python speed composed functions

Question

I'd like to understand why I get the speed differences that I see when I compose functions in different ways. I'm mostly interested in understanding why case (1) is faster than case (2).

Thanks!

import math
from time import time

def f(x):
    return 2*x
def g(x):
    return x*x
def h(x):
    return math.sqrt(x)

time0 = time()
for x in range(1,10**7):
    x_ = h(g(f(x)))
print 'h(g(f(x))): {}'.format( time() - time0)

def fgh(x):
    return h(g(f(x)))
time0 = time()
for x in range(1,10**7):
    x_ = fgh(x)
print 'composed: {}'.format( time() - time0)

time0 = time()
for x in range(1,10**7):
    x_ = f(x)
    x__ = g(x_)
    x___ = h(x__)
print 'subsequent: {}'.format( time() - time0)

As runtimes, I get:

h(g(f(x))): 2.83475399017
composed: 3.29999113083
subsequent: 3.4387819767

Óscar López · Accepted Answer · 2016-11-19 23:35:26Z

1

For starters, case 2 has one extra call - that of fgh(x), whereas in case 1 you're calling h(g(f(x))) directly. Inside a tight loop that gets executed many times, that additional function call can add extra execution time. Case 1 in-lines that call, so it's a bit faster. Case 3 is doing some extra assignments and loading variables, which explains why it's slower.

answered Nov 19, 2016 at 23:35

Óscar López

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2 Comments

Aplln Over a year ago

OK, I thought something like that. Is it fair to say that if each of the composed functions is more complex and time intensive, it doesn't matter for the runtime how I compose them? (i.e. the additional function call in example 2 becomes negligible)

Óscar López Over a year ago

For the general case, it depends on the function - there might be situations where the composition order does matter (for instance: when composing the multiplication of large matrices). For your example it might not matter that much, but one can assume that operations such as taking the square root will be slower for larger numbers, so it'll be slightly slower if we leave it for the end

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