Set of benchmarks to optimize AD?

[gdalle]

Hi there!
Could you suggest a reasonable set of benchmark functions on which to test and optimize AD backends? Beyond the one in the README (which focused much of the attention in #476), there must be a wide variety of input sizes and types, as well as function behaviors, and I would love for DI to strike a decent balance for all of them.

[ChrisRackauckas]

You know the drill, SciMLBenchmarks.

https://docs.sciml.ai/SciMLBenchmarksOutput/stable/NonlinearProblem/nonlinear_solver_23_tests/

https://docs.sciml.ai/SciMLBenchmarksOutput/stable/NonlinearProblem/nonlinear_battery_problem/

https://docs.sciml.ai/SciMLBenchmarksOutput/stable/NonlinearProblem/bruss/