Average Error: 0.0 → 0.0
Time: 3.0s
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 r96053 = x_re;
        double r96054 = y_im;
        double r96055 = r96053 * r96054;
        double r96056 = x_im;
        double r96057 = y_re;
        double r96058 = r96056 * r96057;
        double r96059 = r96055 + r96058;
        return r96059;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r96060 = x_re;
        double r96061 = y_im;
        double r96062 = r96060 * r96061;
        double r96063 = x_im;
        double r96064 = y_re;
        double r96065 = r96063 * r96064;
        double r96066 = r96062 + r96065;
        return r96066;
}

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 2020060 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))