Average Error: 0.6 → 0.5
Time: 15.1s
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 r474183 = re;
        double r474184 = r474183 * r474183;
        double r474185 = im;
        double r474186 = r474185 * r474185;
        double r474187 = r474184 + r474186;
        double r474188 = sqrt(r474187);
        return r474188;
}
↓
double f(double re, double im) {
        double r474189 = re;
        double r474190 = r474189 * r474189;
        double r474191 = /*Error: no posit support in C */;
        double r474192 = im;
        double r474193 = /*Error: no posit support in C */;
        double r474194 = /*Error: no posit support in C */;
        double r474195 = sqrt(r474194);
        return r474195;
}

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 2019165 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt.p16 (+.p16 (*.p16 re re) (*.p16 im im))))