LDP correlation problem

If we have the next case:

• $X^1$ has a uniform distribution on $[0,1]$
• Explanatory variables are perfectly correlated $X^1=X^2$

And we calculate the LDP for $X^1$ function:

$$g_{LD}^{1}(z) = E_{X^2|X^1=z}(z+X^2) = z + E_{X^2|X^1=z}(X^2) = 2z.$$

The value reported is twice larger than the correct one.