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 r1751091 = x_re;
        double r1751092 = y_im;
        double r1751093 = r1751091 * r1751092;
        double r1751094 = x_im;
        double r1751095 = y_re;
        double r1751096 = r1751094 * r1751095;
        double r1751097 = r1751093 + r1751096;
        return r1751097;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1751098 = x_re;
        double r1751099 = y_im;
        double r1751100 = r1751098 * r1751099;
        double r1751101 = x_im;
        double r1751102 = y_re;
        double r1751103 = r1751101 * r1751102;
        double r1751104 = r1751100 + r1751103;
        return r1751104;
}

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 2019134 +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)))