Average Error: 31.0 → 0.0
Time: 1.1s
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 r1786900 = re;
        double r1786901 = r1786900 * r1786900;
        double r1786902 = im;
        double r1786903 = r1786902 * r1786902;
        double r1786904 = r1786901 + r1786903;
        double r1786905 = sqrt(r1786904);
        return r1786905;
}
↓
double f(double re, double im) {
        double r1786906 = re;
        double r1786907 = im;
        double r1786908 = hypot(r1786906, r1786907);
        return r1786908;
}

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 31.0

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

  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 2019172 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))