3,random-128-small-dense,w5,w5,171624\nSAMPLE,3,random-128-small-dense,w5,binary,749481\nSAMPLE,3,random-128-small-dense,w6,w6,191784\nSAMPLE,3,random-128-small-dense,w6,binary,755411\nSAMPLE,3,random-128-small-dense,w7,w7,242700\nSAMPLE,3,random-128-small-dense,w7,binary,758615\nSAMPLE,3,random-128-small-mixed,policy,policy,196240\nSAMPLE,3,random-128-small-mixed,policy,binary,727909\nSAMPLE,3,random-128-small-mixed,w1,w1,634702\nSAMPLE,3,random-128-small-mixed,w1,binary,724655\nSAMPLE,3,random-128-small-mixed,w2,w2,327335\nSAMPLE,3,random-128-small-mixed,w2,binary,717474\nSAMPLE,3,random-128-small-mixed,w3,w3,235599\nSAMPLE,3,random-128-small-mixed,w3,binary,719857\nSAMPLE,3,random-128-small-mixed,w4,w4,184594\nSAMPLE,3,random-128-small-mixed,w4,binary,718165\nSAMPLE,3,random-128-small-mixed,w5,w5,168830\nSAMPLE,3,random-128-small-mixed,w5,binary,718155\nSAMPLE,3,random-128-small-mixed,w6,w6,184264\nSAMPLE,3,random-128-small-mixed,w6,binary,720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dom-128-half-dense,w2,binary,753477\nSAMPLE,3,random-128-half-dense,w3,w3,238985\nSAMPLE,3,random-128-half-dense,w3,binary,750063\nSAMPLE,3,random-128-half-dense,w4,w4,195870\nSAMPLE,3,random-128-half-dense,w4,binary,753527\nSAMPLE,3,random-128-half-dense,w5,w5,207227\nSAMPLE,3,random-128-half-dense,w5,binary,756682\nSAMPLE,3,random-128-half-dense,w6,w6,256770\nSAMPLE,3,random-128-half-dense,w6,binary,760378\nSAMPLE,3,random-128-half-dense,w7,w7,407535\nSAMPLE,3,random-128-half-dense,w7,binary,761349\nSAMPLE,3,random-128-half-mixed,policy,policy,202841\nSAMPLE,3,random-128-half-mixed,policy,binary,724244\nSAMPLE,3,random-128-half-mixed,w1,w1,633009\nSAMPLE,3,random-128-half-mixed,w1,binary,719416\nSAMPLE,3,random-128-half-mixed,w2,w2,332553\nSAMPLE,3,random-128-half-mixed,w2,binary,712176\nSAMPLE,3,random-128-half-mixed,w3,w3,242820\nSAMPLE,3,random-128-half-mixed,w3,binary,719387\nSAMPLE,3,random-128-half-mixed,w4,w4,194629\nSAMPLE,3,random-128-half-mixed,w4,binary,722882\nSAMPLE,3,random-128-half-mixed,w5,w5,193997\nSAMPLE,3,random-128-half-mixed,w5,binary,721440\nSAMPLE,3,random-128-half-mixed,w6,w6,231834\nSAMPLE,3,random-128-half-mixed,w6,binary,715952\nSAMPLE,3,random-128-half-mixed,w7,w7,350620\nSAMPLE,3,random-128-half-mixed,w7,binary,724134\nSAMPLE,3,random-128-half-sparse,policy,policy,191665\nSAMPLE,3,random-128-half-sparse,policy,binary,681151\nSAMPLE,3,random-128-half-sparse,w1,w1,625247\nSAMPLE,3,random-128-half-sparse,w1,binary,678807\nSAMPLE,3,random-128-half-sparse,w2,w2,325263\nSAMPLE,3,random-128-half-sparse,w2,binary,674601\nSAMPLE,3,random-128-half-sparse,w3,w3,230562\nSAMPLE,3,random-128-half-sparse,w3,binary,674570\nSAMPLE,3,random-128-half-sparse,w4,w4,183823\nSAMPLE,3,random-128-half-sparse,w4,binary,673810\nSAMPLE,3,random-128-half-sparse,w5,w5,168339\nSAMPLE,3,random-128-half-sparse,w5,binary,672908\nSAMPLE,3,random-128-half-sparse,w6,w6,186867\nSAMPLE,3,random-128-half-sparse,w6,binary,677816\nSAMPLE,3,random-128-half-sparse,w7,w7,242940\nSAMPLE,3,random-128-half-sparse,w7,binary,679868\nSAMPLE,3,random-128-half-short,policy,policy,104505\nSAMPLE,3,random-128-half-short,policy,binary,327575\nSAMPLE,3,random-128-half-short,w1,w1,285874\nSAMPLE,3,random-128-half-short,w1,binary,324942\nSAMPLE,3,random-128-half-short,w2,w2,157163\nSAMPLE,3,random-128-half-short,w2,binary,319214\nSAMPLE,3,random-128-half-short,w3,w3,114459\nSAMPLE,3,random-128-half-short,w3,binary,317511\nSAMPLE,3,random-128-half-short,w4,w4,98076\nSAMPLE,3,random-128-half-short,w4,binary,317211\nSAMPLE,3,random-128-half-short,w5,w5,95882\nSAMPLE,3,random-128-half-short,w5,binary,316579\nSAMPLE,3,random-128-half-short,w6,w6,121601\nSAMPLE,3,random-128-half-short,w6,binary,326634\nSAMPLE,3,random-128-half-short,w7,w7,152776\nSAMPLE,3,random-128-half-short,w7,binary,321157\nSAMPLE,3,random-128-large-dense,policy,policy,216501\nSAMPLE,3,random-128-large-dense,policy,binary,756262\nSAMPLE,3,random-128-large-dense,w1,w1,631476\nSAMPLE,3,random-128-large-dense,w1,binary,759927\nSAMPLE,3,random-128-large-dense,w2,w2,333275\nSAMPLE,3,random-128-large-dense,w2,binary,747879\nSAMPLE,3,random-128-large-dense,w3,w3,240778\nSAMPLE,3,random-128-large-dense,w3,binary,747649\nSAMPLE,3,random-128-large-dense,w4,w4,207738\nSAMPLE,3,random-128-large-dense,w4,binary,746346\nSAMPLE,3,random-128-large-dense,w5,w5,218805\nSAMPLE,3,random-128-large-dense,w5,binary,753508\nSAMPLE,3,random-128-large-dense,w6,w6,318482\nSAMPLE,3,random-128-large-dense,w6,binary,762471\nSAMPLE,3,random-128-large-dense,w7,w7,558528\nSAMPLE,3,random-128-large-dense,w7,binary,755470\nSAMPLE,3,random-128-large-mixed,policy,policy,206606\nSAMPLE,3,random-128-large-mixed,policy,binary,722392\nSAMPLE,3,random-128-large-mixed,w1,w1,630375\nSAMPLE,3,random-128-large-mixed,w1,binary,717444\nSAMPLE,3,random-128-large-mixed,w2,w2,329999\nSAMPLE,3,random-128-large-mixed,w2,binary,712567\nSAMPLE,3,random-128-large-mixed,w3,w3,240617\nSAMPLE,3,random-128-large-mixed,w3,binary,713839\nSAMPLE,3,random-128-large-mixed,w4,w4,199266\nSAMPLE,3,random-128-large-mixed,w4,binary,711004\nSAMPLE,3,random-128-large-mixed,w5,w5,208439\nSAMPLE,3,random-128-large-mixed,w5,binary,715651\nSAMPLE,3,random-128-large-mixed,w6,w6,266766\nSAMPLE,3,random-128-large-mixed,w6,binary,727459\nSAMPLE,3,random-128-large-mixed,w7,w7,423198\nSAMPLE,3,random-128-large-mixed,w7,binary,731645\nSAMPLE,3,random-128-large-sparse,policy,policy,190984\nSAMPLE,3,random-128-large-sparse,policy,binary,682231\nSAMPLE,3,random-128-large-sparse,w1,w1,626960\nSAMPLE,3,random-128-large-sparse,w1,binary,676033\nSAMPLE,3,random-128-large-sparse,w2,w2,329779\nSAMPLE,3,random-128-large-sparse,w2,binary,674019\nSAMPLE,3,random-128-large-sparse,w3,w3,233186\nSAMPLE,3,random-128-large-sparse,w3,binary,675261\nSAMPLE,3,random-128-large-sparse,w4,w4,184994\nSAMPLE,3,random-128-large-sparse,w4,binary,671185\nSAMPLE,3,random-128-large-sparse,w5,w5,168780\nSAMPLE,3,random-128-large-sparse,w5,binary,678236\nSAMPLE,3,random-128-large-s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LE,3,random-1024-small-dense,w4,binary,7170925\nSAMPLE,3,random-1024-small-dense,w5,w5,5578083\nSAMPLE,3,random-1024-small-dense,w5,binary,7162492\nSAMPLE,3,random-1024-small-mixed,policy,policy,3037114\nSAMPLE,3,random-1024-small-mixed,policy,binary,7298745\nSAMPLE,3,random-1024-small-mixed,w1,w1,5859209\nSAMPLE,3,random-1024-small-mixed,w1,binary,6603743\nSAMPLE,3,random-1024-small-mixed,w2,w2,3375726\nSAMPLE,3,random-1024-small-mixed,w2,binary,6640898\nSAMPLE,3,random-1024-small-mixed,w3,w3,3067479\nSAMPLE,3,random-1024-small-mixed,w3,binary,6632246\nSAMPLE,3,random-1024-small-mixed,w4,w4,3690914\nSAMPLE,3,random-1024-small-mixed,w4,binary,6636332\nSAMPLE,3,random-1024-small-mixed,w5,w5,5555709\nSAMPLE,3,random-1024-small-mixed,w5,binary,6604684\nSAMPLE,3,random-1024-small-sparse,policy,policy,3046478\nSAMPLE,3,random-1024-small-sparse,policy,binary,6122380\nSAMPLE,3,random-1024-small-sparse,w1,w1,5804638\nSAMPLE,3,random-1024-small-sparse,w1,binary,6113286\nSAMPLE,3,random-1024-small-sparse,w2,w2,3364690\nSAMPLE,3,random-1024-small-sparse,w2,binary,6095349\nSAMPLE,3,random-1024-small-sparse,w3,w3,3042902\nSAMPLE,3,random-1024-small-sparse,w3,binary,6124283\nSAMPLE,3,random-1024-small-sparse,w4,w4,3679907\nSAMPLE,3,random-1024-small-sparse,w4,binary,6118213\nSAMPLE,3,random-1024-small-sparse,w5,w5,5540487\nSAMPLE,3,random-1024-small-sparse,w5,binary,6113727\nSAMPLE,3,random-1024-small-short,policy,policy,181359\nSAMPLE,3,random-1024-small-short,policy,binary,370319\nSAMPLE,3,random-1024-small-short,w1,w1,317981\nSAMPLE,3,random-1024-small-short,w1,binary,360695\nSAMPLE,3,random-1024-small-short,w2,w2,189551\nSAMPLE,3,random-1024-small-short,w2,binary,352884\nSAMPLE,3,random-1024-small-short,w3,w3,168630\nSAMPLE,3,random-1024-small-short,w3,binary,355427\nSAMPLE,3,random-1024-small-short,w4,w4,200217\nSAMPLE,3,random-1024-small-short,w4,binary,346625\nSAMPLE,3,random-1024-small-short,w5,w5,294246\nSAMPLE,3,random-1024-small-short,w5,binary,352723\nSAMPLE,3,random-1024-word-dense,policy,policy,3279213\nSAMPLE,3,random-1024-word-dense,policy,binary,7183403\nSAMPLE,3,random-1024-word-dense,w1,w1,5886109\nSAMPLE,3,random-1024-word-dense,w1,binary,7193428\nSAMPLE,3,random-1024-word-dense,w2,w2,3456466\nSAMPLE,3,random-1024-word-dense,w2,binary,7192046\nSAMPLE,3,random-1024-word-dense,w3,w3,3296468\nSAMPLE,3,random-1024-word-dense,w3,binary,7271814\nSAMPLE,3,random-1024-word-dense,w4,w4,4304213\nSAMPLE,3,random-1024-word-dense,w4,binary,7183544\nSAMPLE,3,random-1024-word-dense,w5,w5,6862918\nSAMPLE,3,random-1024-word-dense,w5,binary,7177345\nSAMPLE,3,random-1024-word-mixed,policy,policy,3221938\nSAMPLE,3,random-1024-word-mixed,policy,binary,6636953\nSAMPLE,3,random-1024-word-mixed,w1,w1,5886229\nSAMPLE,3,random-1024-word-mixed,w1,binary,6665605\nSAMPLE,3,random-1024-word-mixed,w2,w2,3460472\nSAMPLE,3,random-1024-word-mixed,w2,binary,6625176\nSAMPLE,3,random-1024-word-mixed,w3,w3,3215439\nSAMPLE,3,random-1024-word-mixed,w3,binary,6632686\nSAMPLE,3,random-1024-word-mixed,w4,w4,4019050\nSAMPLE,3,random-1024-word-mixed,w4,binary,6617594\nSAMPLE,3,random-1024-word-mixed,w5,w5,6333884\nSAMPLE,3,random-1024-word-mixed,w5,binary,6624304\nSAMPLE,3,random-1024-word-sparse,policy,policy,3050033\nSAMPLE,3,random-1024-word-sparse,policy,binary,6105755\nSAMPLE,3,random-1024-word-sparse,w1,w1,5789246\nSAMPLE,3,random-1024-word-sparse,w1,binary,6084122\nSAMPLE,3,random-1024-word-sparse,w2,w2,3350839\nSAMPLE,3,random-1024-word-sparse,w2,binary,6109071\nSAMPLE,3,random-1024-word-sparse,w3,w3,3024826\nSAMPLE,3,random-1024-word-sparse,w3,binary,6113666\nSAMPLE,3,random-1024-word-sparse,w4,w4,3691314\nSAMPLE,3,random-1024-word-sparse,w4,binary,6120376\nSAMPLE,3,random-1024-word-sparse,w5,w5,5557562\nSAMPLE,3,random-1024-word-sparse,w5,binary,6138934\nSAMPLE,3,random-1024-word-short,policy,policy,196692\nSAMPLE,3,random-1024-word-short,policy,binary,373103\nSAMPLE,3,random-1024-word-short,w1,w1,324752\nSAMPLE,3,random-1024-word-short,w1,binary,360785\nSAMPLE,3,random-1024-word-short,w2,w2,201710\nSAMPLE,3,random-1024-word-short,w2,binary,356018\nSAMPLE,3,random-1024-word-short,w3,w3,185905\nSAMPLE,3,random-1024-word-short,w3,binary,356299\nSAMPLE,3,random-1024-word-short,w4,w4,232375\nSAMPLE,3,random-1024-word-short,w4,binary,354726\nSAMPLE,3,random-1024-word-short,w5,w5,373164\nSAMPLE,3,random-1024-word-short,w5,binary,356198\nSAMPLE,3,random-1024-half-dense,policy,policy,4301008\nSAMPLE,3,random-1024-half-dense,policy,binary,7192727\nSAMPLE,3,random-1024-half-dense,w1,w1,6075891\nSAMPLE,3,random-1024-half-dense,w1,binary,7191966\nSAMPLE,3,random-1024-half-dense,w2,w2,4055885\nSAMPLE,3,random-1024-half-dense,w2,binary,7170394\nSAMPLE,3,random-1024-half-dense,w3,w3,4299567\nSAMPLE,3,random-1024-half-dense,w3,binary,7181751\nSAMPLE,3,random-1024-half-dense,w4,w4,6305782\nSAMPLE,3,random-1024-half-dense,w4,binary,7174140\nSAMPLE,3,random-1024-half-dense,w5,w5,11274780\nSAMPLE,3,random-1024-half-dense,w5,binary,7163434\nSAMPLE,3,random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E,3,random-2048-half-short,w1,w1,406563\nSAMPLE,3,random-2048-half-short,w1,binary,447934\nSAMPLE,3,random-2048-half-short,w2,w2,350930\nSAMPLE,3,random-2048-half-short,w2,binary,450077\nSAMPLE,3,random-2048-half-short,w3,w3,474934\nSAMPLE,3,random-2048-half-short,w3,binary,447985\nSAMPLE,3,random-2048-half-short,w4,w4,800457\nSAMPLE,3,random-2048-half-short,w4,binary,448605\nSAMPLE,3,random-2048-large-dense,policy,policy,16273073\nSAMPLE,3,random-2048-large-dense,policy,binary,17907297\nSAMPLE,3,random-2048-large-dense,w1,w1,16756310\nSAMPLE,3,random-2048-large-dense,w1,binary,17876882\nSAMPLE,3,random-2048-large-dense,w2,w2,16290950\nSAMPLE,3,random-2048-large-dense,w2,binary,17898323\nSAMPLE,3,random-2048-large-dense,w3,w3,25236316\nSAMPLE,3,random-2048-large-dense,w3,binary,17927237\nSAMPLE,3,random-2048-large-dense,w4,w4,43843461\nSAMPLE,3,random-2048-large-dense,w4,binary,17924603\nSAMPLE,3,random-2048-large-mixed,policy,policy,13096021\nSAMPLE,3,random-2048-large-mixed,policy,binary,15987180\nSAMPLE,3,random-2048-large-mixed,w1,w1,15285459\nSAMPLE,3,random-2048-large-mixed,w1,binary,16043523\nSAMPLE,3,random-2048-large-mixed,w2,w2,13046097\nSAMPLE,3,random-2048-large-mixed,w2,binary,16039607\nSAMPLE,3,random-2048-large-mixed,w3,w3,17988878\nSAMPLE,3,random-2048-large-mixed,w3,binary,15973439\nSAMPLE,3,random-2048-large-mixed,w4,w4,30952072\nSAMPLE,3,random-2048-large-mixed,w4,binary,16035250\nSAMPLE,3,random-2048-large-sparse,policy,policy,9679796\nSAMPLE,3,random-2048-large-sparse,policy,binary,14148793\nSAMPLE,3,random-2048-large-sparse,w1,w1,13692205\nSAMPLE,3,random-2048-large-sparse,w1,binary,14077767\nSAMPLE,3,random-2048-large-sparse,w2,w2,9690471\nSAMPLE,3,random-2048-large-sparse,w2,binary,14119530\nSAMPLE,3,random-2048-large-sparse,w3,w3,11056758\nSAMPLE,3,random-2048-large-sparse,w3,binary,14045120\nSAMPLE,3,random-2048-large-sparse,w4,w4,16000108\nSAMPLE,3,random-2048-large-sparse,w4,binary,14092089\nSAMPLE,3,random-2048-large-short,policy,policy,413504\nSAMPLE,3,random-2048-large-short,policy,binary,461544\nSAMPLE,3,random-2048-large-short,w1,w1,433593\nSAMPLE,3,random-2048-large-short,w1,binary,454303\nSAMPLE,3,random-2048-large-short,w2,w2,401616\nSAMPLE,3,random-2048-large-short,w2,binary,448635\nSAMPLE,3,random-2048-large-short,w3,w3,593460\nSAMPLE,3,random-2048-large-short,w3,binary,449607\nSAMPLE,3,random-2048-large-short,w4,w4,1022557\nSAMPLE,3,random-2048-large-short,w4,binary,452241\nSAMPLE,3,random-4096-small-dense,policy,policy,36944570\nSAMPLE,3,random-4096-small-dense,policy,binary,59862288\nSAMPLE,3,random-4096-small-dense,w1,w1,40716103\nSAMPLE,3,random-4096-small-dense,w1,binary,60296240\nSAMPLE,3,random-4096-small-dense,w2,w2,37588885\nSAMPLE,3,random-4096-small-dense,w2,binary,57981107\nSAMPLE,3,random-4096-small-dense,w3,w3,49973192\nSAMPLE,3,random-4096-small-dense,w3,binary,57981718\nSAMPLE,3,random-4096-small-mixed,policy,policy,36965110\nSAMPLE,3,random-4096-small-mixed,policy,binary,49358610\nSAMPLE,3,random-4096-small-mixed,w1,w1,40917071\nSAMPLE,3,random-4096-small-mixed,w1,binary,49315435\nSAMPLE,3,random-4096-small-mixed,w2,w2,37329039\nSAMPLE,3,random-4096-small-mixed,w2,binary,49044383\nSAMPLE,3,random-4096-small-mixed,w3,w3,49986591\nSAMPLE,3,random-4096-small-mixed,w3,binary,49263458\nSAMPLE,3,random-4096-small-sparse,policy,policy,37024888\nSAMPLE,3,random-4096-small-sparse,policy,binary,40059239\nSAMPLE,3,random-4096-small-sparse,w1,w1,40710454\nSAMPLE,3,random-4096-small-sparse,w1,binary,39902647\nSAMPLE,3,random-4096-small-sparse,w2,w2,37487184\nSAMPLE,3,random-4096-small-sparse,w2,binary,39667517\nSAMPLE,3,random-4096-small-sparse,w3,w3,50115313\nSAMPLE,3,random-4096-small-sparse,w3,binary,40682323\nSAMPLE,3,random-4096-small-short,policy,policy,477077\nSAMPLE,3,random-4096-small-short,policy,binary,629864\nSAMPLE,3,random-4096-small-short,w1,w1,490046\nSAMPLE,3,random-4096-small-short,w1,binary,612468\nSAMPLE,3,random-4096-small-short,w2,w2,461344\nSAMPLE,3,random-4096-small-short,w2,binary,605729\nSAMPLE,3,random-4096-small-short,w3,w3,612058\nSAMPLE,3,random-4096-small-short,w3,binary,602013\nSAMPLE,3,random-4096-word-dense,policy,policy,58115236\nSAMPLE,3,random-4096-word-dense,policy,binary,58054737\nSAMPLE,3,random-4096-word-dense,w1,w1,41938075\nSAMPLE,3,random-4096-word-dense,w1,binary,59171903\nSAMPLE,3,random-4096-word-dense,w2,w2,38464854\nSAMPLE,3,random-4096-word-dense,w2,binary,58431946\nSAMPLE,3,random-4096-word-dense,w3,w3,52866863\nSAMPLE,3,random-4096-word-dense,w3,binary,58185851\nSAMPLE,3,random-4096-word-mixed,policy,policy,49589072\nSAMPLE,3,random-4096-word-mixed,policy,binary,48892709\nSAMPLE,3,random-4096-word-mixed,w1,w1,41200841\nSAMPLE,3,random-4096-word-mixed,w1,binary,50021212\nSAMPLE,3,random-4096-word-mixed,w2,w2,38401240\nSAMPLE,3,random-4096-word-mixed,w2,binary,49247455\nSAMPLE,3,random-4096-word-mixed,w3,w3,51488508\nSAMPLE,3,random-4096-word-mixed,w3,binary,49143481\nSAMPLE,3,random-4096-word-sparse,policy,policy,39597504\nSAMPLE,3,random-4096-word-sparse,policy,binary,39315535\nSAMPLE,3,random-4096-word-sparse,w1,w1,40384441\nSAMPLE,3,random-4096-word-sparse,w1,binary,39723240\nSAMPLE,3,random-4096-word-sparse,w2,w2,37448197\nSAMPLE,3,random-4096-word-sparse,w2,binary,39741687\nSAMPLE,3,random-4096-word-sparse,w3,w3,49841687\nSAMPLE,3,random-4096-word-sparse,w3,binary,39780795\nSAMPLE,3,random-4096-word-short,policy,policy,654740\nSAMPLE,3,random-4096-word-short,policy,binary,628532\nSAMPLE,3,random-4096-word-short,w1,w1,526832\nSAMPLE,3,random-4096-word-short,w1,binary,635322\nSAMPLE,3,random-4096-word-short,w2,w2,510777\nSAMPLE,3,random-4096-word-short,w2,binary,630745\nSAMPLE,3,random-4096-word-short,w3,w3,698496\nSAMPLE,3,random-4096-word-short,w3,binary,630265\nSAMPLE,3,random-4096-half-dense,policy,policy,58941752\nSAMPLE,3,random-4096-half-dense,policy,binary,58247212\nSAMPLE,3,random-4096-half-dense,w1,w1,53620951\nSAMPLE,3,random-4096-half-dense,w1,binary,58224007\nSAMPLE,3,random-4096-half-dense,w2,w2,59771352\nSAMPLE,3,random-4096-half-dense,w2,binary,58297336\nSAMPLE,3,random-4096-half-dense,w3,w3,94175233\nSAMPLE,3,random-4096-half-dense,w3,binary,58960830\nSAMPLE,3,random-4096-half-mixed,policy,policy,49332341\nSAMPLE,3,random-4096-half-mixed,policy,binary,48890366\nSAMPLE,3,random-4096-half-mixed,w1,w1,47222912\nSAMPLE,3,random-4096-half-mixed,w1,binary,49182158\nSAMPLE,3,random-4096-half-mixed,w2,w2,49410717\nSAMPLE,3,random-4096-half-mixed,w2,binary,49278010\nSAMPLE,3,random-4096-half-mixed,w3,w3,74510691\nSAMPLE,3,random-4096-half-mixed,w3,binary,49565366\nSAMPLE,3,random-4096-half-sparse,policy,policy,40254488\nSAMPLE,3,random-4096-half-sparse,policy,binary,39700557\nSAMPLE,3,random-4096-half-sparse,w1,w1,40842670\nSAMPLE,3,random-4096-half-sparse,w1,binary,40134090\nSAMPLE,3,random-4096-half-sparse,w2,w2,37555265\nSAMPLE,3,random-4096-half-sparse,w2,binary,39962044\nSAMPLE,3,random-4096-half-sparse,w3,w3,49968834\nSAMPLE,3,random-4096-half-sparse,w3,binary,39881906\nSAMPLE,3,random-4096-half-short,policy,policy,673890\nSAMPLE,3,random-4096-half-short,policy,binary,653649\nSAMPLE,3,random-4096-half-short,w1,w1,631176\nSAMPLE,3,random-4096-half-short,w1,binary,655893\nSAMPLE,3,random-4096-half-short,w2,w2,699087\nSAMPLE,3,random-4096-half-short,w2,binary,649593\nSAMPLE,3,random-4096-half-short,w3,w3,1104177\nSAMPLE,3,random-4096-half-short,w3,binary,654571\nSAMPLE,3,random-4096-large-dense,policy,policy,58691321\nSAMPLE,3,random-4096-large-dense,policy,binary,57967507\nSAMPLE,3,random-4096-large-dense,w1,w1,63433042\nSAMPLE,3,random-4096-large-dense,w1,binary,58985486\nSAMPLE,3,random-4096-large-dense,w2,w2,75812891\nSAMPLE,3,random-4096-large-dense,w2,binary,58645812\nSAMPLE,3,random-4096-large-dense,w3,w3,129610535\nSAMPLE,3,random-4096-large-dense,w3,binary,59056101\nSAMPLE,3,random-4096-large-mixed,policy,policy,49312271\nSAMPLE,3,random-4096-large-mixed,policy,binary,49287684\nSAMPLE,3,random-4096-large-mixed,w1,w1,51625842\nSAMPLE,3,random-4096-large-mixed,w1,binary,49389826\nSAMPLE,3,random-4096-large-mixed,w2,w2,57607062\nSAMPLE,3,random-4096-large-mixed,w2,binary,49315406\nSAMPLE,3,random-4096-large-mixed,w3,w3,92354013\nSAMPLE,3,random-4096-large-mixed,w3,binary,49237400\nSAMPLE,3,random-4096-large-sparse,policy,policy,39999080\nSAMPLE,3,random-4096-large-sparse,policy,binary,39582341\nSAMPLE,3,random-4096-large-sparse,w1,w1,40556386\nSAMPLE,3,random-4096-large-sparse,w1,binary,39733205\nSAMPLE,3,random-4096-large-sparse,w2,w2,37518400\nSAMPLE,3,random-4096-large-sparse,w2,binary,39637462\nSAMPLE,3,random-4096-large-sparse,w3,w3,49999160\nSAMPLE,3,random-4096-large-sparse,w3,binary,39696441\nSAMPLE,3,random-4096-large-short,policy,policy,670775\nSAMPLE,3,random-4096-large-short,policy,binary,655922\nSAMPLE,3,random-4096-large-short,w1,w1,665867\nSAMPLE,3,random-4096-large-short,w1,binary,653149\nSAMPLE,3,random-4096-large-short,w2,w2,815900\nSAMPLE,3,random-4096-large-short,w2,binary,650445\nSAMPLE,3,random-4096-large-short,w3,w3,1371764\nSAMPLE,3,random-4096-large-short,w3,binary,656633\nSAMPLE,3,random-8192-small-dense,policy,policy,158832421\nSAMPLE,3,random-8192-small-dense,policy,binary,253735533\nSAMPLE,3,random-8192-small-dense,w1,w1,163998542\nSAMPLE,3,random-8192-small-dense,w1,binary,254301303\nSAMPLE,3,random-8192-small-dense,w2,w2,173092109\nSAMPLE,3,random-8192-small-dense,w2,binary,252224142\nSAMPLE,3,random-8192-small-mixed,policy,policy,159636433\nSAMPLE,3,random-8192-small-mixed,policy,binary,202250040\nSAMPLE,3,random-8192-small-mixed,w1,w1,161771129\nSAMPLE,3,random-8192-small-mixed,w1,binary,203168211\nSAMPLE,3,random-8192-small-mixed,w2,w2,173751466\nSAMPLE,3,random-8192-small-mixed,w2,binary,203176073\nSAMPLE,3,random-8192-small-sparse,policy,policy,158879110\nSAMPLE,3,random-8192-small-sparse,policy,binary,152248767\nSAMPLE,3,random-8192-small-sparse,w1,w1,160255120\nSAMPLE,3,random-8192-small-sparse,w1,binary,150428187\nSAMPLE,3,random-8192-small-sparse,w2,w2,173950010\nSAMPLE,3,random-8192-small-sparse,w2,binary,152960081\nSAMPLE,3,random-8192-small-short,policy,policy,887756\nSAMPLE,3,random-8192-small-short,policy,binary,1181382\nSAMPLE,3,random-8192-small-short,w1,w1,858283\nSAMPLE,3,random-8192-small-short,w1,binary,1141663\nSAMPLE,3,random-8192-small-short,w2,w2,1005200\nSAMPLE,3,random-8192-small-short,w2,binary,1139419\nSAMPLE,3,random-8192-word-dense,policy,policy,159969968\nSAMPLE,3,random-8192-word-dense,policy,binary,252894075\nSAMPLE,3,random-8192-word-dense,w1,w1,163292455\nSAMPLE,3,random-8192-word-dense,w1,binary,255370829\nSAMPLE,3,random-8192-word-dense,w2,w2,177601355\nSAMPLE,3,random-8192-word-dense,w2,binary,252631726\nSAMPLE,3,random-8192-word-mixed,policy,policy,160291734\nSAMPLE,3,random-8192-word-mixed,policy,binary,201894832\nSAMPLE,3,random-8192-word-mixed,w1,w1,162265462\nSAMPLE,3,random-8192-word-mixed,w1,binary,203201429\nSAMPLE,3,random-8192-word-mixed,w2,w2,176183132\nSAMPLE,3,random-8192-word-mixed,w2,binary,202570183\nSAMPLE,3,random-8192-word-sparse,policy,policy,161298667\nSAMPLE,3,random-8192-word-sparse,policy,binary,151448880\nSAMPLE,3,random-8192-word-sparse,w1,w1,160738487\nSAMPLE,3,random-8192-word-sparse,w1,binary,150465531\nSAMPLE,3,random-8192-word-sparse,w2,w2,172708728\nSAMPLE,3,random-8192-word-sparse,w2,binary,150886496\nSAMPLE,3,random-8192-word-short,policy,policy,973313\nSAMPLE,3,random-8192-word-short,policy,binary,1296833\nSAMPLE,3,random-8192-word-short,w1,w1,956518\nSAMPLE,3,random-8192-word-short,w1,binary,1251516\nSAMPLE,3,random-8192-word-short,w2,w2,1123917\nSAMPLE,3,random-8192-word-short,w2,binary,1243794\nSAMPLE,3,random-8192-half-dense,policy,policy,253800088\nSAMPLE,3,random-8192-half-dense,policy,binary,253168701\nSAMPLE,3,random-8192-half-dense,w1,w1,230172758\nSAMPLE,3,random-8192-half-dense,w1,binary,254200511\nSAMPLE,3,random-8192-half-dense,w2,w2,299695100\nSAMPLE,3,random-8192-half-dense,w2,binary,254288542\nSAMPLE,3,random-8192-half-mixed,policy,policy,206505590\nSAMPLE,3,random-8192-half-mixed,policy,binary,203083495\nSAMPLE,3,random-8192-half-mixed,w1,w1,198492216\nSAMPLE,3,random-8192-half-mixed,w1,binary,205264939\nSAMPLE,3,random-8192-half-mixed,w2,w2,241159641\nSAMPLE,3,random-8192-half-mixed,w2,binary,202535441\nSAMPLE,3,random-8192-half-sparse,policy,policy,152901815\nSAMPLE,3,random-8192-half-sparse,policy,binary,151025442\nSAMPLE,3,random-8192-half-sparse,w1,w1,162447741\nSAMPLE,3,random-8192-half-sparse,w1,binary,151384695\nSAMPLE,3,random-8192-half-sparse,w2,w2,173218203\nSAMPLE,3,random-8192-half-sparse,w2,binary,152592235\nSAMPLE,3,random-8192-half-short,policy,policy,1378093\nSAMPLE,3,random-8192-half-short,policy,binary,1330513\nSAMPLE,3,random-8192-half-short,w1,w1,1258236\nSAMPLE,3,random-8192-half-short,w1,binary,1352766\nSAMPLE,3,random-8192-half-short,w2,w2,1746319\nSAMPLE,3,random-8192-half-short,w2,binary,1332877\nSAMPLE,3,random-8192-large-dense,policy,policy,254193471\nSAMPLE,3,random-8192-large-dense,policy,binary,254029216\nSAMPLE,3,random-8192-large-dense,w1,w1,276862539\nSAMPLE,3,random-8192-large-dense,w1,binary,251806621\nSAMPLE,3,random-8192-large-dense,w2,w2,400796633\nSAMPLE,3,random-8192-large-dense,w2,binary,255755586\nSAMPLE,3,random-8192-large-mixed,policy,policy,203726026\nSAMPLE,3,random-8192-large-mixed,policy,binary,203242589\nSAMPLE,3,random-8192-large-mixed,w1,w1,219558175\nSAMPLE,3,random-8192-large-mixed,w1,binary,203027000\nSAMPLE,3,random-8192-large-mixed,w2,w2,289850929\nSAMPLE,3,random-8192-large-mixed,w2,binary,203596584\nSAMPLE,3,random-8192-large-sparse,policy,policy,153929488\nSAMPLE,3,random-8192-large-sparse,policy,binary,152026626\nSAMPLE,3,random-8192-large-sparse,w1,w1,162400610\nSAMPLE,3,random-8192-large-sparse,w1,binary,151756565\nSAMPLE,3,random-8192-large-sparse,w2,w2,173863300\nSAMPLE,3,random-8192-large-sparse,w2,binary,150794468\nSAMPLE,3,random-8192-large-short,policy,policy,1432785\nSAMPLE,3,random-8192-large-short,policy,binary,1361148\nSAMPLE,3,random-8192-large-short,w1,w1,1458523\nSAMPLE,3,random-8192-large-short,w1,binary,1368209\nSAMPLE,3,random-8192-large-short,w2,w2,2145692\nSAMPLE,3,random-8192-large-short,w2,binary,1351885\n",
    "stdout.txt": "COMPLETE\n",
    "stderr.txt": "",
    "summary.md": "# Kernel powMod tuning\n\n144 cases; 7296 retained checks; 4 adjacent AB/BA blocks.\n\nEach cell is the geometric mean of per-case median paired ratios to the binary loop (lower is better).\nDense, mixed, sparse and short exponents receive equal weight. `policy` includes dispatch; width columns time the loops directly.\nA dash means the intermediate-size cap excluded that width. No statistical equivalence or universal optimum is claimed.\n\n| Modulus family/bits | Base (reduced bits) | best fixed gm ms | policy | w1 | w2 | w3 | w4 | w5 | w6 | w7 | best fixed width |\n|---|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|\n| random/32 | small (2) | 0.044 | 0.290 | 0.887 | 0.515 | 0.375 | 0.301 | 0.273 | 0.249 | 0.233 | w7 |\n| random/32 | word (31) | 0.048 | 0.299 | 0.905 | 0.513 | 0.382 | 0.308 | 0.281 | 0.261 | 0.270 | w6 |\n| random/32 | half (16) | 0.047 | 0.292 | 0.904 | 0.506 | 0.382 | 0.308 | 0.277 | 0.252 | 0.254 | w6 |\n| random/32 | large (32) | 0.048 | 0.299 | 0.899 | 0.517 | 0.383 | 0.309 | 0.280 | 0.258 | 0.267 | w6 |\n| random/64 | small (2) | 0.073 | 0.240 | 0.884 | 0.472 | 0.344 | 0.273 | 0.238 | 0.217 | 0.244 | w6 |\n| random/64 | word (62) | 0.084 | 0.272 | 0.887 | 0.482 | 0.351 | 0.282 | 0.253 | 0.254 | 0.325 | w5 |\n| random/64 | half (32) | 0.080 | 0.257 | 0.889 | 0.475 | 0.349 | 0.276 | 0.245 | 0.240 | 0.291 | w6 |\n| random/64 | large (64) | 0.084 | 0.272 | 0.887 | 0.474 | 0.348 | 0.280 | 0.251 | 0.256 | 0.331 | w5 |\n| random/128 | small (2) | 0.143 | 0.278 | 0.873 | 0.464 | 0.334 | 0.267 | 0.244 | 0.265 | 0.332 | w5 |\n| random/128 | word (65) | 0.157 | 0.287 | 0.875 | 0.465 | 0.339 | 0.273 | 0.267 | 0.318 | 0.441 | w5 |\n| random/128 | half (64) | 0.159 | 0.289 | 0.878 | 0.468 | 0.340 | 0.275 | 0.272 | 0.326 | 0.456 | w5 |\n| random/128 | large (126) | 0.166 | 0.296 | 0.883 | 0.468 | 0.341 | 0.284 | 0.287 | 0.365 | 0.534 | w4 |\n| random/256 | small (2) | 0.288 | 0.292 | 0.885 | 0.467 | 0.339 | 0.287 | 0.307 | 0.388 | 0.588 | w4 |\n| random/256 | word (64) | 0.308 | 0.313 | 0.889 | 0.476 | 0.351 | 0.305 | 0.353 | 0.489 | 0.804 | w4 |\n| random/256 | half (128) | 0.321 | 0.325 | 0.894 | 0.475 | 0.354 | 0.318 | 0.379 | 0.546 | 0.918 | w4 |\n| random/256 | large (254) | 0.342 | 0.346 | 0.894 | 0.482 | 0.364 | 0.338 | 0.427 | 0.648 | 1.096 | w4 |\n| random/512 | small (2) | 0.641 | 0.363 | 0.892 | 0.481 | 0.366 | 0.363 | 0.457 | 0.690 | \u2014 | w4 |\n| random/512 | word (64) | 0.676 | 0.397 | 0.894 | 0.484 | 0.383 | 0.392 | 0.526 | 0.864 | \u2014 | w3 |\n| random/512 | half (256) | 0.721 | 0.446 | 0.897 | 0.497 | 0.408 | 0.443 | 0.629 | 1.110 | \u2014 | w3 |\n| random/512 | large (510) | 0.763 | 0.502 | 0.901 | 0.511 | 0.430 | 0.500 | 0.742 | 1.337 | \u2014 | w3 |\n| random/1024 | small (2) | 1.478 | 0.462 | 0.882 | 0.514 | 0.463 | 0.562 | 0.836 | \u2014 | \u2014 | w3 |\n| random/1024 | word (65) | 1.561 | 0.491 | 0.889 | 0.526 | 0.488 | 0.615 | 0.966 | \u2014 | \u2014 | w3 |\n| random/1024 | half (512) | 1.812 | 0.571 | 0.901 | 0.565 | 0.569 | 0.780 | 1.321 | \u2014 | \u2014 | w2 |\n| random/1024 | large (1019) | 1.901 | 0.645 | 0.918 | 0.593 | 0.643 | 0.928 | 1.624 | \u2014 | \u2014 | w2 |\n| random/2048 | small (2) | 3.921 | 0.605 | 0.857 | 0.613 | 0.694 | 0.993 | \u2014 | \u2014 | \u2014 | w2 |\n| random/2048 | word (64) | 4.116 | 0.637 | 0.858 | 0.632 | 0.724 | 1.083 | \u2014 | \u2014 | \u2014 | w2 |\n| random/2048 | half (1024) | 4.818 | 0.744 | 0.912 | 0.739 | 0.950 | 1.535 | \u2014 | \u2014 | \u2014 | w2 |\n| random/2048 | large (2048) | 5.369 | 0.823 | 0.954 | 0.823 | 1.134 | 1.868 | \u2014 | \u2014 | \u2014 | w2 |\n| random/4096 | small (2) | 12.482 | 0.756 | 0.827 | 0.773 | 1.025 | \u2014 | \u2014 | \u2014 | \u2014 | w2 |\n| random/4096 | word (65) | 12.973 | 1.011 | 0.845 | 0.789 | 1.073 | \u2014 | \u2014 | \u2014 | \u2014 | w2 |\n| random/4096 | half (2048) | 15.849 | 1.008 | 0.961 | 1.011 | 1.499 | \u2014 | \u2014 | \u2014 | \u2014 | w1 |\n| random/4096 | large (4096) | 17.105 | 1.004 | 1.036 | 1.154 | 1.809 | \u2014 | \u2014 | \u2014 | \u2014 | w1 |\n| random/8192 | small (2) | 43.591 | 0.794 | 0.801 | 0.878 | \u2014 | \u2014 | \u2014 | \u2014 | \u2014 | w1 |\n| random/8192 | word (64) | 44.715 | 0.799 | 0.803 | 0.889 | \u2014 | \u2014 | \u2014 | \u2014 | \u2014 | w1 |\n| random/8192 | half (4096) | 55.061 | 1.008 | 0.967 | 1.207 | \u2014 | \u2014 | \u2014 | \u2014 | \u2014 | w1 |\n| random/8192 | large (8189) | 61.312 | 1.006 | 1.078 | 1.425 | \u2014 | \u2014 | \u2014 | \u2014 | \u2014 | w1 |\n\n## Largest policy costs relative to the best measured loop\n\nPer-case ratios retain exponent-specific losses that a mean can hide; the baseline is also eligible.\n\n| Case | Policy ms | Policy/binary | Best loop | Policy/best |\n|---|---:|---:|---|---:|\n| random-4096-word-dense | 58.309 | 1.009 | w2 | 1.530 |\n| random-512-large-dense | 1.966 | 0.596 | w3 | 1.334 |\n| random-32-small-dense | 0.055 | 0.308 | w7 | 1.315 |\n| random-4096-word-mixed | 49.348 | 0.999 | w2 | 1.294 |\n| random-4096-word-short | 0.652 | 1.027 | w2 | 1.267 |\n| random-32-small-mixed | 0.051 | 0.306 | w7 | 1.265 |\n| random-32-small-sparse | 0.050 | 0.317 | w7 | 1.250 |\n| random-32-word-sparse | 0.049 | 0.312 | w7 | 1.241 |\n| random-1024-large-dense | 5.455 | 0.759 | w2 | 1.234 |\n| random-32-large-sparse | 0.049 | 0.317 | w7 | 1.234 |\n| random-32-half-sparse | 0.050 | 0.315 | w7 | 1.224 |\n| random-512-large-short | 0.197 | 0.565 | w3 | 1.198 |\n\n## Largest absolute losses\n\nAbsolute differences use per-case medians; the baseline is eligible. All cases remain in the score.\n\n| Case | Policy ms | Best ms | Extra ms |\n|---|---:|---:|---:|\n| random-8192-half-dense | 253.074 | 230.147 | 22.927 |\n| random-4096-word-dense | 58.309 | 38.589 | 19.720 |\n| random-4096-word-mixed | 49.348 | 38.380 | 10.968 |\n| random-8192-word-sparse | 160.854 | 150.803 | 10.051 |\n| random-8192-small-sparse | 159.486 | 150.641 | 8.844 |\n| random-8192-half-mixed | 205.291 | 197.866 | 7.425 |\n| random-4096-half-dense | 58.080 | 53.286 | 4.795 |\n| random-4096-word-sparse | 39.750 | 37.451 | 2.299 |\n\nGeometric mean cost relative to the best measured loop: imported policy 1.067; editable choose() prediction 1.032.\nThe prediction excludes dispatch. Every case has equal weight; minima are a hindsight comparison, not a statistical lower bound.\n\nElapsed wall time: 122.3 s. CPU: 83 (AMD EPYC 9455 48-Core Processor). Host: Linux-6.12.100-x86_64-with-glibc2.42.\n\nAll samples, inputs, source snapshots, return status and toolchain metadata accompany this summary.\n"
  },
  "validation": {
    "Tune.lean": "/-\nCopyright (c) 2026 Lean FRO, LLC. All rights reserved.\nReleased under Apache 2.0 license as described in the Lean repository LICENSE.\nAuthors: Kim Morrison\n-/\nmodule\nimport Lean\nmeta import Lean\n\n/-! Standalone kernel powMod tuning. No declarations are added to the library.\nThe JSON cases and every timed sample are retained by tune.py. -/\n\nopen Lean\n\nstructure Case where\n  id : String\n  b : Nat\n  e : Nat\n  m : Nat\n  widths : List Nat\n  expected : Nat\n  deriving FromJson\n\ndef power (c : Case) (width : Option Nat) : Expr := Id.run do\n  let b := mkRawNatLit c.b\n  let e := mkRawNatLit c.e\n  let m := mkRawNatLit c.m\n  let base := mkApp2 (mkConst ``Nat.mod) b m\n  let fuel := mkApp (mkConst ``Nat.succ) e\n  match width with\n  | none => return mkApp3 (mkConst ``Nat.powMod) b e m\n  | some 0 => return mkApp5 (mkConst ``Nat.powMod.go) m fuel base e (mkRawNatLit 1)\n  | some w => return mkApp5 (mkConst ``Nat.powMod.window) base m (mkRawNatLit (2^w)) fuel e\n\n-- Checking the identity application forces the supplied equality's endpoints\n-- to agree; merely checking Eq.refl's inferred type would not test the power.\ndef proof (lhs : Expr) (value : Nat) : Expr :=\n  let n := mkConst ``Nat\n  let rhs := mkRawNatLit value\n  let type := mkApp3 (mkConst ``Eq [.succ .zero]) n lhs rhs\n  mkApp (mkLambda `h .default type (mkBVar 0))\n    (mkApp2 (mkConst ``Eq.refl [.succ .zero]) n rhs)\n\nrun_cmd do\n  let path \u2190 IO.getEnv \"POWMOD_CASES\"\n  let some path := path | throwError \"set POWMOD_CASES to the generated JSON file\"\n  let cases : List Case \u2190 ofExcept <| (Json.parse (\u2190 IO.FS.readFile path)).bind fromJson?\n  let some output \u2190 IO.getEnv \"POWMOD_SAMPLES\" | throwError \"set POWMOD_SAMPLES\"\n  let samples \u2190 IO.FS.Handle.mk output .write\n  let blocks := ((\u2190 IO.getEnv \"POWMOD_BLOCKS\").getD \"4\").toNat!\n  -- Drain asynchronous checking before creating the reusable import environment.\n  let ready \u2190 IO.mkRef (\u2190 getEnv).toKernelEnv\n  let env := Environment.ofKernelEnv (\u2190 ready.get)\n  for block in [:blocks] do\n    for c in cases do\n      -- The compiled GMP implementation supplies an untrusted reference outside\n      -- the timer. Each fresh kernel checker must establish the equality itself.\n      let value := Nat.powMod c.b c.e c.m\n      if value != c.expected then throwError \"GMP disagrees with Python reference\"\n      let candidates := (\"policy\", none) :: c.widths.map (fun w => (s!\"w{w}\", some w))\n      if block == 0 then\n        for width in some 0 :: candidates.map Prod.snd do\n          let bad \u2190 IO.mkRef (Kernel.check env {} (proof (power c width) (value + 1)))\n          if (\u2190 bad.get).isOk then throwError \"incorrect-result control was accepted\"\n      -- Equal preparation in every block; kernel caches are still fresh per call.\n      let warm \u2190 IO.mkRef (Kernel.check env {} (proof (power c none) value))\n      let _ \u2190 ofExceptKernelException (\u2190 warm.get)\n      for (name, width) in candidates do\n        let arms := [(\"binary\", some 0), (name, width)]\n        let arms := if block % 2 == 0 then arms else arms.reverse\n        for (arm, width) in arms do\n          -- References prevent the pure check from moving across the IO timer.\n          let input \u2190 IO.mkRef (env, proof (power c width) value)\n          let (env, term) \u2190 input.get\n          let start \u2190 IO.monoNanosNow\n          let checked \u2190 IO.mkRef (Kernel.check env {} term)\n          let checked \u2190 checked.get\n          let stop \u2190 IO.monoNanosNow\n          let _ \u2190 ofExceptKernelException checked\n          samples.putStrLn s!\"SAMPLE,{block},{c.id},{name},{arm},{stop - start}\"\n          samples.flush\n  IO.println \"COMPLETE\"\n",
    "tune.py": "#!/usr/bin/env python3\n\"\"\"Standalone powMod kernel tuning; Python standard library, no CI integration.\nCopyright (c) 2026 Lean FRO, LLC. Apache-2.0 (Lean repository LICENSE).\n\"\"\"\nimport argparse\nimport collections\nimport csv\nimport hashlib\nimport json\nimport math\nimport os\nfrom pathlib import Path\nimport platform\nimport statistics as stats\nimport subprocess\nimport sys\nimport tempfile\nimport time\n\n# These are the experiment, not the policy. Edit them or supply --cases JSON.\nBITS = [32, 64, 128, 256, 512, 1024, 2048, 4096, 8192]\nPATTERNS = [\"dense\", \"mixed\", \"sparse\", \"short\"]\nBASES = [\"small\", \"word\", \"half\", \"large\"]\nWIDTHS = list(range(1, 8))\nMAX_INTERMEDIATE_BITS = 65536  # excludes costly cells, explicitly recorded\n\n\ndef random_bits(n, label):\n    data = hashlib.shake_256(label.encode()).digest((n+7)//8)\n    return (int.from_bytes(data, \"little\") & ((1 << n)-1)) | (1 << (n-1))\n\n\ndef choose(c):\n    \"\"\"Editable policy: returns 0 for binary, otherwise the window width.\n    --summarize scores edits from existing samples; rebuild Lean to time dispatch.\n    \"\"\"\n    m, b = c[\"m\"], c[\"b\"] % c[\"m\"]\n    if m <= 1 << 64: return 6\n    if m <= 1 << 512: return 4\n    if m <= 1 << 1024: return 3\n    if m <= 1 << 2048: return 2\n    if b >= 1 << 64: return 0\n    if m <= 1 << 4096: return 2\n    return 1\n\n\ndef cases(bits, family, bases=BASES):\n    out = []\n    for n in bits:\n        seed = f\"powmod-{family}-{n}\"\n        if family == \"irregular\": m = ((1 << (n-1))*8//7 + 147) | 1\n        else: m = random_bits(n, seed+\"m\") | 1\n        used = set()\n        for base in bases:\n            b = (2 if base == \"small\" else (1 << 64)-1 if base == \"word\" else\n                 random_bits(n//2, seed+\"half\") if base == \"half\" else\n                 random_bits(n, seed+\"full\") if base == \"large\" else (1 << int(base))-1)\n            b %= m\n            while math.gcd(b, m) != 1:\n                b = (b+1) % m\n            if b in used: continue\n            used.add(b)\n            for pattern in PATTERNS:\n                e = {\"dense\": (1 << n)-1,\n                     \"mixed\": random_bits(n, seed+\"e\") if family == \"random\" else ((1 << n)-1)//3,\n                     \"sparse\": (1 << (n-1))+1,\n                     \"short\": random_bits(62, seed+\"short\") if family == \"random\" else 65537}[pattern]\n                widths = [w for w in WIDTHS\n                          if n*(1 << w) + b.bit_length()*((1 << w)-1) <= MAX_INTERMEDIATE_BITS]\n                out.append(dict(id=f\"{family}-{n}-{base}-{pattern}\", bits=n, family=family,\n                                base=base, pattern=pattern, b=b, e=e, m=m, widths=widths))\n    return out\n\n\ndef gm(xs):\n    return math.exp(stats.mean(math.log(x) for x in xs))\n\n\ndef summarize(out):\n    meta = json.loads((out / \"metadata.json\").read_text())\n    inputs = json.loads((out / \"cases.json\").read_text())\n    samples = []\n    raw = out / \"raw.csv\"\n    if not raw.exists(): raw = out / \"stdout.txt\"  # retained exploratory records\n    for line in raw.read_text().splitlines():\n        if line.startswith(\"SAMPLE,\"):\n            _, block, case, candidate, arm, ns = line.split(\",\")\n            samples.append((int(block), case, candidate, arm, int(ns)))\n    with (out / \"samples.csv\").open(\"w\") as f:\n        writer = csv.writer(f)\n        writer.writerow([\"block\", \"case\", \"candidate\", \"arm\", \"kernel_ns\"])\n        writer.writerows(samples)\n    expected = meta[\"blocks\"] * 2 * sum(1+len(c[\"widths\"]) for c in inputs)\n    if len(samples) != expected or meta[\"returncode\"] != 0 or \"COMPLETE\" not in (out/\"stdout.txt\").read_text():\n        raise SystemExit(f\"Incomplete run: retained {len(samples)}/{expected} samples in {out}\")\n    pairs = collections.defaultdict(dict)\n    for block, case, candidate, arm, ns in samples:\n        key = (block, case, candidate)\n        if arm in pairs[key]:\n            raise SystemExit(f\"duplicate sample: {key} {arm}\")\n        pairs[key][arm] = ns\n    ratios = collections.defaultdict(list)\n    absolute = collections.defaultdict(list)\n    for (block, case, candidate), arms in pairs.items():\n        ratios[case, candidate].append(arms[candidate] / arms[\"binary\"])\n        absolute[case, candidate].append(arms[candidate] / 1e6)\n        absolute[case, \"binary\"].append(arms[\"binary\"] / 1e6)\n    med = {key: stats.median(values) for key, values in ratios.items()}\n    lines = [\"# Kernel powMod tuning\", \"\", f\"{len(inputs)} cases; {len(samples)} retained checks; {meta['blocks']} adjacent AB/BA blocks.\",\n             \"\", \"Each cell is the geometric mean of per-case median paired ratios to the binary loop (lower is better).\",\n             \"Dense, mixed, sparse and short exponents receive equal weight. `policy` includes dispatch; width columns time the loops directly.\",\n             \"A dash means the intermediate-size cap excluded that width. No statistical equivalence or universal optimum is claimed.\", \"\",\n             \"| Modulus family/bits | Base (reduced bits) | best fixed gm ms | policy | \" + \" | \".join(f\"w{w}\" for w in WIDTHS) + \" | best fixed width |\",\n             \"|---|---|---:|---:|\" + \"---:|\"*len(WIDTHS) + \"---:|\"]\n    groups = collections.defaultdict(list)\n    for c in inputs:\n        groups[c[\"family\"], c[\"bits\"], c[\"base\"]].append(c)\n    for (family, bits, base), cs in groups.items():\n        values = {}\n        for name in [\"policy\"]+[f\"w{w}\" for w in WIDTHS]:\n            if all((c[\"id\"], name) in med for c in cs):\n                values[name] = gm(med[c[\"id\"], name] for c in cs)\n        best = min((k for k in values if k != \"policy\"), key=values.get)\n        lines.append(f\"| {family}/{bits} | {base} ({cs[0]['b'].bit_length()}) | {gm(stats.median(absolute[c['id'], best]) for c in cs):.3f} | \" + \" | \".join(f\"{values[k]:.3f}\" if k in values else \"\u2014\" for k in [\"policy\"]+[f\"w{w}\" for w in WIDTHS]) + f\" | {best} |\")\n    lines += [\"\", \"## Largest policy costs relative to the best measured loop\", \"\",\n              \"Per-case ratios retain exponent-specific losses that a mean can hide; the baseline is also eligible.\", \"\",\n              \"| Case | Policy ms | Policy/binary | Best loop | Policy/best |\", \"|---|---:|---:|---|---:|\"]\n    regrets = []\n    for c in inputs:\n        scores = {\"binary\": 1.0, **{f\"w{w}\": med[c[\"id\"], f\"w{w}\"] for w in c[\"widths\"]}}\n        best = min(scores, key=scores.get)\n        policy = med[c[\"id\"], \"policy\"]\n        regrets.append((policy/scores[best], c[\"id\"], best, policy))\n    for regret, case, best, policy in sorted(regrets, reverse=True)[:12]:\n        lines.append(f\"| {case} | {stats.median(absolute[case, 'policy']):.3f} | {policy:.3f} | {best} | {regret:.3f} |\")\n    lines += [\"\", \"## Largest absolute losses\", \"\",\n              \"Absolute differences use per-case medians; the baseline is eligible. All cases remain in the score.\", \"\",\n              \"| Case | Policy ms | Best ms | Extra ms |\", \"|---|---:|---:|---:|\"]\n    losses = []\n    for c in inputs:\n        policy_ms = stats.median(absolute[c[\"id\"], \"policy\"])\n        best_ms = min(stats.median(absolute[c[\"id\"], name]) for name in\n                      [\"binary\"]+[f\"w{w}\" for w in c[\"widths\"]])\n        losses.append((policy_ms-best_ms, c[\"id\"], policy_ms, best_ms))\n    for loss, case, current, best in sorted(losses, reverse=True)[:8]:\n        lines.append(f\"| {case} | {current:.3f} | {best:.3f} | {loss:.3f} |\")\n    predicted = []\n    actual = []\n    for c in inputs:\n        costs = [1.0]+[med[c[\"id\"], f\"w{w}\"] for w in c[\"widths\"]]\n        w = choose(c)\n        chosen = 1.0 if w == 0 else med.get((c[\"id\"], f\"w{w}\"))\n        if chosen is None: raise SystemExit(f\"policy selects unmeasured w{w} at {c['id']}\")\n        predicted.append(chosen/min(costs))\n        actual.append(med[c[\"id\"], \"policy\"]/min(costs))\n    lines += [\"\", f\"Geometric mean cost relative to the best measured loop: imported policy {gm(actual):.3f}; editable choose() prediction {gm(predicted):.3f}.\",\n              \"The prediction excludes dispatch. Every case has equal weight; minima are a hindsight comparison, not a statistical lower bound.\"]\n    lines += [\"\", f\"Elapsed wall time: {meta['elapsed_seconds']:.1f} s. CPU: {meta['cpu']} ({meta.get('cpu_model', 'model absent in this archived run')}). Host: {meta['host']}.\",\n              \"\", \"All samples, inputs, source snapshots, return status and toolchain metadata accompany this summary.\"]\n    (out / \"summary.md\").write_text(\"\\n\".join(lines)+\"\\n\")\n    print(out / \"summary.md\")\n\n\ndef pin():\n    \"\"\"Reserve an available affinity CPU among simultaneous copies of this runner.\"\"\"\n    if not hasattr(os, \"sched_getaffinity\"):\n        return None, None\n    import fcntl\n    allowed = sorted(os.sched_getaffinity(0))\n    start = os.getpid() % len(allowed)\n    for cpu in allowed[start:]+allowed[:start]:\n        lock = open(Path(tempfile.gettempdir()) / f\"powmod-tuning-{cpu}.lock\", \"a\")\n        try:\n            fcntl.flock(lock, fcntl.LOCK_EX | fcntl.LOCK_NB)\n        except BlockingIOError:\n            lock.close()\n            continue\n        os.sched_setaffinity(0, {cpu})\n        return cpu, lock\n    raise SystemExit(\"All affinity CPUs reserved by other tuning runners\")\n\n\ndef main():\n    parser = argparse.ArgumentParser(description=__doc__)\n    parser.add_argument(\"--restore\", type=Path, help=\"unpack one run from evidence.json\")\n    parser.add_argument(\"--run\", default=\"calibration\", help=\"archived run to restore\")\n    parser.add_argument(\"--repo\", type=Path, default=Path.cwd())\n    parser.add_argument(\"--out\", type=Path, required=True)\n    parser.add_argument(\"--blocks\", type=int, default=4)\n    parser.add_argument(\"--bits\", help=\"comma-separated sweep sizes\")\n    parser.add_argument(\"--cases\", type=Path, help=\"replace the generated corpus with this JSON\")\n    parser.add_argument(\"--suite\", choices=[\"sweep\", \"heldout\", \"boundaries\", \"smoke\"], default=\"sweep\")\n    parser.add_argument(\"--summarize\", action=\"store_true\")\n    args = parser.parse_args()\n    out = args.out.resolve()\n    if args.restore:\n        files = json.loads(args.restore.read_text())[args.run]\n        if any(Path(name).name != name for name in files): parser.error(\"invalid archive filename\")\n        out.mkdir(parents=True, exist_ok=False)\n        for name, content in files.items(): (out/name).write_text(content)\n        return\n    if args.summarize:\n        summarize(out)\n        return\n    if args.blocks < 2 or args.blocks % 2:\n        parser.error(\"--blocks must be positive and even (AB/BA)\")\n    repo = args.repo.resolve()\n    lean = repo / \"build/release/stage1/bin/lean\"\n    if not lean.is_file():\n        parser.error(\"build Lean first: make -j$(nproc) -C build/release\")\n    if args.cases:\n        inputs = json.loads(args.cases.read_text())\n    elif args.suite == \"smoke\":\n        inputs = cases([32], \"random\")[:1]\n    elif args.suite == \"heldout\":\n        inputs = cases([48, 80, 160, 320, 640, 1280, 2560, 5120, 10240], \"validation\")\n    elif args.suite == \"boundaries\":\n        inputs = cases([2048, 8192], \"irregular\", [\"32\", \"63\", \"64\", \"65\", \"96\", \"128\"])\n        for c in inputs:\n            c[\"b\"] = (1 << int(c[\"base\"]))-1  # exact bases, even when non-coprime\n        extra = []\n        for c in inputs:\n            if c[\"base\"] == \"64\":\n                for delta in [0, 1]:\n                    extra.append(dict(c, id=c[\"id\"]+f\"-plus{delta}\", base=f\"2^64+{delta}\", b=(1 << 64)+delta))\n        inputs += extra\n        for c in cases([4096, 8192], \"irregular\", [\"small\", \"large\"]):\n            if c[\"pattern\"] != \"dense\": continue\n            for bits, delta in [(32, -1), (63, -1), (64, -1), (64, 0), (64, 1), (65, -1), (96, -1)]:\n                extra_id = f\"{bits}{delta:+}\"\n                inputs.append(dict(c, id=c[\"id\"]+\"-e\"+extra_id, family=\"exponent-cutoff\",\n                                   pattern=\"e\"+extra_id, e=(1 << bits)+delta))\n    else:\n        inputs = cases([int(n) for n in args.bits.split(\",\")] if args.bits else BITS, \"random\")\n    if len({c[\"id\"] for c in inputs}) != len(inputs): parser.error(\"duplicate case IDs\")\n    for c in inputs:\n        if min(c[\"m\"], c[\"b\"]+1, c[\"e\"]+1) <= 0: parser.error(\"positive modulus and natural inputs required\")\n        c[\"expected\"] = pow(c[\"b\"], c[\"e\"], c[\"m\"])\n    out.mkdir(parents=True, exist_ok=False)\n    cpu, lock = pin()\n    source = Path(__file__).resolve().parent\n    for name in [\"tune.py\", \"Tune.lean\"]:\n        (out/name).write_bytes((source/name).read_bytes())\n    (out / \"cases.json\").write_text(json.dumps(inputs, indent=2)+\"\\n\")\n    def git(*xs):\n        return subprocess.check_output([\"git\", \"-C\", str(repo), *xs], text=True).strip()\n    meta = dict(host=platform.platform(), machine=platform.node(), cpu=cpu, returncode=None, blocks=args.blocks, suite=args.suite,\n                commit=git(\"rev-parse\", \"HEAD\"), diff=git(\"diff\", \"HEAD\"),\n                lean=subprocess.check_output([str(lean), \"--version\"], text=True).strip(),\n                load_before=os.getloadavg(), command=sys.argv,\n                hashes={n: hashlib.sha256((out/n).read_bytes()).hexdigest() for n in [\"tune.py\", \"Tune.lean\", \"cases.json\"]})\n    info = Path(\"/proc/cpuinfo\")\n    meta[\"cpu_model\"] = next((line.split(\":\", 1)[1].strip() for line in info.read_text().splitlines()\n                              if line.startswith(\"model name\")), \"unknown\") if info.exists() else platform.processor()\n    meta[\"source_sha256\"] = hashlib.sha256((repo/\"src/Init/Data/Nat/PowMod.lean\").read_bytes()).hexdigest()\n    (out/\"metadata.json\").write_text(json.dumps(meta, indent=2)+\"\\n\")\n    start = time.monotonic()\n    env = dict(os.environ, POWMOD_CASES=str(out/\"cases.json\"), POWMOD_BLOCKS=str(args.blocks), POWMOD_SAMPLES=str(out/\"raw.csv\"))\n    env.pop(\"LEAN_PATH\", None)\n    with (out/\"stdout.txt\").open(\"w\") as stdout, (out/\"stderr.txt\").open(\"w\") as stderr:\n        try:\n            result = subprocess.run([str(lean), str(out/\"Tune.lean\")], cwd=repo, env=env, stdout=stdout, stderr=stderr)\n            meta[\"returncode\"] = result.returncode\n        finally:\n            meta.update(elapsed_seconds=time.monotonic()-start, load_after=os.getloadavg())\n            (out/\"metadata.json\").write_text(json.dumps(meta, indent=2)+\"\\n\")\n    summarize(out)\n\n\nif __name__ == \"__main__\":\n    main()\n",
    "cases.json": "[\n  {\n    \"id\": \"validation-48-small-dense\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"small\",\n    \"pattern\": \"dense\",\n    \"b\": 2,\n    \"e\": 281474976710655,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 91972237658504\n  },\n  {\n    \"id\": \"validation-48-small-mixed\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"small\",\n    \"pattern\": \"mixed\",\n    \"b\": 2,\n    \"e\": 93824992236885,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 122273320722233\n  },\n  {\n    \"id\": \"validation-48-small-sparse\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"small\",\n    \"pattern\": \"sparse\",\n    \"b\": 2,\n    \"e\": 140737488355329,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 59373579923429\n  },\n  {\n    \"id\": \"validation-48-small-short\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"small\",\n    \"pattern\": \"short\",\n    \"b\": 2,\n    \"e\": 65537,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 131606366913677\n  },\n  {\n    \"id\": \"validation-48-word-dense\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"word\",\n    \"pattern\": \"dense\",\n    \"b\": 127005738909832,\n    \"e\": 281474976710655,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 8080992716434\n  },\n  {\n    \"id\": \"validation-48-word-mixed\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"word\",\n    \"pattern\": \"mixed\",\n    \"b\": 127005738909832,\n    \"e\": 93824992236885,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 100215350232817\n  },\n  {\n    \"id\": \"validation-48-word-sparse\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"word\",\n    \"pattern\": \"sparse\",\n    \"b\": 127005738909832,\n    \"e\": 140737488355329,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 102535846508278\n  },\n  {\n    \"id\": \"validation-48-word-short\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"word\",\n    \"pattern\": \"short\",\n    \"b\": 127005738909832,\n    \"e\": 65537,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 77618247834409\n  },\n  {\n    \"id\": \"validation-48-half-dense\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"half\",\n    \"pattern\": \"dense\",\n    \"b\": 13673749,\n    \"e\": 281474976710655,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 88841103996481\n  },\n  {\n    \"id\": \"validation-48-half-mixed\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"half\",\n    \"pattern\": \"mixed\",\n    \"b\": 13673749,\n    \"e\": 93824992236885,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 116655375957349\n  },\n  {\n    \"id\": \"validation-48-half-sparse\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"half\",\n    \"pattern\": \"sparse\",\n    \"b\": 13673749,\n    \"e\": 140737488355329,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 20776559867032\n  },\n  {\n    \"id\": \"validation-48-half-short\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"half\",\n    \"pattern\": \"short\",\n    \"b\": 13673749,\n    \"e\": 65537,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 19687790311378\n  },\n  {\n    \"id\": \"validation-48-large-dense\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"large\",\n    \"pattern\": \"dense\",\n    \"b\": 106798214995777,\n    \"e\": 281474976710655,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 33812220619744\n  },\n  {\n    \"id\": \"validation-48-large-mixed\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"large\",\n    \"pattern\": \"mixed\",\n    \"b\": 106798214995777,\n    \"e\": 93824992236885,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 122800401257656\n  },\n  {\n    \"id\": \"validation-48-large-sparse\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"large\",\n    \"pattern\": \"sparse\",\n    \"b\": 106798214995777,\n    \"e\": 140737488355329,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 60104550142135\n  },\n  {\n    \"id\": \"validation-48-large-short\",\n    \"bits\": 48,\n    \"family\": \"validation\",\n    \"base\": \"large\",\n    \"pattern\": \"short\",\n    \"b\": 106798214995777,\n    \"e\": 65537,\n    \"m\": 148198928819097,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 62764706270749\n  },\n  {\n    \"id\": \"validation-80-small-dense\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"small\",\n    \"pattern\": \"dense\",\n    \"b\": 2,\n    \"e\": 1208925819614629174706175,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 828177219580910643739583\n  },\n  {\n    \"id\": \"validation-80-small-mixed\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"small\",\n    \"pattern\": \"mixed\",\n    \"b\": 2,\n    \"e\": 402975273204876391568725,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 973672937692147063207433\n  },\n  {\n    \"id\": \"validation-80-small-sparse\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"small\",\n    \"pattern\": \"sparse\",\n    \"b\": 2,\n    \"e\": 604462909807314587353089,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 400930750186775647740308\n  },\n  {\n    \"id\": \"validation-80-small-short\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"small\",\n    \"pattern\": \"short\",\n    \"b\": 2,\n    \"e\": 65537,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 779457270610282534173824\n  },\n  {\n    \"id\": \"validation-80-word-dense\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"word\",\n    \"pattern\": \"dense\",\n    \"b\": 18446744073709551616,\n    \"e\": 1208925819614629174706175,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 345281589695062925481928\n  },\n  {\n    \"id\": \"validation-80-word-mixed\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"word\",\n    \"pattern\": \"mixed\",\n    \"b\": 18446744073709551616,\n    \"e\": 402975273204876391568725,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 307429596934750827050026\n  },\n  {\n    \"id\": \"validation-80-word-sparse\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"word\",\n    \"pattern\": \"sparse\",\n    \"b\": 18446744073709551616,\n    \"e\": 604462909807314587353089,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 149545286400980505123859\n  },\n  {\n    \"id\": \"validation-80-word-short\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"word\",\n    \"pattern\": \"short\",\n    \"b\": 18446744073709551616,\n    \"e\": 65537,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 641602645073378814409735\n  },\n  {\n    \"id\": \"validation-80-half-dense\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"half\",\n    \"pattern\": \"dense\",\n    \"b\": 655739857942,\n    \"e\": 1208925819614629174706175,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 951960153217558479068761\n  },\n  {\n    \"id\": \"validation-80-half-mixed\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"half\",\n    \"pattern\": \"mixed\",\n    \"b\": 655739857942,\n    \"e\": 402975273204876391568725,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 404661424140379446490885\n  },\n  {\n    \"id\": \"validation-80-half-sparse\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"half\",\n    \"pattern\": \"sparse\",\n    \"b\": 655739857942,\n    \"e\": 604462909807314587353089,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 657254126412974470409968\n  },\n  {\n    \"id\": \"validation-80-half-short\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"half\",\n    \"pattern\": \"short\",\n    \"b\": 655739857942,\n    \"e\": 65537,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 215001043978701180968755\n  },\n  {\n    \"id\": \"validation-80-large-dense\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"large\",\n    \"pattern\": \"dense\",\n    \"b\": 668182355160813845799593,\n    \"e\": 1208925819614629174706175,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 446106084641754166168055\n  },\n  {\n    \"id\": \"validation-80-large-mixed\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"large\",\n    \"pattern\": \"mixed\",\n    \"b\": 668182355160813845799593,\n    \"e\": 402975273204876391568725,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 722876782914782696534543\n  },\n  {\n    \"id\": \"validation-80-large-sparse\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"large\",\n    \"pattern\": \"sparse\",\n    \"b\": 668182355160813845799593,\n    \"e\": 604462909807314587353089,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 272657453007543363344948\n  },\n  {\n    \"id\": \"validation-80-large-short\",\n    \"bits\": 80,\n    \"family\": \"validation\",\n    \"base\": \"large\",\n    \"pattern\": \"short\",\n    \"b\": 668182355160813845799593,\n    \"e\": 65537,\n    \"m\": 1154191276030655777466363,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 978096952294134951749183\n  },\n  {\n    \"id\": \"validation-160-small-dense\",\n    \"bits\": 160,\n    \"family\": \"validation\",\n    \"base\": \"small\",\n    \"pattern\": \"dense\",\n    \"b\": 2,\n    \"e\": 1461501637330902918203684832716283019655932542975,\n    \"m\": 984737284307687991303539619998556041048796153411,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 427018360415438860117862704191120597011639824835\n  },\n  {\n    \"id\": \"validation-160-small-mixed\",\n    \"bits\": 160,\n    \"family\": \"validation\",\n    \"base\": \"small\",\n    \"pattern\": \"mixed\",\n    \"b\": 2,\n    \"e\": 487167212443634306067894944238761006551977514325,\n    \"m\": 984737284307687991303539619998556041048796153411,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 690472066215862633430669837491813081659089689673\n  },\n  {\n    \"id\": \"validation-160-small-sparse\",\n    \"bits\": 160,\n    \"family\": \"validation\",\n    \"base\": \"small\",\n    \"pattern\": \"sparse\",\n    \"b\": 2,\n    \"e\": 730750818665451459101842416358141509827966271489,\n    \"m\": 984737284307687991303539619998556041048796153411,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 275112200774960336880613889824895029739176456265\n  },\n  {\n    \"id\": \"validation-160-small-short\",\n    \"bits\": 160,\n    \"family\": \"validation\",\n    \"base\": \"small\",\n    \"pattern\": \"short\",\n    \"b\": 2,\n    \"e\": 65537,\n    \"m\": 984737284307687991303539619998556041048796153411,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 735099959334022447976351795359738650304043943302\n  },\n  {\n    \"id\": \"validation-160-word-dense\",\n    \"bits\": 160,\n    \"family\": \"validation\",\n    \"base\": \"word\",\n    \"pattern\": \"dense\",\n    \"b\": 18446744073709551616,\n    \"e\": 1461501637330902918203684832716283019655932542975,\n    \"m\": 984737284307687991303539619998556041048796153411,\n    \"widths\": [\n      1,\n      2,\n      3,\n      4,\n      5,\n      6,\n      7\n    ],\n    \"expected\": 71647890373774025751436753060336072468523530441\n  },\n  {\n    \"id\": \"validation-160-word-mixed\",\n    \"bits\": 160,\n    \"family\": \"validation\",\n    \"base\": \"word\",\n    \"pattern\": \"mixed\",\n    \"b\": 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   \"widths\": [\n      1,\n      2\n    ],\n    \"expected\": 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 },\n  {\n    \"id\": \"validation-5120-large-short\",\n    \"bits\": 5120,\n    \"family\": \"validation\",\n    \"base\": \"large\",\n    \"pattern\": \"short\",\n    \"b\": 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large.py

tune.py