Average Error: 31.4 → 0.0
Time: 453.0ms
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 r85783 = re;
        double r85784 = r85783 * r85783;
        double r85785 = im;
        double r85786 = r85785 * r85785;
        double r85787 = r85784 + r85786;
        double r85788 = sqrt(r85787);
        return r85788;
}
↓
double f(double re, double im) {
        double r85789 = re;
        double r85790 = im;
        double r85791 = hypot(r85789, r85790);
        return r85791;
}

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 31.4

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

  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 2019351 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))