Average Error: 31.5 → 0.0
Time: 10.5s
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 r1584679 = re;
        double r1584680 = r1584679 * r1584679;
        double r1584681 = im;
        double r1584682 = r1584681 * r1584681;
        double r1584683 = r1584680 + r1584682;
        double r1584684 = sqrt(r1584683);
        return r1584684;
}
↓
double f(double re, double im) {
        double r1584685 = re;
        double r1584686 = im;
        double r1584687 = hypot(r1584685, r1584686);
        return r1584687;
}

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 31.5

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

  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 2019179 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))