Average Error: 0.3 → 0.3
Time: 3.7s
Precision: 64
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[x.re \cdot y.im + x.im \cdot y.re\]
double f(double x_re, double x_im, double y_re, double y_im) {
        double r600866 = x_re;
        double r600867 = y_im;
        double r600868 = r600866 * r600867;
        double r600869 = x_im;
        double r600870 = y_re;
        double r600871 = r600869 * r600870;
        double r600872 = r600868 + r600871;
        return r600872;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r600873 = x_re;
        double r600874 = y_im;
        double r600875 = r600873 * r600874;
        double r600876 = x_im;
        double r600877 = y_re;
        double r600878 = r600876 * r600877;
        double r600879 = r600875 + r600878;
        return r600879;
}


x.re \cdot y.im + x.im \cdot y.re
↓
x.re \cdot y.im + x.im \cdot y.re

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 2019102 +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)))