Average Error: 0.3 → 0.3
Time: 3.8s
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 r1552775 = x_re;
        double r1552776 = y_im;
        double r1552777 = r1552775 * r1552776;
        double r1552778 = x_im;
        double r1552779 = y_re;
        double r1552780 = r1552778 * r1552779;
        double r1552781 = r1552777 + r1552780;
        return r1552781;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1552782 = x_re;
        double r1552783 = y_im;
        double r1552784 = r1552782 * r1552783;
        double r1552785 = x_im;
        double r1552786 = y_re;
        double r1552787 = r1552785 * r1552786;
        double r1552788 = r1552784 + r1552787;
        return r1552788;
}

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