Average Error: 0.3 → 0.3
Time: 3.7s
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 r871807 = x_re;
        double r871808 = y_im;
        double r871809 = r871807 * r871808;
        double r871810 = x_im;
        double r871811 = y_re;
        double r871812 = r871810 * r871811;
        double r871813 = r871809 + r871812;
        return r871813;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r871814 = x_re;
        double r871815 = y_im;
        double r871816 = r871814 * r871815;
        double r871817 = x_im;
        double r871818 = y_re;
        double r871819 = r871817 * r871818;
        double r871820 = r871816 + r871819;
        return r871820;
}

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 2019120 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))