[Rafael-SOWNet]

sin(x)^tanh(x) at 0 from the right was left unevaluated, where it is 1. tan(2x)^sin(tanh(x)) declined after 13 s, and 2.6.0 does not finish it in 2 minutes.

Read through its exponent, the power becomes a quotient that l'Hôpital's rule takes. The rule differentiated every factor of both parts. That included factors tending to a non-zero number, such as the 1 - tanh(x)^2 that tanh's derivative brings. tanh is written through exponentials, so each such factor doubled the derivative, which then outgrew the rule's bound.

Now a factor that is continuous at a finite destination, with a finite, non-zero real value there, is taken out as that value and kept exact: lim c(x) f(x)/g(x) = c(a) lim f(x)/g(x).

• Only a factor that TreeAnalyzer.IsRealValued says is real for real x, and that has no floor, ceil, round, sign or piecewise in it. So its value at the point is its limit from either side.
• A limit that is an infinity stays that infinity. A finite one is the exact product, so tanh(1 + x)·(x - 1)/(x^2 - 1) at 1 is (e^4 - 1)/(2(e^4 + 1)) and not a decimal.

Input, at 0⁺	2.6.0	master	Now
sin(x)^tanh(x)	unevaluated	unevaluated	1
tan(x)^sin(tanh(x))	unevaluated	unevaluated	1
tan(2*x)^sin(tanh(x))	did not finish in 2 min	unevaluated after 13 s	1, in 0.4 s

Measured

• limitcheck at DEPTH=3 on 18 seeds (14 to 45), master against this branch: 10 more rows compared across 6 seeds, and 4 fewer that did not finish in 5 s. No row moved to another value or to NaN.
• The new tests fail on master: the three rows above. The three rows that check the value taken out pass on both.
• Suite: 18982 passed, 0 failed. AOT passed. BoundCheck, RootCheck, CasBench, PropCheck, SimpSweep, RuleCheck, CanonCheck and Confluence are clean.

Not fixed here: (1 - tanh(x)^2)·x·(1 + x^2)/tanh(x) at 0⁺ still takes about 19 s. Nearly all of that is Simplify on the expression itself, which takes 7 s without any limit. That is a separate defect.

Found by limitcheck at seed 42. Recorded in BREAKING-CHANGES.md.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 95.65217% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 86.75%. Comparing base (4c203f0) to head (4a4e752).

Files with missing lines	Patch %	Lines
...ath/Functions/Continuous/Limits/Transformations.cs	95.65%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #2370   +/-   ##
=======================================
  Coverage   86.75%   86.75%           
=======================================
  Files         312      312           
  Lines       68877    68897   +20     
  Branches    20071    20078    +7     
=======================================
+ Hits        59755    59774   +19     
+ Misses       4926     4925    -1     
- Partials     4196     4198    +2     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.30% <95.65%> (+<0.01%)	⬆️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
...ath/Functions/Continuous/Limits/Transformations.cs	88.05% <95.65%> (+0.22%)	⬆️

... and 9 files with indirect coverage changes

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[Rafael-SOWNet]

Merged without the two macOS jobs. They were cancelled before they started ("The job was not acquired by Runner of type hosted even after multiple attempts"), the same macOS arm64 outage as on #2368 and #2369. In their place:

• I ran this PR's rows on a 512 KB thread, the tightest stack the macOS leg gives, along with x * ln(x) and Ask the whole limit of a quotient of two infinities in the descent #2369's e^log(1/x, arcsin(x)). Each limit came out as the tests expect.
• The branch sits on current master, so there was nothing to trial-merge.
• Every Linux and Windows check is green.
• The local chain, suite and harnesses all passed.