Average Error: 0.3 → 0.2
Time: 3.6m
Precision: 64
\[\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)\]
↓
\[\left(\mathsf{qms}\left(\left(\left(x.re \cdot y.re\right)\right), x.im, y.im\right)\right)\]
\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)
↓
\left(\mathsf{qms}\left(\left(\left(x.re \cdot y.re\right)\right), x.im, y.im\right)\right)
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2674768 = x_re;
        double r2674769 = y_re;
        double r2674770 = r2674768 * r2674769;
        double r2674771 = x_im;
        double r2674772 = y_im;
        double r2674773 = r2674771 * r2674772;
        double r2674774 = r2674770 - r2674773;
        return r2674774;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2674775 = x_re;
        double r2674776 = y_re;
        double r2674777 = r2674775 * r2674776;
        double r2674778 = /*Error: no posit support in C */;
        double r2674779 = x_im;
        double r2674780 = y_im;
        double r2674781 = /*Error: no posit support in C */;
        double r2674782 = /*Error: no posit support in C */;
        return r2674782;
}

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. Using strategy rm

  3. Applied introduce-quire0.3

    \[\leadsto \color{blue}{\left(\left(\left(x.re \cdot y.re\right)\right)\right)} - \left(x.im \cdot y.im\right)\]

  4. Applied insert-quire-fdp-sub0.2

    \[\leadsto \color{blue}{\left(\mathsf{qms}\left(\left(\left(x.re \cdot y.re\right)\right), x.im, y.im\right)\right)}\]

  5. Final simplification0.2

    \[\leadsto \left(\mathsf{qms}\left(\left(\left(x.re \cdot y.re\right)\right), x.im, y.im\right)\right)\]

Reproduce

herbie shell --seed 2019162 +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)))