Average Error: 0.6 → 0.6
Time: 2.4s
Precision: 64
\[\sqrt{\left(\frac{\left(re \cdot re\right)}{\left(im \cdot im\right)}\right)}\]
↓
\[\sqrt{re \cdot re + im \cdot im}\]
\sqrt{\left(\frac{\left(re \cdot re\right)}{\left(im \cdot im\right)}\right)}
↓
\sqrt{re \cdot re + im \cdot im}
double f(double re, double im) {
        double r843377 = re;
        double r843378 = r843377 * r843377;
        double r843379 = im;
        double r843380 = r843379 * r843379;
        double r843381 = r843378 + r843380;
        double r843382 = sqrt(r843381);
        return r843382;
}
↓
double f(double re, double im) {
        double r843383 = re;
        double r843384 = r843383 * r843383;
        double r843385 = im;
        double r843386 = r843385 * r843385;
        double r843387 = r843384 + r843386;
        double r843388 = sqrt(r843387);
        return r843388;
}

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.6

    \[\sqrt{\left(\frac{\left(re \cdot re\right)}{\left(im \cdot im\right)}\right)}\]

  2. Final simplification0.6

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

Reproduce

herbie shell --seed 2019121 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt.p16 (+.p16 (*.p16 re re) (*.p16 im im))))