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Introduce new monomials in Horner when shared factors have bounded linear combinations
When solve-eqs eliminates a variable x (= a - b) that appears as a factor in a nonlinear product x*y, the product splits into a*y - b*y. The NLA solver then reasons about a*y and b*y independently, losing the tight bounds that x had. This can cause severe performance degradation (e.g., timeout on a QF_UFNIA verification condition that solves in 3s without solve-eqs). The Horner module's cross-nested factoring already recovers the factored form y*(a-b), and interval_from_term (fixed in the previous commit) finds the LP column for (a-b) with its tight bounds. However, only Horner's zero-exclusion check used this — the rest of the NLA solver (order lemmas, tangent planes, bounds propagation) continued reasoning about the split monomials independently. This commit adds a new mechanism: when Horner discovers that a linear sub-expression maps to a bounded LP column, it introduces a new monomial pairing that column with the shared factor. For example, if y*(a-b) is discovered and (a-b) maps to LP column j with bounds [L,U], we create a new monomial m := y*j via add_mul_def and assert the equality m = a*y - b*y via literals. This allows all NLA modules to generate lemmas using j's tight bounds. The feature is gated by smt.arith.nl.horner_max_new_monomials (default 2, 0 to disable). On the motivating benchmark, this changes simplify+propagate-values+solve-eqs+smt from timeout (30s) to UNSAT in ~15s with no regressions on other configurations. Files changed: - horner.cpp: introduce_monomials_from_term_columns() and find_binary_monic() - horner.h: m_introduced_monomials dedup set - nla_intervals.cpp/h: m_term_columns to record interval_from_term discoveries - smt_params_helper.pyg: arith.nl.horner_max_new_monomials parameter Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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5 changed files with 124 additions and 2 deletions
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@ -292,6 +292,7 @@ bool intervals::interval_from_term(const nex& e, scoped_dep_interval& i) {
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if (j + 1 == 0)
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return false;
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m_term_columns.push_back(j);
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set_var_interval<wd>(j, i);
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interval bi;
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m_dep_intervals.mul<wd>(a, i, bi);
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