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 r1409987 = x_re;
        double r1409988 = y_im;
        double r1409989 = r1409987 * r1409988;
        double r1409990 = x_im;
        double r1409991 = y_re;
        double r1409992 = r1409990 * r1409991;
        double r1409993 = r1409989 + r1409992;
        return r1409993;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1409994 = x_re;
        double r1409995 = y_im;
        double r1409996 = r1409994 * r1409995;
        double r1409997 = x_im;
        double r1409998 = y_re;
        double r1409999 = r1409997 * r1409998;
        double r1410000 = r1409996 + r1409999;
        return r1410000;
}

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 2019107 +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)))