Average Error: 0.3 → 0.3
Time: 14.1s
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 r2459395 = x_re;
        double r2459396 = y_re;
        double r2459397 = r2459395 * r2459396;
        double r2459398 = x_im;
        double r2459399 = y_im;
        double r2459400 = r2459398 * r2459399;
        double r2459401 = r2459397 - r2459400;
        return r2459401;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2459402 = x_re;
        double r2459403 = y_re;
        double r2459404 = r2459402 * r2459403;
        double r2459405 = x_im;
        double r2459406 = y_im;
        double r2459407 = r2459405 * r2459406;
        double r2459408 = r2459404 - r2459407;
        return r2459408;
}

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 +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)))