Audit performance of captured variables in closures

One of the benefits of ChainRules' design is that rules for multiple arguments can share intermediate computations by virtue of defining variables outside of the individual Rules then capturing them in the wrapped closures. However, this approach likely incurs the infamous https://github.com/JuliaLang/julia/issues/15276. To get around this, we could potentially define a macro that does a Rule definition but scans the closure expression for uses of variables not defined therein, and wrapping those in let. That would be heinously hacky but might buy us some performance improvements.

Start by reading Julia issue 15276 and auditing how ChainRules defines Rule closures that capture variables from their surrounding scope. Compare the current captured-variable behavior with the proposed let-wrapped form; done requires evidence that the approach improves performance and a settled implementation direction.