Average Error: 0.6 → 0.5
Time: 5.5s
Precision: 64
\[\sqrt{\left(\frac{\left(re \cdot re\right)}{\left(im \cdot im\right)}\right)}\]
↓
\[\sqrt{\left(\mathsf{qma}\left(\left(\left(re \cdot re\right)\right), im, im\right)\right)}\]
\sqrt{\left(\frac{\left(re \cdot re\right)}{\left(im \cdot im\right)}\right)}
↓
\sqrt{\left(\mathsf{qma}\left(\left(\left(re \cdot re\right)\right), im, im\right)\right)}
double f(double re, double im) {
        double r2581984 = re;
        double r2581985 = r2581984 * r2581984;
        double r2581986 = im;
        double r2581987 = r2581986 * r2581986;
        double r2581988 = r2581985 + r2581987;
        double r2581989 = sqrt(r2581988);
        return r2581989;
}
↓
double f(double re, double im) {
        double r2581990 = re;
        double r2581991 = r2581990 * r2581990;
        double r2581992 = /*Error: no posit support in C */;
        double r2581993 = im;
        double r2581994 = /*Error: no posit support in C */;
        double r2581995 = /*Error: no posit support in C */;
        double r2581996 = sqrt(r2581995);
        return r2581996;
}

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. Using strategy rm

  3. Applied introduce-quire0.6

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

  4. Applied insert-quire-fdp-add0.5

    \[\leadsto \sqrt{\color{blue}{\left(\left(\mathsf{qma}\left(\left(\left(re \cdot re\right)\right), im, im\right)\right)\right)}}\]

  5. Final simplification0.5

    \[\leadsto \sqrt{\left(\mathsf{qma}\left(\left(\left(re \cdot re\right)\right), im, im\right)\right)}\]

Reproduce

herbie shell --seed 2019142 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt.p16 (+.p16 (*.p16 re re) (*.p16 im im))))