Average Error: 29.7 → 0.0
Time: 1.8s
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 r885724 = re;
        double r885725 = r885724 * r885724;
        double r885726 = im;
        double r885727 = r885726 * r885726;
        double r885728 = r885725 + r885727;
        double r885729 = sqrt(r885728);
        return r885729;
}
↓
double f(double re, double im) {
        double r885730 = re;
        double r885731 = im;
        double r885732 = hypot(r885730, r885731);
        return r885732;
}

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 2019156 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))