Turn code samples into doctests on first page of docs

[gdalle]

Fix #1188

In the section on caveats, the code samples are not run when the documentation is built, which means they can get outdated.
I realized that because I tried the first one (on temporary storage and it threw an error).

This PR:

• turns the remaining code samples into doctests
• fixes the error I spotted in one of them (a missing Reverse as the first argument to autodiff)
• modified the test for duplicated temporary storage to circumvent Julia being more clever now

[gdalle]

Also I wasn't able to build the documentation locally (see #1189), so if you have any tips I'll gladly take them

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (7313c99) 75.39% compared to head (3f27a9d) 75.61%.
Report is 4 commits behind head on main.

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Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1187      +/-   ##
==========================================
+ Coverage   75.39%   75.61%   +0.21%     
==========================================
  Files          35       35              
  Lines        9788     9891     +103     
==========================================
+ Hits         7380     7479      +99     
- Misses       2408     2412       +4     

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[gdalle]

This is good to go