When computing transcendental functions (e.g., \(\sin \) , \(\exp \) , \(\tanh \) ), there is a risk for rounding errors even if the function is computed to a very high precision. This well-known phenomenon is called “The Table-Maker’s Dilemma”. In this paper we describe a probabilistic model for estimating the expected number of rounding errors for a given function implementation. We show that this model is robust, even when using crude assumptions about the function. Furthermore, one can use this model to optimize the function implementations, without the need for exhaustive testing, which are often very expensive or entirely impractical.