Average Error: 1.1 → 1.0
Time: 19.5s
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 r560231 = x_re;
        double r560232 = y_re;
        double r560233 = r560231 * r560232;
        double r560234 = x_im;
        double r560235 = y_im;
        double r560236 = r560234 * r560235;
        double r560237 = r560233 + r560236;
        double r560238 = r560232 * r560232;
        double r560239 = r560235 * r560235;
        double r560240 = r560238 + r560239;
        double r560241 = r560237 / r560240;
        return r560241;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r560242 = x_re;
        double r560243 = y_re;
        double r560244 = r560242 * r560243;
        double r560245 = /*Error: no posit support in C */;
        double r560246 = x_im;
        double r560247 = y_im;
        double r560248 = /*Error: no posit support in C */;
        double r560249 = /*Error: no posit support in C */;
        double r560250 = r560243 * r560243;
        double r560251 = /*Error: no posit support in C */;
        double r560252 = /*Error: no posit support in C */;
        double r560253 = /*Error: no posit support in C */;
        double r560254 = r560249 / r560253;
        return r560254;
}

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 2019153 
(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))))