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Recent research has shown that dynamic zeros in shader programs of gaming applications can be effectively leveraged with a profile-guided, code-versioning transform. This transform duplicates code, specializes one path assuming certain key program operands, called versioning variables, are zero, and leaves the other path unspecialized. Dynamically, depending on the versioning variable's value, either the specialized fast path or the default slow path will execute. Prior work applied this transform manually and showed promising gains on gaming applications. In this paper, we present AZP, an automatic compiler approach to perform the above code-versioning transform. Our framework automatically determines which versioning variables or combinations of them are profitable, and determines the code region to duplicate and specialize (called the versioning scope). AZP takes operand zero value probabilities as input and it then uses classical techniques such as constant folding and dead-code elimination to determine the most profitable versioning variables and their versioning scopes. This information is then used to affect the final transform in a straightforward manner. We demonstrate that AZP is able to achieve an average speedup of 16.4% for targeted shader programs, amounting to an average frame-rate speedup of 3.5% across a collection of modern gaming applications on an NVIDIA GeForce RTX 2080 GPU GPU.