Average Error: 0.3 → 0.3
Time: 3.2s
Precision: 64
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[x.re \cdot y.im + x.im \cdot y.re\]
double f(double x_re, double x_im, double y_re, double y_im) {
        double r805312 = x_re;
        double r805313 = y_im;
        double r805314 = r805312 * r805313;
        double r805315 = x_im;
        double r805316 = y_re;
        double r805317 = r805315 * r805316;
        double r805318 = r805314 + r805317;
        return r805318;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r805319 = x_re;
        double r805320 = y_im;
        double r805321 = r805319 * r805320;
        double r805322 = x_im;
        double r805323 = y_re;
        double r805324 = r805322 * r805323;
        double r805325 = r805321 + r805324;
        return r805325;
}


x.re \cdot y.im + x.im \cdot y.re
↓
x.re \cdot y.im + x.im \cdot y.re

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 2019101 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))