When simulating a practical present day analog circuit, device model evaluations alone can take several days of compute time. This is largely because of the complexity of the physical devices that these models represent. These models typically have only a few inputs, so approximating them with polynomials is feasible and attractive. In this thesis, we build a general purpose framework for translating any given compact model into a table-based approximation. We show that with diﬀerent interpolants, various improvements can be achieved over conventional analytically-derived ‘compact models’. Low order cubic splines provide multiple orders of magnitude in speed improvement. Chebyshev polynomials implemented using Barycentric-Lagrange Interpolation can yield near machine precision in terms of accuracy while still yielding a signiﬁcant speedup. Chebyshev polynomials can also be used to diagnose hard-to-ﬁnd modeling errors, like derivative discontinuities. We also discuss the construction of table-based models from sparse measurements of compact models using compressed sensing.