Average Error: 0.3 → 0.3
Time: 3.2s
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 r1225861 = x_re;
        double r1225862 = y_im;
        double r1225863 = r1225861 * r1225862;
        double r1225864 = x_im;
        double r1225865 = y_re;
        double r1225866 = r1225864 * r1225865;
        double r1225867 = r1225863 + r1225866;
        return r1225867;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1225868 = x_re;
        double r1225869 = y_im;
        double r1225870 = r1225868 * r1225869;
        double r1225871 = x_im;
        double r1225872 = y_re;
        double r1225873 = r1225871 * r1225872;
        double r1225874 = r1225870 + r1225873;
        return r1225874;
}

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 2019125 +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)))