Performance improvements

[g-bauer]

Following some guidelines of the Rust Performance Book here are some things we can try to improve performance:

• Add codegen-units = 1 to release build
• Use a faster allocator. E.g. mimalloc works on all operating systems

Not so easy:

• properly profile to identify hot parts
• remove clones/allocations where not needed
• use profile-guided optimization (e.g. via cargo-pgo)
  • unfortunately this is currently not working with LTO and the PGO version is 10-20% slower than LTO
  • might be available in the future in maturin directly, see here

---

Quick tests with codegen-units = 1 added to release-lto (see here) show performance improvements of benchmarks of up to 12% (mean is about 7%) while for dual_number, changes are a bit smaller (see below).

Proper benchmarks (across all benchmarks) with comparison to current release workflow are needed but this might be an easy-to-get improvement if it turns out to be faster for all cases.

• Benchmark: dual_numbers
• System: methane/CO2
• main: main branch + lto
• main_codegen: main branch + lto + codegen-units = 1
• develop_: like main

Execution times in µs

name	f64	dual	dual2	hyperdual	dual3
main	1.1382	1.2325	1.4539	1.6267	1.7563
main_codegen	1.0229	1.1741	1.3708	1.5777	1.6316
develop	1.0138	1.1989	1.4465	1.589	1.7549
develop_codegen	0.9761	1.1681	1.4195	1.5446	1.6304

Slowdown t_f64/t_d for each branch/option

	f64	dual	dual2	hyperdual	dual3
main	1	1.08285	1.27737	1.42919	1.54305
main_codegen	1	1.14782	1.34011	1.54238	1.59507
develop	1	1.18258	1.42681	1.56737	1.73101
develop_codegen	1	1.1967	1.45426	1.58242	1.67032

Relative difference in % w.r.t. main + lto for each dual number (t_d_branch - t_d_main) / t_d_main * 100

name	f64	dual	dual2	hyperdual	dual3
main_codegen	-10.13	-4.74	-5.72	-3.01	-7.10
develop	-10.93	-2.73	-0.51	-2.32	-0.08
develop_codegen	-14.24	-5.23	-2.37	-5.05	-7.17