## Problem
Maximizing/minimizing under a **strict** inequality has a delta-rational
optimum. For
```smt2
(declare-const r Real)
(assert (< r 1))
(maximize r)
(check-sat)
(get-objectives)
```
the optimum is the supremum `1 - epsilon`, but z3 reported `r = 0`.
The same defect makes shared-symbol objectives report a value matching
**neither the model nor the true optimum** (issue #10028 follow-up).
Minimal reproducer — a 6-mark Golomb ruler (a `>32`-arg `distinct`, so
the objective is coupled to EUF) with a strict real objective `obj >
x5`, whose true optimum is `17 + epsilon`:
| case | before | after |
|---|---|---|
| `maximize r`, `r < 1` | `0` ❌ | `1 - epsilon` ✅ |
| `minimize r`, `r > 1` | `0` ❌ | `1 + epsilon` ✅ |
| Golomb `minimize obj`, `obj > x5` | `35/2` / `7+eps` ❌ | `17 +
epsilon` ✅ |
## Root cause
`check_bound` validates the LP hint by asserting `objective >= optimum`.
For a supremum `1 - epsilon` this is a **lower** bound whose value
carries a **negative** infinitesimal `(1, -1)`.
No `lconstraint_kind` can express that. The kind->infinitesimal map only
yields the *matching-sign* cases — `GT` -> lower `(r, +1)`, `LT` ->
upper `(r, -1)` — or zero (`GE`/`LE`). The opposite-sign lower bound
`(r, -1)` (i.e. `r >= r0 - delta`) is a *relaxation* that no strict
inequality produces. `opt_solver::mk_ge` therefore projected the
`-epsilon` away, turning `r >= 1 - epsilon` into the over-strong,
unsatisfiable `r >= 1`; validation failed and the strictly smaller
current model value was reported instead.
## Fix — carry the infinitesimal faithfully through the bound pipeline
- **`lp_api::bound`** gains an `eps` component so `get_value` returns
the true delta value (no spurious rational fixed-variable equality is
propagated to EUF).
- **`lar_base_constraint`** stores its right-hand side as a
delta-rational `impq` pair; `rhs()` returns the rational component,
`bound_eps()` the infinitesimal one.
- **`lar_solver`** bound activation/update threads the whole `impq`
bound, so a lower bound `(r, -1)` can be asserted. `constraint_holds`
accounts for it using the **same** strict-bounds delta that flattens the
model, computed **once per model**.
- **`theory_lra::mk_ge`** builds a *fresh* predicate for the `(r, -1)`
lower bound (to avoid colliding with an already-internalized `v >= r`
literal) and attaches `eps = -1`. **`opt_solver::mk_ge`** passes the
unprojected value to `theory_lra` / `theory_mi_arith` /
`theory_inf_arith` (whose bounds are already `inf_rational`).
The pair machinery is what makes the supremum both representable
(optimum `1 - epsilon`) and validatable; the reported witness model
remains the flattened rational (`find_delta_for_strict_bounds`),
consistent with the existing epsilon semantics.
## Validation
- Strict optima correct: `1-eps`, `1+eps`, bounded `2<r<5 -> 5-eps`, and
lex/box variants.
- Integer optima and the #10028 shared-symbol cases unchanged (Golomb
n=6/7/8 -> 17/25/34, consistent with the model).
- Unit tests **92/92** (release); no new debug-suite failures.
- Opt regression corpus (73 files, `model_validate=true`)
**byte-identical** to baseline.
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
---------
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Co-authored-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This removes the temporary `lp.batch_explain_fixed_in_row` knob added
with the recent LP changes. The batched fixed-column explanation path is
kept as the only implementation, matching the follow-up review comments.
- **Problem**
- The new LP setting exposed a temporary fallback path that is no longer
needed.
- Keeping both paths added parameter surface area and settings plumbing
without a lasting behavioral distinction.
- **Changes**
- **Remove parameter definition**
- Delete `lp.batch_explain_fixed_in_row` from LP parameter generation.
- **Remove settings plumbing**
- Drop the stored field, accessor methods, and parameter update wiring
from `lp_settings`.
- **Keep batched explanation as default behavior**
- Remove the runtime branch in `lar_solver::explain_fixed_in_row`.
- Always linearize fixed-column witnesses together in a single
dependency pass.
- **Resulting simplification**
- The solver no longer carries a dead configuration toggle for fixed-row
explanation.
- The batched dependency-linearization path remains intact and is now
the sole code path.
```c++
void lar_solver::explain_fixed_in_row(unsigned row, explanation& ex) {
auto& witnesses = m_imp->m_tmp_witnesses;
witnesses.reset();
for (auto const& c : get_row(row)) {
if (!column_is_fixed(c.var()))
continue;
const column& ul = m_imp->m_columns[c.var()];
witnesses.push_back(ul.lower_bound_witness());
witnesses.push_back(ul.upper_bound_witness());
}
m_imp->m_tmp_dependencies.reset();
m_imp->m_dependencies.linearize(witnesses, m_imp->m_tmp_dependencies);
for (auto ci : m_imp->m_tmp_dependencies)
ex.push_back(ci);
}
```
Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: Nikolaj Bjorner <nbjorner@microsoft.com>
### Summary
`lp_bound_propagator::explain_fixed_in_row` explained every fixed column
of a row
independently, calling `lar_solver::explain_fixed_column` once per fixed
column
(`src/math/lp/lar_solver.cpp`). Each such call linearizes the lower- and
upper-bound witnesses of a single column — a BFS over the `u_dependency`
DAG using
the dependency manager's mark bits — and inserts every reached leaf
constraint into
the `explanation`.
Fixed columns of the same row routinely share large portions of their
bound-witness
sub-DAGs (common ancestor constraints). The per-column scheme therefore
re-traverses
those shared sub-DAGs and re-inserts their leaves once for *every*
column, with an
independent mark/unmark cycle per column.
### Change
Add `lar_solver::explain_fixed_in_row(row, ex)`, which collects the
lower/upper
witnesses of all fixed columns in the row and linearizes them together
in a single
`u_dependency_manager::linearize` pass.
`lp_bound_propagator::explain_fixed_in_row`
and `explain_fixed_in_row_and_get_base` now delegate to it; the
base-column lookup in
the latter is unchanged. `explain_fixed_column` is kept for its
single-column caller.
### Why it is correct
`explanation` is a set — `push_back` deduplicates. Dependency
reachability is
monotone, so the union of the per-column leaf sets equals the leaf set
of the union
of all roots: the batched pass yields exactly the same explanation. The
manager's
mark bits guarantee each shared sub-DAG node is visited once, and the
`linearize(ptr_vector, ...)` overload already skips null/duplicate
roots.
### Complexity
For a row with `N` fixed columns:
- before: `O(Σ_j |witness-DAG(j)|)` traversal + `O(Σ_j leaves(j))` set
insertions, with `N` mark/unmark cycles;
- after: `O(|⋃_j witness-DAG(j)|)` traversal + `O(#distinct leaves)` set
insertions, with a single mark/unmark cycle.
Shared sub-DAGs are walked and their leaves inserted once instead of
once per column.
### Measured effect
Profiled with callgrind on a representative conflict-heavy `QF_SLIA`
input
(`model_validate=true`, bounded run), baseline vs. patched:
- `lp::lar_solver::explain_fixed_column` on the hot path:
`24,337,671,616 → 0`
retired instructions (59.2% → 0% of the run), replaced by the single
batched
traversal;
- total retired instructions: `41,113,093,210 → 35,983,363,256` (×0.875,
≈ 12.5%
fewer) — the net work removed by de-duplicating shared sub-DAGs;
- wall-clock: `6.428 s → 6.079 s` (≈ 5.4% faster);
- differential correctness preserved (identical results across the
validation inputs).
<!-- gh-aw-workflow-id: coz3-deepperf-fix -->
<!-- gh-aw-workflow-call-id: Z3Prover/bench/coz3-deepperf-fix -->
---------
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Implemented the largest cube heuristic from Bromberger and Weidenbach's
paper on cubes. Also fixes an overflow bug in mzp.
Use vswhere to find the visual studio version on windows in the build's ymls.
---------
Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
Co-authored-by: Claude Fable 5 <noreply@anthropic.com>
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
* Fix broken term_comparer in m_normalized_terms_to_columns lookup
The `m_normalized_terms_to_columns` map in `lar_solver` uses a
`term_comparer` that delegates to `lar_term::operator==`, which
intentionally returns `false` (with comment "take care not to create
identical terms"). This makes `fetch_normalized_term_column` unable to
find any term, rendering the Horner module's `interval_from_term`
bounds-recovery path dead code.
History: `lar_term::operator==` returning `false` has been present since
the original "merge LRA" commit (911b24784, 2018). The
`m_normalized_terms_to_columns` lookup was added later (dfe0e856,
c95f66e0, Aug 2019) as "toward fetching existing terms intervals from
lar_solver". The initial code had `lp_assert(find == end)` on
registration (always true with broken ==) and `lp_assert(find != end)`
on deregister (always false). The very next commit (207c1c50, one day
later) removed both asserts, replacing them with soft checks. The
`term_comparer` struct delegating to `operator==` was introduced during
a later PIMPL refactor (b375faa77).
Fix: Replace the `term_comparer` implementation with a structural
comparison that checks size and then verifies each coefficient-variable
pair via `coeffs().find_core()`. This is localized to the
`m_normalized_terms_to_columns` map and does not change
`lar_term::operator==`, preserving its intentional semantics elsewhere.
Validated: on a QF_UFNIA benchmark, `interval_from_term` lookups go
from 0/573 successful to 34/573 successful. Unit test added for the
`fetch_normalized_term_column` round-trip.
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
* Disable operator== for lar_term
The operator== for lar_term was never intended to be used.
This changes physically disables it to identify what happens to depend
on the operator.
* Work around missing lar_term==
Previous commit disabled lar_term==. This is the only use of the
operator that seems meaningful. Changed it to compare by references
instead.
Compiles, but not sure this is the best solution.
* replace with e
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
* Delete unused ineq::operator==
The operator is unused, so there is no need to figure what is
the best fix for it.
* Remove lp tests that use ineq::operator==
---------
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Co-authored-by: Nikolaj Bjorner <nbjorner@microsoft.com>
- Relax restore_x() to handle backup/current size mismatches: when
backup is shorter (new columns added), call
move_non_basic_columns_to_bounds() to find a feasible solution.
- Fix 100x performance regression in nonlinear optimization: save LP
optimum before check_nla and return it as bound regardless of NLA
result, so opt_solver::check_bound() can validate via full re-solve
with accumulated NLA lemmas.
- Refactor theory_lra::maximize() into three helpers: max_with_lp(),
max_with_nl(), and max_result().
- Add mk_gt(theory_var, impq const&) overload for building blockers
from saved LP optimum values.
- Add BNH multi-objective optimization test (7/7 sat in <1s vs 1/7
in 30s before fix).
- Add restore_x test for backup size mismatch handling.
Fixes#8890
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
* Initial plan
* Add try_get_value for std::map and use it in var_register.h and dioph_eq.cpp
Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>
* Add try_get_value overload for unordered_map with custom hash and use in lar_solver.cpp
Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>
* Remove redundant try_get_value template overload
Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>
* Remove std::map include and try_get_value overload from lp_utils.h
Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>
---------
Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>
#7791 reports on using model values during lex optimization that break soft constraints.
This is an artifact of using optimization where optimal values can be arbitrarily close to a rational.
In a way it is by design, but we give the user now an option to control the starting point for epsilon when converting infinitesimals into rationals.
* Introduce X-macro-based trace tag definition
- Created trace_tags.def to centralize TRACE tag definitions
- Each tag includes a symbolic name and description
- Set up enum class TraceTag for type-safe usage in TRACE macros
* Add script to generate Markdown documentation from trace_tags.def
- Python script parses trace_tags.def and outputs trace_tags.md
* Refactor TRACE_NEW to prepend TraceTag and pass enum to is_trace_enabled
* trace: improve trace tag handling system with hierarchical tagging
- Introduce hierarchical tag-class structure: enabling a tag class activates all child tags
- Unify TRACE, STRACE, SCTRACE, and CTRACE under enum TraceTag
- Implement initial version of trace_tag.def using X(tag, tag_class, description)
(class names and descriptions to be refined in a future update)
* trace: replace all string-based TRACE tags with enum TraceTag
- Migrated all TRACE, STRACE, SCTRACE, and CTRACE macros to use enum TraceTag values instead of raw string literals
* trace : add cstring header
* trace : Add Markdown documentation generation from trace_tags.def via mk_api_doc.py
* trace : rename macro parameter 'class' to 'tag_class' and remove Unicode comment in trace_tags.h.
* trace : Add TODO comment for future implementation of tag_class activation
* trace : Disable code related to tag_class until implementation is ready (#7663).
