Average Error: 0.3 → 0.3
Time: 12.5s
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 r2484906 = x_re;
        double r2484907 = y_re;
        double r2484908 = r2484906 * r2484907;
        double r2484909 = x_im;
        double r2484910 = y_im;
        double r2484911 = r2484909 * r2484910;
        double r2484912 = r2484908 - r2484911;
        return r2484912;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2484913 = x_re;
        double r2484914 = y_re;
        double r2484915 = r2484913 * r2484914;
        double r2484916 = x_im;
        double r2484917 = y_im;
        double r2484918 = r2484916 * r2484917;
        double r2484919 = r2484915 - r2484918;
        return r2484919;
}

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 2019135 +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)))