Average Error: 0.3 → 0.2
Time: 42.5s
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 r1691476 = x_re;
        double r1691477 = y_re;
        double r1691478 = r1691476 * r1691477;
        double r1691479 = x_im;
        double r1691480 = y_im;
        double r1691481 = r1691479 * r1691480;
        double r1691482 = r1691478 - r1691481;
        return r1691482;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1691483 = x_re;
        double r1691484 = y_re;
        double r1691485 = r1691483 * r1691484;
        double r1691486 = /*Error: no posit support in C */;
        double r1691487 = x_im;
        double r1691488 = y_im;
        double r1691489 = /*Error: no posit support in C */;
        double r1691490 = /*Error: no posit support in C */;
        return r1691490;
}

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 2019163 +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)))