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We propose a generalization of separability in the context of global optimization. Our results apply to objective functions implemented as differentiable computer programs. They are presented in the context of a simple branch and bound method. The often significant search space reduction can be expected to yield an acceleration of any global optimization method. We show how to utilize interval derivatives calculated by adjoint algorithmic differentiation to examine the monotonicity of the objective with respect to so called structural separators and how to verify the latter automatically.