We propose a novel tool, AquaSense, to automatically reason about the sensitivity analysis of probabilistic programs. In the context of probabilistic programs, sensitivity analysis investigates how the perturbation in the parameters of prior distributions affects the program’s result, i.e., the program’s posterior distribution. AquaSense leverages quantized inference, an efficient and accurate approximate inference algorithm that represents distributions of random variables with quantized intervals. AquaSense is the first tool to support sensitivity analysis of probabilistic programs that is at the same time symbolic, differentiable, and practical. Our evaluation compares AquaSense with an existing system PSense (a system that relies on fully symbolic inference). AquaSense can compute the sensitivity of all 45 parameters from 12 programs, compared to 11/45 that PSense computes. AquaSense is particularly effective on programs with continuous distributions: it achieves an average speedup of 18.10 × over PSense (which, in contrast, can solve only a handful of problems). Our evaluation shows that AquaSense computes exact results on discrete programs. On 91% of evaluated continuous parameters, AquaSense computed the sensitivity results within 40 s with high accuracy (below 5% error). The paper also discusses AquaSense’s performance-accuracy trade-offs, which can enable different operational points for programs with different input data sizes.