  In order to compare and benchmark the mathematical software, the performance
profiles have been introduced [1]. However, it has been proved that the
algorithm is not flawless. The main issue with the performance profile is that
it may rank the solvers with respect to the best solver, by excluding the best
one and running the algorithm on the remaining set of the solvers, the method
may rank the solvers in a different way. We characterize such systems of
problems-solvers and propose an efficient and reliable algorithm to overcome
this negative side effect. The proposed method is unbiased in comparing the
solvers and is successful in detecting the top ones
