Average Error: 0.3 → 0.3
Time: 9.8s
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 r633722 = x_re;
        double r633723 = y_re;
        double r633724 = r633722 * r633723;
        double r633725 = x_im;
        double r633726 = y_im;
        double r633727 = r633725 * r633726;
        double r633728 = r633724 - r633727;
        return r633728;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r633729 = x_re;
        double r633730 = y_re;
        double r633731 = r633729 * r633730;
        double r633732 = x_im;
        double r633733 = y_im;
        double r633734 = r633732 * r633733;
        double r633735 = r633731 - r633734;
        return r633735;
}

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 2019107 +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)))