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 r1142827 = x_re;
        double r1142828 = y_im;
        double r1142829 = r1142827 * r1142828;
        double r1142830 = x_im;
        double r1142831 = y_re;
        double r1142832 = r1142830 * r1142831;
        double r1142833 = r1142829 + r1142832;
        return r1142833;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1142834 = x_re;
        double r1142835 = y_im;
        double r1142836 = r1142834 * r1142835;
        double r1142837 = x_im;
        double r1142838 = y_re;
        double r1142839 = r1142837 * r1142838;
        double r1142840 = r1142836 + r1142839;
        return r1142840;
}

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 2019130 +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)))