Hardware accelerators (HAs) underpin high-performance and energy-efficient digital systems. Correctness of these systems thus depends on the correctness of constituent HAs. Self-consistency-based pre-silicon verification techniques, like A-QED (Accelerator Quick Error Detection), provide a quick and provably thorough HA verification framework that does not require extensive design-specific properties or a full functional specification. However, A-QED is limited to verifying HAs which are non-interfering – i.e., they produce the same result for a given input independent of its context within a sequence of inputs. We present a new technique called G-QED (Generalized QED) which goes beyond non-interfering HAs while retaining A-QED’s benefits. Our extensive results as well as a detailed industrial case study show that: G-QED is highly thorough in detecting critical bugs in well-verified designs that otherwise escape traditional verification flows while simultaneously improving verification productivity 18-fold (from 370 person days to 21 person days). These results are backed by theoretical guarantees of soundness and completeness.