Average Error: 1.1 → 1.0
Time: 25.0s
Precision: 64
\[\frac{\left(\left(x.im \cdot y.re\right) - \left(x.re \cdot y.im\right)\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
↓
\[\frac{\left(\mathsf{qms}\left(\left(\left(x.im \cdot y.re\right)\right), x.re, y.im\right)\right)}{\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)}\]
\frac{\left(\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(\mathsf{qms}\left(\left(\left(x.im \cdot y.re\right)\right), x.re, 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 r1689318 = x_im;
        double r1689319 = y_re;
        double r1689320 = r1689318 * r1689319;
        double r1689321 = x_re;
        double r1689322 = y_im;
        double r1689323 = r1689321 * r1689322;
        double r1689324 = r1689320 - r1689323;
        double r1689325 = r1689319 * r1689319;
        double r1689326 = r1689322 * r1689322;
        double r1689327 = r1689325 + r1689326;
        double r1689328 = r1689324 / r1689327;
        return r1689328;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1689329 = x_im;
        double r1689330 = y_re;
        double r1689331 = r1689329 * r1689330;
        double r1689332 = /*Error: no posit support in C */;
        double r1689333 = x_re;
        double r1689334 = y_im;
        double r1689335 = /*Error: no posit support in C */;
        double r1689336 = /*Error: no posit support in C */;
        double r1689337 = r1689330 * r1689330;
        double r1689338 = /*Error: no posit support in C */;
        double r1689339 = /*Error: no posit support in C */;
        double r1689340 = /*Error: no posit support in C */;
        double r1689341 = r1689336 / r1689340;
        return r1689341;
}

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-add1.0

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

  8. Final simplification1.0

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, 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))))