Average Error: 31.9 → 0.0
Time: 639.0ms
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 r100487 = re;
        double r100488 = r100487 * r100487;
        double r100489 = im;
        double r100490 = r100489 * r100489;
        double r100491 = r100488 + r100490;
        double r100492 = sqrt(r100491);
        return r100492;
}
↓
double f(double re, double im) {
        double r100493 = re;
        double r100494 = im;
        double r100495 = hypot(r100493, r100494);
        return r100495;
}

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 31.9

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

  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 2020034 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))