Average Error: 0.6 → 0.6
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 r4120504 = re;
        double r4120505 = r4120504 * r4120504;
        double r4120506 = im;
        double r4120507 = r4120506 * r4120506;
        double r4120508 = r4120505 + r4120507;
        double r4120509 = sqrt(r4120508);
        return r4120509;
}
↓
double f(double re, double im) {
        double r4120510 = re;
        double r4120511 = r4120510 * r4120510;
        double r4120512 = /*Error: no posit support in C */;
        double r4120513 = im;
        double r4120514 = /*Error: no posit support in C */;
        double r4120515 = /*Error: no posit support in C */;
        double r4120516 = sqrt(r4120515);
        return r4120516;
}

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-add0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019152 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt.p16 (+.p16 (*.p16 re re) (*.p16 im im))))