A roadmap for autotuning task-based numerical libraries is presented. Carefully chosen experiments are carried out when the numerical library is being installed to assess its performance. Real and simulated executions are considered to optimize the routine. The discussion is illustrated with a task-based tile Cholesky factorization, and the aim is to find the optimum tile size for any problem size, using the Chameleon numerical linear algebra package on top of the StarPU runtime system and also with the SimGrid simulator. The study shows that combining a smart exploration strategy of the search space with both real and simulated executions results in a fast, reliable autotuning process.