Which is faster in Python: x**.5 or math.sqrt(x)?

math.sqrt(x) is significantly faster than x**0.5.

import math
N = 1000000

%%timeit
for i in range(N):
    z=i**.5

10 loops, best of 3: 156 ms per loop

%%timeit
for i in range(N):
    z=math.sqrt(i)

10 loops, best of 3: 91.1 ms per loop

Using Python 3.6.9 (notebook).


  • first rule of optimization: don't do it
  • second rule: don't do it, yet

Here's some timings (Python 2.5.2, Windows):

$ python -mtimeit -s"from math import sqrt; x = 123" "x**.5"
1000000 loops, best of 3: 0.445 usec per loop

$ python -mtimeit -s"from math import sqrt; x = 123" "sqrt(x)"
1000000 loops, best of 3: 0.574 usec per loop

$ python -mtimeit -s"import math; x = 123" "math.sqrt(x)"
1000000 loops, best of 3: 0.727 usec per loop

This test shows that x**.5 is slightly faster than sqrt(x).

For the Python 3.0 the result is the opposite:

$ \Python30\python -mtimeit -s"from math import sqrt; x = 123" "x**.5"
1000000 loops, best of 3: 0.803 usec per loop

$ \Python30\python -mtimeit -s"from math import sqrt; x = 123" "sqrt(x)"
1000000 loops, best of 3: 0.695 usec per loop

$ \Python30\python -mtimeit -s"import math; x = 123" "math.sqrt(x)"
1000000 loops, best of 3: 0.761 usec per loop

math.sqrt(x) is always faster than x**.5 on another machine (Ubuntu, Python 2.6 and 3.1):

$ python -mtimeit -s"from math import sqrt; x = 123" "x**.5"
10000000 loops, best of 3: 0.173 usec per loop
$ python -mtimeit -s"from math import sqrt; x = 123" "sqrt(x)"
10000000 loops, best of 3: 0.115 usec per loop
$ python -mtimeit -s"import math; x = 123" "math.sqrt(x)"
10000000 loops, best of 3: 0.158 usec per loop
$ python3.1 -mtimeit -s"from math import sqrt; x = 123" "x**.5"
10000000 loops, best of 3: 0.194 usec per loop
$ python3.1 -mtimeit -s"from math import sqrt; x = 123" "sqrt(x)"
10000000 loops, best of 3: 0.123 usec per loop
$ python3.1 -mtimeit -s"import math; x = 123" "math.sqrt(x)"
10000000 loops, best of 3: 0.157 usec per loop

In these micro-benchmarks, math.sqrt will be slower, because of the slight time it takes to lookup the sqrt in the math namespace. You can improve it slightly with 

 from math import sqrt

Even then though, running a few variations through timeit, show a slight (4-5%) performance advantage for x**.5

Interestingly, doing

 import math
 sqrt = math.sqrt

sped it up even more, to within 1% difference in speed, with very little statistical significance.

I will repeat Kibbee, and say that this is probably a premature optimization.

Tags:

Python

Performance

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