Average Error: 0.3 → 0.3
Time: 4.3s
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 r229234 = x_re;
        double r229235 = y_im;
        double r229236 = r229234 * r229235;
        double r229237 = x_im;
        double r229238 = y_re;
        double r229239 = r229237 * r229238;
        double r229240 = r229236 + r229239;
        return r229240;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r229241 = x_re;
        double r229242 = y_im;
        double r229243 = r229241 * r229242;
        double r229244 = x_im;
        double r229245 = y_re;
        double r229246 = r229244 * r229245;
        double r229247 = r229243 + r229246;
        return r229247;
}

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 2019133 +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)))