Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[x.im \cdot y.re + x.re \cdot y.im\]
x.re \cdot y.im + x.im \cdot y.re
↓
x.im \cdot y.re + x.re \cdot y.im
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2357882 = x_re;
        double r2357883 = y_im;
        double r2357884 = r2357882 * r2357883;
        double r2357885 = x_im;
        double r2357886 = y_re;
        double r2357887 = r2357885 * r2357886;
        double r2357888 = r2357884 + r2357887;
        return r2357888;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2357889 = x_im;
        double r2357890 = y_re;
        double r2357891 = r2357889 * r2357890;
        double r2357892 = x_re;
        double r2357893 = y_im;
        double r2357894 = r2357892 * r2357893;
        double r2357895 = r2357891 + r2357894;
        return r2357895;
}

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

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

Reproduce

herbie shell --seed 2019138 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))