Average Error: 29.8 → 0.0
Time: 3.0s
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 r5157021 = re;
        double r5157022 = r5157021 * r5157021;
        double r5157023 = im;
        double r5157024 = r5157023 * r5157023;
        double r5157025 = r5157022 + r5157024;
        double r5157026 = sqrt(r5157025);
        return r5157026;
}
↓
double f(double re, double im) {
        double r5157027 = re;
        double r5157028 = im;
        double r5157029 = hypot(r5157027, r5157028);
        return r5157029;
}

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 29.8

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

  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 2019104 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))