Average Error: 31.7 → 0.0
Time: 411.0ms
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 r89744 = re;
        double r89745 = r89744 * r89744;
        double r89746 = im;
        double r89747 = r89746 * r89746;
        double r89748 = r89745 + r89747;
        double r89749 = sqrt(r89748);
        return r89749;
}
↓
double f(double re, double im) {
        double r89750 = re;
        double r89751 = im;
        double r89752 = hypot(r89750, r89751);
        return r89752;
}

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 31.7

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

  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 2020062 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))