Add comprehensive docstrings for all public API functions

This commit adds missing docstrings and updates the API documentation:

Added docstrings for core functions:
- term: Create symbolic terms
- showraw: Display raw structure of expressions
- hasmetadata, getmetadata, setmetadata: Metadata manipulation
- sorted_arguments: Get canonically sorted arguments

Added docstrings for rule system:
- @acrule: Associative-commutative rule macro

Added docstrings for all rewriter types:
- Empty, IfElse, If, Chain, RestartedChain
- Fixpoint, Postwalk, Prewalk, PassThrough

Added docstrings for code generation utilities:
- AtIndex: Array indexing representation
- Multithreaded: Threading parallelism type
- cse: Common subexpression elimination

Updated docs/src/api.md:
- Reorganized into logical sections
- Added all documented exported symbols
- Improved categorization of API elements

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <[email protected]>

Author: ChrisRackauckas

docs/src/api.md

@@ -1,33 +1,118 @@
 # API Reference
 
 ## Symbols and Terms
+
+### Creating Symbols and Terms
 ```@docs
 SymbolicUtils.@syms
+SymbolicUtils.term
 SymbolicUtils.Sym
+```
+
+### Inspecting Terms
+```@docs
 SymbolicUtils.issym
 SymbolicUtils.symtype
+SymbolicUtils.iscall
+SymbolicUtils.operation
+SymbolicUtils.arguments
+SymbolicUtils.sorted_arguments
+SymbolicUtils.showraw
+```
+
+### Term Types
+```@docs
 SymbolicUtils.Term
 SymbolicUtils.Add
 SymbolicUtils.Mul
 SymbolicUtils.Pow
+```
+
+### Metadata
+```@docs
+SymbolicUtils.hasmetadata
+SymbolicUtils.getmetadata
+SymbolicUtils.setmetadata
+```
+
+### Type Promotion
+```@docs
 SymbolicUtils.promote_symtype
 ```
 
-## Rewriters
+## Rewriting System
 
+### Rule Creation
 ```@docs
 @rule
+@acrule
+```
+
+### Rewriters
+```@docs
 SymbolicUtils.Rewriters
+SymbolicUtils.Rewriters.Empty
+SymbolicUtils.Rewriters.IfElse
+SymbolicUtils.Rewriters.If
+SymbolicUtils.Rewriters.Chain
+SymbolicUtils.Rewriters.RestartedChain
+SymbolicUtils.Rewriters.Fixpoint
+SymbolicUtils.Rewriters.FixpointNoCycle
+SymbolicUtils.Rewriters.Postwalk
+SymbolicUtils.Rewriters.Prewalk
+SymbolicUtils.Rewriters.PassThrough
 ```
 
-## Simplify
+## Simplification and Transformation
 
 ```@docs
 SymbolicUtils.simplify
 SymbolicUtils.expand
 SymbolicUtils.substitute
 ```
 
+## Polynomial Forms
+
+```@docs
+SymbolicUtils.PolyForm
+SymbolicUtils.simplify_fractions
+SymbolicUtils.quick_cancel
+SymbolicUtils.flatten_fractions
+```
+
+## Code Generation
+
+### Core Functions
+```@docs
+SymbolicUtils.toexpr
+SymbolicUtils.cse
+```
+
+### Code Generation Types
+```@docs
+SymbolicUtils.Assignment
+SymbolicUtils.Let
+SymbolicUtils.Func
+SymbolicUtils.DestructuredArgs
+SymbolicUtils.LiteralExpr
+SymbolicUtils.ForLoop
+```
+
+### Array Operations
+```@docs
+SymbolicUtils.SetArray
+SymbolicUtils.MakeArray
+SymbolicUtils.MakeSparseArray
+SymbolicUtils.MakeTuple
+SymbolicUtils.AtIndex
+```
+
+### Parallelism
+```@docs
+SymbolicUtils.SpawnFetch
+SymbolicUtils.Multithreaded
+```
+
 ## Utilities
 
 ```@docs

src/code.jl

@@ -446,6 +446,17 @@ SetArray
 
 SetArray(inbounds, arr, elems) = SetArray(inbounds, arr, elems, false)
 
+"""
+    AtIndex(i, elem)
+
+Represent an element at a specific index in an array.
+
+This is used internally for array indexing operations in code generation.
+
+# Fields
+- `i`: The index
+- `elem`: The element at that index
+"""
 @matchable struct AtIndex <: CodegenPrimitive
     i
     elem
@@ -666,6 +677,21 @@ function toexpr(a::MakeTuple, st)
     :(($(toexpr.(a.elems, (st,))...),))
 end
 
+"""
+    Multithreaded
+
+A parallelism type for `SpawnFetch` that uses Julia's threading system.
+
+When used with `SpawnFetch{Multithreaded}`, expressions are executed
+in parallel using `Threads.@spawn`.
+
+# Examples
+```julia
+julia> SpawnFetch{Multithreaded}([func1, func2], combine_func)
+```
+
+See also: [`SpawnFetch`](@ref)
+"""
 struct Multithreaded end
 """
     SpawnFetch{ParallelType}(funcs [, args], reduce)
@@ -837,6 +863,26 @@ end
 Perform Common Subexpression Elimination on the given expression `expr`. Return an
 equivalent `expr` with optimized computation.
 """
+"""
+    cse(expr)
+
+Perform common subexpression elimination on an expression.
+
+This optimization identifies repeated subexpressions and replaces them with
+variables to avoid redundant computation.
+
+# Arguments
+- `expr`: The expression to optimize
+
+# Returns
+An optimized expression with common subexpressions eliminated
+
+# Examples
+```julia
+julia> expr = :(sin(x) + sin(x) * cos(y))
+julia> cse(expr)  # sin(x) is computed only once
+```
+"""
 function cse(expr)
     state = CSEState()
     newexpr = cse!(expr, state)