Average Error: 31.1 → 0.0
Time: 440.0ms
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 r30548 = re;
        double r30549 = r30548 * r30548;
        double r30550 = im;
        double r30551 = r30550 * r30550;
        double r30552 = r30549 + r30551;
        double r30553 = sqrt(r30552);
        return r30553;
}
↓
double f(double re, double im) {
        double r30554 = re;
        double r30555 = im;
        double r30556 = hypot(r30554, r30555);
        return r30556;
}

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 31.1

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

  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 2019350 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))