Average Error: 0.3 → 0.3
Time: 7.6s
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 r1381621 = x_re;
        double r1381622 = y_re;
        double r1381623 = r1381621 * r1381622;
        double r1381624 = x_im;
        double r1381625 = y_im;
        double r1381626 = r1381624 * r1381625;
        double r1381627 = r1381623 - r1381626;
        return r1381627;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1381628 = x_re;
        double r1381629 = y_re;
        double r1381630 = r1381628 * r1381629;
        double r1381631 = x_im;
        double r1381632 = y_im;
        double r1381633 = r1381631 * r1381632;
        double r1381634 = r1381630 - r1381633;
        return r1381634;
}

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 2019125 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))