Average Error: 0.3 → 0.3
Time: 6.5s
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 r334746 = x_re;
        double r334747 = y_re;
        double r334748 = r334746 * r334747;
        double r334749 = x_im;
        double r334750 = y_im;
        double r334751 = r334749 * r334750;
        double r334752 = r334748 - r334751;
        return r334752;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r334753 = x_re;
        double r334754 = y_re;
        double r334755 = r334753 * r334754;
        double r334756 = x_im;
        double r334757 = y_im;
        double r334758 = r334756 * r334757;
        double r334759 = r334755 - r334758;
        return r334759;
}

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 2019120 +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)))