Verilog simulators and synthesizers play a critical role in chip design and verification. However, due to the complexity of simulation and synthesis processes, they easily introduce various types of bugs. Among them, Behavioral Deviation Bugs (BDBs) are particularly severe, as they can cause incorrect results by introducing subtle semantic deviations that make the chip behave differently from its intended design, potentially enabling hardware backdoors.

In this work, we propose VeriEQ, an automated framework based on the idea of metamorphic testing, which detects BDBs by generating semantically equivalent Verilog programs. First, to increase the likelihood of triggering BDB, we analyze the structural patterns of historical BDB and design a Verilog code template. Second, we generate semantically equivalent variants by applying equivalence circuit transformation rules. These rules include constraints on bit-width and signedness to ensure logical consistency before and after the transformation. Finally, we design an inlined deviation checking mechanism that embeds multiple equivalent modules within a single testbench to improve testing efficiency. We implement and evaluate VeriEQ on four mainstream Verilog simulators and synthesizer. Experimental results show that VeriEQ achieves a 138.1% to 4161.9% speedup over state-of-the-art tools. In total, VeriEQ successfully detects 33 previously unknown bugs, including 29 BDBs, along with 4 hang bugs as additional findings. All discovered bugs have been confirmed, with 27 already fixed. In contrast, the other tools are able to detect only 1 to 7 bugs.