Average Error: 0.3 → 0.3
Time: 8.8s
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 r1460210 = x_re;
        double r1460211 = y_re;
        double r1460212 = r1460210 * r1460211;
        double r1460213 = x_im;
        double r1460214 = y_im;
        double r1460215 = r1460213 * r1460214;
        double r1460216 = r1460212 - r1460215;
        return r1460216;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1460217 = x_re;
        double r1460218 = y_re;
        double r1460219 = r1460217 * r1460218;
        double r1460220 = x_im;
        double r1460221 = y_im;
        double r1460222 = r1460220 * r1460221;
        double r1460223 = r1460219 - r1460222;
        return r1460223;
}

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 2019124 +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)))