Added following optimizations:

theano/tensor/opt.py

@@ -1553,6 +1553,16 @@ def local_useless_elemwise(node):
 
     """
     if isinstance(node.op, T.Elemwise):
+        def zeros_like(node, in_idx):
+            #it is the same var in the graph. That will always be true
+            return [T.fill(node.inputs[in_idx],
+                           T.constant(0.0, dtype=node.outputs[0].type.dtype))]
+            
+        def ones_like(node, in_idx):
+            #it is the same var in the graph. That will always be true
+            return [T.fill(node.inputs[in_idx],
+                           T.constant(1.0, dtype=node.outputs[0].type.dtype))]
+
         if node.op.scalar_op == theano.scalar.eq and len(node.inputs) == 2:
             if node.inputs[0] == node.inputs[1]:
                 # it is the same var in the graph. That will always be true
@@ -1577,13 +1587,90 @@ def local_useless_elemwise(node):
         elif node.op.scalar_op == theano.scalar.mul and len(node.inputs) == 1:
             # No need to copy over any stack trace
             return [node.inputs[0]]
+            
         elif node.op.scalar_op == theano.scalar.add and len(node.inputs) == 1:
             # No need to copy over any stack trace
             return [node.inputs[0]]
-        elif (node.op.scalar_op == theano.scalar.identity and
-              len(node.inputs) == 1):
-            # No need to copy over any stack trace
+        if (
+                node.op.scalar_op == theano.scalar.identity and
+                len(node.inputs) == 1
+        ):
             return [node.inputs[0]]
+            
+        if (
+                isinstance(node.op.scalar_op, theano.scalar.basic.AND) and
+                len(node.inputs) == 2
+        ):
+            
+            if (
+                    isinstance(node.inputs[0], T.TensorConstant) and
+                    node.inputs[0].data == 1.0
+            ):
+                return [node.inputs[1]]
+                
+            if (
+                    isinstance(node.inputs[1], T.TensorConstant) and
+                    node.inputs[1].data == 1.0
+            ):
+                return [node.inputs[0]]
+                
+            if (
+                    isinstance(node.inputs[0], T.TensorConstant) and
+                    node.inputs[0].data == 0.0
+            ):
+                return zeros_like(node, 1)
+                
+            if (
+                    isinstance(node.inputs[1], T.TensorConstant) and
+                    node.inputs[1].data == 0.0
+            ):
+                return zeros_like(node, 0)
+                
+        if (
+                isinstance(node.op.scalar_op, theano.scalar.basic.OR) and
+                len(node.inputs) == 2
+        ):
+            
+            if (
+                    isinstance(node.inputs[0], T.TensorConstant) and
+                    node.inputs[0].data == 0.0
+            ):
+                return [node.inputs[1]]
+                
+            if (
+                    isinstance(node.inputs[1], T.TensorConstant) and
+                    node.inputs[1].data == 0.0
+            ):
+                return [node.inputs[0]]
+                
+            if (
+                    isinstance(node.inputs[0], T.TensorConstant) and
+                    node.inputs[0].data == 1.0
+            ):
+                return ones_like(node, 1)
+                
+            if (
+                    isinstance(node.inputs[1], T.TensorConstant) and
+                    node.inputs[1].data == 1.0
+            ):
+                return ones_like(node, 0)
+                
+        if (
+                isinstance(node.op.scalar_op, theano.scalar.basic.XOR) and
+                len(node.inputs) == 2
+        ):
+            if node.inputs[0] == node.inputs[1]:
+                return zeros_like(node, 0)
+                
+        if (
+                (
+                    isinstance(node.op.scalar_op, theano.scalar.basic.LE) or
+                    isinstance(node.op.scalar_op, theano.scalar.basic.GE)
+                ) and
+                len(node.inputs) == 2
+        ):
+            if node.inputs[0] == node.inputs[1]:
+                return ones_like(node, 0)
 
 
 @register_specialize