Average Error: 0.3 → 0.3
Time: 3.1s
Precision: 64
\[\frac{\left(x.re \cdot y.im\right)}{\left(x.im \cdot y.re\right)}\]
↓
\[x.re \cdot y.im + x.im \cdot y.re\]
\frac{\left(x.re \cdot y.im\right)}{\left(x.im \cdot y.re\right)}
↓
x.re \cdot y.im + x.im \cdot y.re
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1919195 = x_re;
        double r1919196 = y_im;
        double r1919197 = r1919195 * r1919196;
        double r1919198 = x_im;
        double r1919199 = y_re;
        double r1919200 = r1919198 * r1919199;
        double r1919201 = r1919197 + r1919200;
        return r1919201;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1919202 = x_re;
        double r1919203 = y_im;
        double r1919204 = r1919202 * r1919203;
        double r1919205 = x_im;
        double r1919206 = y_re;
        double r1919207 = r1919205 * r1919206;
        double r1919208 = r1919204 + r1919207;
        return r1919208;
}

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 0.3

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

  2. Final simplification0.3

    \[\leadsto x.re \cdot y.im + x.im \cdot y.re\]

Reproduce

herbie shell --seed 2019128 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))