Average Error: 1.1 → 1.0
Time: 20.5s
Precision: 64
\[\frac{\left(\frac{\left(x.re \cdot y.re\right)}{\left(x.im \cdot y.im\right)}\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
↓
\[\frac{\left(\mathsf{qma}\left(\left(\left(x.re \cdot y.re\right)\right), y.im, x.im\right)\right)}{\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)}\]
\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), y.im, x.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 r2517391 = x_re;
        double r2517392 = y_re;
        double r2517393 = r2517391 * r2517392;
        double r2517394 = x_im;
        double r2517395 = y_im;
        double r2517396 = r2517394 * r2517395;
        double r2517397 = r2517393 + r2517396;
        double r2517398 = r2517392 * r2517392;
        double r2517399 = r2517395 * r2517395;
        double r2517400 = r2517398 + r2517399;
        double r2517401 = r2517397 / r2517400;
        return r2517401;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2517402 = x_re;
        double r2517403 = y_re;
        double r2517404 = r2517402 * r2517403;
        double r2517405 = /*Error: no posit support in C */;
        double r2517406 = y_im;
        double r2517407 = x_im;
        double r2517408 = /*Error: no posit support in C */;
        double r2517409 = /*Error: no posit support in C */;
        double r2517410 = r2517403 * r2517403;
        double r2517411 = /*Error: no posit support in C */;
        double r2517412 = /*Error: no posit support in C */;
        double r2517413 = /*Error: no posit support in C */;
        double r2517414 = r2517409 / r2517413;
        return r2517414;
}

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 *-commutative1.1

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

  4. Applied introduce-quire1.1

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

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

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

  7. Applied introduce-quire1.1

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

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

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

  9. Final simplification1.0

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

Reproduce

herbie shell --seed 2019158 
(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))))