Average Error: 0.3 → 0.3
Time: 22.2s
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 r2983431 = x_re;
        double r2983432 = y_re;
        double r2983433 = r2983431 * r2983432;
        double r2983434 = x_im;
        double r2983435 = y_im;
        double r2983436 = r2983434 * r2983435;
        double r2983437 = r2983433 - r2983436;
        return r2983437;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2983438 = x_re;
        double r2983439 = y_re;
        double r2983440 = r2983438 * r2983439;
        double r2983441 = x_im;
        double r2983442 = y_im;
        double r2983443 = r2983441 * r2983442;
        double r2983444 = r2983440 - r2983443;
        return r2983444;
}

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 2019134 +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)))