Average Error: 0.0 → 0.0
Time: 6.6s
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 r2001775 = x_re;
        double r2001776 = y_im;
        double r2001777 = r2001775 * r2001776;
        double r2001778 = x_im;
        double r2001779 = y_re;
        double r2001780 = r2001778 * r2001779;
        double r2001781 = r2001777 + r2001780;
        return r2001781;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2001782 = x_im;
        double r2001783 = y_re;
        double r2001784 = r2001782 * r2001783;
        double r2001785 = x_re;
        double r2001786 = y_im;
        double r2001787 = r2001785 * r2001786;
        double r2001788 = r2001784 + r2001787;
        return r2001788;
}

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 2019171 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))