Average Error: 0.3 → 0.3
Time: 3.1s
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 r520462 = x_re;
        double r520463 = y_im;
        double r520464 = r520462 * r520463;
        double r520465 = x_im;
        double r520466 = y_re;
        double r520467 = r520465 * r520466;
        double r520468 = r520464 + r520467;
        return r520468;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r520469 = x_re;
        double r520470 = y_im;
        double r520471 = r520469 * r520470;
        double r520472 = x_im;
        double r520473 = y_re;
        double r520474 = r520472 * r520473;
        double r520475 = r520471 + r520474;
        return r520475;
}

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 2019128 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))