Average Error: 29.5 → 0.0
Time: 1.2s
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 r437349 = re;
        double r437350 = r437349 * r437349;
        double r437351 = im;
        double r437352 = r437351 * r437351;
        double r437353 = r437350 + r437352;
        double r437354 = sqrt(r437353);
        return r437354;
}
↓
double f(double re, double im) {
        double r437355 = re;
        double r437356 = im;
        double r437357 = hypot(r437355, r437356);
        return r437357;
}

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 2019128 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))