Average Error: 29.6 → 0.0
Time: 860.0ms
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 r1103689 = re;
        double r1103690 = r1103689 * r1103689;
        double r1103691 = im;
        double r1103692 = r1103691 * r1103691;
        double r1103693 = r1103690 + r1103692;
        double r1103694 = sqrt(r1103693);
        return r1103694;
}
↓
double f(double re, double im) {
        double r1103695 = re;
        double r1103696 = im;
        double r1103697 = hypot(r1103695, r1103696);
        return r1103697;
}

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 29.6

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

  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 2019162 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))