A brief example

ex.py

import time
import numpy as np

def naive():
  x = 0
  y = 0
  for i in range(1, 1001):
    x += pow(i, 2)
    y += i
  return pow(y, 2) - x

def excellence():
  x = np.arange(1001, dtype='int64')
  sumsq = np.sum(x ** 2)
  sqsum = x.sum() ** 2

  return sqsum - sumsq

start = time.time()
for i in range(4):
  naive()
end = time.time()
print "Naive duration %.5f" % (end - start)

start = time.time()
for i in range(4):
  excellence()
end = time.time()
print "Excellent duration %.5f" % (end - start)