To design faster and more energy-efficient systems, numerous inexact arithmetic operators have been proposed, generally obtained by modifying the logic structure of conventional circuits. However, as the quality of service of an application has to be ensured, these operators need to be precisely characterized to be usable in commercial or real-life applications. The characterization of the error induced by inexact operators is commonly achieved with exhaustive or stochastic bit-accurate gate-level simulations. However, for high bit-widths, the time and memory required for such simulations become prohibitive. To overcome these limitations, a new characterization framework for inexact operators is proposed. The proposed framework characterizes the error induced by inexact operators in terms of mean error distance, error rate and maximum error distance, allowing to completely define the error probability mass function. By exploiting statistical properties of the approximation error, the number of simulations needed for precise characterization is minimized. From user-defined confidence requirements, the proposed method computes the minimal number of simulations to obtain the desired accuracy on the characterization for the error rate and mean error distance. The maximum error distance value is then extracted from the simulated samples using the extreme value theory. For 32-bit adders, the proposed method reduces the number of simulations needed up to a few tens of thousands points.