[Rafael-SOWNet]

A hang since #2306, and a wrong answer since before 2.6.0, in one l'Hôpital chain. limitcheck found it at DEPTH=3, SEED=23. No issue was filed.

at 0 from the right	2.6.0	master	now
(-ln(2)/ln(x))^(exp(x) - 1)	1, 4.5 s	does not finish in 10 min	1, 6.1 s
(log(x, 1/2))^(exp(x) - sgn(x))	0	does not finish	1, 3.4 s

The chain. It's the form 0^0, and its exponent's logarithm is a 0·∞ product. Written as x^n / (1 / g^k) with g = e^(-1/x) - 1 after the substitution to +oo, each application differentiates 1/g^k into a quotient over g^(2k). So k went 6, 12, 24, …, every quotient was asked twice per depth, and the inner limits expanded the growing powers (stack: PolynomialLongDivision → DivideOnePolynomial → Expand). GrewTooMuch turns a step away by node count, and (…)^12 and (…)^24 have the same nodes. MaxlHopitalApplications was never reached, because the cost is inside each application.

Why it started. Bisected to #2306 ("A factor a numerator's terms hold to a power cancels"). Before it, the limit took a different arrangement at its fourth step and settled in 4.4 s. The l'Hôpital traces of the two builds agree through three levels and their simplified results. #2306 changed which route is reached afterwards, not the simplification of these quotients, so this does not undo it.

The fix. GrewTooMuch also adds up the quotient's whole exponents, with the same room as for nodes: the larger of eight more and three fifths again. A chain that is getting somewhere lowers its degrees.

limitcheck at SEED=16, and at DEPTH=3 on SEED=19 and 23, changes only the limit that did not finish, which now agrees with the values. Every other answer and decline is master's. The 752 limit tests pass, 1/x^2 - 1/sin(x)^2 among them; its chain is the one the node budget's comment was written for.

Tests: AQuotientWhosePowersGrowIsNotDifferentiatedTest, 5 cases. The two 0^0 limits fail on master by the one-minute cap; the three chains that settle pass on both. The full suite, AOT and the nine harnesses pass. There is a BREAKING-CHANGES entry, measured on 2.6.0.

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.77%. Comparing base (195da7f) to head (b0bb3ae).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2357      +/-   ##
==========================================
+ Coverage   86.76%   86.77%   +0.01%     
==========================================
  Files         312      312              
  Lines       68783    68786       +3     
  Branches    20037    20039       +2     
==========================================
+ Hits        59679    59692      +13     
+ Misses       4915     4909       -6     
+ Partials     4189     4185       -4     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.32% <100.00%> (+0.01%)	⬆️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

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Files with missing lines	Coverage Δ
...ath/Functions/Continuous/Limits/Transformations.cs	87.82% <100.00%> (+0.06%)	⬆️

... and 9 files with indirect coverage changes

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