Average Error: 1.1 → 1.0
Time: 16.9s
Precision: 64
\[\frac{\left(\left(x.im \cdot y.re\right) - \left(x.re \cdot y.im\right)\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
↓
\[\frac{\left(\mathsf{qms}\left(\left(\left(x.im \cdot y.re\right)\right), x.re, y.im\right)\right)}{\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)}\]
\frac{\left(\left(x.im \cdot y.re\right) - \left(x.re \cdot y.im\right)\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}
↓
\frac{\left(\mathsf{qms}\left(\left(\left(x.im \cdot y.re\right)\right), x.re, y.im\right)\right)}{\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)}
double f(double x_re, double x_im, double y_re, double y_im) {
        double r734608 = x_im;
        double r734609 = y_re;
        double r734610 = r734608 * r734609;
        double r734611 = x_re;
        double r734612 = y_im;
        double r734613 = r734611 * r734612;
        double r734614 = r734610 - r734613;
        double r734615 = r734609 * r734609;
        double r734616 = r734612 * r734612;
        double r734617 = r734615 + r734616;
        double r734618 = r734614 / r734617;
        return r734618;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r734619 = x_im;
        double r734620 = y_re;
        double r734621 = r734619 * r734620;
        double r734622 = /*Error: no posit support in C */;
        double r734623 = x_re;
        double r734624 = y_im;
        double r734625 = /*Error: no posit support in C */;
        double r734626 = /*Error: no posit support in C */;
        double r734627 = r734620 * r734620;
        double r734628 = /*Error: no posit support in C */;
        double r734629 = /*Error: no posit support in C */;
        double r734630 = /*Error: no posit support in C */;
        double r734631 = r734626 / r734630;
        return r734631;
}

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 1.1

    \[\frac{\left(\left(x.im \cdot y.re\right) - \left(x.re \cdot y.im\right)\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
  2. Using strategy rm

  3. Applied introduce-quire1.1

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

  4. Applied insert-quire-fdp-add1.1

    \[\leadsto \frac{\left(\left(x.im \cdot y.re\right) - \left(x.re \cdot y.im\right)\right)}{\color{blue}{\left(\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)\right)}}\]
  5. Using strategy rm

  6. Applied introduce-quire1.1

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

  7. Applied insert-quire-fdp-sub1.0

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

  8. Final simplification1.0

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

Reproduce

herbie shell --seed 2019154 
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, imaginary part"
  (/.p16 (-.p16 (*.p16 x.im y.re) (*.p16 x.re y.im)) (+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im))))