Average Error: 0.3 → 0.3
Time: 7.0s
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 r925842 = x_re;
        double r925843 = y_re;
        double r925844 = r925842 * r925843;
        double r925845 = x_im;
        double r925846 = y_im;
        double r925847 = r925845 * r925846;
        double r925848 = r925844 - r925847;
        return r925848;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r925849 = x_re;
        double r925850 = y_re;
        double r925851 = r925849 * r925850;
        double r925852 = x_im;
        double r925853 = y_im;
        double r925854 = r925852 * r925853;
        double r925855 = r925851 - r925854;
        return r925855;
}

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 2019104 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))