[Rafael-SOWNet]

exp(log(1/x, arcsin(x))) at 0 from the right was left unevaluated. The logarithm alone tends to -1, so the limit is 1/e.

The logarithm reaches the descent as ln(arcsin(x)) / ln(1/x). That went wrong in two places:

• Its derivatives' quotient came back with the limit 0 * +oo / 0, a form with no value. The quotient's descent returned that form at once as the exponent's limit.
• The parts tend to -oo and +oo. The descent asked for the quotient's whole limit only when substituting finite parts came back NaN, and two infinite parts never go through that substitution.

A sine of the logarithm was left unevaluated too, and so was a hyperbolic sine, after ten seconds. 2.6.0 gives the same results.

Now a form with no value from the first reading is kept for the end, where it was returned before, and the parts are read first. The whole limit is also asked where the parts' limits make oo/oo and the substitution has no value. Only a value is taken from it.

Input	2.6.0 and master	Now
e^log(1/x, arcsin(x)) at 0⁺	unevaluated	1 / e
sin(log(1/x, arcsin(x))) at 0⁺	unevaluated	sin(-1)
sinh(log(1/x, arcsin(x))) at 0⁺	unevaluated, in 10 s	(1 / e - e) / 2, in 2.6 s
tanh(log(x, arcsin(x))) at 0⁻	unevaluated, in 6 s	tanh(1), in 0.9 s

The product was left alone. Changing the 0·oo reading in the product broke the two-sided convention. I tried two changes: making that case decline, and asking for the product's whole limit. Both turned x * ln(x) at 0 into 0 where it is pinned at NaN. From both sides the descent reads ln(x) at 0 as -oo, and the NaN that 0 * -oo comes back as is what holds the convention. The convention is open on #2365. A test here pins that it still holds.

Measured

• limitcheck at DEPTH=3 on 15 seeds (14, 16, 19, 23, 26, 28, 29, 31, 33, 34, 36, 38, 40, 41, 42), master against this branch: 22 more rows compared, across 11 seeds. No row moved from a value to another value or to NaN.
• One row crossed the harness's 5 s cap: (log(pi, x))^sinh(x) * sin(1) at 0⁻. Measured alone it declines in 7.05 s on this branch and 7.09 s on master, so the time is the same.
• The new tests fail on master: the three right-hand rows that have a composition. The sinh row took 8 minutes to fail under the test runner.
• Suite: 18968 passed, 0 failed. AOT passed. BoundCheck, RootCheck, CasBench, PropCheck, SimpSweep, RuleCheck, CanonCheck and Confluence are clean.

Found by limitcheck at seed 40. Recorded in BREAKING-CHANGES.md.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.78%. Comparing base (88e0661) to head (099de6f).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2369      +/-   ##
==========================================
- Coverage   86.78%   86.78%   -0.01%     
==========================================
  Files         312      312              
  Lines       68867    68873       +6     
  Branches    20069    20070       +1     
==========================================
+ Hits        59766    59769       +3     
- Misses       4910     4911       +1     
- Partials     4191     4193       +2     

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
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	75.00% <100.00%> (+1.61%)	⬆️

... and 10 files with indirect coverage changes

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[Rafael-SOWNet]

Merged without the macOS jobs. Each one was cancelled before it started, with "The job was not acquired by Runner of type hosted even after multiple attempts" (macOS arm64 capacity), the same outage as on #2368. In their place:

• I trial-merged this branch with master as it is after Read an even power of a real base as never negative in a limit #2368. On that tree all 6484 limit and calculus tests passed.
• On the same tree I ran this PR's rows and Read an even power of a real base as never negative in a limit #2368's on a 512 KB thread, the tightest stack the macOS leg gives. Each limit came out as the tests expect, including x * ln(x) and sin(x) * ln(x) still NaN at 0.
• Every Linux and Windows check is green.
• The local chain, suite and harnesses all passed.