_multiplyComplex, imaginary part

Average Error: 0.3 → 0.2

Time: 6.5s

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 r2093239 = x_re;
        double r2093240 = y_im;
        double r2093241 = r2093239 * r2093240;
        double r2093242 = x_im;
        double r2093243 = y_re;
        double r2093244 = r2093242 * r2093243;
        double r2093245 = r2093241 + r2093244;
        return r2093245;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r2093246 = x_re;
        double r2093247 = y_im;
        double r2093248 = r2093246 * r2093247;
        double r2093249 = /*Error: no posit support in C */;
        double r2093250 = x_im;
        double r2093251 = y_re;
        double r2093252 = /*Error: no posit support in C */;
        double r2093253 = /*Error: no posit support in C */;
        return r2093253;
}

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 2019152 +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)))