Average Error: 0.6 → 0.6
Time: 5.4s
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 r432155 = re;
        double r432156 = r432155 * r432155;
        double r432157 = im;
        double r432158 = r432157 * r432157;
        double r432159 = r432156 + r432158;
        double r432160 = sqrt(r432159);
        return r432160;
}
↓
double f(double re, double im) {
        double r432161 = re;
        double r432162 = r432161 * r432161;
        double r432163 = /*Error: no posit support in C */;
        double r432164 = im;
        double r432165 = /*Error: no posit support in C */;
        double r432166 = /*Error: no posit support in C */;
        double r432167 = sqrt(r432166);
        return r432167;
}

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