  The Fast Multipole Method (FMM) offers an acceleration for pairwise
interaction calculation, known as $N$-body problems, from $\mathcal{O}(N^2)$ to
$\mathcal{O}(N)$ with $N$ particles. This has brought dramatic increase in the
capability of particle simulations in many application areas, such as
electrostatics, particle formulations of fluid mechanics, and others. Although
the literature on the subject provides theoretical error bounds for the FMM
approximation, there are not many reports of the measured errors in a suite of
computational experiments. We have performed such an experimental
investigation, and summarized the results of about 1000 calculations using the
FMM algorithm, to characterize the accuracy of the method in relation with the
different parameters available to the user. In addition to the more standard
diagnostic of the maximum error, we supply illustrations of the spatial
distribution of the errors, which offers visual evidence of all the
contributing factors to the overall approximation accuracy: multipole
expansion, local expansion, hierarchical spatial decomposition (interaction
lists, local domain, far domain). This presentation is a contribution to any
researcher wishing to incorporate the FMM acceleration to their application
code, as it aids in understanding where accuracy is gained or compromised.
