Average Error: 1.1 → 1.1
Time: 15.9s
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 r3624401 = x_im;
        double r3624402 = y_re;
        double r3624403 = r3624401 * r3624402;
        double r3624404 = x_re;
        double r3624405 = y_im;
        double r3624406 = r3624404 * r3624405;
        double r3624407 = r3624403 - r3624406;
        double r3624408 = r3624402 * r3624402;
        double r3624409 = r3624405 * r3624405;
        double r3624410 = r3624408 + r3624409;
        double r3624411 = r3624407 / r3624410;
        return r3624411;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r3624412 = x_im;
        double r3624413 = y_re;
        double r3624414 = r3624412 * r3624413;
        double r3624415 = x_re;
        double r3624416 = y_im;
        double r3624417 = r3624415 * r3624416;
        double r3624418 = r3624414 - r3624417;
        double r3624419 = r3624413 * r3624413;
        double r3624420 = r3624416 * r3624416;
        double r3624421 = r3624419 + r3624420;
        double r3624422 = r3624418 / r3624421;
        return r3624422;
}

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 2019133 
(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))))