Average Error: 0.3 → 0.3
Time: 13.5s
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 r2052020 = x_re;
        double r2052021 = y_re;
        double r2052022 = r2052020 * r2052021;
        double r2052023 = x_im;
        double r2052024 = y_im;
        double r2052025 = r2052023 * r2052024;
        double r2052026 = r2052022 - r2052025;
        return r2052026;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2052027 = x_re;
        double r2052028 = y_re;
        double r2052029 = r2052027 * r2052028;
        double r2052030 = x_im;
        double r2052031 = y_im;
        double r2052032 = r2052030 * r2052031;
        double r2052033 = r2052029 - r2052032;
        return r2052033;
}

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 2019130 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))