Average Error: 29.7 → 0.0
Time: 1.2s
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 r630038 = re;
        double r630039 = r630038 * r630038;
        double r630040 = im;
        double r630041 = r630040 * r630040;
        double r630042 = r630039 + r630041;
        double r630043 = sqrt(r630042);
        return r630043;
}
↓
double f(double re, double im) {
        double r630044 = re;
        double r630045 = im;
        double r630046 = hypot(r630044, r630045);
        return r630046;
}

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 29.7

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

  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 2019112 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))