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One of the potential solutions for model interpretation is to train a surrogate model: a more transparent model that approximates the behavior of the model to be explained. Typically, classification rules or decision trees are used due to the intelligibility of their logic-based expressions. However, decision trees can grow too deep and rule sets can become too large to approximate a complex model. Unlike paths on a decision tree that must share ancestor nodes (conditions), rules are more flexible. However, the unstructured visual representation of rules makes it hard to make inferences across rules. To address these issues, we present a workflow that includes novel algorithmic and interactive solutions. First, we present Hierarchical Surrogate Rules (HSR), an algorithm that generates hierarchical rules based on user-defined parameters. We also contribute SuRE, a visual analytics (VA) system that integrates HSR and interactive surrogate rule visualizations. Particularly, we present a novel feature-aligned tree to overcome the shortcomings of existing rule visualizations. We evaluate the algorithm in terms of parameter sensitivity, time performance, and comparison with surrogate decision trees and find that it scales reasonably well and outperforms decision trees in many respects. We also evaluate the visualization and the VA system by a usability study with 24 volunteers and an observational study with 7 domain experts. Our investigation shows that the participants can use feature-aligned trees to perform non-trivial tasks with very high accuracy. We also discuss many interesting observations that can be useful for future research on designing effective rule-based VA systems.