Average Error: 31.4 → 0.0
Time: 432.0ms
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 r49703 = re;
        double r49704 = r49703 * r49703;
        double r49705 = im;
        double r49706 = r49705 * r49705;
        double r49707 = r49704 + r49706;
        double r49708 = sqrt(r49707);
        return r49708;
}
↓
double f(double re, double im) {
        double r49709 = re;
        double r49710 = im;
        double r49711 = hypot(r49709, r49710);
        return r49711;
}

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 31.4

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

  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 2020003 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))