The effects of economic growth on the environment have received increased attention as global warming and other environmental problems become more serious. Many empirical studies explain the nexus between carbon dioxide emissions and economic growth with such models as the environmental Kuznets curve (EKC) theory. However, the assumptions of these models have never received strict verification with a large available data set and therefore may not be appropriate to describe the relationship. In this study, the nexus is modeled for 67 countries from 1971 to 2010 using a novel symbolic regression method. From the experimental results, several conclusions as follows could be reached. Firstly, there is no universal model fitting every country, and symbolic regression could discover a set of reasonable models for a specific country or region. Secondly, four models, including the inverted N-shaped, M-shaped, inverted U-shaped and monotonically increasing, are frequently found without domain experts' intervention in these countries, whereas the M-shaped model has received little attention in previous studies but exhibits promising performance. Thirdly, the relationship is diversified due to the difference of regions and economic development, where developed countries generally follow the inverted N-shaped and M-shaped models to explain the relationship, whereas developing countries are more likely to refer to the inverted N-shaped, inverted U-shaped and monotonically increasing models. Finally, several policy suggestions are presented. (c) 2015 Elsevier Ltd. All rights reserved.