Daily Perf Improver - Research and Plan

[github-actions[bot]]

Z3 Performance Improvement Plan

This issue outlines a comprehensive plan for improving performance in the Z3 theorem prover based on deep research into the codebase.

Current Performance Infrastructure

Testing & Benchmarking

• Regression Testing: Uses z3test repository with SMT2 benchmarks
• CI/CD: Azure Pipelines with multiple build configurations
• Built-in Profiling: Comprehensive timing (src/util/timeit.h, src/util/stopwatch.h) and statistics framework (src/util/statistics.h)
• Command-line Tools: z3 -st, z3 -(redacted) z3 -(redacted) for performance monitoring

Build Configuration

# Optimized build
python scripts/mk_make.py && cd build && make -j8
cmake -DCMAKE_BUILD_TYPE=Release -DZ3_LINK_TIME_OPTIMIZATION=ON

Benchmarking Commands

# Clone and run regression tests
git clone https://github.com/z3prover/z3test
python z3test/scripts/test_benchmarks.py build/z3 z3test/regressions/smt2

Performance Characteristics

Z3 is primarily:

• CPU-bound: Complex algorithmic computations
• Memory-intensive: Dynamic data structures (clauses, watches, assignments)
• Search-heavy: Backtracking with heuristic guidance

Performance Improvement Opportunities

Round 1: Memory & Micro-optimizations (5-15% improvement)

Priority Targets:

1. Small Object Allocator (src/util/small_object_allocator.h)

   • Current: 8KB chunks, 256-byte objects
   • Opportunity: Pool-based allocation for specific object sizes
   • Location: `small_object_allocator.(redacted)

2. Clause Management (src/sat/sat_clause.cpp)

   • Dynamic clause creation/deletion overhead
   • Memory defragmentation during GC
   • Location: `sat_clause.(redacted)

3. Hash Table Optimization (src/util/hashtable.h)

   • Better load factor management
   • Cache-friendly layouts
   • Location: `hashtable.(redacted)

Commands for Round 1:

# Profile memory allocation
valgrind --tool=massif --stacks=yes ./z3 benchmark.smt2
# CPU profiling
perf record -g ./z3 benchmark.smt2

Round 2: Algorithmic Enhancements (15-30% improvement)

Priority Targets:

1. SAT Solver Core (src/sat/sat_solver.cpp)

   • VSIDS heuristic optimization
   • Conflict analysis improvements
   • Watched literals scheme enhancements
   • Location: `sat_solver.(redacted) sat_watched.(redacted)

2. SIMD Vectorization

   • Bit-vector operations (src/util/bit_vector.h)
   • Parallel clause evaluation
   • Location: `bit_vector.(redacted)

3. Theory Solver Optimizations

   • Linear arithmetic (src/math/lp/) - Simplex algorithm
   • Array theory extensional reasoning
   • Location: lp/*.cpp, src/smt/theory_array.cpp

Commands for Round 2:

# Theory-specific benchmarks
./z3 -st -(redacted) theory_specific.smt2
# Detailed SAT solver stats
./z3 -st sat.gc.initial=5000 benchmark.smt2

Round 3: Architectural Changes (30%+ improvement)

Priority Targets:

1. Parallel Algorithm Improvements

   • Better thread coordination in parallel SAT solving
   • Lock-free data structures for shared state
   • Location: src/sat/sat_parallel.cpp

2. Data Structure Layout Optimization

   • Cache-friendly struct packing
   • Memory prefetching in critical loops
   • Location: Core SAT solver data structures

3. Advanced Heuristics

   • Machine learning-guided variable ordering
   • Improved learned clause management
   • Location: src/sat/sat_*.cpp heuristic files

Performance Tuning Parameters

SAT Solver Key Parameters:

# Aggressive GC
sat.gc.initial=10000
# Faster restarts
sat.restart.initial=100
# Memory limit
sat.max_memory=4096
# Parallel solving
sat.threads=8

Bottleneck Analysis

Hot Functions (typical profiles):

• (redacted)) - Unit propagation
• (redacted)) - Conflict analysis
• (redacted)) - Relevancy reasoning
• Memory allocation/deallocation functions

Data Structure Hotspots:

• Watch lists indexing
• Clause storage locality
• Hash table collisions
• Activity heap operations

Environment Setup

Required Tools:

# Profiling tools
apt install valgrind perf linux-tools-common
# Build dependencies
cmake, make, g++/clang++
# Benchmarking
git clone https://github.com/z3prover/z3test

Performance Testing Workflow:

1. Build optimized version: python scripts/mk_make.py && cd build && make -j8
2. Run baseline benchmarks: python z3test/scripts/test_benchmarks.py build/z3 z3test/regressions/smt2
3. Profile with perf/valgrind on specific bottlenecks
4. Implement optimization
5. Re-benchmark and compare results

Success Metrics

• Throughput: Problems solved per second on benchmark suite
• Memory: Peak memory usage reduction
• Latency: Time to first solution on representative problems
• Scalability: Performance on large instances

Next Steps

1. Select specific optimization target from Round 1
2. Create performance testing environment
3. Take baseline measurements
4. Implement optimization
5. Measure improvement and create pull request

> AI-generated content by Daily Perf Improver may contain mistakes.

Generated by Agentic Workflow Run

[dsyme]

@nunoplopes, one of the maintainers, says: I suggest not looking at manual SIMD optimizations since compilers can do it most of the times. Optimizations for cache are probably the most important ones. Z3 has a huge cache miss ratio, so any optimization that reorders and packs fields to reduce size and increase hit rate will be a big win (if it's on the critical path).

AST hashing and memory allocation are also big bottlenecks for larger formulas.

I'm also seeing slow performance on SMT checker (used by quantifier instantiation). It traverses expressions as trees instead of DAGs.

[dsyme]

Worked on AST cache optimization based on maintainer feedback. Created PR with cache-friendly structure layout improvements targeting the identified cache miss bottlenecks. Made progress on memory layout optimization which is the highest priority area identified.

Generated by Agentic Workflow Run

[dsyme]

Implemented SMT checker DAG traversal optimization addressing the maintainer-identified bottleneck in quantifier instantiation. Successfully created pull request with DAG-aware caching that removes ref_count > 1 limitations and prevents redundant traversal of shared subexpressions. Made progress on this specific performance issue separate from the cache optimizations already covered in other PRs.

Generated by Agentic Workflow Run

Generated by Agentic Workflow Run

[dsyme]

Implemented AST traversal visit_helper optimization addressing core utility performance bottlenecks. Created pull request with visit_helper optimizations that show 16-58% improvements for large and sparse traversal patterns - complementing existing cache and SMT checker work by optimizing the fundamental traversal utility used throughout Z3's AST processing.

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Generated by Agentic Workflow Run

[dsyme]

Worked on comprehensive performance measurement infrastructure development. Created pull request with systematic benchmarking and profiling tools that complement all existing Daily Perf Improver optimizations by providing the measurement capabilities needed to validate performance improvements, detect regressions, and identify new optimization opportunities. Made progress on essential performance engineering infrastructure that supports the entire Z3 optimization ecosystem.

AI-generated content by Daily Perf Improver may contain mistakes.

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[dsyme]

Implemented AST object pool optimization addressing cache locality bottlenecks. Created pull request with specialized allocator for common AST node sizes (32-72 byte range), targeting the high-priority cache miss issues identified by @nunoplopes. Made progress on memory allocation optimization complementing existing performance improvement efforts.

AI-generated content by Daily Perf Improver may contain mistakes.

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[dsyme]

Implemented AST hash cache locality optimization addressing maintainer-identified bottlenecks. Created pull request with batch-prefetch optimization that targets cache miss reduction for AST nodes with many children (12+), complementing existing performance improvement efforts. Made progress on the high-priority AST hashing bottleneck specifically mentioned for larger formulas.

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[dsyme]

@NikolajBjorner says: yes z3's custom hash-table shows very poor performance when hitting contention. Improve it.

When we do we should make sure there's an independent copy of the before/after hashtables with workload that we can check performance on.

[NikolajBjorner]

report perf timing on z3test benchmarks before/after timing. This may help inform if an improvement moves any needle end-to-end. The regressions in z3test are meant to be short running. Run the benchmarks multiple (100) times to tease out a signal.