LLVM contains thousands of bitwidth-dependent rewrites that are hard to maintain and reason about. We introduce new parametric bitvector algorithms that automatically generalize these rewrites across all widths. By applying a mixed unary–binary encoding and finite-state reasoning, our solver lifts concrete LLVM test cases into true width-independent identities, recovering  parametric rewrites from LLVM's test suite that has fixed width rewrites. This moves LLVM toward a declarative InstCombine specification, where rewrite rules are uniform, provably correct, and mechanically derived.