Average Error: 31.1 → 0.0
Time: 774.0ms
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 r88794 = re;
        double r88795 = r88794 * r88794;
        double r88796 = im;
        double r88797 = r88796 * r88796;
        double r88798 = r88795 + r88797;
        double r88799 = sqrt(r88798);
        return r88799;
}
↓
double f(double re, double im) {
        double r88800 = re;
        double r88801 = im;
        double r88802 = hypot(r88800, r88801);
        return r88802;
}

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 2020100 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))