Average Error: 31.4 → 0.0
Time: 24.6s
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 r1679422 = re;
        double r1679423 = r1679422 * r1679422;
        double r1679424 = im;
        double r1679425 = r1679424 * r1679424;
        double r1679426 = r1679423 + r1679425;
        double r1679427 = sqrt(r1679426);
        return r1679427;
}
↓
double f(double re, double im) {
        double r1679428 = re;
        double r1679429 = im;
        double r1679430 = hypot(r1679428, r1679429);
        return r1679430;
}

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 31.4

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

  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 2019165 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))