math.abs on complex

Average Error: 0.6 → 0.5

Time: 4.9s

Precision: 64

Math

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

↓

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

C

double f(double re, double im) {
        double r563349 = re;
        double r563350 = r563349 * r563349;
        double r563351 = im;
        double r563352 = r563351 * r563351;
        double r563353 = r563350 + r563352;
        double r563354 = sqrt(r563353);
        return r563354;
}

↓

double f(double re, double im) {
        double r563355 = re;
        double r563356 = r563355 * r563355;
        double r563357 = /*Error: no posit support in C */;
        double r563358 = im;
        double r563359 = /*Error: no posit support in C */;
        double r563360 = /*Error: no posit support in C */;
        double r563361 = sqrt(r563360);
        return r563361;
}

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-quire 0.6

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

4. Applied insert-quire-fdp-add 0.5

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

5. Final simplification 0.5

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

Reproduce

herbie shell --seed 2019153 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt.p16 (+.p16 (*.p16 re re) (*.p16 im im))))