diff --git a/src/copapy/_basic_types.py b/src/copapy/_basic_types.py
index e3ef3e5..b32828c 100644
--- a/src/copapy/_basic_types.py
+++ b/src/copapy/_basic_types.py
@@ -49,12 +49,22 @@ class Node:
         name (str): The name of the operation this Node represents.
     """
     def __init__(self) -> None:
-        self.args: Sequence[Net] = []
+        self.args: tuple[Net, ...] = tuple()
         self.name: str = ''
+        self.node_hash = 0
 
     def __repr__(self) -> str:
         return f"Node:{self.name}({', '.join(str(a) for a in self.args) if self.args else (self.value if isinstance(self, CPConstant) else '')})"
 
+    def get_node_hash(self, commutative: bool = False) -> int:
+        if commutative:
+            return hash(self.name) ^ hash(frozenset(a.source.node_hash for a in self.args))
+        return hash(self.name) ^ hash(tuple(a.source.node_hash for a in self.args))
+
+
+    def __hash__(self) -> int:
+        return self.node_hash
+
 
 class Net:
     """A Net represents a variable in the computation graph - or more generally it
@@ -67,14 +77,13 @@ class Net:
     def __init__(self, dtype: str, source: Node):
         self.dtype = dtype
         self.source = source
-        self.grad: NumLike = 1
 
     def __repr__(self) -> str:
         names = get_var_name(self)
-        return f"{'name:' + names[0] if names else 'id:' + str(id(self))[-5:]}"
+        return f"{'name:' + names[0] if names else 'id:' + str(hash(self))[-5:]}"
 
     def __hash__(self) -> int:
-        return id(self)
+        return self.source.node_hash
 
 
 class variable(Generic[TNum], Net):
@@ -104,8 +113,6 @@ class variable(Generic[TNum], Net):
         else:
             self.source = CPConstant(source)
             self.dtype = 'int'
-        
-        self.grad = 1
 
     @overload
     def __add__(self: 'variable[TNum]', other: 'variable[TNum] | TNum') -> 'variable[TNum]': ...
@@ -118,7 +125,7 @@ class variable(Generic[TNum], Net):
     @overload
     def __add__(self, other: TVarNumb) -> 'variable[float] | variable[int]': ...
     def __add__(self, other: TVarNumb) -> Any:
-        if isinstance(other, int | float) and other == 0:
+        if not isinstance(other, variable) and other == 0:
             return self
         return add_op('add', [self, other], True)
 
@@ -129,9 +136,7 @@ class variable(Generic[TNum], Net):
     @overload
     def __radd__(self, other: float) -> 'variable[float]': ...
     def __radd__(self, other: NumLike) -> Any:
-        if isinstance(other, int | float) and other == 0:
-            return self
-        return add_op('add', [self, other], True)
+        return self + other
 
     @overload
     def __sub__(self: 'variable[TNum]', other: 'variable[TNum] | TNum') -> 'variable[TNum]': ...
@@ -144,6 +149,8 @@ class variable(Generic[TNum], Net):
     @overload
     def __sub__(self, other: TVarNumb) -> 'variable[float] | variable[int]': ...
     def __sub__(self, other: TVarNumb) -> Any:
+        if isinstance(other, int | float) and other == 0:
+            return self
         return add_op('sub', [self, other])
 
     @overload
@@ -168,6 +175,11 @@ class variable(Generic[TNum], Net):
     def __mul__(self, other: TVarNumb) -> Any:
         if self.dtype == 'float' and isinstance(other, int):
             other = float(other)  # Prevent runtime conversion of consts; TODO: add this for other operations
+        if not isinstance(other, variable):
+            if other == 1:
+                return self
+            elif other == 0:
+                return 0
         return add_op('mul', [self, other], True)
 
     @overload
@@ -177,7 +189,7 @@ class variable(Generic[TNum], Net):
     @overload
     def __rmul__(self, other: float) -> 'variable[float]': ...
     def __rmul__(self, other: NumLike) -> Any:
-        return add_op('mul', [self, other], True)
+        return self * other
 
     def __truediv__(self, other: NumLike) -> 'variable[float]':
         return add_op('div', [self, other])
@@ -319,7 +331,8 @@ class CPConstant(Node):
     def __init__(self, value: int | float):
         self.dtype, self.value = _get_data_and_dtype(value)
         self.name = 'const_' + self.dtype
-        self.args = []
+        self.args = tuple()
+        self.node_hash = id(self)
 
 
 class Write(Node):
@@ -331,14 +344,16 @@ class Write(Node):
             net = Net(node.dtype, node)
 
         self.name = 'write_' + transl_type(net.dtype)
-        self.args = [net]
+        self.args = (net,)
+        self.node_hash = hash(self.name) ^ hash(net.source.node_hash)
 
 
 class Op(Node):
-    def __init__(self, typed_op_name: str, args: Sequence[Net]):
+    def __init__(self, typed_op_name: str, args: Sequence[Net], commutative: bool = False):
         assert not args or any(isinstance(t, Net) for t in args), 'args parameter must be of type list[Net]'
         self.name: str = typed_op_name
-        self.args: Sequence[Net] = args
+        self.args: tuple[Net, ...] = tuple(args)
+        self.node_hash = self.get_node_hash(commutative)
 
 
 def net_from_value(value: Any) -> variable[Any]:
@@ -378,9 +393,9 @@ def add_op(op: str, args: list[variable[Any] | int | float], commutative: bool =
     result_type = generic_sdb.stencil_definitions[typed_op].split('_')[0]
 
     if result_type == 'float':
-        return variable[float](Op(typed_op, arg_nets), result_type)
+        return variable[float](Op(typed_op, arg_nets, commutative), result_type)
     else:
-        return variable[int](Op(typed_op, arg_nets), result_type)
+        return variable[int](Op(typed_op, arg_nets, commutative), result_type)
 
 
 def _get_data_and_dtype(value: Any) -> tuple[str, float | int]: