math.abs on complex

Average Error: 0.6 → 0.5

Time: 5.7s

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 r327232 = re;
        double r327233 = r327232 * r327232;
        double r327234 = im;
        double r327235 = r327234 * r327234;
        double r327236 = r327233 + r327235;
        double r327237 = sqrt(r327236);
        return r327237;
}

↓

double f(double re, double im) {
        double r327238 = re;
        double r327239 = r327238 * r327238;
        double r327240 = /*Error: no posit support in C */;
        double r327241 = im;
        double r327242 = /*Error: no posit support in C */;
        double r327243 = /*Error: no posit support in C */;
        double r327244 = sqrt(r327243);
        return r327244;
}

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 2019155 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt.p16 (+.p16 (*.p16 re re) (*.p16 im im))))