Average Error: 1.1 → 1.1
Time: 21.7s
Precision: 64
\[\frac{\left(\frac{\left(x.re \cdot y.re\right)}{\left(x.im \cdot y.im\right)}\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
↓
\[\frac{\left(\mathsf{qma}\left(\left(\left(x.re \cdot y.re\right)\right), x.im, y.im\right)\right)}{y.re \cdot y.re + y.im \cdot y.im}\]
\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), x.im, y.im\right)\right)}{y.re \cdot y.re + y.im \cdot y.im}
double f(double x_re, double x_im, double y_re, double y_im) {
        double r654667 = x_re;
        double r654668 = y_re;
        double r654669 = r654667 * r654668;
        double r654670 = x_im;
        double r654671 = y_im;
        double r654672 = r654670 * r654671;
        double r654673 = r654669 + r654672;
        double r654674 = r654668 * r654668;
        double r654675 = r654671 * r654671;
        double r654676 = r654674 + r654675;
        double r654677 = r654673 / r654676;
        return r654677;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r654678 = x_re;
        double r654679 = y_re;
        double r654680 = r654678 * r654679;
        double r654681 = /*Error: no posit support in C */;
        double r654682 = x_im;
        double r654683 = y_im;
        double r654684 = /*Error: no posit support in C */;
        double r654685 = /*Error: no posit support in C */;
        double r654686 = r654679 * r654679;
        double r654687 = r654683 * r654683;
        double r654688 = r654686 + r654687;
        double r654689 = r654685 / r654688;
        return r654689;
}

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

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

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

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

  5. Final simplification1.1

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

Reproduce

herbie shell --seed 2019155 
(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))))