Racer: Hunting GPU Kernel Bugs with Symbolic Equivalence Checking

Tuan Truong Vu, Cheng Tan

GPU kernels are critical to the performance of today's AI services, yet the same operators are rewritten repeatedly: for each GPU generation, numeric format, serving regime, and kernel language. Every rewrite must preserve the function computed by the implementation it replaces. Today, this obligation depends almost entirely on differential testing: run the new kernel and a trusted reference on randomly sampled tensors, then compare their outputs within a tolerance. This approach has blind spots that additional test cases cannot eliminate. For example, a logical bug may produce an error smaller than the tolerance required to accommodate a correct optimized kernel. We propose symbolic equivalence checking, which executes a kernel and its reference on symbolic inputs, turning each output cell into an exact algebraic expression, and then checks whether the paired expressions agree for all inputs. Because these expressions are exact, symbolic equivalence checking distinguishes floating-point error from logical bugs, while a single check covers the entire input space. We implement Racer, a PTX-level symbolic equivalence checking engine, with three techniques that make this approach…