Average Error: 0.3 → 0.3
Time: 13.1s
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 r1083495 = x_re;
        double r1083496 = y_re;
        double r1083497 = r1083495 * r1083496;
        double r1083498 = x_im;
        double r1083499 = y_im;
        double r1083500 = r1083498 * r1083499;
        double r1083501 = r1083497 - r1083500;
        return r1083501;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1083502 = x_re;
        double r1083503 = y_re;
        double r1083504 = r1083502 * r1083503;
        double r1083505 = x_im;
        double r1083506 = y_im;
        double r1083507 = r1083505 * r1083506;
        double r1083508 = r1083504 - r1083507;
        return r1083508;
}

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 2019133 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))