math.abs on complex

Average Error: 0.6 → 0.5

Time: 5.3s

Precision: 64

Math

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

↓

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

C

double f(double re, double im) {
        double r1127933 = re;
        double r1127934 = r1127933 * r1127933;
        double r1127935 = im;
        double r1127936 = r1127935 * r1127935;
        double r1127937 = r1127934 + r1127936;
        double r1127938 = sqrt(r1127937);
        return r1127938;
}

↓

double f(double re, double im) {
        double r1127939 = re;
        double r1127940 = r1127939 * r1127939;
        double r1127941 = /*Error: no posit support in C */;
        double r1127942 = im;
        double r1127943 = /*Error: no posit support in C */;
        double r1127944 = /*Error: no posit support in C */;
        double r1127945 = sqrt(r1127944);
        return r1127945;
}

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

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

Reproduce

herbie shell --seed 2019168 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt.p16 (+.p16 (*.p16 re re) (*.p16 im im))))