Average Error: 0.0 → 0.0
Time: 8.2s
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 r1416622 = x_re;
        double r1416623 = y_re;
        double r1416624 = r1416622 * r1416623;
        double r1416625 = x_im;
        double r1416626 = y_im;
        double r1416627 = r1416625 * r1416626;
        double r1416628 = r1416624 - r1416627;
        return r1416628;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1416629 = x_re;
        double r1416630 = y_re;
        double r1416631 = r1416629 * r1416630;
        double r1416632 = x_im;
        double r1416633 = y_im;
        double r1416634 = r1416632 * r1416633;
        double r1416635 = r1416631 - r1416634;
        return r1416635;
}

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 2019165 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))