Average Error: 30.1 → 0.0
Time: 20.3s
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 r2499717 = re;
        double r2499718 = r2499717 * r2499717;
        double r2499719 = im;
        double r2499720 = r2499719 * r2499719;
        double r2499721 = r2499718 + r2499720;
        double r2499722 = sqrt(r2499721);
        return r2499722;
}
↓
double f(double re, double im) {
        double r2499723 = re;
        double r2499724 = im;
        double r2499725 = hypot(r2499723, r2499724);
        return r2499725;
}

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 30.1

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

  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 2019142 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))