Average Error: 1.1 → 1.1
Time: 10.4s
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 r2745375 = x_im;
        double r2745376 = y_re;
        double r2745377 = r2745375 * r2745376;
        double r2745378 = x_re;
        double r2745379 = y_im;
        double r2745380 = r2745378 * r2745379;
        double r2745381 = r2745377 - r2745380;
        double r2745382 = r2745376 * r2745376;
        double r2745383 = r2745379 * r2745379;
        double r2745384 = r2745382 + r2745383;
        double r2745385 = r2745381 / r2745384;
        return r2745385;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2745386 = x_im;
        double r2745387 = y_re;
        double r2745388 = r2745386 * r2745387;
        double r2745389 = x_re;
        double r2745390 = y_im;
        double r2745391 = r2745389 * r2745390;
        double r2745392 = r2745388 - r2745391;
        double r2745393 = r2745387 * r2745387;
        double r2745394 = r2745390 * r2745390;
        double r2745395 = r2745393 + r2745394;
        double r2745396 = r2745392 / r2745395;
        return r2745396;
}

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 2019125 
(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))))