Fearless taylor version

[oscardssmith]

If we're willing to use the information that derivatives are linear operators, we can remove a lot of complexity from forward mode differentiation (and improve type stability in the process). I know @Keno doesn't believe this is valid to assume, but IMO the simplification enabled provides a pretty strong justification that this is the right approach.

[Keno]

This is unsound as is, even if you want to make the assumption that taylor-ness is preserved. This just makes everything taylor which is unconditionally unsound.

[oscardssmith]

in that case we definitely need test cases that break the assumption that everything is taylor because locally all the tests pass with this PR. (also, can you decipher the error message on CI I'm not able to understand or reproduce it).

[codecov-commenter]

Codecov Report

Base: 50.87% // Head: 50.77% // Decreases project coverage by -0.10% ⚠️

Coverage data is based on head (9b56ede) compared to base (0241872).
Patch coverage: 55.26% of modified lines in pull request are covered.

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Additional details and impacted files

@@            Coverage Diff             @@
##             main     #109      +/-   ##
==========================================
- Coverage   50.87%   50.77%   -0.10%     
==========================================
  Files          27       27              
  Lines        2632     2572      -60     
==========================================
- Hits         1339     1306      -33     
+ Misses       1293     1266      -27     

Impacted Files	Coverage Δ
src/codegen/forward_demand.jl	29.29% <0.00%> (-1.56%)	⬇️
src/stage1/mixed.jl	0.00% <0.00%> (ø)
src/stage1/recurse_fwd.jl	86.84% <0.00%> (-2.64%)	⬇️
src/jet.jl	41.02% <46.66%> (+1.35%)	⬆️
src/tangent.jl	25.75% <55.55%> (+1.22%)	⬆️
src/extra_rules.jl	41.81% <60.00%> (-2.73%)	⬇️
src/stage1/forward.jl	70.96% <71.42%> (+0.96%)	⬆️
src/stage1/recurse.jl	96.27% <75.00%> (-0.47%)	⬇️
src/interface.jl	67.92% <80.00%> (-1.17%)	⬇️
src/stage1/generated.jl	71.49% <93.75%> (-1.44%)	⬇️
... and 7 more

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