In this paper, we introduce PANDORA—a framework that complements existing parallelizing compilers by automatically discovering application- and architecture-specialized approximations. We demonstrate that PANDORA creates approximations that extract massive amounts of parallelism from inherently sequential code by eliminating loop-carried dependencies—a long-time goal of the compiler research community. Compared to exact parallel baselines, preliminary results show speedups ranging from 2x to 80x, with acceptable error for many usage scenarios. We also highlight PANDORA’s discovery capabilities by removing loop-carried dependencies from a recurrence relation with no known closed-form solution.