profiling solutions for http://stackoverflow.com/questions/17497281/most-efficient-way-to-check-3-lists-for-a-common-integer-in-haskell see also https://s3.amazonaws.com/jd2-4a7cb8e3affb4a7f0cf8229a481d0dc3-us/public/ProfileIntersect.html

ProfileIntersect.hs

module Main where
import Criterion.Main
import qualified Data.List.Ordered as O
import qualified Data.List as L
import qualified Data.Set as S
import qualified Data.IntSet as IS

repeatsTail, orderedIntersect, listIntersect, setIntersect :: [Integer] -> [Integer] -> [Integer] -> [Integer]
intsetIntersect :: [Int] -> [Int] -> [Int] -> [Int]

repeatsTail f s t = go f s t []
   where go [] _ _  acc = reverse acc 
         go  _ [] _ acc = reverse acc 
         go  _ _ [] acc = reverse acc 
         go a@(x:xs) b@(y:ys) c@(z:zs) acc 
            | x == y && y == z     = go xs ys zs (x:acc)
            | x <= y && x <= z     = go xs b c acc 
            | y <= x && y <= z     = go a ys c acc 
            | otherwise            = go a b zs acc 

orderedIntersect a b c = O.isect a $ O.isect b c

listIntersect a b c = L.intersect a $ L.intersect b c

setIntersect a b c = S.toList (S.intersection (S.fromList a) (S.intersection (S.fromList b) (S.fromList c)))

intsetIntersect a b c = IS.toList (IS.intersection (IS.fromList a) (IS.intersection (IS.fromList b) (IS.fromList c)))

fibsLessThan100 :: Integral a => [a]
fibsLessThan100 = takeWhile (<100) . drop 1 $ fibs
  where fibs = 1 : 1 : zipWith (+) fibs (tail fibs)

primesLessThan100 :: Integral a => [a]
primesLessThan100 = takeWhile (<100) primes
  where primes = (2:) $ [3..] `O.minus` composites
        composites = foldr merge [] [ map (p*) [p..] | p <- primes ]
        merge (x:xs) ys = x : O.union xs ys

oddsLessThan100 :: Integral a => [a]
oddsLessThan100 = [1, 3..99]

go f = f fibsLessThan100 primesLessThan100 oddsLessThan100

main = defaultMain [
        bench "repeatsTail"               . flip nf integerArgs $ \(a,b,c) -> repeatsTail a b c,
        bench "Data.List.Ordered.isect"   . flip nf integerArgs $ \(a,b,c) -> orderedIntersect a b c,
        bench "Data.List.intersect"       . flip nf integerArgs $ \(a,b,c) -> listIntersect a b c,
        bench "Data.Set.intersect"        . flip nf integerArgs $ \(a,b,c) -> setIntersect a b c,
        bench "Data.IntSet.intersect"     . flip nf intArgs     $ \(a,b,c) -> intsetIntersect a b c
      ]
  where integerArgs :: ([Integer], [Integer], [Integer])
        integerArgs = (fibsLessThan100, primesLessThan100, oddsLessThan100)
        intArgs :: ([Int], [Int], [Int])
        intArgs = (fibsLessThan100, primesLessThan100, oddsLessThan100)
  

results.txt

warming up
estimating clock resolution...
mean is 3.262077 us (160001 iterations)
found 28401 outliers among 159999 samples (17.8%)
  25368 (15.9%) low severe
  3033 (1.9%) high severe
estimating cost of a clock call...
mean is 90.74326 ns (26 iterations)
found 3 outliers among 26 samples (11.5%)
  3 (11.5%) high severe

benchmarking repeatsTail
mean: 11.09914 us, lb 10.57613 us, ub 12.23400 us, ci 0.950
std dev: 3.764360 us, lb 2.101762 us, ub 7.015260 us, ci 0.950
found 19 outliers among 100 samples (19.0%)
  4 (4.0%) high mild
  15 (15.0%) high severe
variance introduced by outliers: 97.870%
variance is severely inflated by outliers

benchmarking Data.List.Ordered.isect
mean: 2.889594 us, lb 2.764070 us, ub 3.193310 us, ci 0.950
std dev: 944.8768 ns, lb 461.2368 ns, ub 1.863115 us, ci 0.950
found 18 outliers among 100 samples (18.0%)
  5 (5.0%) high mild
  13 (13.0%) high severe
variance introduced by outliers: 97.860%
variance is severely inflated by outliers

benchmarking Data.List.intersect
mean: 21.58114 us, lb 20.56325 us, ub 23.98248 us, ci 0.950
std dev: 7.593801 us, lb 3.694492 us, ub 13.91247 us, ci 0.950
found 15 outliers among 100 samples (15.0%)
  4 (4.0%) high mild
  11 (11.0%) high severe
variance introduced by outliers: 98.876%
variance is severely inflated by outliers

benchmarking Data.Set.intersect
mean: 29.81241 us, lb 28.30306 us, ub 33.72211 us, ci 0.950
std dev: 11.52247 us, lb 5.509201 us, ub 23.43350 us, ci 0.950
found 15 outliers among 100 samples (15.0%)
  3 (3.0%) high mild
  12 (12.0%) high severe
variance introduced by outliers: 98.897%
variance is severely inflated by outliers

benchmarking Data.IntSet.intersect
mean: 5.586984 us, lb 5.329440 us, ub 6.230935 us, ci 0.950
std dev: 1.943859 us, lb 871.9458 ns, ub 3.892892 us, ci 0.950
found 18 outliers among 100 samples (18.0%)
  5 (5.0%) high mild
  13 (13.0%) high severe
variance introduced by outliers: 97.876%
variance is severely inflated by outliers