Average Error: 0.3 → 0.3
Time: 7.3s
Precision: 64
\[\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)\]
↓
\[x.re \cdot y.re - x.im \cdot y.im\]
\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)
↓
x.re \cdot y.re - x.im \cdot y.im
double f(double x_re, double x_im, double y_re, double y_im) {
        double r761621 = x_re;
        double r761622 = y_re;
        double r761623 = r761621 * r761622;
        double r761624 = x_im;
        double r761625 = y_im;
        double r761626 = r761624 * r761625;
        double r761627 = r761623 - r761626;
        return r761627;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r761628 = x_re;
        double r761629 = y_re;
        double r761630 = r761628 * r761629;
        double r761631 = x_im;
        double r761632 = y_im;
        double r761633 = r761631 * r761632;
        double r761634 = r761630 - r761633;
        return r761634;
}

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

    \[\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)\]

  2. Final simplification0.3

    \[\leadsto x.re \cdot y.re - x.im \cdot y.im\]

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))