[Rafael-SOWNet]

When the descent's sides come back NaN, a two-sided limit asks each side outright. Since #2419, a side that stops at an indeterminate form with an infinity in it is undecided. A side that stops at a form of finite parts only, 0 / 0 or c / 0, still counted as a side with no limit, which made the two-sided limit NaN.

That is right for (x - x) / (x - x), which has no value anywhere. It is wrong for erf(abs(x)) / x^4 at 0: that limit is +oo from each side, and the form only shows that two rates were never compared.

Such a side now counts as undecided where the expression has a finite real value at 10^-6 and 10^-9 from the point on that side. Where it has no real value there, the side still has no limit. That covers (x - x) / (x - x), and ln(-2) / ln(x) at 1, which is complex beside the point.

Input, at 0, two-sided	true value	2.6.0	master	this branch
erf(abs(x)) / x^4	+oo	unevaluated	NaN	unevaluated
erf(abs(x)) / (x^3 * sinh(x))	+oo	unevaluated	NaN	unevaluated
1 / log(x^2, cos(x))	+oo	-oo	NaN	unevaluated
abs(x)^erf(x)	1	unevaluated	NaN	unevaluated
tan(1/2 + x) + abs(x)^erf(x)	tan(1/2) + 1	unevaluated	NaN	unevaluated
1 / (x * arccot(x))	+oo	NaN	NaN	unevaluated
(x - x) / (x - x)	none	NaN	NaN	NaN
(x - x) * sin(x) / ((x - x) * x)	none	NaN	NaN	NaN
ln(-2) / ln(x), at 1	none	NaN	NaN	NaN
sin(1/x), floor(2/x), floor(x), 1/x, abs(x)/x	none	NaN	NaN	NaN

Against 2.6.0, the 1 / log(x^2, cos(x)) and 1 / (x * arccot(x)) rows change, and both are in BREAKING-CHANGES.md. The other wrong NaNs appeared during this cycle and never shipped. The test pins all of them as unevaluated, and the cases with no limit as NaN.

The check runs only on the path where a side has already stopped at an indeterminate form, so no limit that was already answered pays for it.

Checked on this branch:

• Tests: UnitTests 19355 passed, plus the MCP, Terminal, InteractiveWrapper and F# wrapper suites, and the AOT smoke test. A 1 / (x * arccot(x)) test row and its BREAKING-CHANGES.md row were added after that run; the test passes.
• Harnesses: BoundCheck, RootCheck, CasBench, PropCheck, SimpSweep, RuleCheck, CanonCheck and Confluence all pass.
• limitcheck at DEPTH=3, COUNT=600, on 42 seeds against master: seven rows went from NaN to unevaluated, and no row gained a value. Each is an expression that is real beside the point through a complex intermediate.
  • abs(arctan(x^x)) at 0 is pi/4 from each side, and abs(sinh(2)^log(x, -1)) at 1 is 1 from each side, so their NaN was wrong.
  • cos(sinh(log(x, -1))) at 1 oscillates, so it had no limit and NaN was right; unevaluated is not wrong.
  • x^x at 0 itself is not real to the left and stays NaN, as LimitTest.TestNoLimit pins it.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 77.77778% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.80%. Comparing base (fe19c27) to head (1785c0e).

Files with missing lines	Patch %	Lines
...ns/Continuous/Limits/Solvers/Solvers.Definition.cs	77.77%	1 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2426      +/-   ##
==========================================
- Coverage   86.82%   86.80%   -0.03%     
==========================================
  Files         312      312              
  Lines       69545    69551       +6     
  Branches    20312    20316       +4     
==========================================
- Hits        60380    60371       -9     
- Misses       4929     4944      +15     
  Partials     4236     4236              

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.34% <77.77%> (-0.03%)	⬇️
fsharp	32.97% <ø> (ø)
interactive	39.81% <ø> (ø)

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Files with missing lines	Coverage Δ
...ns/Continuous/Limits/Solvers/Solvers.Definition.cs	92.10% <77.77%> (-0.52%)	⬇️

... and 9 files with indirect coverage changes

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