I have tried both Derive 6.10 under Windows and 4.11 under DOS. Both fail.
I am trying to solve:
sinh(x) = 2^-16382
That gives weird results.
So, take a two term Taylor series of sinh(x) and try to solve that:
x^3/6+x=2^(-16382)
I aborted it after a few minutes.
Now, try taking asinh() of both sides and approximate that:
asinh(2^(-16382))
I aborted it after a few minutes.
So, take a two term Taylor series of asinh(x), getting:
x-x^3/6
and substitute 2^-16382 for x getting:
2^(-16382)-(2^(-16382))^3/6
Now, approximate that and we get a negative value (when it should be 2^-16382,
unless precision is greater than about 4932 digits). Actually, Derive 4.11
gets this last part correct.
Suggestions?
Here is a saved mth file of what I did:
SINH(x)=2^(-16382)
;Solve(#1,x)
APPROX(SOLVE(SINH(x)=2^(-16382),x,Real))
;Simp(Solve(#1,x))
x=inf OR x=0
SINH(x)
;Taylor(#4,x)
TAYLOR(SINH(x),x,0,3)
;Simp(Taylor(#4,x))
x^3/6+x
x^3/6+x=2^(-16382)
;Solve(#7,x)
APPROX(SOLVE(x^3/6+x=2^(-16382),x,Real))
ASINH(2^(-16382))
ASINH(x)
;Taylor(#10,x)
TAYLOR(ASINH(x),x,0,3)
;Simp(Taylor(#10,x))
x-x^3/6
;Sub(#12)
2^(-16382)-(2^(-16382))^3/6
;Approx(#13)
-6.334055188*10^(-1.4796*10^4)
;Approx(#13)
-6.33405525478398227448680315211021631619558599986975956120092730820865273771~
2858556814759621258195555*10^(-1.4796*10^4)
---
Fred J. Tydeman Tydeman Consulting
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+1 (775) 287-5904 Vice-chair of PL22.11 (ANSI "C")
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