_multiplyComplex, imaginary part

Average Error: 0.3 → 0.2

Time: 6.9s

Precision: 64

Math

\[\frac{\left(x.re \cdot y.im\right)}{\left(x.im \cdot y.re\right)}\]

↓

\[\left(\mathsf{qma}\left(\left(\left(x.re \cdot y.im\right)\right), x.im, y.re\right)\right)\]

C

double f(double x_re, double x_im, double y_re, double y_im) {
        double r1650283 = x_re;
        double r1650284 = y_im;
        double r1650285 = r1650283 * r1650284;
        double r1650286 = x_im;
        double r1650287 = y_re;
        double r1650288 = r1650286 * r1650287;
        double r1650289 = r1650285 + r1650288;
        return r1650289;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r1650290 = x_re;
        double r1650291 = y_im;
        double r1650292 = r1650290 * r1650291;
        double r1650293 = /*Error: no posit support in C */;
        double r1650294 = x_im;
        double r1650295 = y_re;
        double r1650296 = /*Error: no posit support in C */;
        double r1650297 = /*Error: no posit support in C */;
        return r1650297;
}

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Derivation

1. Initial program 0.3

   \[\frac{\left(x.re \cdot y.im\right)}{\left(x.im \cdot y.re\right)}\]
2. Using strategy rm

3. Applied introduce-quire 0.3

   \[\leadsto \frac{\color{blue}{\left(\left(\left(x.re \cdot y.im\right)\right)\right)}}{\left(x.im \cdot y.re\right)}\]

4. Applied insert-quire-fdp-add 0.2

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

5. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019149 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))