Automated feature engineering (AutoFE) is the process of automatically building and selecting new features that help improve downstream predictive performance. While traditional feature engineering requires significant domain expertise and time-consuming iterative testing, AutoFE strives to make feature engineering easy and accessible to all data science practitioners. We introduce a new AutoFE algorithm, IIFE, based on determining which feature pairs synergize well through an information-theoretic perspective called interaction information. We demonstrate the superior performance of IIFE over existing algorithms. We also show how interaction information can be used to improve existing AutoFE algorithms. Finally, we highlight several critical experimental setup issues in the existing AutoFE literature and their effects on performance.