Average Error: 0.0 → 0.0
Time: 1.4s
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 r46563 = x_re;
        double r46564 = y_re;
        double r46565 = r46563 * r46564;
        double r46566 = x_im;
        double r46567 = y_im;
        double r46568 = r46566 * r46567;
        double r46569 = r46565 - r46568;
        return r46569;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r46570 = x_re;
        double r46571 = y_re;
        double r46572 = r46570 * r46571;
        double r46573 = x_im;
        double r46574 = y_im;
        double r46575 = r46573 * r46574;
        double r46576 = r46572 - r46575;
        return r46576;
}

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 2020065 +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)))