Average Error: 0.0 → 0.0
Time: 6.2s
Precision: 64
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[x.re \cdot y.re - x.im \cdot y.im\]
x.re \cdot y.re - x.im \cdot y.im
↓
x.re \cdot y.re - x.im \cdot y.im
double f(double x_re, double x_im, double y_re, double y_im) {
        double r37980 = x_re;
        double r37981 = y_re;
        double r37982 = r37980 * r37981;
        double r37983 = x_im;
        double r37984 = y_im;
        double r37985 = r37983 * r37984;
        double r37986 = r37982 - r37985;
        return r37986;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r37987 = x_re;
        double r37988 = y_re;
        double r37989 = r37987 * r37988;
        double r37990 = x_im;
        double r37991 = y_im;
        double r37992 = r37990 * r37991;
        double r37993 = r37989 - r37992;
        return r37993;
}

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

    \[x.re \cdot y.re - x.im \cdot y.im\]

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))