Average Error: 0.3 → 0.3
Time: 3.9s
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 r514156 = x_re;
        double r514157 = y_im;
        double r514158 = r514156 * r514157;
        double r514159 = x_im;
        double r514160 = y_re;
        double r514161 = r514159 * r514160;
        double r514162 = r514158 + r514161;
        return r514162;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r514163 = x_re;
        double r514164 = y_im;
        double r514165 = r514163 * r514164;
        double r514166 = x_im;
        double r514167 = y_re;
        double r514168 = r514166 * r514167;
        double r514169 = r514165 + r514168;
        return r514169;
}

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 2019112 +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)))