followed by the usage of a grid of \(N\times N\) equidistant points on \(u\) and \(w\). A two‑dimensional spline (either bicubic or univariate) is then used to interpolate between points on the considered interval. The implementation of Piantadosi’s encoding procedure is then identical to the previous case, with the only difference that the series of points are now constructed as \(x \in \left[(0,0),\text{...},(0,N),(1,0),\text{...},(1,N)\right]\). The implementation of the encoding procedure for all meta-GGA exchange functionals in the LibXC library is presented in a Jupyter notebook in XXX. Once again, the accuracy of the procedure depends only on two variables, the number of points used to interpolate the enhancement factor, \(N^{2}\), and the accuracy of the encoder parameter, \(\beta\). The major hurdle in the procedure is that the number of digits required to represent the parameter is now much higher than for the previous case. Interpolations with \(N>20\) become computationally expensive since they require > 400 points, and result in parameters with more than 1500 digits, regardless of the value of \(\beta\). For well-behaved functionals, however, \(N=20\) and \(\beta=8\) result in parameters with ~1000 digits, and overall errors < 1 %, similarly to the GGA case.