  Previous studies have introduced a weakly-supervised paradigm for solving
math word problems requiring only the answer value annotation. While these
methods search for correct value equation candidates as pseudo labels, they
search among a narrow sub-space of the enormous equation space. To address this
problem, we propose a novel search algorithm with combinatorial strategy
\textbf{ComSearch}, which can compress the search space by excluding
mathematically equivalent equations. The compression allows the searching
algorithm to enumerate all possible equations and obtain high-quality data. We
investigate the noise in the pseudo labels that hold wrong mathematical logic,
which we refer to as the \textit{false-matching} problem, and propose a ranking
model to denoise the pseudo labels. Our approach holds a flexible framework to
utilize two existing supervised math word problem solvers to train pseudo
labels, and both achieve state-of-the-art performance in the weak supervision
task.
