Average Error: 31.8 → 0.0
Time: 394.0ms
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 r36932 = re;
        double r36933 = r36932 * r36932;
        double r36934 = im;
        double r36935 = r36934 * r36934;
        double r36936 = r36933 + r36935;
        double r36937 = sqrt(r36936);
        return r36937;
}
↓
double f(double re, double im) {
        double r36938 = re;
        double r36939 = im;
        double r36940 = hypot(r36938, r36939);
        return r36940;
}

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 2020020 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))