Average Error: 31.5 → 0.0
Time: 9.4s
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 r43413 = re;
        double r43414 = r43413 * r43413;
        double r43415 = im;
        double r43416 = r43415 * r43415;
        double r43417 = r43414 + r43416;
        double r43418 = sqrt(r43417);
        return r43418;
}
↓
double f(double re, double im) {
        double r43419 = re;
        double r43420 = im;
        double r43421 = hypot(r43419, r43420);
        return r43421;
}

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 31.5

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

  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 2019179 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))