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Find a common partial application of a pair of functions

Suppose we have two functions f(a,b,c) and g(a,b,d) that we can express as expressions in Sympy.
How can we find the functions h(a,b), f'(x,c), g'(x,d) such that f'(h(a,b),c) = f(a,b,c) and g'(h(a,b),d)=g(a,b,d) via SymPy?