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In recent years, the MLIR framework has had explosive growth due to the need for extensible deep learning compilers for hardware accelerators. Such examples include Triton, CIRCT, and ONNX-MLIR. MLIR compilers introduce significant complexities in localizing bugs or inefficiencies because of their layered optimization and transformation process with compilation passes. While existing delta debugging techniques can be used to identify a minimum subset of IR code that reproduces a given bug symptom, their naive application to MLIR is time-consuming because real-world MLIR compilers usually involve a large number of compilation passes. Compiler developers must identify a minimized set of relevant compilation passes to reduce the footprint of MLIR compiler code to be inspected for a bug fix. We propose DuoReduce, a dual-dimensional reduction approach for MLIR bug localization. DuoReduce leverages three key ideas in tandem to design an efficient MLIR delta debugger. First, DuoReduce reduces compiler passes that are irrelevant to the bug by identifying ordering dependencies among the different compilation passes. Second, DuoReduce uses MLIR-semantics-aware transformations to expedite IR code reduction. Finally, DuoReduce leverages cross-dependence between the IR code dimension and the compilation pass dimension by accounting for which IR code segments are related to which compilation passes to reduce unused passes. Experiments with three large-scale MLIR compiler projects find that DuoReduce outperforms syntax-aware reducers such as Perses and Vulcan in terms of IR code reduction by 31.6% and 21.5% respectively. If one uses these reducers by enumerating all possible compilation passes (on average 18 passes), it could take up to 145 hours. By identifying ordering dependencies among compilation passes, DuoReduce reduces this time to 9.5 minutes. By identifying which compilation passes are unused for compiling reduced IR code, DuoReduce reduces the number of passes by 14.6%. This translates to not needing to examine 281 lines of MLIR compiler code on average to fix the bugs. DuoReduce has the potential to significantly reduce debugging effort in MLIR compilers, which serves as the foundation for the current landscape of machine learning and hardware accelerators.