Average Error: 1.1 → 1.1
Time: 4.7s
Precision: 64
\[\frac{\left(\frac{\left(x.re \cdot y.re\right)}{\left(x.im \cdot y.im\right)}\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
↓
\[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
\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 r331164 = x_re;
        double r331165 = y_re;
        double r331166 = r331164 * r331165;
        double r331167 = x_im;
        double r331168 = y_im;
        double r331169 = r331167 * r331168;
        double r331170 = r331166 + r331169;
        double r331171 = r331165 * r331165;
        double r331172 = r331168 * r331168;
        double r331173 = r331171 + r331172;
        double r331174 = r331170 / r331173;
        return r331174;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r331175 = x_re;
        double r331176 = y_re;
        double r331177 = r331175 * r331176;
        double r331178 = x_im;
        double r331179 = y_im;
        double r331180 = r331178 * r331179;
        double r331181 = r331177 + r331180;
        double r331182 = r331176 * r331176;
        double r331183 = r331179 * r331179;
        double r331184 = r331182 + r331183;
        double r331185 = r331181 / r331184;
        return r331185;
}

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 2019119 
(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))))