Average Error: 29.7 → 0.0
Time: 1.3s
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 r488412 = re;
        double r488413 = r488412 * r488412;
        double r488414 = im;
        double r488415 = r488414 * r488414;
        double r488416 = r488413 + r488415;
        double r488417 = sqrt(r488416);
        return r488417;
}
↓
double f(double re, double im) {
        double r488418 = re;
        double r488419 = im;
        double r488420 = hypot(r488418, r488419);
        return r488420;
}

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 2019119 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))