Average Error: 28.9 → 0.0
Time: 9.1s
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 r1932470 = re;
        double r1932471 = r1932470 * r1932470;
        double r1932472 = im;
        double r1932473 = r1932472 * r1932472;
        double r1932474 = r1932471 + r1932473;
        double r1932475 = sqrt(r1932474);
        return r1932475;
}
↓
double f(double re, double im) {
        double r1932476 = re;
        double r1932477 = im;
        double r1932478 = hypot(r1932476, r1932477);
        return r1932478;
}

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 28.9

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

  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 2019158 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))