We derived an approximate non-linear interference (NLI) closed-form model (CFM), capable of handling a very broad range of optical WDM system scenarios. We tested the CFM over 8500 randomized C-band WDM systems, of which 6250 were fully-loaded and 2250 were partially loaded. The systems had highly diversified channel formats, symbol rates, fibers, as well as other parameters. We improved the CFM accuracy by augmenting the formula with simple machine-learning factors, optimized by leveraging the system test-set. We further improvedthe CFM by adding a term which models special situations where NLI has high self-coherence. In the end, we obtained a very good match with the results found using the numerically-integrated Enhanced GN-model (or EGN-model). We also checked the CFM accuracy by comparing its predictions with full-C-Band split-step simulations of 300 randomized systems. The combined high accuracy and very fast computation time (milliseconds) of the CFM potentially make it an effective tool for real-time physical-layer-aware optical network management and control.