Average Error: 29.1 → 0.0
Time: 1.1s
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 r1502623 = re;
        double r1502624 = r1502623 * r1502623;
        double r1502625 = im;
        double r1502626 = r1502625 * r1502625;
        double r1502627 = r1502624 + r1502626;
        double r1502628 = sqrt(r1502627);
        return r1502628;
}
↓
double f(double re, double im) {
        double r1502629 = re;
        double r1502630 = im;
        double r1502631 = hypot(r1502629, r1502630);
        return r1502631;
}

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 29.1

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

  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 2019125 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))