Average Error: 0.6 → 0.5
Time: 5.6s
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 r315566 = re;
        double r315567 = r315566 * r315566;
        double r315568 = im;
        double r315569 = r315568 * r315568;
        double r315570 = r315567 + r315569;
        double r315571 = sqrt(r315570);
        return r315571;
}
↓
double f(double re, double im) {
        double r315572 = re;
        double r315573 = r315572 * r315572;
        double r315574 = /*Error: no posit support in C */;
        double r315575 = im;
        double r315576 = /*Error: no posit support in C */;
        double r315577 = /*Error: no posit support in C */;
        double r315578 = sqrt(r315577);
        return r315578;
}

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 2019151 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt.p16 (+.p16 (*.p16 re re) (*.p16 im im))))