Average Error: 1.1 → 1.0
Time: 17.9s
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 r527289 = x_re;
        double r527290 = y_re;
        double r527291 = r527289 * r527290;
        double r527292 = x_im;
        double r527293 = y_im;
        double r527294 = r527292 * r527293;
        double r527295 = r527291 + r527294;
        double r527296 = r527290 * r527290;
        double r527297 = r527293 * r527293;
        double r527298 = r527296 + r527297;
        double r527299 = r527295 / r527298;
        return r527299;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r527300 = x_re;
        double r527301 = y_re;
        double r527302 = r527300 * r527301;
        double r527303 = /*Error: no posit support in C */;
        double r527304 = x_im;
        double r527305 = y_im;
        double r527306 = /*Error: no posit support in C */;
        double r527307 = /*Error: no posit support in C */;
        double r527308 = r527301 * r527301;
        double r527309 = /*Error: no posit support in C */;
        double r527310 = /*Error: no posit support in C */;
        double r527311 = /*Error: no posit support in C */;
        double r527312 = r527307 / r527311;
        return r527312;
}

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 2019156 
(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))))