Average Error: 1.1 → 1.0
Time: 1.6m
Precision: 64
\[\frac{\left(\frac{\left(x.re \cdot y.re\right)}{\left(x.im \cdot y.im\right)}\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
↓
\[\frac{\left(\mathsf{qma}\left(\left(\left(x.re \cdot y.re\right)\right), x.im, y.im\right)\right)}{\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)}\]
\frac{\left(\frac{\left(x.re \cdot y.re\right)}{\left(x.im \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{qma}\left(\left(\left(x.re \cdot y.re\right)\right), x.im, 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 r2074828 = x_re;
        double r2074829 = y_re;
        double r2074830 = r2074828 * r2074829;
        double r2074831 = x_im;
        double r2074832 = y_im;
        double r2074833 = r2074831 * r2074832;
        double r2074834 = r2074830 + r2074833;
        double r2074835 = r2074829 * r2074829;
        double r2074836 = r2074832 * r2074832;
        double r2074837 = r2074835 + r2074836;
        double r2074838 = r2074834 / r2074837;
        return r2074838;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2074839 = x_re;
        double r2074840 = y_re;
        double r2074841 = r2074839 * r2074840;
        double r2074842 = /*Error: no posit support in C */;
        double r2074843 = x_im;
        double r2074844 = y_im;
        double r2074845 = /*Error: no posit support in C */;
        double r2074846 = /*Error: no posit support in C */;
        double r2074847 = r2074840 * r2074840;
        double r2074848 = /*Error: no posit support in C */;
        double r2074849 = /*Error: no posit support in C */;
        double r2074850 = /*Error: no posit support in C */;
        double r2074851 = r2074846 / r2074850;
        return r2074851;
}

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

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

  3. Applied introduce-quire1.1

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

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

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

  6. Applied introduce-quire1.1

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

  7. Applied insert-quire-fdp-add1.0

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

  8. Final simplification1.0

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, real part"
  (/.p16 (+.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)) (+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im))))