Average Error: 0.3 → 0.2
Time: 10.9s
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 r591270 = x_re;
        double r591271 = y_re;
        double r591272 = r591270 * r591271;
        double r591273 = x_im;
        double r591274 = y_im;
        double r591275 = r591273 * r591274;
        double r591276 = r591272 - r591275;
        return r591276;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r591277 = x_re;
        double r591278 = y_re;
        double r591279 = r591277 * r591278;
        double r591280 = /*Error: no posit support in C */;
        double r591281 = x_im;
        double r591282 = y_im;
        double r591283 = /*Error: no posit support in C */;
        double r591284 = /*Error: no posit support in C */;
        return r591284;
}

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 2019156 +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)))