  Symbolic regression (SR) is a data analysis problem where we search for the
mathematical expression that best fits a numerical dataset. It is a global
optimization problem. The most popular approach to SR is by genetic programming
(SRGP). It is a common paradigm to compare an algorithm's performance to that
of random search, but the data comparing SRGP to random search is lacking. We
describe a novel algorithm for SR, namely SR by uniform random global search
(SRURGS), also known as pure random search. We conduct experiments comparing
SRURGS with SRGP using 100 randomly generated equations. Our results suggest
that a SRGP is faster than SRURGS in producing equations with good R^2 for
simple problems. However, our experiments suggest that SRURGS is more robust
than SRGP, able to produce good output in more challenging problems. As SRURGS
is arguably the simplest global search algorithm, we believe it should serve as
a control algorithm against which other symbolic regression algorithms are
compared. SRURGS has only one tuning parameter, and is conceptually very
simple, making it a useful tool in solving SR problems. The method produces
random equations, which is useful for the generation of symbolic regression
benchmark problems. We have released well documented and open-source python
code, currently under formal peer-review, so that interested researchers can
deploy the tool in practice.
