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Mozilla Research is developing Servo, a parallel web browser engine, to exploit the benefits of parallelism and concurrency in the web rendering pipeline. Parallelization results in improved performance for pinterest.com but not for google.com. This is because the workload of a browser is dependent on the web page it is rendering. In many cases, the overhead of creating, deleting, and coordinating parallel work outweighs any of its benefits. In this paper, we model the relationship between web page primitives and a web browser's parallel performance using supervised learning. We discover a feature space that is representative of the parallelism available in a web page and characterize it using seven key features. Additionally, we consider energy usage trade-offs for different levels of performance improvements using automated labeling algorithms. Such a model allows us to predict the degree of parallelism available in a web page and decide whether or not to render a web page in parallel. This modeling is critical for improving the browser's performance and minimizing its energy usage. We evaluate our model by using Servo's layout stage as a case study. Experiments on a quad-core Intel Ivy Bridge (i7-3615QM) laptop show that we can improve performance and energy usage by up to 94.52% and 46.32% respectively on the 535 web pages considered in this study. Looking forward, we identify opportunities to apply this model to other stages of a browser's architecture as well as other performance- and energy-critical devices.