diff --git a/code/code_gen/code_gen.py b/code/code_gen/code_gen.py
index 0662779..351724c 100644
--- a/code/code_gen/code_gen.py
+++ b/code/code_gen/code_gen.py
@@ -7,6 +7,7 @@ from post import (
     CompilationContext,
     ParserStage,
     DerivativeExpansionStage,
+    SympySimplificationStage,
     DependencyResolutionStage,
     SympyOptimizationStage,
     FortranProgramWriter,
@@ -74,11 +75,11 @@ class VersionInfo(object):
 
 
 def compile_terms(terms_raw):
-    """Parses DSL terms spec and runs it through the four compiler stages.
+    """Parses DSL terms spec and runs it through the five compiler stages.
 
     This function initializes a new `CompilationContext` and executes the compiler pipeline
-    sequentially: parsing, derivative/fluctuation expansion, data dependency resolution,
-    and SymPy optimization (including buffer pooling).
+    sequentially: parsing, derivative/fluctuation expansion, SymPy expression simplification,
+    data dependency resolution, and array buffer pooling.
 
     Args:
         terms_raw (str): The raw string contents of the DSL terms specification input file.
@@ -89,6 +90,7 @@ def compile_terms(terms_raw):
     ctx = CompilationContext()
     ParserStage().execute(terms_raw, ctx)
     DerivativeExpansionStage().execute(ctx)
+    SympySimplificationStage().execute(ctx)
     DependencyResolutionStage().execute(ctx)
     SympyOptimizationStage().execute(ctx)
     return ctx
diff --git a/code/code_gen/post.py b/code/code_gen/post.py
index 11db601..143ebbd 100644
--- a/code/code_gen/post.py
+++ b/code/code_gen/post.py
@@ -2497,21 +2497,19 @@ class DependencyResolutionStage(object):
         return order
 
 
-class SympyOptimizationStage(object):
-    """Compiler pipeline Stage 4: Optimizes mathematical equations and shares memory buffers.
+class SympySimplificationStage(object):
+    """Compiler pipeline Stage 3: Expands, simplifies equations and prunes dependencies.
 
     This stage:
-    1. Invokes the SympyOptimizer to apply algebraic simplification and CSE.
-    2. Updates variable dependencies to reflect optimized equations.
-    3. Runs liveness window analysis to map multiple non-overlapping temporary variables
-       to a limited set of shared XYZ buffers (array pooling) to prevent RAM exhaustion.
+    1. Invokes the SympyOptimizer to substitute and simplify equations.
+    2. Updates variable dependencies in CompilationContext to reflect optimized equations.
     """
 
     def execute(self, ctx):
-        """Executes Stage 4 mathematical optimization and array buffer sharing.
+        """Executes Stage 3 mathematical expression expansion and dependency pruning.
 
         Args:
-            ctx (CompilationContext): Active compilation context.
+            ctx (CompilationContext): Active compilation context to update.
         """
         # 1. SymPy 수식 최적화 엔진 초기화
         opt = SympyOptimizer.get_instance(ctx.derived)
@@ -2531,9 +2529,23 @@ class SympyOptimizationStage(object):
                 updated_dependency[name] = dep_set
         ctx.dependency = updated_dependency
 
+
+class SympyOptimizationStage(object):
+    """Compiler pipeline Stage 5: Performs liveness analysis and memory buffer sharing.
+
+    This stage runs liveness window analysis to map multiple non-overlapping temporary
+    variables to a limited set of shared XYZ buffers (array pooling) to prevent RAM exhaustion.
+    """
+
+    def execute(self, ctx):
+        """Executes Stage 5 array buffer sharing based on topologically sorted lists.
+
+        Args:
+            ctx (CompilationContext): Active compilation context.
+        """
         self.array_name = "xyzbuffer{}"
 
-        # 3. Pass 1 및 Pass 2 연산 순서 배열들에 대해 각각 버퍼 공유 매핑(Pooling) 수행
+        # 1. Pass 1 및 Pass 2 연산 순서 배열들에 대해 각각 버퍼 공유 매핑(Pooling) 수행
         narr1, alloc1 = (self.allocate_arr(ctx, ctx.pass1))
         narr2, alloc2 = (self.allocate_arr(ctx, ctx.pass2))