Average Error: 31.0 → 0.0
Time: 765.0ms
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 r12408 = re;
        double r12409 = r12408 * r12408;
        double r12410 = im;
        double r12411 = r12410 * r12410;
        double r12412 = r12409 + r12411;
        double r12413 = sqrt(r12412);
        return r12413;
}
↓
double f(double re, double im) {
        double r12414 = re;
        double r12415 = im;
        double r12416 = hypot(r12414, r12415);
        return r12416;
}

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 31.0

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

  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 2019315 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))