## Issue

In numpy, the square root and power by 1/2 is almost indistinguishable in speed. However, when doing the inverse square root vs the power by -1/2, the latter is about 10x slower.

```
# Python 3.10.2; numpy 1.22.1; clang-1205.0.22.11; macOS 12.1
import numpy as np
arr = np.random.uniform(0, 1, 10000)
%timeit -n 10000 np.sqrt(arr)
%timeit -n 10000 arr**(1/2)
%timeit -n 10000 1 / np.sqrt(arr)
%timeit -n 10000 arr**(-1/2)
```

```
10.8 µs ± 472 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
9.97 µs ± 449 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
18.2 µs ± 673 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
187 µs ± 13.1 µs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
```

Can someone with more familiarity of the source implementation explain the difference?

## Solution

`numpy`

makes special cases of exponents in `{-1, 0, 0.5, 1, 2}`

, but no others. There was an issue opened in 2017 to add to add -2 and -0.5 to this set, but it appears that nothing yet has been done in that direction.

Answered By – Tim Peters

Answer Checked By – Timothy Miller (BugsFixing Admin)