While we can apply Eq. 5 after simulation to solve for the changes in free energy, we can also use the information about uncertainties to engage in design and find a set of transformations that are likely to decrease error. The added information we need about potential designs is the covariance matrix of the parameter errors, 𝐂, which describes the free energy changes' variances, 𝐶 𝑖𝑖 , and covariances, 𝐶 𝑖𝑗 where 𝑖 ≠ 𝑗. To find 𝐂, we use