Average Error: 1.1 → 1.1
Time: 33.5s
Precision: 64
\[\frac{\left(\frac{\left(x.re \cdot y.re\right)}{\left(x.im \cdot y.im\right)}\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
↓
\[\frac{\left(\frac{\left(x.re \cdot y.re\right)}{\left(x.im \cdot y.im\right)}\right)}{\left(\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)\right)}\]
\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(\frac{\left(x.re \cdot y.re\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)}
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1636326 = x_re;
        double r1636327 = y_re;
        double r1636328 = r1636326 * r1636327;
        double r1636329 = x_im;
        double r1636330 = y_im;
        double r1636331 = r1636329 * r1636330;
        double r1636332 = r1636328 + r1636331;
        double r1636333 = r1636327 * r1636327;
        double r1636334 = r1636330 * r1636330;
        double r1636335 = r1636333 + r1636334;
        double r1636336 = r1636332 / r1636335;
        return r1636336;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1636337 = x_re;
        double r1636338 = y_re;
        double r1636339 = r1636337 * r1636338;
        double r1636340 = x_im;
        double r1636341 = y_im;
        double r1636342 = r1636340 * r1636341;
        double r1636343 = r1636339 + r1636342;
        double r1636344 = r1636338 * r1636338;
        double r1636345 = /*Error: no posit support in C */;
        double r1636346 = /*Error: no posit support in C */;
        double r1636347 = /*Error: no posit support in C */;
        double r1636348 = r1636343 / r1636347;
        return r1636348;
}

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. Final simplification1.1

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

Reproduce

herbie shell --seed 2019168 
(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))))