Fix #480: tanh derivative saturates instead of collapsing to a wrong finite value

[petlenz]

Closes #480.

Fix level: the composition (option a), with a documented residual. tanh was (exp(2x) − 1) / (exp(2x) + 1), whose quotient-rule derivative is two terms near +2 and −2 that cancel; once (exp(2x)+1)² overflows one term drops out and the sum is a finite wrong number on the t2s side, NaN on the scalar side, and the value itself was NaN past x ≈ 355. Both domains now build 2 / (1 + exp(−2x)) − 1: still one exp term (so the #180 duplicate-insert hazard stays closed), and the derivative is a single product 4·exp(−2x)·(1+exp(−2x))⁻² that cannot cancel.

argument	main	this PR	true
value, x = ±400	NaN	±1	±1
d/dx, x = 50	0	1.49e-43	1.49e-43
d/dx, x = 200	NaN	7.66068e-174	7.66068e-174
d/dA tanh(tr A)₀₀, tr = +197.324	41.2392 (t2s)	1.61663e-171	1.61663e-171
positive side, 0 → 420	−inf / NaN above 179	exact (worst 1 ulp)

Residual — this PR moves a narrow defect from the positive side to the negative side. Below x ≈ −179 the squared denominator leaves the double range and pow returns a denormal, so the derivative over-estimates: +0.26 % at −185, +29 % at −186, +75 % at −186.25; it is zero from −186.5 (truth ~4e-162) and NaN past −354.25. Main is exact in that band. The trade is deliberate: main's worst undetectable error on the positive side is ~171 orders of magnitude (41.2 vs 1.6e-171), this PR's is a factor of 1.75 in a ~7-wide band. tanh(−y) folds to −tanh(y) and stays exact, so only a bare argument that evaluates negative at runtime reaches it.

The symmetric form the review suggested was tried and is worse. (eˣ − e⁻ˣ)/(eˣ + e⁻ˣ) differentiates to 1 − sinh²/cosh², i.e. catastrophic cancellation: at ±186.25 it returns 1.11e-16 where the truth is 6.72e-162 — wrong by 145 orders of magnitude, on both sides, versus 1.75× here. The mirror form 1 − 2/(exp(2x)+1) is exactly this PR's behaviour reflected, so it only swaps which sign is wrong. A single-term derivative requires a constant numerator, and no such composition is stable on both sides — 4/(eˣ+e⁻ˣ)² is the stable expression but no composition differentiates to it without an algebraic rewrite. Dedicated hyperbolic nodes with a sech² rule (#126) are the only complete fix; an if_then_else split was considered and rejected (it would put a branch in every emitted tanh).

Tests. CoreBugFix.TanhStaysSoundForLargeArguments and TensorToScalarDifferentiationTest.TanhOfLargeTraceGradientIsSound pin the fixed behaviour. CoreBugFix.TanhDerivativeDegradesOnlyInTheKnownBand and TanhGradientDegradesOnlyInTheKnownBand sweep −179.25 → −354 in 0.25 steps (0.5 for t2s, whose evaluation is heavier) and assert the degradation is one-sided and bounded by 2×, so it cannot widen unnoticed; the first version of these tests sampled −50 and −200 and straddled the band, which an adversarial review caught.

Negative control (both headers restored from main, rebuilt): all four tanh tests fail — the positive-side ones on the value and derivative, the band ones on the far tail and on the negation-fold case (main returns inf there). The negative-band assertions themselves pass on main, since main is exact there; they are characterisation of this PR's residual, not a demonstration of a main bug, and are labelled as such.

Siblings checked at large and extreme arguments in both signs: sinh, cosh grow consistently to inf; acosh, atanh, log10 exact. asinh has the same class on its negative side (−1e7 → value 0.03 % and derivative 1.5 % wrong; −1e8 → −inf/NaN); a symmetric identity was probed and rejected because it degrades the currently-exact positive side. Filed as #502.

Full suite 2409/2409 in Debug and in Release (gcc-14); clang-format clean.

Follow-up: PR #481's fuzz generators bound hyperbolic arguments to dodge this limitation; the tanh bound can be relaxed to the positive side once this lands, while asinh keeps its bound until #502.