Average Error: 0.3 → 0.3
Time: 21.0s
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 r2471921 = x_re;
        double r2471922 = y_re;
        double r2471923 = r2471921 * r2471922;
        double r2471924 = x_im;
        double r2471925 = y_im;
        double r2471926 = r2471924 * r2471925;
        double r2471927 = r2471923 - r2471926;
        return r2471927;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2471928 = x_re;
        double r2471929 = y_re;
        double r2471930 = r2471928 * r2471929;
        double r2471931 = x_im;
        double r2471932 = y_im;
        double r2471933 = r2471931 * r2471932;
        double r2471934 = r2471930 - r2471933;
        return r2471934;
}

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 2019134 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))