Constrained EML Grammars in Symbolic Regression: Structural Inflation and Throughput Loss

EML Framework v2 — Validity-Aware Symbolic Search Under Constrained Grammars This release accompanies the AICTA 2026 submission studying how constrained operator grammars reshape symbolic search behavior in evolutionary symbolic regression under strict real-domain validity constraints. The repository implements a constrained symbolic grammar built around the nonlinear primitive eml(x, y) = exp(x) − ln(y) within a strictly positive-domain symbolic setting. The project investigates how recursive macro-expansion, strict validity enforcement, and fixed-budget evolutionary search interact to alter effective search behavior under constrained grammars. Unlike the earlier representation-focused release, this version reframes the project as a controlled empirical characterization study of validity-aware symbolic search dynamics under operator-space restriction. Core findings from this release include: - recursive EML macro-expansion systematically increases symbolic tree depth and node count- constrained validity enforcement produces substantially sparser valid search regions- elevated rejection density reduces effective evolutionary throughput under fixed evaluation budgets- rejection-aware accounting reveals that invalid candidate generation directly consumes computational search budget- structural depth overflow emerges as the dominant operational bottleneck under constrained macro-expansion Key additions in v2: - rejection-aware evaluation accounting- grammar-pure mutation without repair- decomposition of rejection into domain, depth, and numeric sources- multi-trial statistical aggregation with mean ± standard deviation reporting- constrained evolutionary symbolic regression experiments across 18 domain-safe targets- updated AICTA 2026 manuscript, figures, tables, and reproducibility pipeline Repository contents include: - complete experiment and benchmark code- figure and table generation scripts- LaTeX manuscript sources- statistical aggregation pipeline- cleaned notebooks and demonstrations- reproducibility instructions and release metadata This release supersedes the earlier structural-analysis framing and reflects the finalized experimental and methodological direction of the project. Keywords:symbolic regression, constrained grammars, evolutionary computation, validity-aware search, grammar-guided search, search-space sparsity, expression trees, domain-safe symbolic computation