Average Error: 0.3 → 0.3
Time: 5.5s
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 r609593 = x_re;
        double r609594 = y_re;
        double r609595 = r609593 * r609594;
        double r609596 = x_im;
        double r609597 = y_im;
        double r609598 = r609596 * r609597;
        double r609599 = r609595 - r609598;
        return r609599;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r609600 = x_re;
        double r609601 = y_re;
        double r609602 = r609600 * r609601;
        double r609603 = x_im;
        double r609604 = y_im;
        double r609605 = r609603 * r609604;
        double r609606 = r609602 - r609605;
        return r609606;
}

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 2019120 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))