We present an enumerative program synthesis framework called component-based refactoring that can refactor “direct” style code that does not use library components into equivalent “combinator” style code that does use library components. This framework introduces a sound but incomplete technique to check the equivalence of direct code and combinator code called equivalence by canonicalization that does not rely on input-output examples or logical specifications. Moreover, our approach can repurpose existing compiler optimizations, leveraging decades of research from the programming languages community. We instantiated our new synthesis framework in two contexts: (i) higher-order functional combinators such as map and filter in the statically-typed functional programming language Elm and (ii) high-performance numerical computing combinators provided by the NumPy library for Python. We implemented both instantiations in a tool called Cobbler and evaluated it on thousands of real programs to test the performance of the component-based refactoring framework in terms of execution time and output quality. Our work offers evidence that synthesis-backed refactoring can apply across a range of domains without specification beyond the input program.