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

❌ Patch coverage is 62.90323% with 23 lines in your changes missing coverage. Please review.
✅ Project coverage is 50.77%. Comparing base (5b3a846) to head (9b56ede).
⚠️ Report is 336 commits behind head on main.

Files with missing lines	Patch %	Lines
src/jet.jl	46.66%	8 Missing ⚠️
src/stage1/mixed.jl	0.00%	4 Missing ⚠️
src/tangent.jl	55.55%	4 Missing ⚠️
src/extra_rules.jl	60.00%	2 Missing ⚠️
src/stage1/forward.jl	71.42%	2 Missing ⚠️
src/interface.jl	80.00%	1 Missing ⚠️
src/stage1/generated.jl	93.75%	1 Missing ⚠️
src/stage1/recurse_fwd.jl	0.00%	1 Missing ⚠️

Additional details and impacted files

@@ Coverage Diff @@## main #109 +/- ##
==========================================
+ Coverage 50.50% 50.77% +0.26% 
==========================================
Files 27 27 Lines 2651 2572 -79 ==========================================
- Hits 1339 1306 -33 + Misses 1312 1266 -46 

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