Average Error: 0.0 → 0.0
Time: 2.4s
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 r42925 = x_re;
        double r42926 = y_im;
        double r42927 = r42925 * r42926;
        double r42928 = x_im;
        double r42929 = y_re;
        double r42930 = r42928 * r42929;
        double r42931 = r42927 + r42930;
        return r42931;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r42932 = x_re;
        double r42933 = y_im;
        double r42934 = r42932 * r42933;
        double r42935 = x_im;
        double r42936 = y_re;
        double r42937 = r42935 * r42936;
        double r42938 = r42934 + r42937;
        return r42938;
}

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 2020035 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))