Average Error: 0.0 → 0.0
Time: 1.6s
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 r57853 = x_re;
        double r57854 = y_re;
        double r57855 = r57853 * r57854;
        double r57856 = x_im;
        double r57857 = y_im;
        double r57858 = r57856 * r57857;
        double r57859 = r57855 - r57858;
        return r57859;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r57860 = x_re;
        double r57861 = y_re;
        double r57862 = r57860 * r57861;
        double r57863 = x_im;
        double r57864 = y_im;
        double r57865 = r57863 * r57864;
        double r57866 = r57862 - r57865;
        return r57866;
}

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 2020045 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))