Average Error: 1.1 → 1.0
Time: 22.8s
Precision: 64
\[\frac{\left(\left(x.re \cdot y.re\right) + \left(x.im \cdot y.im\right)\right)}{\left(\left(y.re \cdot y.re\right) + \left(y.im \cdot y.im\right)\right)}\]
↓
\[\frac{\left(\left(\mathsf{qma}\left(\left(\left(x.re \cdot y.re\right)\right), x.im, y.im\right)\right)\right)}{\left(\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)\right)}\]
\frac{\left(\left(x.re \cdot y.re\right) + \left(x.im \cdot y.im\right)\right)}{\left(\left(y.re \cdot y.re\right) + \left(y.im \cdot y.im\right)\right)}
↓
\frac{\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)}
double f(double x_re, double x_im, double y_re, double y_im) {
        double r3872788 = x_re;
        double r3872789 = y_re;
        double r3872790 = r3872788 * r3872789;
        double r3872791 = x_im;
        double r3872792 = y_im;
        double r3872793 = r3872791 * r3872792;
        double r3872794 = r3872790 + r3872793;
        double r3872795 = r3872789 * r3872789;
        double r3872796 = r3872792 * r3872792;
        double r3872797 = r3872795 + r3872796;
        double r3872798 = r3872794 / r3872797;
        return r3872798;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r3872799 = x_re;
        double r3872800 = y_re;
        double r3872801 = r3872799 * r3872800;
        double r3872802 = /*Error: no posit support in C */;
        double r3872803 = x_im;
        double r3872804 = y_im;
        double r3872805 = /*Error: no posit support in C */;
        double r3872806 = /*Error: no posit support in C */;
        double r3872807 = r3872800 * r3872800;
        double r3872808 = /*Error: no posit support in C */;
        double r3872809 = /*Error: no posit support in C */;
        double r3872810 = /*Error: no posit support in C */;
        double r3872811 = r3872806 / r3872810;
        return r3872811;
}

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

    \[\frac{\left(\left(x.re \cdot y.re\right) + \left(x.im \cdot y.im\right)\right)}{\left(\left(y.re \cdot y.re\right) + \left(y.im \cdot y.im\right)\right)}\]
  2. Using strategy rm

  3. Applied introduce-quire1.1

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

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

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

  6. Applied introduce-quire1.1

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

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

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

  8. Final simplification1.0

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

Reproduce

herbie shell --seed 0 
(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))))