Average Error: 31.7 → 0.0
Time: 410.0ms
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 r46484 = re;
        double r46485 = r46484 * r46484;
        double r46486 = im;
        double r46487 = r46486 * r46486;
        double r46488 = r46485 + r46487;
        double r46489 = sqrt(r46488);
        return r46489;
}
↓
double f(double re, double im) {
        double r46490 = re;
        double r46491 = im;
        double r46492 = hypot(r46490, r46491);
        return r46492;
}

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 31.7

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

  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 2020060 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))