Average Error: 29.6 → 0.0
Time: 1.1s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\sqrt{re^2 + im^2}^*\]
\sqrt{re \cdot re + im \cdot im}
↓
\sqrt{re^2 + im^2}^*
double f(double re, double im) {
        double r4509178 = re;
        double r4509179 = r4509178 * r4509178;
        double r4509180 = im;
        double r4509181 = r4509180 * r4509180;
        double r4509182 = r4509179 + r4509181;
        double r4509183 = sqrt(r4509182);
        return r4509183;
}
↓
double f(double re, double im) {
        double r4509184 = re;
        double r4509185 = im;
        double r4509186 = hypot(r4509184, r4509185);
        return r4509186;
}

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

    \[\leadsto \color{blue}{\sqrt{re^2 + im^2}^*}\]

  3. Final simplification0.0

    \[\leadsto \sqrt{re^2 + im^2}^*\]

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))