  Many promising approaches to symbolic regression have been presented in
recent years, yet progress in the field continues to suffer from a lack of
uniform, robust, and transparent benchmarking standards. In this paper, we
address this shortcoming by introducing an open-source, reproducible
benchmarking platform for symbolic regression. We assess 14 symbolic regression
methods and 7 machine learning methods on a set of 252 diverse regression
problems. Our assessment includes both real-world datasets with no known model
form as well as ground-truth benchmark problems, including physics equations
and systems of ordinary differential equations. For the real-world datasets, we
benchmark the ability of each method to learn models with low error and low
complexity relative to state-of-the-art machine learning methods. For the
synthetic problems, we assess each method's ability to find exact solutions in
the presence of varying levels of noise. Under these controlled experiments, we
conclude that the best performing methods for real-world regression combine
genetic algorithms with parameter estimation and/or semantic search drivers.
When tasked with recovering exact equations in the presence of noise, we find
that deep learning and genetic algorithm-based approaches perform similarly. We
provide a detailed guide to reproducing this experiment and contributing new
methods, and encourage other researchers to collaborate with us on a common and
living symbolic regression benchmark.
