calculating the number of k-combinations with and without SciPy

Question

I'm puzzled by the fact that the function comb of SciPy appears to be slower than a naive Python implementation. This is the measured time for two equivalent programs solving the Problem 53 of Project Euler.

---

With SciPy:

%%timeit
from scipy.misc import comb

result = 0
for n in range(1, 101):
    for k in range(1, n + 1):
        if comb(n, k) > 1000000:
            result += 1
result

Output:

1 loops, best of 3: 483 ms per loop

---

Without SciPy:

%%timeit
from math import factorial

def comb(n, k):
    return factorial(n) / factorial(k) / factorial(n - k)

result = 0
for n in range(1, 101):
    for k in range(1, n + 1):
        if comb(n, k) > 1000000:
            result += 1
result

Output:

10 loops, best of 3: 86.9 ms per loop

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The second version is about 5 times faster (tested on two Macs, python-2.7.9-1, IPython 2.3.1-py27_0). Is this an expected behaviour of the comb function of SciPy (source code)? What am I doing wrong?

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Edit (SciPy from the Anaconda 3.7.3-py27_0 distribution):

import scipy; print scipy.version.version
0.12.0

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Edit (same difference outside IPython):

$ time python with_scipy.py
real    0m0.700s
user    0m0.610s
sys     0m0.069s

$ time python without_scipy.py
real    0m0.134s
user    0m0.099s
sys     0m0.015s

Answer 1

It looks like you may be running the timings incorrectly and measuring the time it takes to load scipy into memory. When I run:

import timeit
from scipy.misc import comb
from math import factorial

def comb2(n, k):
    return factorial(n) / factorial(k) / factorial(n - k)

def test():
    result = 0
    for n in range(1, 101):
        for k in range(1, n + 1):
            if comb(n, k) > 1000000:
                result += 1

def test2():
    result = 0
    for n in range(1, 101):
        for k in range(1, n + 1):
            if comb2(n, k) > 1000000:
                result += 1

T = timeit.Timer(test)
print T.repeat(3,50)

T2 = timeit.Timer(test2)
print T2.repeat(3,50)

I get:

[2.2370951175689697, 2.2209839820861816, 2.2142510414123535]
[2.136591911315918, 2.138144016265869, 2.1437559127807617]

which indicates that scipy is slightly faster than the python version.