Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information beyond just values at some inputs, but also effectively constrain the search space. We identify the asymptotic constraints of leading polynomial powers as the function approaches zero and infinity as useful constraints and create a system to use them for symbolic regression. The first part of the system is a conditional production rule generating neural network which preferentially generates production rules to construct expressions with the desired leading powers, producing novel expressions outside the training domain. The second part, which we call Neural-Guided Monte Carlo Tree Search, uses the network during a search to find an expression that conforms to a set of data points and desired leading powers. Lastly, we provide an extensive experimental validation on thousands of target expressions showing the efficacy of our system compared to exiting methods for finding unknown functions outside of the training set.