Abstract We test the mutual consistency between the baryon acoustic oscillation measurements from the eBOSS SDSS final release and the Pantheon supernova compilation in a model-independent fashion using Gaussian process regression. We also test their joint consistency with the ΛCDM model in a model-independent fashion. We also use Gaussian process regression to reconstruct the expansion history that is preferred by these two data sets. While this methodology finds no significant preference for model flexibility beyond ΛCDM, we are able to generate a number of reconstructed expansion histories that fit the data better than the best-fit ΛCDM model. These example expansion histories may point the way toward modifications to ΛCDM. We also constrain the parameters Ω k and H 0 r d both with ΛCDM and with Gaussian process regression. We find that H 0 r d = 10,030 ± 130 km s−1 and Ω k = 0.05 ± 0.10 for ΛCDM and that H 0 r d = 10,040 ± 140 km s−1 and Ω k = 0.02 ± 0.20 for the Gaussian process case.