Average Error: 1.1 → 1.1
Time: 4.2s
Precision: 64
\[\frac{\left(\frac{\left(x.re \cdot y.re\right)}{\left(x.im \cdot y.im\right)}\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
↓
\[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
\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{x.re \cdot y.re + x.im \cdot y.im}{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 r1802763 = x_re;
        double r1802764 = y_re;
        double r1802765 = r1802763 * r1802764;
        double r1802766 = x_im;
        double r1802767 = y_im;
        double r1802768 = r1802766 * r1802767;
        double r1802769 = r1802765 + r1802768;
        double r1802770 = r1802764 * r1802764;
        double r1802771 = r1802767 * r1802767;
        double r1802772 = r1802770 + r1802771;
        double r1802773 = r1802769 / r1802772;
        return r1802773;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1802774 = x_re;
        double r1802775 = y_re;
        double r1802776 = r1802774 * r1802775;
        double r1802777 = x_im;
        double r1802778 = y_im;
        double r1802779 = r1802777 * r1802778;
        double r1802780 = r1802776 + r1802779;
        double r1802781 = r1802775 * r1802775;
        double r1802782 = r1802778 * r1802778;
        double r1802783 = r1802781 + r1802782;
        double r1802784 = r1802780 / r1802783;
        return r1802784;
}

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. Final simplification1.1

    \[\leadsto \frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]

Reproduce

herbie shell --seed 2019128 
(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))))