Average Error: 28.9 → 0.0
Time: 9.9s
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 r2196289 = re;
        double r2196290 = r2196289 * r2196289;
        double r2196291 = im;
        double r2196292 = r2196291 * r2196291;
        double r2196293 = r2196290 + r2196292;
        double r2196294 = sqrt(r2196293);
        return r2196294;
}
↓
double f(double re, double im) {
        double r2196295 = re;
        double r2196296 = im;
        double r2196297 = hypot(r2196295, r2196296);
        return r2196297;
}

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 28.9

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

  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 2019158 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))