square-root performance test between native implementation and Newton's method.

sqrt.py

import random
import operator
from datetime import datetime
from math import sqrt
from functools import reduce

def better_gues(number,gues):
    return ((number/gues) + gues) /2

def sqrt1(number,gues=None):
    if gues is None:
        gues = number/2

    if abs(number - gues*gues) <0.001:
        return gues
    else:
        return sqrt1(number,better_gues(number,gues))

#tests
if __name__ == '__main__':
    SIZE = 10000000
    # create test lists
    l = [random.random()*SIZE*10 for i in range(SIZE)]
    l1 = l[:]
    l2 = l[:]

    start = datetime.now()
    l1 = map(sqrt,l1)
    end = datetime.now()
    print('native',str(end-start))

    start = datetime.now()
    l2 = map(sqrt1,l2)
    end = datetime.now()
    print('our version',str(end-start))
    
    avrg = reduce(operator.add, map(lambda x,y:x-y,l1,l2))/SIZE
    print('l3 =', avrg)

##########################
# PRINTED SAMPLE RESULTS #
##########################
    
# Results for python 2.6.6
# ('native', '0:00:01.095318')
# ('our version', '0:01:50.710895')
# ('l3 =', -7.1736151821178763e-09)

# Results for python 3.2
# native 0:00:00.000084
# our version 0:00:00.000005
# l3 = -7.18527774924e-09

sqrt.scm

(define (average x y) (/ (+ x y) 2))

(define (square x) (* x x))

(define (abs x)(if (< x 0) (- x) x))

(define (better_guess number guess)
  (average (/ number guess) guess)
  )

(define (calculate_square_root number guess)
  (if (< (abs (- (square guess) number)) 0.001)
	  guess
	  (calculate_square_root number (better_guess number guess))
	  )
  )
  
(define (sqrt1 x)
  (calculate_square_root x (/ x 2)))