Average Error: 29.7 → 0.0
Time: 1.6s
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 r1789974 = re;
        double r1789975 = r1789974 * r1789974;
        double r1789976 = im;
        double r1789977 = r1789976 * r1789976;
        double r1789978 = r1789975 + r1789977;
        double r1789979 = sqrt(r1789978);
        return r1789979;
}
↓
double f(double re, double im) {
        double r1789980 = re;
        double r1789981 = im;
        double r1789982 = hypot(r1789980, r1789981);
        return r1789982;
}

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 2019144 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))