Add benchmarks

[g-bauer]

Following #65, we should add benchmarks for possible future performance investigations. Feel free to add to the list of functions to benchmark.

• [x] direct calls to the residual Helmholtz energy function given a StateHD (circumventing closure construction and cache) [#89 ].
  • [x] Helmholtz energy
  • [x] first derivative using Dual64
  • [x] second derivative using HyperDual64
  • [x] third derivative using Dual3
• [x] Properties of State (creating a State inside benchmark or manually clearing cache) [#89]
• [x] functions including algorithms / solver
  • [x] PhaseEquilibrium: constructors
  • [x] critical point
• [ ] DFT
  • [ ] surface tension
  • [x] pores
• [ ] Python
  • [ ] identifying overhead

Notes

• Compare impact of compiler options
  • lto = "thin" versus lto = true
  • target-cpu=native
  • and more?

[prehner]

I added DFT benchmarks in #103. Comparing different solvers in a benchmark is not useful imo, because it gives a very limited insight into the capabilities of the solver.

Do you have a specific thought on how to identify Python overhead? For DFT it appears to be of the order of 2-3 ms, but very difficult to assess property.

[g-bauer]

Do you have a specific thought on how to identify Python overhead? For DFT it appears to be of the order of 2-3 ms

I am note sure. There are options to run Python code using pyo3 (run, eval, from_code, etc.) but I am not sure if we can use these to make proper comparisons or get an idea of the overhead of a function/method. 2-3 ms seems to be a lot, though. Does that include calling a property that returns a numpy array?