  Symbolic Regression (SR) can generate interpretable, concise expressions that
fit a given dataset, allowing for more human understanding of the structure
than black-box approaches. The addition of background knowledge (in the form of
symbolic mathematical constraints) allows for the generation of expressions
that are meaningful with respect to theory while also being consistent with
data. We specifically examine the addition of constraints to traditional
genetic algorithm (GA) based SR (PySR) as well as a Markov-chain Monte Carlo
(MCMC) based Bayesian SR architecture (Bayesian Machine Scientist), and apply
these to rediscovering adsorption equations from experimental, historical
datasets. We find that, while hard constraints prevent GA and MCMC SR from
searching, soft constraints can lead to improved performance both in terms of
search effectiveness and model meaningfulness, with computational costs
increasing by about an order-of-magnitude. If the constraints do not correlate
well with the dataset or expected models, they can hinder the search of
expressions. We find Bayesian SR is better these constraints (as the Bayesian
prior) than by modifying the fitness function in the GA
