Average Error: 0.0 → 0.0
Time: 775.0ms
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 r33823 = x_re;
        double r33824 = y_im;
        double r33825 = r33823 * r33824;
        double r33826 = x_im;
        double r33827 = y_re;
        double r33828 = r33826 * r33827;
        double r33829 = r33825 + r33828;
        return r33829;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r33830 = x_re;
        double r33831 = y_im;
        double r33832 = r33830 * r33831;
        double r33833 = x_im;
        double r33834 = y_re;
        double r33835 = r33833 * r33834;
        double r33836 = r33832 + r33835;
        return r33836;
}

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 2020064 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))