Evaluating a quadratic form with an inverse of a sparse PD matrix, comparison between using the inverse vs using a Cholseky decomposition

Question

I have the following quadratic form I need to evaluate:

$x^T A^{-1} y$, where $A$ is a sparse positive definite matrix, $x, y$ are sparse vectors.

Now assume that I am given for free both $A^{-1}$ and the Cholesky decomposition $A = L D L^T$. I understand that it be faster to evaluate $x^T A^{-1} y$ using a Cholseky decomposition, rather than directly.

Can anyone relate to the computational complexity (+ references) of each alternative?

Thanks a lot!