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Visual thinking with diagrams is a crucial skill for learning and problem-solving in STEM subjects. To improve in this area, students need a variety of visual problems for deliberate practice. However, in our interviews, educators shared that they struggle to create these practice exercises because of limitations of existing tools. We introduce Edgeworth, a tool designed to help educators easily create visual problems. Edgeworth works in two main ways: firstly, it takes a single diagram from the user and systematically alters it to produce many variations, which the educator can then choose from to create multiple problems. Secondly, it automates the layout of diagrams, ensuring consistent high quality without the need for manual adjustments. To assess Edgeworth, we carried out case studies, a technical evaluation, and expert walkthrough demonstrations. We show that Edgeworth can create problems in three domains: geometry, chemistry, and discrete math. These problems were authored in just 15 lines of Edgeworth code on average. Edgeworth generated usable answer options within the first 10 diagram variations in 87% of authored problems. Finally, educators gave positive feedback on Edgeworth's utility and the real-world applicability of its outputs. 

Reverse-mode automatic differentiation (autodiff) has been popularized by deep learning, but its ability to compute gradients is also valuable for interactive use cases such as bidirectional computer-aided design, embedded physics simulations, visualizing causal inference, and more. Unfortunately, the web is ill-served by existing autodiff frameworks, which use autodiff strategies that perform poorly on dynamic scalar programs, and pull in heavy dependencies that would result in unacceptable webpage sizes. This work introduces Rose, a lightweight autodiff framework for the web using a new hybrid approach to reverse-mode autodiff, blending conventional tracing and transformation techniques in a way that uses the host language for metaprogramming while also allowing the programmer to explicitly define reusable functions that comprise a larger differentiable computation. We demonstrate the value of the Rose design by porting two differentiable physics simulations, and evaluate its performance on an optimization-based diagramming application, showing Rose outperforming the state-of-the-art in web-based autodiff by multiple orders of magnitude.