Sum hints for the optimizer

[hecmas]

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[Copilot]

Pull Request Overview

This PR introduces "sum hints for the optimizer" which adds significant optimizations to the sum and product check mechanisms in PIL2 components. The main changes focus on improving the performance of rational expression handling through optimized intermediate value generation and introducing support for a new "one instance" mode.

Key changes include:

• Enhanced sum and product expression optimization with configurable reduction levels
• Introduction of STD_MODE_ONE_INSTANCE for special optimization scenarios
• Comprehensive refactoring of intermediate value handling to support variable degrees

Reviewed Changes

Copilot reviewed 33 out of 33 changed files in this pull request and generated 4 comments.

Show a summary per file

File	Description
pil2-components/test/std/special/intermediate_sums.pil	Completely refactored to use new sum optimization APIs with configurable degree arrays
pil2-components/test/std/special/intermediate_prods.pil	New file implementing product optimization tests with assume/prove scenarios
pil2-components/lib/std/pil/std_sum.pil	Major refactoring with new expression grouping, one-instance mode support, and optimizer hints
pil2-components/lib/std/pil/std_prod.pil	Comprehensive rewrite with sophisticated high/low degree term handling and intermediate optimization
pil2-components/lib/std/pil/std_constants.pil	Added STD_MODE constants and MAX_CONSTRAINT_DEGREE configuration
pil2-components/lib/std/rs/src/std_sum.rs	Updated to support one-instance mode with conditional result handling
pil2-components/lib/std/rs/src/std_prod.rs	Enhanced with intermediate multiplication hints and one-instance mode support