Fix Caldara model failing to solve with precompile=true: expand trivial algebraic simplification

[Copilot]

With @model ... precompile=true, SymPy's simplify() is skipped, leaving ratio expressions like c[1]/c[0] and (1-l[1])/(1-l[0]) unsimplified at steady state. These become spurious auxiliary variables (➕₄, ➕₅) with initial guess 1e12, causing ➕₅^ν = (1e12)^(1e12) → overflow → solver failure.

Changes

• src/macros.jl — Replace the bare passthrough with trivial_simplify(): converts the expression to SS form (strips time subscripts so l[1], l[0] → l), then applies a full set of algebraic rewrites using postwalk (from MacroTools) in bottom-up order, so reductions chain:

  Rule	Example
  A/A → 1	c[1]/c[0] → 1, (1-l[1])/(1-l[0]) → 1
  A - A → 0	log(σ[0]) - log(σ[-1]) → 0
  A^0 → 1, A^1 → A, 1^A → 1	1^(1-ν) → 1
  A*1 → A, 1*A → A, A*0 → 0	eliminates trivial products
  A+0 → A, 0+A → A, A-0 → A	eliminates trivial additions
  A/1 → A, 0/A → 0	eliminates trivial divisions

  Chaining is automatic: (c[1]/c[0]) * (k[0]/k[0]) reduces each ratio to 1, then 1*1 → 1. Applied in all precompile branches: nonneg-expression bases under ^, log, norminvcdf, and full SS equations.

function trivial_simplify(ex)
    ss_ex = convert_to_ss_equation(ex)   # strip time subscripts: l[1], l[0] → l
    result = postwalk(ss_ex) do x
        # ... algebraic rewrite rules applied bottom-up ...
    end
    return result
end

• src/nsss_solver.jl — In make_equation_robust_to_domain_errors, widen x.args[2] isa Float64 ? x : to x.args[2] isa Number ? x :. After trivial simplification, expressions like 1^(1-ν) reach this function with an Int base; accessing .head on Int64 was throwing a FieldError. Also applies trivial_simplify in all five precompile branches.

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[codecov-commenter]

Codecov Report

❌ Patch coverage is 83.28343% with 335 lines in your changes missing coverage. Please review.
✅ Project coverage is 83.84%. Comparing base (180b1e1) to head (fc707f2).
⚠️ Report is 30 commits behind head on main.

Files with missing lines	Patch %	Lines
src/moments.jl	58.29%	88 Missing ⚠️
src/custom_autodiff_rules/forwarddiff.jl	70.11%	75 Missing ⚠️
src/algorithms/lyapunov.jl	64.67%	59 Missing ⚠️
src/algorithms/fast_lapack_wrappers.jl	58.57%	29 Missing ⚠️
src/algorithms/sylvester.jl	86.40%	28 Missing ⚠️
src/options_and_caches.jl	90.96%	27 Missing ⚠️
src/nsss_solver.jl	89.04%	8 Missing ⚠️
src/macros.jl	89.36%	5 Missing ⚠️
src/algorithms/quadratic_matrix_equation.jl	95.50%	4 Missing ⚠️
src/filter/inversion.jl	97.75%	4 Missing ⚠️
... and 4 more

Additional details and impacted files

@@             Coverage Diff             @@
##             main     #279       +/-   ##
===========================================
+ Coverage   65.87%   83.84%   +17.97%     
===========================================
  Files          23       25        +2     
  Lines       14063    20357     +6294     
===========================================
+ Hits         9264    17069     +7805     
+ Misses       4799     3288     -1511     

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