Average Error: 0.3 → 0.3
Time: 3.8s
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 r739727 = x_re;
        double r739728 = y_im;
        double r739729 = r739727 * r739728;
        double r739730 = x_im;
        double r739731 = y_re;
        double r739732 = r739730 * r739731;
        double r739733 = r739729 + r739732;
        return r739733;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r739734 = x_re;
        double r739735 = y_im;
        double r739736 = r739734 * r739735;
        double r739737 = x_im;
        double r739738 = y_re;
        double r739739 = r739737 * r739738;
        double r739740 = r739736 + r739739;
        return r739740;
}

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 2019104 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))