Average Error: 0.3 → 0.3
Time: 3.3s
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 r144816 = x_re;
        double r144817 = y_im;
        double r144818 = r144816 * r144817;
        double r144819 = x_im;
        double r144820 = y_re;
        double r144821 = r144819 * r144820;
        double r144822 = r144818 + r144821;
        return r144822;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r144823 = x_re;
        double r144824 = y_im;
        double r144825 = r144823 * r144824;
        double r144826 = x_im;
        double r144827 = y_re;
        double r144828 = r144826 * r144827;
        double r144829 = r144825 + r144828;
        return r144829;
}

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 +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)))