math.abs on complex

Average Error: 0.6 → 0.6

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 r4120542 = re;
        double r4120543 = r4120542 * r4120542;
        double r4120544 = im;
        double r4120545 = r4120544 * r4120544;
        double r4120546 = r4120543 + r4120545;
        double r4120547 = sqrt(r4120546);
        return r4120547;
}

↓

double f(double re, double im) {
        double r4120548 = re;
        double r4120549 = r4120548 * r4120548;
        double r4120550 = /*Error: no posit support in C */;
        double r4120551 = im;
        double r4120552 = /*Error: no posit support in C */;
        double r4120553 = /*Error: no posit support in C */;
        double r4120554 = sqrt(r4120553);
        return r4120554;
}

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 0.6

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

5. Final simplification 0.6

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

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))))