Average Error: 0.3 → 0.3
Time: 8.5s
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 r748882 = x_re;
        double r748883 = y_re;
        double r748884 = r748882 * r748883;
        double r748885 = x_im;
        double r748886 = y_im;
        double r748887 = r748885 * r748886;
        double r748888 = r748884 - r748887;
        return r748888;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r748889 = x_re;
        double r748890 = y_re;
        double r748891 = r748889 * r748890;
        double r748892 = x_im;
        double r748893 = y_im;
        double r748894 = r748892 * r748893;
        double r748895 = r748891 - r748894;
        return r748895;
}

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 2019112 +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)))