# MathCompile Development Roadmap
## Project Overview
MathCompile is a high-performance mathematical expression compiler that transforms symbolic expressions into optimized machine code. The project combines symbolic computation, automatic differentiation, and just-in-time compilation to achieve maximum performance for mathematical computations.
## Current Status: Phase 3 - Advanced Optimization (100% Complete)
### ✅ Completed Features
#### Phase 1: Core Infrastructure (100% Complete)
- ✅ **Expression AST**: Complete algebraic data type for mathematical expressions
- ✅ **Basic Operations**: Addition, subtraction, multiplication, division, power
- ✅ **Transcendental Functions**: sin, cos, ln, exp, sqrt with optimized implementations
- ✅ **Variable Management**: Support for named variables and indexed variables
- ✅ **Type Safety**: Generic type system with f64 specialization
#### Phase 2: Compilation Pipeline (100% Complete)
- ✅ **Cranelift Backend**: High-performance JIT compilation to native machine code
- ✅ **Rust Code Generation**: Alternative backend for debugging and cross-compilation
- ✅ **Memory Management**: Efficient variable allocation and stack management
- ✅ **Function Compilation**: Complete pipeline from AST to executable functions
- ✅ **Performance Optimization**: Register allocation and instruction optimization
#### Phase 3: Advanced Optimization (100% Complete)
- ✅ **Symbolic Optimization**: Comprehensive algebraic simplification engine
- ✅ **Automatic Differentiation**: Forward and reverse mode AD with optimization
- ✅ **Egglog Integration**: Equality saturation for advanced symbolic optimization
- ✅ **Egglog Extraction**: Hybrid extraction system combining egglog equality saturation with pattern-based optimization
- ✅ **Advanced Summation Engine**: Multi-dimensional summations with separability analysis
- ✅ **Convergence Analysis**: Infinite series convergence testing with ratio, root, and comparison tests
- ✅ **Pattern Recognition**: Arithmetic, geometric, power, and telescoping series detection
- ✅ **Closed-Form Evaluation**: Automatic conversion to closed-form expressions where possible
- ✅ **Variable System Refactoring**: ✨ **NEWLY COMPLETED** - Replaced global registry with per-function ExpressionBuilder approach for improved thread safety and isolation
### 🔄 Recently Completed (Phase 3 Final Features)
#### Developer Documentation & Architecture Clarity ✅
**Completed**: January 2025
- **✅ DEVELOPER_NOTES.md**: Comprehensive documentation explaining the different AST and expression types, their roles, and relationships
- **Architecture Overview**: Detailed explanation of the Final Tagless approach and how it solves the expression problem
- **Expression Type Hierarchy**: Complete documentation of all expression types from core traits to concrete implementations
- **Usage Patterns**: Examples showing when and how to use each expression type (`DirectEval`, `ASTEval`, `PrettyPrint`, etc.)
- **Design Benefits**: Clear explanation of performance, type safety, and extensibility advantages
- **Common Pitfalls**: Documentation of potential issues and how to avoid them
#### README Improvements & Tested Examples ✅
**Completed**: January 2025
- **✅ Tested README Examples**: Created `examples/readme.rs` with all README code examples to ensure they actually work
- **✅ Compile-and-Load API**: Implemented `RustCompiler::compile_and_load()` method with auto-generated file paths
- **✅ Working Code Snippets**: All README examples are now tested and functional, copied directly from working code
- **✅ Comprehensive Examples**: Covers symbolic optimization, automatic differentiation, and multiple compilation backends
- **✅ Error-Free Documentation**: No more non-existent functions or incorrect API usage in README
#### Variable System Architecture Overhaul ✅
**Completed**: January 2025
- **Removed Global Variable Registry** to eliminate thread safety issues and test isolation problems
- **Implemented ExpressionBuilder Pattern** with per-function variable registries for better encapsulation
- **Enhanced Thread Safety**: Each ExpressionBuilder maintains its own isolated variable registry
- **Improved Test Reliability**: Eliminated test interference from shared global state
- **Maintained Performance**: Index-based variable access with efficient HashMap lookups
- **Simplified API**: Clean separation between expression building and evaluation phases
- **Real-world Ready**: Designed for concurrent usage in production environments
- **Backend Integration**: ✨ **NEWLY COMPLETED** - Updated Rust and Cranelift backends to use variable registry system
**Technical Details**:
- `ExpressionBuilder` provides isolated variable management per function
- `VariableRegistry` struct with bidirectional name↔index mapping
- Removed all global state dependencies from core modules
- Updated summation engine, symbolic AD, and compilation backends
- **Backend Variable Mapping**: Both Rust codegen and Cranelift backends now use `VariableRegistry` for proper variable name-to-index mapping
- **Improved Code Generation**: Multi-variable functions generate correct parameter extraction from arrays
- **Test Coverage**: All backend tests updated and passing with new variable system
- Comprehensive test coverage with proper isolation
- Zero breaking changes to existing functionality
#### Previously Completed Features
1. **Egglog Extraction System** ✅
- Hybrid approach combining egglog equality saturation with pattern-based extraction
- Comprehensive rewrite rules for algebraic simplification
- Robust fallback mechanisms for complex expressions
- Integration with existing symbolic optimization pipeline
2. **Multi-Dimensional Summation Support** ✅
- `MultiDimRange` for nested summation ranges
- `MultiDimFunction` for multi-variable functions
- Separability analysis for factorizable multi-dimensional sums
- Closed-form evaluation for separable dimensions
- Comprehensive test coverage with 6 new test cases
3. **Convergence Analysis Framework** ✅
- `ConvergenceAnalyzer` with configurable test strategies
- Ratio test, root test, and comparison test implementations
- Support for infinite series convergence determination
- Integration with summation simplification pipeline
### 🎯 Next Steps (Phase 4: Specialized Applications)
#### ✅ Priority 0: Ergonomics & Usability Improvements ✨ **COMPLETED**
1. **✅ Unified Expression Builder API**
- ✅ Single, intuitive entry point for creating mathematical expressions (`MathBuilder`)
- ✅ Fluent builder pattern with method chaining
- ✅ Automatic variable management with smart defaults
- ✅ Type-safe expression construction with compile-time validation
- ✅ **Native operator overloading** for `ASTRepr<f64>` (+ - * / operators)
- ✅ **Reference-based operations** to avoid unnecessary cloning
2. **✅ Enhanced Error Messages & Debugging**
- ✅ Context-aware error messages with suggestions
- ✅ Expression validation with helpful diagnostics (`validate()` method)
- ✅ Debug utilities for inspecting expression structure
- ✅ Performance profiling helpers
3. **✅ Convenience Functions & Presets**
- ✅ Common mathematical function library (`poly()`, `quadratic()`, `linear()`)
- ✅ Built-in mathematical constants (π, e, τ, √2, ln(2), ln(10))
- ✅ High-level statistical functions (`gaussian()`, `logistic()`, `tanh()`)
- ✅ Machine learning presets (`relu()`, `mse_loss()`, `cross_entropy_loss()`)
- ✅ Preset mathematical expressions for common use cases
4. **✅ Documentation & Examples**
- ✅ Comprehensive API documentation with examples
- ✅ Updated examples showcasing ergonomic features
- ✅ Migration guide from verbose to ergonomic API
- ✅ **Cleaned up legacy verbose `ASTEval` usage** throughout codebase
- ✅ **Updated benchmarks** to use ergonomic API
- ✅ **Modernized all examples** with operator overloading
5. **✅ Integration & Compatibility**
- ✅ Seamless integration with existing optimization pipeline
- ✅ Automatic differentiation support with ergonomic API
- ✅ Backward compatibility with traditional final tagless approach
- ✅ **Performance optimization** - no wrapper overhead with direct `