Average Error: 0.0 → 0.0
Time: 14.0s
Precision: 64
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[x.re \cdot y.im + x.im \cdot y.re\]
x.re \cdot y.im + x.im \cdot y.re
↓
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 r47736 = x_re;
        double r47737 = y_im;
        double r47738 = r47736 * r47737;
        double r47739 = x_im;
        double r47740 = y_re;
        double r47741 = r47739 * r47740;
        double r47742 = r47738 + r47741;
        return r47742;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r47743 = x_re;
        double r47744 = y_im;
        double r47745 = r47743 * r47744;
        double r47746 = x_im;
        double r47747 = y_re;
        double r47748 = r47746 * r47747;
        double r47749 = r47745 + r47748;
        return r47749;
}

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019347 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))