Test-time compute has emerged as a powerful paradigm in function-level code generation. However, previous proposed strategies have been viewed as disparate, thus lacking a fair apples-to-apples analysis enabling understanding of their operational mechanisms in execution-based benchmarks. Therefore, we present a mathematical framework that unifies generation and reranking with theoretical justifications through the lens of Minimum Bayes Risk (MBR) decoding. Our proposed framework leads to key research questions regarding the effectiveness of using parallel and/or iterative sampling, design choices of reranking signals and soft/hard MBR utility functions, and behaviors of the final selected program across different methods. Our empirical findings highlight the importance of the diversity of sampled candidates (over self-improvement), reranking with simple and high-quality signals, and the effectiveness of test-time compute to select programs that manifest general and edge test case robustness. We will open-source our analysis toolkit and implementation to enable reproducible research.We open-source our analysis toolkit and implementation to enable reproducible research.