Average Error: 0.3 → 0.3
Time: 3.0s
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 r806151 = x_re;
        double r806152 = y_im;
        double r806153 = r806151 * r806152;
        double r806154 = x_im;
        double r806155 = y_re;
        double r806156 = r806154 * r806155;
        double r806157 = r806153 + r806156;
        return r806157;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r806158 = x_re;
        double r806159 = y_im;
        double r806160 = r806158 * r806159;
        double r806161 = x_im;
        double r806162 = y_re;
        double r806163 = r806161 * r806162;
        double r806164 = r806160 + r806163;
        return r806164;
}

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 2019125 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))