Average Error: 31.4 → 0.0
Time: 2.9s
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 r48716 = re;
        double r48717 = r48716 * r48716;
        double r48718 = im;
        double r48719 = r48718 * r48718;
        double r48720 = r48717 + r48719;
        double r48721 = sqrt(r48720);
        return r48721;
}
↓
double f(double re, double im) {
        double r48722 = re;
        double r48723 = im;
        double r48724 = hypot(r48722, r48723);
        return r48724;
}

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 31.4

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

  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 2019325 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))