Average Error: 32.0 → 0.0
Time: 1.2s
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 r47729 = re;
        double r47730 = r47729 * r47729;
        double r47731 = im;
        double r47732 = r47731 * r47731;
        double r47733 = r47730 + r47732;
        double r47734 = sqrt(r47733);
        return r47734;
}
↓
double f(double re, double im) {
        double r47735 = re;
        double r47736 = im;
        double r47737 = hypot(r47735, r47736);
        return r47737;
}

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 32.0

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

  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 2019354 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))