[DO NOT MERGE] Testing the new NonlinearSolveBase.jl

[avik-pal]

This is VERY Breaking

• Move to NonlinearSolveBase, which is a significantly lighter version of DiffEqBase
• ForwardDiff and FiniteDiff are moved into extensions, so no AD package is loaded by default

Package load time goes from ~0.5s to ~0.15s

This needs a 2.0 tag.

Precompile Timings:

# OLD
(@temp) pkg> precompile
Precompiling project...
  79 dependencies successfully precompiled in 30 seconds. 6 already precompiled.

# NEW
(SimpleNonlinearSolve) pkg> precompile
Precompiling project...
  41 dependencies successfully precompiled in 19 seconds. 3 already precompiled.
Precompiling project...  # If we don't have a precompile workload
  41 dependencies successfully precompiled in 12 seconds. 3 already precompiled.

Roots.jl precompilation:

(@temp) pkg> precompile
Precompiling project...
  12 dependencies successfully precompiled in 5 seconds. 1 already precompiled.

Current Dependencies

Project SimpleNonlinearSolve v1.6.0
Status `/mnt/research/ongoing/nlsolve/SimpleNonlinearSolve.jl/Manifest.toml`
  [47edcb42] ADTypes v0.2.6
  [79e6a3ab] Adapt v4.0.1
  [4fba245c] ArrayInterface v7.7.1
  [38540f10] CommonSolve v0.2.4
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.5.4
  [9a962f9c] DataAPI v1.16.0
  [e2d170a0] DataValueInterfaces v1.0.0
  [ffbed154] DocStringExtensions v0.9.3
  [4e289a0a] EnumX v1.0.4
  [e2ba6199] ExprTools v0.1.10
  [9aa1b823] FastClosures v0.3.2
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [46192b85] GPUArraysCore v0.1.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1914dd2f] MacroTools v0.5.13
  [bb5d69b7] MaybeInplace v0.1.1
  [be0214bd] NonlinearSolveBase v1.0.0 `https://github.com/SciML/NonlinearSolveBase.jl#master`
  [bac558e1] OrderedCollections v1.6.3
  [aea7be01] PrecompileTools v1.2.0
  [21216c6a] Preferences v1.4.1
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.10.1
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.12
  [0bca4576] SciMLBase v2.29.0
  [c0aeaf25] SciMLOperators v0.3.8
  [efcf1570] Setfield v1.1.1
  [1e83bf80] StaticArraysCore v1.4.2
  [2efcf032] SymbolicIndexingInterface v0.3.8
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.11.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [9fa8497b] Future
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [ca575930] NetworkOptions v1.2.0
  [de0858da] Printf
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [4536629a] OpenBLAS_jll v0.3.23+4
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [8e850b90] libblastrampoline_jll v5.8.0+1

cc @oscardssmith, @ChrisRackauckas

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 187 lines in your changes are missing coverage. Please review.

Project coverage is 0.00%. Comparing base (fd7d216) to head (2d21b01).

Files	Patch %	Lines
...onlinearSolveDiffResultsForwardDiffExt/jacobian.jl	0.00%	50 Missing ⚠️
src/utils.jl	0.00%	36 Missing ⚠️
ext/SimpleNonlinearSolveFiniteDiffExt.jl	0.00%	33 Missing ⚠️
...linearSolveDiffResultsForwardDiffExt/forward_ad.jl	0.00%	20 Missing ⚠️
...NonlinearSolveDiffResultsForwardDiffExt/hessian.jl	0.00%	15 Missing ⚠️
src/SimpleNonlinearSolve.jl	0.00%	9 Missing ⚠️
...t/SimpleNonlinearSolveDiffResultsForwardDiffExt.jl	0.00%	7 Missing ⚠️
ext/SimpleNonlinearSolvePolyesterForwardDiffExt.jl	0.00%	6 Missing ⚠️
src/linesearch.jl	0.00%	3 Missing ⚠️
...SimpleNonlinearSolveChainRulesCoreDiffEqBaseExt.jl	0.00%	2 Missing ⚠️
... and 6 more

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #132       +/-   ##
==========================================
- Coverage   90.90%   0.00%   -90.91%     
==========================================
  Files          21      25        +4     
  Lines        1286    1212       -74     
==========================================
- Hits         1169       0     -1169     
- Misses        117    1212     +1095     

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