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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>
55 lines
1.4 KiB
C++
55 lines
1.4 KiB
C++
/*++
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Copyright (c) 2017 Microsoft Corporation
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Module Name:
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<name>
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Abstract:
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<abstract>
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Author:
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Nikolaj Bjorner (nbjorner)
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Lev Nachmanson (levnach)
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Revision History:
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--*/
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#pragma once
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#include "math/lp/nla_common.h"
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#include "math/lp/nla_intervals.h"
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#include "math/lp/nex.h"
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#include "math/lp/cross_nested.h"
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#include "util/uint_set.h"
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namespace nla {
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class core;
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class horner : common {
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nex_creator::sum_factory m_row_sum;
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unsigned m_row_index;
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svector<std::pair<lpvar, lpvar>> m_introduced_monomials; // track what we've already created
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public:
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typedef intervals::interval interv;
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horner(core *core);
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bool horner_lemmas();
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template <typename T> // T has an iterator of (coeff(), var())
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bool lemmas_on_row(const T&);
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template <typename T> bool row_is_interesting(const T&) const;
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intervals::interval interval_of_sum_with_deps(const nex_sum*);
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intervals::interval interval_of_sum_no_term_with_deps(const nex_sum*);
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void set_var_interval_with_deps(lpvar j, intervals::interval&) const;
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bool lemmas_on_expr(cross_nested&, nex_sum*);
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template <typename T> // T has an iterator of (coeff(), var())
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bool row_has_monomial_to_refine(const T&) const;
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bool interval_from_term_with_deps(const nex* e, intervals::interval&) const;
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void introduce_monomials_from_term_columns();
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}; // end of horner
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}
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