math.abs on complex

Average Error: 0.6 → 0.5

Time: 3.3s

Precision: 64

Math

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

↓

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

C

double f(double re, double im) {
        double r3235139 = re;
        double r3235140 = r3235139 * r3235139;
        double r3235141 = im;
        double r3235142 = r3235141 * r3235141;
        double r3235143 = r3235140 + r3235142;
        double r3235144 = sqrt(r3235143);
        return r3235144;
}

↓

double f(double re, double im) {
        double r3235145 = re;
        double r3235146 = r3235145 * r3235145;
        double r3235147 = /*Error: no posit support in C */;
        double r3235148 = im;
        double r3235149 = /*Error: no posit support in C */;
        double r3235150 = /*Error: no posit support in C */;
        double r3235151 = sqrt(r3235150);
        return r3235151;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.6

   \[\sqrt{\left(\left(re \cdot re\right) + \left(im \cdot im\right)\right)}\]
2. Using strategy rm

3. Applied introduce-quire 0.6

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

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 0 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt.p16 (+.p16 (*.p16 re re) (*.p16 im im))))