Average Error: 0.3 → 0.3
Time: 4.2s
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 r1944123 = x_re;
        double r1944124 = y_im;
        double r1944125 = r1944123 * r1944124;
        double r1944126 = x_im;
        double r1944127 = y_re;
        double r1944128 = r1944126 * r1944127;
        double r1944129 = r1944125 + r1944128;
        return r1944129;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1944130 = x_re;
        double r1944131 = y_im;
        double r1944132 = r1944130 * r1944131;
        double r1944133 = x_im;
        double r1944134 = y_re;
        double r1944135 = r1944133 * r1944134;
        double r1944136 = r1944132 + r1944135;
        return r1944136;
}

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 2019130 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))