Average Error: 31.0 → 0.0
Time: 1.4s
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 r38789 = re;
        double r38790 = r38789 * r38789;
        double r38791 = im;
        double r38792 = r38791 * r38791;
        double r38793 = r38790 + r38792;
        double r38794 = sqrt(r38793);
        return r38794;
}
↓
double f(double re, double im) {
        double r38795 = re;
        double r38796 = im;
        double r38797 = hypot(r38795, r38796);
        return r38797;
}

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 31.0

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

  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 2020001 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))