Average Error: 0.3 → 0.3
Time: 4.0s
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 r730271 = x_re;
        double r730272 = y_im;
        double r730273 = r730271 * r730272;
        double r730274 = x_im;
        double r730275 = y_re;
        double r730276 = r730274 * r730275;
        double r730277 = r730273 + r730276;
        return r730277;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r730278 = x_re;
        double r730279 = y_im;
        double r730280 = r730278 * r730279;
        double r730281 = x_im;
        double r730282 = y_re;
        double r730283 = r730281 * r730282;
        double r730284 = r730280 + r730283;
        return r730284;
}

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 2019119 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))