Average Error: 0.3 → 0.3
Time: 3.1s
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 r562493 = x_re;
        double r562494 = y_im;
        double r562495 = r562493 * r562494;
        double r562496 = x_im;
        double r562497 = y_re;
        double r562498 = r562496 * r562497;
        double r562499 = r562495 + r562498;
        return r562499;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r562500 = x_re;
        double r562501 = y_im;
        double r562502 = r562500 * r562501;
        double r562503 = x_im;
        double r562504 = y_re;
        double r562505 = r562503 * r562504;
        double r562506 = r562502 + r562505;
        return r562506;
}


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 +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)))