Average Error: 1.1 → 1.1
Time: 41.9s
Precision: 64
\[\frac{\left(\frac{\left(x.re \cdot y.re\right)}{\left(x.im \cdot y.im\right)}\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
↓
\[\frac{x.re \cdot y.re + x.im \cdot y.im}{\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)}\]
\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{x.re \cdot y.re + x.im \cdot y.im}{\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 r2304729 = x_re;
        double r2304730 = y_re;
        double r2304731 = r2304729 * r2304730;
        double r2304732 = x_im;
        double r2304733 = y_im;
        double r2304734 = r2304732 * r2304733;
        double r2304735 = r2304731 + r2304734;
        double r2304736 = r2304730 * r2304730;
        double r2304737 = r2304733 * r2304733;
        double r2304738 = r2304736 + r2304737;
        double r2304739 = r2304735 / r2304738;
        return r2304739;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2304740 = x_re;
        double r2304741 = y_re;
        double r2304742 = r2304740 * r2304741;
        double r2304743 = x_im;
        double r2304744 = y_im;
        double r2304745 = r2304743 * r2304744;
        double r2304746 = r2304742 + r2304745;
        double r2304747 = r2304741 * r2304741;
        double r2304748 = /*Error: no posit support in C */;
        double r2304749 = /*Error: no posit support in C */;
        double r2304750 = /*Error: no posit support in C */;
        double r2304751 = r2304746 / r2304750;
        return r2304751;
}

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

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

Reproduce

herbie shell --seed 2019152 
(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))))