math.abs on complex

Average Error: 0.6 → 0.5

Time: 27.0s

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 r509940 = re;
        double r509941 = r509940 * r509940;
        double r509942 = im;
        double r509943 = r509942 * r509942;
        double r509944 = r509941 + r509943;
        double r509945 = sqrt(r509944);
        return r509945;
}

↓

double f(double re, double im) {
        double r509946 = re;
        double r509947 = r509946 * r509946;
        double r509948 = /*Error: no posit support in C */;
        double r509949 = im;
        double r509950 = /*Error: no posit support in C */;
        double r509951 = /*Error: no posit support in C */;
        double r509952 = sqrt(r509951);
        return r509952;
}

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 2019158 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt.p16 (+.p16 (*.p16 re re) (*.p16 im im))))