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The derivative of an answer at a large hyperbolic argument evaluates to NaN or loses its imaginary part

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Bewertung

Schwierigkeit
4/5
Geschätzter Aufwand
3-5 Tage
Anfängerfreundlichkeit
43/100
Issue-Typ
Bug
Klarheit
Größtenteils klar
Aktivitätsstatus
Aktiv
Tech-Stack
csharp
Bereich
backend

Rechercherichtung

Start by reproducing the derivative evaluation with the exact parameters and x from the issue, comparing it with the integrand at 50, 300, and 2000 digits. Trace the derivative evaluation path and identify which subexpression causes NaN or loses the imaginary component; the issue does not name a file or test. Done means the derivative agrees with the integrand at the reported large argument and at x = 2 across those precisions.

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Beschreibung

Found while checking Rubi 6.1.5, row 94 (1/sqrt(a + i a sinh(c + d x))) for 2.6.0. The answer is right. The library's own numerical evaluation of its derivative is not, at large arguments.

With a, c, d = 21/10, 19/10, 17/10 and x = 227283/1250 (so t = c + d x ≈ 311), the true value of the derivative is r(1 − i) with r ≈ 2.0185e-68. That is what mpmath gives at dps 400, and what the library gives when it evaluates the integrand itself.

The derivative of the answer, Differentiate(x) then substituted with exact rationals and evaluated, gives:

digits value
50 NaN
300 1.5329…, which is wrong in magnitude too
2000 2.0185…e-68: the real part is right and the imaginary part −2.0185…e-68 i is missing

The relative difference at 2000 digits is exactly −1/2 + i/2. At x = 2 all three precisions agree with the integrand to the last digit.

The derivative holds e^(±t/2) and e^(±t) beside a + i a sinh(t), so large cancellations are expected. Losing a whole component at 2000 digits is not explained by that, though, and NaN at 50 digits should have been "could not evaluate". I have not narrowed it to a single subexpression.

Because of this, the Rubi harness reports this row as wrong, and anything that checks an answer by evaluating would do the same.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

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C#
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Gemergte PRs (30 T.)
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Entwicklungsumgebung

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  4. Öffnen Sie einen Pull Request, der die Issue-Nummer nennt.

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