Average Error: 31.1 → 0.0
Time: 794.0ms
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\mathsf{hypot}\left(re, im\right)\]
\sqrt{re \cdot re + im \cdot im}
↓
\mathsf{hypot}\left(re, im\right)
double f(double re, double im) {
        double r52735 = re;
        double r52736 = r52735 * r52735;
        double r52737 = im;
        double r52738 = r52737 * r52737;
        double r52739 = r52736 + r52738;
        double r52740 = sqrt(r52739);
        return r52740;
}
↓
double f(double re, double im) {
        double r52741 = re;
        double r52742 = im;
        double r52743 = hypot(r52741, r52742);
        return r52743;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 31.1

    \[\sqrt{re \cdot re + im \cdot im}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{hypot}\left(re, im\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{hypot}\left(re, im\right)\]

Reproduce

herbie shell --seed 2019346 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))