refactor: several TTFX improvements

[AayushSabharwal]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Add any other context about the problem here.

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	master	711172e...	master / 711172e...
ODEProblem	13.8 ± 1.9 ms	19.8 ± 5.4 ms	0.698 ± 0.21
init	0.0825 ± 0.013 ms	0.159 ± 0.025 ms	0.519 ± 0.12
large_parameter_init/ODEProblem	0.0457 ± 0.0075 s	0.0568 ± 0.011 s	0.805 ± 0.21
large_parameter_init/init	0.0934 ± 0.012 ms	0.124 ± 0.046 ms	0.755 ± 0.3
mtkcompile	14.3 ± 1.6 ms	18.4 ± 2.7 ms	0.776 ± 0.14
sparse_analytical_jacobian/ODEProblem	0.0413 ± 0.0069 s	0.0533 ± 0.0098 s	0.776 ± 0.19
sparse_analytical_jacobian/f_iip	0.114 ± 0.004 μs	0.119 ± 0.001 μs	0.958 ± 0.035
sparse_analytical_jacobian/f_oop	0.19 ± 0.0063 ms	0.357 ± 0.2 ms	0.533 ± 0.29
time_to_load	9.99 ± 0.34 s	11.3 ± 3.2 s	0.882 ± 0.25

Memory benchmarks

	master	711172e...	master / 711172e...
ODEProblem	0.0432 M allocs: 2.34 MB	0.0435 M allocs: 2.34 MB	0.998
init	0.345 k allocs: 0.0447 MB	0.345 k allocs: 0.0447 MB	1
large_parameter_init/ODEProblem	0.261 M allocs: 9.98 MB	0.261 M allocs: 10 MB	0.993
large_parameter_init/init	0.685 k allocs: 0.144 MB	0.685 k allocs: 0.144 MB	1
mtkcompile	0.0621 M allocs: 2.71 MB	0.0621 M allocs: 2.71 MB	1
sparse_analytical_jacobian/ODEProblem	0.195 M allocs: 7.2 MB	0.196 M allocs: 7.24 MB	0.995
sparse_analytical_jacobian/f_iip	0 allocs: 0 B	0 allocs: 0 B
sparse_analytical_jacobian/f_oop	0.848 k allocs: 27 kB	0.848 k allocs: 27 kB	1
time_to_load	0.153 k allocs: 12 kB	0.153 k allocs: 12 kB	1

[github-actions]

Benchmark Results (Julia vlts)

Time benchmarks

	master	711172e...	master / 711172e...
ODEProblem	8.45 ± 0.17 ms	8.42 ± 0.077 ms	1 ± 0.022
init	0.0478 ± 0.026 ms	0.0541 ± 0.026 ms	0.885 ± 0.64
large_parameter_init/ODEProblem	24.4 ± 0.32 ms	24.5 ± 0.55 ms	0.995 ± 0.026
large_parameter_init/init	0.0669 ± 0.0024 ms	0.0672 ± 0.0027 ms	0.996 ± 0.054
mtkcompile	9.02 ± 0.068 ms	9.03 ± 0.082 ms	0.999 ± 0.012
sparse_analytical_jacobian/ODEProblem	27.7 ± 0.18 ms	27.6 ± 0.29 ms	1 ± 0.012
sparse_analytical_jacobian/f_iip	0.07 ± 0.01 μs	0.069 ± 0.01 μs	1.01 ± 0.21
sparse_analytical_jacobian/f_oop	0.347 ± 0.013 ms	0.345 ± 0.012 ms	1.01 ± 0.051
time_to_load	5.19 ± 0.061 s	5.82 ± 0.32 s	0.892 ± 0.051

Memory benchmarks

	master	711172e...	master / 711172e...
ODEProblem	0.046 M allocs: 2.72 MB	0.046 M allocs: 2.73 MB	0.998
init	0.384 k allocs: 0.065 MB	0.384 k allocs: 0.065 MB	1
large_parameter_init/ODEProblem	0.26 M allocs: 9.83 MB	0.26 M allocs: 9.83 MB	1
large_parameter_init/init	0.551 k allocs: 0.166 MB	0.551 k allocs: 0.166 MB	1
mtkcompile	0.0657 M allocs: 3.43 MB	0.0657 M allocs: 3.43 MB	1
sparse_analytical_jacobian/ODEProblem	0.209 M allocs: 8.39 MB	0.209 M allocs: 8.39 MB	1
sparse_analytical_jacobian/f_iip	0 allocs: 0 B	0 allocs: 0 B
sparse_analytical_jacobian/f_oop	0.634 k allocs: 19.6 kB	0.634 k allocs: 19.6 kB	1
time_to_load	0.153 k allocs: 14.7 kB	0.153 k allocs: 14.7 kB	1

[KristofferC]

Is this for invalidation reasons?

Edit: Ok,I see this was already there before this PR.

[github-actions]

[Runic] _{reported by reviewdog 🐶}

Suggested change

	@eval Base.Experimental.@compiler_options max_methods=1
	@eval Base.Experimental.@compiler_options max_methods = 1

[github-actions]

[Runic] _{reported by reviewdog 🐶}

Suggested change