Also you said that your interval arithmetics will not support
expressions like integrals and so on. You said that it is because the
behavior between the end points is important for the calculations. But
I think that it is extremely important to support all expressions in
sympy, thus my question:

Is it possible just to have a simpler and inexact interval arithmetics
for all the expressions that are not explicitly supported by your
code?

A simple linear or quadratic interpolation should do the trick in most cases.

Otherwise your code will be useful only for a very constrained subset
of sympy functions (no special functions (gamma or bessel), integrals,
nsolve expressions and so on).

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