The benefits of exercise are well demonstrated in the scientific literature. In fact, the physical exercise is recommended in the prevention and management of various medical conditions, however, an often-overlooked aspect of exercise is the effect it has on cognition and the brain. In this paper, we present a study the aim of which is to investigate and identify the relationship between physical exercise and cognitive performance measured through a number of cognitive tests taken from Cambridge Brain Science (CBS). The dynamic autonomic responses during physical exercise can be measured by analyzing the ElectroCardioGram signal, i.e. the Heart Rate Variability (HRV). This suggests that the relationship between physical exercise and cognitive performance can be analyzed by studying the correlation between HRV and cognitive performance. This study involves thirty subjects, divided into two groups, each with specific physical activity. Twelve cognitive tests from CBS are used. Comparison between the pre- and post-exercise results in terms of cognitive performance differences is effected. Then, a regression analysis between HRV features and CBS tests results is performed. Several machine learning algorithms are considered. The results of the study numerically appraise, both before and after physical training, the improvement, the conservation, or the worsening on different aspects of cognition, each represented by a CBStest. Additionally, the found mathematical relationship between physical exercise and cognitive performance suggests that it is possible to predict the beneficial effect of various exercise programs (aerobics or muscle strength) on executive and attentive control (work memory, distributed focus, inhibition of response, interference on control).