It’s much more explicit than that in the docs.
https://diffeq.sciml.ai/stable/solvers/dae_solve/#Rosenbrock-Methods
Rodas5- A 5th order A-stable stiffly stable Rosenbrock method. Currently has a Hermite interpolant because its stiff-aware 3rd order interpolant is not yet implemented. This means the interpolation is inaccurate on algebraic variables, meaning this algorithm should not be used withsaveator post-solution interpolation on DAEs.
So if the non-smooth behavior was in the algebraic variables, then that would be the explanation. If it’s in the differential variables, and that explosion… I think you might be doing something wrong in your f function. See:
One guess, do you happen to modify u?