Average Error: 1.1 → 1.1
Time: 19.4s
Precision: 64
\[\frac{\left(\left(x.im \cdot y.re\right) - \left(x.re \cdot y.im\right)\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
↓
\[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
\frac{\left(\left(x.im \cdot y.re\right) - \left(x.re \cdot y.im\right)\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}
↓
\frac{x.im \cdot y.re - x.re \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 r1430650 = x_im;
        double r1430651 = y_re;
        double r1430652 = r1430650 * r1430651;
        double r1430653 = x_re;
        double r1430654 = y_im;
        double r1430655 = r1430653 * r1430654;
        double r1430656 = r1430652 - r1430655;
        double r1430657 = r1430651 * r1430651;
        double r1430658 = r1430654 * r1430654;
        double r1430659 = r1430657 + r1430658;
        double r1430660 = r1430656 / r1430659;
        return r1430660;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1430661 = x_im;
        double r1430662 = y_re;
        double r1430663 = r1430661 * r1430662;
        double r1430664 = x_re;
        double r1430665 = y_im;
        double r1430666 = r1430664 * r1430665;
        double r1430667 = r1430663 - r1430666;
        double r1430668 = r1430662 * r1430662;
        double r1430669 = r1430665 * r1430665;
        double r1430670 = r1430668 + r1430669;
        double r1430671 = r1430667 / r1430670;
        return r1430671;
}

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

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

  2. Final simplification1.1

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

Reproduce

herbie shell --seed 2019134 
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, imaginary part"
  (/.p16 (-.p16 (*.p16 x.im y.re) (*.p16 x.re y.im)) (+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im))))