Average Error: 32.0 → 0.0
Time: 2.2s
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 r89632 = re;
        double r89633 = r89632 * r89632;
        double r89634 = im;
        double r89635 = r89634 * r89634;
        double r89636 = r89633 + r89635;
        double r89637 = sqrt(r89636);
        return r89637;
}
↓
double f(double re, double im) {
        double r89638 = re;
        double r89639 = im;
        double r89640 = hypot(r89638, r89639);
        return r89640;
}

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 2020089 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))