refactor: various performance 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 vlts)

Time benchmarks

	master	4873ecf...	master / 4873ecf...
ODEProblem	11.5 ± 0.32 ms	11.8 ± 0.65 ms	0.969 ± 0.06
init	0.0591 ± 0.0018 ms	0.0578 ± 0.0019 ms	1.02 ± 0.047
large_parameter_init/ODEProblem	28.7 ± 0.77 ms	30.4 ± 1.1 ms	0.944 ± 0.043
large_parameter_init/init	0.0763 ± 0.003 ms	0.0774 ± 0.0036 ms	0.985 ± 0.06
mtkcompile	13.1 ± 0.22 ms	13.7 ± 0.33 ms	0.959 ± 0.028
sparse_analytical_jacobian/ODEProblem	30.9 ± 1.1 ms	0.0332 ± 0.0012 s	0.932 ± 0.046
sparse_analytical_jacobian/f_iip	0.07 ± 0 μs	0.07 ± 0 μs	1 ± 0
sparse_analytical_jacobian/f_oop	0.378 ± 0.013 ms	0.378 ± 0.012 ms	1 ± 0.047
time_to_load	5.57 ± 0.029 s	5.82 ± 0.0045 s	0.957 ± 0.0051

Memory benchmarks

	master	4873ecf...	master / 4873ecf...
ODEProblem	0.056 M allocs: 3.2 MB	0.056 M allocs: 3.2 MB	1
init	0.377 k allocs: 0.0621 MB	0.377 k allocs: 0.0621 MB	1
large_parameter_init/ODEProblem	0.263 M allocs: 9.98 MB	0.263 M allocs: 9.98 MB	1
large_parameter_init/init	0.398 k allocs: 0.15 MB	0.398 k allocs: 0.15 MB	1
mtkcompile	0.0816 M allocs: 4.02 MB	0.0816 M allocs: 4.02 MB	1
sparse_analytical_jacobian/ODEProblem	0.21 M allocs: 8.48 MB	0.21 M allocs: 8.48 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: 14.5 kB	0.153 k allocs: 14.5 kB	1

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	master	4873ecf...	master / 4873ecf...
ODEProblem	8.19 ± 0.27 ms	8.15 ± 0.38 ms	1.01 ± 0.057
init	31.5 ± 11 μs	0.0317 ± 0.011 ms	0.994 ± 0.48
large_parameter_init/ODEProblem	24.9 ± 2.1 ms	22.6 ± 0.88 ms	1.1 ± 0.1
large_parameter_init/init	0.0473 ± 0.0031 ms	0.0478 ± 0.0031 ms	0.988 ± 0.09
mtkcompile	8.42 ± 0.32 ms	8.38 ± 0.26 ms	1 ± 0.05
sparse_analytical_jacobian/ODEProblem	23.6 ± 2.5 ms	22.9 ± 1.5 ms	1.03 ± 0.13
sparse_analytical_jacobian/f_iip	0.06 ± 0.01 μs	0.07 ± 0.01 μs	0.857 ± 0.19
sparse_analytical_jacobian/f_oop	0.104 ± 0.011 ms	0.103 ± 0.011 ms	1.01 ± 0.15
time_to_load	4.86 ± 0.05 s	4.87 ± 0.025 s	0.999 ± 0.012

Memory benchmarks

	master	4873ecf...	master / 4873ecf...
ODEProblem	0.052 M allocs: 2.73 MB	0.052 M allocs: 2.73 MB	1
init	0.331 k allocs: 0.0408 MB	0.331 k allocs: 0.0408 MB	1
large_parameter_init/ODEProblem	0.264 M allocs: 10.1 MB	0.264 M allocs: 10.1 MB	1
large_parameter_init/init	0.391 k allocs: 0.128 MB	0.391 k allocs: 0.128 MB	1
mtkcompile	0.074 M allocs: 3.14 MB	0.074 M allocs: 3.14 MB	1
sparse_analytical_jacobian/ODEProblem	0.201 M allocs: 7.41 MB	0.201 M allocs: 7.42 MB	0.999
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	0.145 k allocs: 11 kB	0.145 k allocs: 11 kB	1