Average Error: 0.3 → 0.3
Time: 7.5s
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 r395161 = x_re;
        double r395162 = y_re;
        double r395163 = r395161 * r395162;
        double r395164 = x_im;
        double r395165 = y_im;
        double r395166 = r395164 * r395165;
        double r395167 = r395163 - r395166;
        return r395167;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r395168 = x_re;
        double r395169 = y_re;
        double r395170 = r395168 * r395169;
        double r395171 = x_im;
        double r395172 = y_im;
        double r395173 = r395171 * r395172;
        double r395174 = r395170 - r395173;
        return r395174;
}

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 2019119 +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)))