Average Error: 1.1 → 1.1
Time: 32.3s
Precision: 64
\[\frac{\left(\frac{\left(x.re \cdot y.re\right)}{\left(x.im \cdot y.im\right)}\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
↓
\[\frac{\left(\frac{\left(x.re \cdot y.re\right)}{\left(x.im \cdot y.im\right)}\right)}{\left(\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)\right)}\]
\frac{\left(\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(\frac{\left(x.re \cdot y.re\right)}{\left(x.im \cdot y.im\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 r2734712 = x_re;
        double r2734713 = y_re;
        double r2734714 = r2734712 * r2734713;
        double r2734715 = x_im;
        double r2734716 = y_im;
        double r2734717 = r2734715 * r2734716;
        double r2734718 = r2734714 + r2734717;
        double r2734719 = r2734713 * r2734713;
        double r2734720 = r2734716 * r2734716;
        double r2734721 = r2734719 + r2734720;
        double r2734722 = r2734718 / r2734721;
        return r2734722;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2734723 = x_re;
        double r2734724 = y_re;
        double r2734725 = r2734723 * r2734724;
        double r2734726 = x_im;
        double r2734727 = y_im;
        double r2734728 = r2734726 * r2734727;
        double r2734729 = r2734725 + r2734728;
        double r2734730 = r2734724 * r2734724;
        double r2734731 = /*Error: no posit support in C */;
        double r2734732 = /*Error: no posit support in C */;
        double r2734733 = /*Error: no posit support in C */;
        double r2734734 = r2734729 / r2734733;
        return r2734734;
}

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

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(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))))