Average Error: 1.1 → 1.1
Time: 29.4s
Precision: 64
\[\frac{\left(\left(x.im \cdot y.re\right) - \left(x.re \cdot y.im\right)\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
↓
\[\frac{\left(\left(\mathsf{qms}\left(\left(\left(x.im \cdot y.re\right)\right), x.re, y.im\right)\right)\right)}{\left(\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)\right)}\]
\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(\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)}
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2442720 = x_im;
        double r2442721 = y_re;
        double r2442722 = r2442720 * r2442721;
        double r2442723 = x_re;
        double r2442724 = y_im;
        double r2442725 = r2442723 * r2442724;
        double r2442726 = r2442722 - r2442725;
        double r2442727 = r2442721 * r2442721;
        double r2442728 = r2442724 * r2442724;
        double r2442729 = r2442727 + r2442728;
        double r2442730 = r2442726 / r2442729;
        return r2442730;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2442731 = x_im;
        double r2442732 = y_re;
        double r2442733 = r2442731 * r2442732;
        double r2442734 = /*Error: no posit support in C */;
        double r2442735 = x_re;
        double r2442736 = y_im;
        double r2442737 = /*Error: no posit support in C */;
        double r2442738 = /*Error: no posit support in C */;
        double r2442739 = r2442732 * r2442732;
        double r2442740 = /*Error: no posit support in C */;
        double r2442741 = /*Error: no posit support in C */;
        double r2442742 = /*Error: no posit support in C */;
        double r2442743 = r2442738 / r2442742;
        return r2442743;
}

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

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

  4. Applied insert-quire-fdp-sub1.1

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

  6. Applied introduce-quire1.1

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

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

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

  8. Final simplification1.1

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

Reproduce

herbie shell --seed 2019164 
(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))))