which is uniquely defined by a single parameter \(\alpha \in \mathbb{R}\), and a constant \(\beta \in \mathbb{N}\) that controls the accuracy of the encoding procedure. It is important to notice that eq. \ref{eqn:5}  only reproduces the position of the points, while the spline interpolation is still required to obtain a continuous function over the considered interval (an exact fit would require \(N\to\infty\), and therefore an infinitely long encoding parameter). The drawback of this procedure is that eq. \ref{eqn: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 \(\beta\). In general, \(N=20\) interpolation points and \(\beta=8\) can be used to represent simple GGA exchange functionals—such as PBE \cite{perdew_generalized_1996}—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 \cite{peverati_generalized_2011}\(N=100\) interpolation points and a value of \(\beta=12\) are required for similar accuracies, resulting in parameters with ~ 350 digits. The single parameters for both the PBE and SOGGA11 functionals are reported in Fig. \ref{468093}, together with the corresponding plots of the enhancement factors, \(F_{\text{x}}\), as a function of \(u\) and \(s\). A Jupyter notebook with the details of the encoding procedure—as well as an algorithm to evaluate the errors for both the spline implementation and the encoding procedure—is also associated with the Figure and is available on github.