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 r2013981 = x_re;
        double r2013982 = y_im;
        double r2013983 = r2013981 * r2013982;
        double r2013984 = x_im;
        double r2013985 = y_re;
        double r2013986 = r2013984 * r2013985;
        double r2013987 = r2013983 + r2013986;
        return r2013987;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2013988 = x_re;
        double r2013989 = y_im;
        double r2013990 = r2013988 * r2013989;
        double r2013991 = x_im;
        double r2013992 = y_re;
        double r2013993 = r2013991 * r2013992;
        double r2013994 = r2013990 + r2013993;
        return r2013994;
}

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 2019132 +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)))