Average Error: 29.5 → 0.0
Time: 11.6s
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 r1512501 = re;
        double r1512502 = r1512501 * r1512501;
        double r1512503 = im;
        double r1512504 = r1512503 * r1512503;
        double r1512505 = r1512502 + r1512504;
        double r1512506 = sqrt(r1512505);
        return r1512506;
}
↓
double f(double re, double im) {
        double r1512507 = re;
        double r1512508 = im;
        double r1512509 = hypot(r1512507, r1512508);
        return r1512509;
}

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 29.5

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

  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 2019134 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))