Average Error: 30.2 → 0.0
Time: 5.5s
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 r922610 = re;
        double r922611 = r922610 * r922610;
        double r922612 = im;
        double r922613 = r922612 * r922612;
        double r922614 = r922611 + r922613;
        double r922615 = sqrt(r922614);
        return r922615;
}
↓
double f(double re, double im) {
        double r922616 = re;
        double r922617 = im;
        double r922618 = hypot(r922616, r922617);
        return r922618;
}

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 30.2

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

  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 2019133 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))