Average Error: 0.3 → 0.3
Time: 6.8s
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 r1206266 = x_re;
        double r1206267 = y_re;
        double r1206268 = r1206266 * r1206267;
        double r1206269 = x_im;
        double r1206270 = y_im;
        double r1206271 = r1206269 * r1206270;
        double r1206272 = r1206268 - r1206271;
        return r1206272;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1206273 = x_re;
        double r1206274 = y_re;
        double r1206275 = r1206273 * r1206274;
        double r1206276 = x_im;
        double r1206277 = y_im;
        double r1206278 = r1206276 * r1206277;
        double r1206279 = r1206275 - r1206278;
        return r1206279;
}

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 2019125 +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)))