Average Error: 31.2 → 0.0
Time: 1.0s
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 r93076 = re;
        double r93077 = r93076 * r93076;
        double r93078 = im;
        double r93079 = r93078 * r93078;
        double r93080 = r93077 + r93079;
        double r93081 = sqrt(r93080);
        return r93081;
}
↓
double f(double re, double im) {
        double r93082 = re;
        double r93083 = im;
        double r93084 = hypot(r93082, r93083);
        return r93084;
}

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 31.2

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

  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 2020065 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))