Average Error: 29.7 → 0.0
Time: 10.3s
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 r1762921 = re;
        double r1762922 = r1762921 * r1762921;
        double r1762923 = im;
        double r1762924 = r1762923 * r1762923;
        double r1762925 = r1762922 + r1762924;
        double r1762926 = sqrt(r1762925);
        return r1762926;
}
↓
double f(double re, double im) {
        double r1762927 = re;
        double r1762928 = im;
        double r1762929 = hypot(r1762927, r1762928);
        return r1762929;
}

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 29.7

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

  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 2019129 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))