Average Error: 31.8 → 0.0
Time: 429.0ms
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 r33717 = re;
        double r33718 = r33717 * r33717;
        double r33719 = im;
        double r33720 = r33719 * r33719;
        double r33721 = r33718 + r33720;
        double r33722 = sqrt(r33721);
        return r33722;
}
↓
double f(double re, double im) {
        double r33723 = re;
        double r33724 = im;
        double r33725 = hypot(r33723, r33724);
        return r33725;
}

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 31.8

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

  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 2020039 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))