Sensitivity Analysis (SA) is a novel compiler technique that complements, and integrates with, static automatic parallelization analysis for the cases when relevant program behavior is input sensitive. In this paper we show how SA can extract all the input dependent, statically unavailable, conditions for which loops can be dynamically parallelized. SA generates a sequence of sufficient conditions which, when evaluated dynamically in order of their complexity, can each validate the dynamic parallel execution of the corresponding loop. For example, SA can first attempt to validate parallelization by checking simple conditions related to loop bounds. If such simple conditions cannot be met, then validating dynamic parallelization may require evaluating conditions related to the entire memory reference trace of a loop, thus decreasing the benefits of parallel execution. We have implemented Sensitivity Analysis in the Polaris compiler and evaluated its performance using 22 industry standard benchmark codes running on two multicore systems. In most cases we have obtained speedups superior to the Intel Ifort compiler because with SA we could complement static analysis with minimum cost dynamic analysis and extract most of the available coarse grained parallelism.