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 r2594510 = x_re;
        double r2594511 = y_re;
        double r2594512 = r2594510 * r2594511;
        double r2594513 = x_im;
        double r2594514 = y_im;
        double r2594515 = r2594513 * r2594514;
        double r2594516 = r2594512 - r2594515;
        return r2594516;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2594517 = x_re;
        double r2594518 = y_re;
        double r2594519 = r2594517 * r2594518;
        double r2594520 = /*Error: no posit support in C */;
        double r2594521 = x_im;
        double r2594522 = y_im;
        double r2594523 = /*Error: no posit support in C */;
        double r2594524 = /*Error: no posit support in C */;
        return r2594524;
}

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 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))