Average Error: 0.3 → 0.3
Time: 3.6s
Precision: 64
\[\frac{\left(x.re \cdot y.im\right)}{\left(x.im \cdot y.re\right)}\]
↓
\[x.re \cdot y.im + x.im \cdot y.re\]
\frac{\left(x.re \cdot y.im\right)}{\left(x.im \cdot y.re\right)}
↓
x.re \cdot y.im + x.im \cdot y.re
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1343289 = x_re;
        double r1343290 = y_im;
        double r1343291 = r1343289 * r1343290;
        double r1343292 = x_im;
        double r1343293 = y_re;
        double r1343294 = r1343292 * r1343293;
        double r1343295 = r1343291 + r1343294;
        return r1343295;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1343296 = x_re;
        double r1343297 = y_im;
        double r1343298 = r1343296 * r1343297;
        double r1343299 = x_im;
        double r1343300 = y_re;
        double r1343301 = r1343299 * r1343300;
        double r1343302 = r1343298 + r1343301;
        return r1343302;
}

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. Final simplification0.3

    \[\leadsto x.re \cdot y.im + x.im \cdot y.re\]

Reproduce

herbie shell --seed 2019124 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))