The expressiveness of Linear Programming (LP) has motivated research on an LP compiler that generates polynomial-size LPs for polynomial-time solvable problems, including those having exponential extension complexity. By automating modeling from high-level algorithmic descriptions, the compiler offers a promising alternative to algebraic modelling languages. However, the resulting LPs are extremely large, posing challenges for existing solvers. Recently, we have introduced two LP compiler optimizations, namely Hierarachical Synchronization Barriers (HSB) and Constraint Sharing (CS), that address this challenge by exploiting structural and similarity-based patterns derived from the source code and the design of compiler-generated LPs, beyond what conventional compiler and presolve techniques can achieve in isolation. In this paper, we provide a comprehensive evaluation of these optimization methods on fundamental combinatorial algorithms and introduce the Execution Domain Aware (EDA) optimization framework to address a limitation revealed by this analysis. The framework reinterprets structural synchronizations as a time abstraction layer within which other optimizations can target localized reductions while remaining agnostic to time-step transitions. Across a broad suite of benchmarks, HSB and CS consistently generate smaller LPs, achieving LP file-size reductions of up to 96% and 53%, respectively, while also improving numerical conditioning, solver performance, and solution quality. HSB provides the strongest and most robust overall gains. The EDA framework further broadens the range of benchmarks that can benefit from HSB when its underlying structural assumptions are less effective. We view this work as a step toward systematic generation of Compact Integer Programming formulations for problems with exponential-size Integer Programs having polynomial-time separation oracles.

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