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 r731145 = x_re;
        double r731146 = y_im;
        double r731147 = r731145 * r731146;
        double r731148 = x_im;
        double r731149 = y_re;
        double r731150 = r731148 * r731149;
        double r731151 = r731147 + r731150;
        return r731151;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r731152 = x_re;
        double r731153 = y_im;
        double r731154 = r731152 * r731153;
        double r731155 = x_im;
        double r731156 = y_re;
        double r731157 = r731155 * r731156;
        double r731158 = r731154 + r731157;
        return r731158;
}

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 2019107 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))