Reduce unnecessary allocations and reuse code

[avik-pal]

Fixes #291

Checklist

• [x] https://github.com/SciML/LinearSolve.jl/pull/436
• [x] https://github.com/avik-pal/MaybeInplace.jl/pull/3
• [x] https://github.com/JuliaDiff/SparseDiffTools.jl/pull/276
• [x] Test out reinit!
• [x] Change the compat of SimpleNonlinearSolve
• [x] Update all the algorithms
  • [x] Newton Raphson
  • [x] Broyden
  • [x] Klement
  • [x] LBroyden
  • [x] Trust Region
  • [x] LM
  • [x] Gauss Newton
  • [x] DFSane
  • [x] Pseudo Transient
• [x] Fix Tests (if needed)
• [x] Reenable Precompilation

Additional context

Add any other context about the problem here.

[avik-pal]

Tests should pass once the linked PRs are merged

[codecov[bot]]

Codecov Report

Attention: 62 lines in your changes are missing coverage. Please review.

Comparison is base (657c549) 93.07% compared to head (3b52a5a) 87.40%. Report is 2 commits behind head on master.

Files	Patch %	Lines
src/utils.jl	82.90%	20 Missing :warning:
src/levenberg.jl	91.48%	8 Missing :warning:
src/trace.jl	58.82%	7 Missing :warning:
src/gaussnewton.jl	81.81%	6 Missing :warning:
src/jacobian.jl	92.95%	5 Missing :warning:
src/lbroyden.jl	92.18%	5 Missing :warning:
src/trustRegion.jl	95.79%	5 Missing :warning:
src/NonlinearSolve.jl	89.47%	4 Missing :warning:
src/pseudotransient.jl	94.11%	2 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #297 +/- ## ========================================== - Coverage 93.07% 87.40% -5.68% ========================================== Files 21 21 Lines 2065 1683 -382 ========================================== - Hits 1922 1471 -451 - Misses 143 212 +69 ```

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[ChrisRackauckas]

The docs build needs to be fixed though