Average Error: 31.3 → 0.0
Time: 9.3s
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 r39748 = re;
        double r39749 = r39748 * r39748;
        double r39750 = im;
        double r39751 = r39750 * r39750;
        double r39752 = r39749 + r39751;
        double r39753 = sqrt(r39752);
        return r39753;
}
↓
double f(double re, double im) {
        double r39754 = re;
        double r39755 = im;
        double r39756 = hypot(r39754, r39755);
        return r39756;
}

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 31.3

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

  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 2019326 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))