Here’s my attempt at drawing what I understand to be the set in your docs:
Unfortunately currently the mechanism for creating separators from functions is broken
(Package is broken due to changes in ModelingToolkit · Issue #162 · JuliaIntervals/IntervalConstraintProgramming.jl · GitHub)
But actually I’m not sure this is the right tool for the job, since as far as I can see this is just a union of 1D curves (?). @Xing_Shi_Cai pointed me towards Cylindrical Algebraic Decomposition the other day. This can give you all the “pieces” of the solution.