Anytime performance assessment of black-box optimization algorithms assumes that the performance of an algorithm at a specific time does not depend on the total budget of function evaluations at its disposal. It therefore should not be used for benchmarking budget-depending algorithms, i.e., algorithms whose performance depends on the total budget of function evaluations, such as some surrogate-assisted or hybrid algorithms. This paper presents an anytime bench-marking approach suited for budget-depending algorithms. The approach is illustrated on a budget-dependent variant of the Differential Evolution algorithm.