Add Mooncake to Lux benchmarking suite

[yebai]

For more comprehensive benchmarking, let's add Mooncake to the Lux's benchmarking set:

• results: https://lux.csail.mit.edu/benchmarks/
• code: https://github.com/LuxDL/Lux.jl/tree/main/benchmarks

Cc @avik-pal, who might be able to provide pointers on what is needed.

(this issue is copied from #361 (comment))

[avik-pal]

Yes, let's do this. I need to cleanup the benchmarks on Lux end (the benchmarks are somewhat broken since the monorepo setup). I will update here once that is done

[yebai]

It'd be incredibly helpful if we could have a set of (Lux + basic NN library functions) benchmark cases and a benchmarking script that leads to an (autograd) community leaderboard like this one for probabilistic programming:

https://nsiccha.github.io/StanBlocks.jl/performance.html#visualization

@avik-pal, what are your thoughts? The Turing.jl team would be happy to contribute to a leaderboard if you could lead it.

Related Flux benchmark cases: #361 (comment)