Avoid inserting useless nodes in the graph during optimization

theano/tensor/opt.py

@@ -3906,12 +3906,17 @@ def local_sum_prod_mul_by_scalar(node):
             # If node.op is a T.elemwise.Prod, then the scalars need to be
             # raised to the power of the number of elements in the input
             # to the Prod
-            if isinstance(node.op, T.elemwise.Prod):
+            if (isinstance(node.op, T.elemwise.Prod) and
+                new_op_input_nb_elements != 1):
+
                 scalars = [s ** new_op_input_nb_elements for s in scalars]
 
             # Scale the output of the op by the scalars and return as
             # replacement for the original output
-            mul_inputs = scalars + [new_op_output]
+            mul_inputs = scalars
+            if new_op_input_nb_elements != 1:
+                mul_inputs.append(new_op_output)
+
             return [T.mul(*mul_inputs)]
 
         if isinstance(node.op, T.Sum) and node_inps.owner and node_inps.owner.op == T.neg: