SplitFunction can not be handled with TaylorIntegration.jl (and probably others that rely on different types)

[nathanaelbosch]

The IIP implementation of SplitFunction in the IIP case evaluates f.f1 and f.f2 separately and then adds the results, but having f.f2 write into du but f.f1 write into some f.cache:

SciMLBase.jl/src/scimlfunctions.jl

Lines 2139 to 2143 in be26e21

	function (f::SplitFunction)(du, u, p, t)
	f.f1(f.cache, u, p, t)
	f.f2(du, u, p, t)
	du .+= f.cache
	end

f.cache is not guaranteed to have the same type as du. This then creates errors with packages such as TaylorIntegration.jl, since f.cache::AbstractVector{Float64}, but to work it needs to be the same as du::AbstractVector{TaylorSeries.Taylor1{Float64}}.

This also prevents solvers that rely on Jacobians to compute them with ForwardDiff (at least OrdinaryDiffEq.calc_J! does not work and returns the standard autodiff-not-possible error message).

Are there any improvements to the SplitODEFunction implementation that could be made to enable these cases?