Average Error: 0.3 → 0.3
Time: 4.1s
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 r2472400 = x_re;
        double r2472401 = y_im;
        double r2472402 = r2472400 * r2472401;
        double r2472403 = x_im;
        double r2472404 = y_re;
        double r2472405 = r2472403 * r2472404;
        double r2472406 = r2472402 + r2472405;
        return r2472406;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2472407 = x_re;
        double r2472408 = y_im;
        double r2472409 = r2472407 * r2472408;
        double r2472410 = x_im;
        double r2472411 = y_re;
        double r2472412 = r2472410 * r2472411;
        double r2472413 = r2472409 + r2472412;
        return r2472413;
}

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 +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)))