Average Error: 1.1 → 1.0
Time: 25.4s
Precision: 64
\[\frac{\left(\left(x.im \cdot y.re\right) - \left(x.re \cdot y.im\right)\right)}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
↓
\[\frac{\left(\mathsf{qms}\left(\left(\left(x.im \cdot y.re\right)\right), x.re, y.im\right)\right)}{\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)}\]
\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{\left(\mathsf{qms}\left(\left(\left(x.im \cdot y.re\right)\right), x.re, y.im\right)\right)}{\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)}
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1242301 = x_im;
        double r1242302 = y_re;
        double r1242303 = r1242301 * r1242302;
        double r1242304 = x_re;
        double r1242305 = y_im;
        double r1242306 = r1242304 * r1242305;
        double r1242307 = r1242303 - r1242306;
        double r1242308 = r1242302 * r1242302;
        double r1242309 = r1242305 * r1242305;
        double r1242310 = r1242308 + r1242309;
        double r1242311 = r1242307 / r1242310;
        return r1242311;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1242312 = x_im;
        double r1242313 = y_re;
        double r1242314 = r1242312 * r1242313;
        double r1242315 = /*Error: no posit support in C */;
        double r1242316 = x_re;
        double r1242317 = y_im;
        double r1242318 = /*Error: no posit support in C */;
        double r1242319 = /*Error: no posit support in C */;
        double r1242320 = r1242313 * r1242313;
        double r1242321 = /*Error: no posit support in C */;
        double r1242322 = /*Error: no posit support in C */;
        double r1242323 = /*Error: no posit support in C */;
        double r1242324 = r1242319 / r1242323;
        return r1242324;
}

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. Using strategy rm

  3. Applied introduce-quire1.1

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

  4. Applied insert-quire-fdp-sub1.1

    \[\leadsto \frac{\color{blue}{\left(\left(\mathsf{qms}\left(\left(\left(x.im \cdot y.re\right)\right), x.re, y.im\right)\right)\right)}}{\left(\frac{\left(y.re \cdot y.re\right)}{\left(y.im \cdot y.im\right)}\right)}\]
  5. Using strategy rm

  6. Applied introduce-quire1.1

    \[\leadsto \frac{\left(\left(\mathsf{qms}\left(\left(\left(x.im \cdot y.re\right)\right), x.re, y.im\right)\right)\right)}{\left(\frac{\color{blue}{\left(\left(\left(y.re \cdot y.re\right)\right)\right)}}{\left(y.im \cdot y.im\right)}\right)}\]

  7. Applied insert-quire-fdp-add1.0

    \[\leadsto \frac{\left(\left(\mathsf{qms}\left(\left(\left(x.im \cdot y.re\right)\right), x.re, y.im\right)\right)\right)}{\color{blue}{\left(\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)\right)}}\]

  8. Final simplification1.0

    \[\leadsto \frac{\left(\mathsf{qms}\left(\left(\left(x.im \cdot y.re\right)\right), x.re, y.im\right)\right)}{\left(\mathsf{qma}\left(\left(\left(y.re \cdot y.re\right)\right), y.im, y.im\right)\right)}\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(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))))