Average Error: 0.0 → 0.0
Time: 2.4s
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 r98788 = x_re;
        double r98789 = y_re;
        double r98790 = r98788 * r98789;
        double r98791 = x_im;
        double r98792 = y_im;
        double r98793 = r98791 * r98792;
        double r98794 = r98790 - r98793;
        return r98794;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r98795 = x_re;
        double r98796 = y_re;
        double r98797 = r98795 * r98796;
        double r98798 = x_im;
        double r98799 = y_im;
        double r98800 = r98798 * r98799;
        double r98801 = r98797 - r98800;
        return r98801;
}

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 2020047 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))