Average Error: 0.0 → 0.0
Time: 3.6s
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 r46572 = x_re;
        double r46573 = y_re;
        double r46574 = r46572 * r46573;
        double r46575 = x_im;
        double r46576 = y_im;
        double r46577 = r46575 * r46576;
        double r46578 = r46574 - r46577;
        return r46578;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r46579 = x_re;
        double r46580 = y_re;
        double r46581 = r46579 * r46580;
        double r46582 = x_im;
        double r46583 = y_im;
        double r46584 = r46582 * r46583;
        double r46585 = r46581 - r46584;
        return r46585;
}

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 2019356 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))