Average Error: 31.6 → 0.0
Time: 3.7s
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 r114383 = re;
        double r114384 = r114383 * r114383;
        double r114385 = im;
        double r114386 = r114385 * r114385;
        double r114387 = r114384 + r114386;
        double r114388 = sqrt(r114387);
        return r114388;
}
↓
double f(double re, double im) {
        double r114389 = re;
        double r114390 = im;
        double r114391 = hypot(r114389, r114390);
        return r114391;
}

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 31.6

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

  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 2019323 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))