Average Error: 0.3 → 0.3
Time: 9.3s
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 r937258 = x_re;
        double r937259 = y_re;
        double r937260 = r937258 * r937259;
        double r937261 = x_im;
        double r937262 = y_im;
        double r937263 = r937261 * r937262;
        double r937264 = r937260 - r937263;
        return r937264;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r937265 = x_re;
        double r937266 = y_re;
        double r937267 = r937265 * r937266;
        double r937268 = x_im;
        double r937269 = y_im;
        double r937270 = r937268 * r937269;
        double r937271 = r937267 - r937270;
        return r937271;
}

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 2019124 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))