Question

A quote from “Python Programming: An Introduction to Computer Science“

We could have taken the square root
using exponentiation **. Using
math.sqrt is somewhat more efficient.

“Somewhat”, but to what extent, and how?

Answer 1

Theoretically, hammar’s answer and duffymo’s answer are good guesses. But in practice, on my machine, it’s not more efficient:

>>> import timeit
>>> timeit.timeit(stmt='[n ** 0.5 for n in range(100)]', setup='import math', number=10000)
0.15518403053283691
>>> timeit.timeit(stmt='[math.sqrt(n) for n in range(100)]', setup='import math', number=10000)
0.17707490921020508

Part of the problem is the . operation. If you import sqrt directly into the namespace, you get a slight improvement.

>>> timeit.timeit(stmt='[sqrt(n) for n in range(100)]', setup='from math import sqrt', number=10000)
0.15312695503234863

Key word there: slight.

Further testing indicates that as the number gets larger, the benefit you get from using sqrt increases. But still not by a lot!

>>> timeit.timeit(stmt='[n ** 0.5 for n in range(1000000)]', setup='import math', number=1)
0.18888211250305176
>>> timeit.timeit(stmt='[math.sqrt(n) for n in range(1000000)]', setup='import math', number=1)
0.18425297737121582
>>> timeit.timeit(stmt='[sqrt(n) for n in range(1000000)]', setup='from math import sqrt', number=1)
0.1571958065032959