The drawback of this procedure is that eq. (5) is extremely sensitive to the value of the parameter. Hence \(\alpha\) has to be represented using a huge number of significant digits. In fact, the entire point of this exercise is to encode the full complexity of the GGA exchange enhancement into the length of the single parameter. Such length (i.e. the number of significant digits required to write \(\alpha\)) depends on both the number of interpolation points that are used to represent the functional on the grid, and the accuracy parameter \(\beta\). A simple algorithm to evaluate the errors in both the spline implementation and the encoding procedure is implemented in the code reported in XXX. In general, \(N=20\) interpolation points and \(\beta=8\) can be used to represent simple GGA exchange functionals—such as PBE and B88—with relative errors in the description of the enhancement factor smaller than 1%, resulting in parameters that require ~ 60 digits. For functionals that have some oscillation over the entire interval of \(u\)—such as SOGGA11 and SOGGA11-X—\(N=100\) interpolation points and a value of \(\beta=12\) are required for similar accuracies, resulting in parameters with ~ 350 digits.