Average Error: 0.3 → 0.3
Time: 3.0s
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 r557584 = x_re;
        double r557585 = y_im;
        double r557586 = r557584 * r557585;
        double r557587 = x_im;
        double r557588 = y_re;
        double r557589 = r557587 * r557588;
        double r557590 = r557586 + r557589;
        return r557590;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r557591 = x_re;
        double r557592 = y_im;
        double r557593 = r557591 * r557592;
        double r557594 = x_im;
        double r557595 = y_re;
        double r557596 = r557594 * r557595;
        double r557597 = r557593 + r557596;
        return r557597;
}

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 2019121 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))