  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.
