Add a code generation pipeline that compiles Expr DAGs into flat Python
functions, eliminating recursive tree-walk dispatch in the Newton-Raphson
inner loop.
Key changes:
- Add to_code() method to all 11 Expr node types (expr.py)
- New codegen.py module with CSE (common subexpression elimination),
sparsity detection, and compile()/exec() compilation pipeline
- Add ParamTable.env_ref() to avoid dict copies per iteration (params.py)
- Newton and BFGS solvers accept pre-built jac_exprs and compiled_eval
to avoid redundant diff/simplify and enable compiled evaluation
- count_dof() and diagnostics accept pre-built jac_exprs
- solver.py builds symbolic Jacobian once, compiles once, passes to all
consumers (_monolithic_solve, count_dof, diagnostics)
- Automatic fallback: if codegen fails, tree-walk eval is used
Expected performance impact:
- ~10-20x faster Jacobian evaluation (no recursive dispatch)
- ~2-5x additional from CSE on quaternion-heavy systems
- ~3x fewer entries evaluated via sparsity detection
- Eliminates redundant diff().simplify() in DOF/diagnostics
