Reduce unnecessary allocations and reuse code

[avik-pal]

Fixes #291

Checklist

• Support StaticArrays Properly LinearSolve.jl#436
• Adding support for NonlinearSolve.jl MaybeInplace.jl#3
• Non allocating versions for StaticArrays JuliaDiff/SparseDiffTools.jl#276
• Test out reinit!
• Change the compat of SimpleNonlinearSolve
• Update all the algorithms
  • Newton Raphson
  • Broyden
  • Klement
  • LBroyden
  • Trust Region
  • LM
  • Gauss Newton
  • DFSane
  • Pseudo Transient
• Fix Tests (if needed)
• Reenable Precompilation

Additional context

Add any other context about the problem here.

[avik-pal]

Tests should pass once the linked PRs are merged

[codecov]

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 ⚠️
src/levenberg.jl	91.48%	8 Missing ⚠️
src/trace.jl	58.82%	7 Missing ⚠️
src/gaussnewton.jl	81.81%	6 Missing ⚠️
src/jacobian.jl	92.95%	5 Missing ⚠️
src/lbroyden.jl	92.18%	5 Missing ⚠️
src/trustRegion.jl	95.79%	5 Missing ⚠️
src/NonlinearSolve.jl	89.47%	4 Missing ⚠️
src/pseudotransient.jl	94.11%	2 Missing ⚠️

Additional details and impacted files

@@            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