Average Error: 0.3 → 0.2
Time: 9.8s
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 r806100 = x_re;
        double r806101 = y_re;
        double r806102 = r806100 * r806101;
        double r806103 = x_im;
        double r806104 = y_im;
        double r806105 = r806103 * r806104;
        double r806106 = r806102 - r806105;
        return r806106;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r806107 = x_re;
        double r806108 = y_re;
        double r806109 = r806107 * r806108;
        double r806110 = /*Error: no posit support in C */;
        double r806111 = x_im;
        double r806112 = y_im;
        double r806113 = /*Error: no posit support in C */;
        double r806114 = /*Error: no posit support in C */;
        return r806114;
}

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