Average Error: 29.5 → 0.0
Time: 1.5s
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 r1471781 = re;
        double r1471782 = r1471781 * r1471781;
        double r1471783 = im;
        double r1471784 = r1471783 * r1471783;
        double r1471785 = r1471782 + r1471784;
        double r1471786 = sqrt(r1471785);
        return r1471786;
}
↓
double f(double re, double im) {
        double r1471787 = re;
        double r1471788 = im;
        double r1471789 = hypot(r1471787, r1471788);
        return r1471789;
}

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 29.5

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

  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 2019128 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))