Interpretable machine learning models trade off accuracy for simplicity to make explanations more readable and easier to comprehend. Drawing from cognitive psychology theories in graph comprehension, we formalize readability as visual cognitive chunks to measure and moderate the cognitive load in explanation visualizations. We present Cognitive-GAM (COGAM) to generate explanations with desired cognitive load and accuracy by combining the expressive nonlinear generalized additive models (GAM) with simpler sparse linear models. We calibrated visual cognitive chunks with reading time in a user study, characterized the trade-off between cognitive load and accuracy for four datasets in simulation studies, and evaluated COGAM against baselines with users. We found that COGAM can decrease cognitive load without decreasing accuracy and/or increase accuracy without increasing cognitive load. Our framework and empirical measurement instruments for cognitive load will enable more rigorous assessment of the human interpretability of explainable AI.