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 r1628661 = x_re;
        double r1628662 = y_im;
        double r1628663 = r1628661 * r1628662;
        double r1628664 = x_im;
        double r1628665 = y_re;
        double r1628666 = r1628664 * r1628665;
        double r1628667 = r1628663 + r1628666;
        return r1628667;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1628668 = x_re;
        double r1628669 = y_im;
        double r1628670 = r1628668 * r1628669;
        double r1628671 = x_im;
        double r1628672 = y_re;
        double r1628673 = r1628671 * r1628672;
        double r1628674 = r1628670 + r1628673;
        return r1628674;
}

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 2019135 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))