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In many scientific and engineering applications, we often encounter mathematical expressions that require differentiation, and efficiently computing derivatives is a key challenge. The `ChainRules.jl` package in Julia provides a flexible framework to define custom derivative rules for complex functions and compositions. By writing your own rrules, you can optimize the computation of derivatives in your specific use case, making it easier to handle non-standard or complex operations that are not supported out-of-the-box.
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## Motivation
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In our research, we often find that the bottleneck in experiments lies in the performance of basic functions. A common issue arises when working with loops and indexing, as Julia needs to track each index separately, which can slow down gradient computations significantly. However, if you understand your function well, you can write a custom rrule to bypass these limitations and achieve speedups of up to 1000 times. In this lab, you’ll experience this firsthand in one of the exercises you'll solve.
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## ChainRules ecosystem
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