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Science Forum Index » Math - Symbolic Forum » An exact simplification challenge - 14
Page 1 of 1
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| Author |
Message |
| Vladimir Bondarenko |
 Posted: Sun Apr 29, 2007 5:54 am |
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Guest
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Oh you brave computer algebra warriors,
Needless to speak that again, neither Maple nor Mathematica
nor MuPAD nor Derive is able to simplify this expression
directly... within a reasonable span of Core 2 duo time...
Is there a simplification field marshal who can come up with
and implement a war scenario, in terms of a CAS commands to
defeat the enemy and savour the victory of the exact answer?
Best wishes,
Vladimir Bondarenko
VM and GEMM architect
Co-founder, CEO, Mathematical Director
http://www.cybertester.com/ Cyber Tester, LLC
http://maple.bug-list.org/ Maple Bugs Encyclopaedia
http://www.CAS-testing.org/ CAS Testing
.............................................................
cos(- 1/4*2^(3/4)*arctan(1/cos(2^(1/2)*(- 1/2*arctan(1/cos(\
2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*\
sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^\
(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 \
+ 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) \
+ 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(\
1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2)\
*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) +\
1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*\
(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))^2)))^2*exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln\
(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2))) + exp(-2^(1/2)*(arctan(1/cos(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln\
(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)\
^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/\
2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2)\
+ 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(\
2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))^2)))^2)))*sin(2^(1/2)*(- 1/2*arctan(1/cos(2^(1/2)*(1\
/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/\
2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/\
2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arct\
an(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2\
))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/\
2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^\
2*exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2\
*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))^2))) + exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*si\
n(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*ar\
ctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(\
1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))\
)^2))))*(2^(1/2) + 2)^(1/2) - 1/8*2^(3/4)*ln(exp(2*2^(1/2)*\
(1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1\
/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2\
) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(\
1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/\
2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*\
cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) \
+ 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + \
1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2)))^2*exp(-2^(1/2)*(arctan(1/cos(ln\
(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(\
1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + exp(-2^(1\
/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + \
1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(\
1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln\
(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))*cos(2^(1/2)*(- 1/2*arcta\
n(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)\
^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2\
*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(\
1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/\
2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos\
(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
+ 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2)))^2*exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) \
- 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(\
1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + exp(-2^(1/2)*(arcta\
n(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(\
1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2)\
)*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2\
) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*s\
in(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2\
*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))^2)))^2)))^2 + exp(2*2^(1/2)*(1/2*arctan(1/co\
s(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*\
2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^\
2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) \
- 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*si\
n(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/\
2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2)\
+ 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(\
2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))^2)))^2*exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*\
ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))^2))) + exp(-2^(1/2)*(arctan(1/co\
s(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/\
2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(\
1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/\
2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2)))^2)))*sin(2^(1/2)*(- 1/2*arctan(1/cos(2^(1/2)*\
(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + \
1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(\
1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln\
(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*ar\
ctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(\
1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))\
)^2*exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1\
/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/\
2) - 1/2)^(1/2))^2))) + exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*\
sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*\
arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/\
2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^\
(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
)))^2)))^2)*(- 2^(1/2) + 2)^(1/2))*exp(1/8*2^(3/4)*ln(exp(2\
*2^(1/2)*(1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2)\
)*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/\
2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(\
1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2\
)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2\
*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) +\
1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*exp(-2^(1/2)*(arctan\
(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))\
*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2)\
+ 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + \
exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
+ 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)))\
+ 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))*cos(2^(1/2)*(- \
1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/\
2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/\
4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1\
/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2\
) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*c\
os(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) +\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1\
/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/\
2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^\
(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)\
^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))^2)))^2*exp(-2^(1/2)*(arctan(1/cos(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)\
^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)\
*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + exp(-2^(1/\
2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)\
*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1\
/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1\
/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(\
2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/\
2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/\
2*2^(1/2) - 1/2)^(1/2))^2)))^2)))^2 + exp(2*2^(1/2)*(1/2*ar\
ctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/\
2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^\
(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(\
cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/\
2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2\
) - 1/2)^(1/2))^2)))^2*exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/\
2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*s\
in(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + exp(-2^(1/2)*(ar\
ctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(\
1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))\
)*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(\
1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(\
1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))^2)))^2)))*sin(2^(1/2)*(- 1/2*arctan(1/cos\
(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
+ 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)))\
+ 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2\
)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln\
(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) \
+ 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2\
*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(\
1/2))^2)))^2*exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) \
- 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*l\
n(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(\
1/2*2^(1/2) - 1/2)^(1/2))^2))) + exp(-2^(1/2)*(arctan(1/cos\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2\
)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1\
/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2\
) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^\
(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)\
^(1/2))^2)))^2)))^2)*(2^(1/2) + 2)^(1/2) - 1/4*2^(3/4)*arct\
an(1/cos(2^(1/2)*(- 1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/\
cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*co\
s(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + \
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2\
^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*s\
in(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(\
1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 +\
2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)\
^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)\
*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*exp(-2^(1/\
2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)\
*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1\
/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1\
/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))^2))) + exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/\
2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^\
(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))*sin(2\
^(1/2)*(- 1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2)\
)*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/\
2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(\
1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2\
)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2\
*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) +\
1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*exp(-2^(1/2)*(arctan\
(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))\
*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2)\
+ 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + \
exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
+ 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)))\
+ 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2))))*(- 2^(1/2) + 2\
)^(1/2)) + (sin(- 1/4*2^(3/4)*arctan(1/cos(2^(1/2)*(- 1/2*a\
rctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(\
2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/\
2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/\
2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln\
(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)\
^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln\
(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1\
/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/\
2) - 1/2)^(1/2))^2)))^2*exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*\
sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + exp(-2^(1/2)*(a\
rctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(\
1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^\
(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)\
))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*\
(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(\
1/2) - 1/2)^(1/2))^2)))^2)))*sin(2^(1/2)*(- 1/2*arctan(1/co\
s(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*\
2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^\
2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) \
- 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*si\
n(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/\
2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2)\
+ 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(\
2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))^2)))^2*exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*\
ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))^2))) + exp(-2^(1/2)*(arctan(1/co\
s(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/\
2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(\
1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/\
2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2)))^2))))*(2^(1/2) + 2)^(1/2) - 1/8*2^(3/4)*ln(ex\
p(2*2^(1/2)*(1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)\
^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)\
*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*\
(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + \
1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(\
1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*si\
n(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*exp(-2^(1/2)*(arc\
tan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/\
2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1\
/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))\
+ exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/\
2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2\
) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*\
sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))*cos(2^(1/2)*\
(- 1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) +\
1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arcta\
n(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(\
1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2)\
)*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2\
) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) \
+ 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln\
(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2)))^2*exp(-2^(1/2)*(arctan(1/cos(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln\
(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)\
^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + exp(-2^\
(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln\
(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) \
+ 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2\
*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(\
1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*\
ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))^2 + exp(2*2^(1/2)*(1/2\
*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) \
- 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*l\
n(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(\
1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/co\
s(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/\
2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*\
ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*\
(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(\
1/2) - 1/2)^(1/2))^2)))^2*exp(-2^(1/2)*(arctan(1/cos(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2)\
)*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + exp(-2^(1/2)*\
(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)\
^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*\
2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^\
2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(\
2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))^2)))^2)))*sin(2^(1/2)*(- 1/2*arctan(1/\
cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/\
2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2\
) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*\
sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(\
1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/\
2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2)))^2*exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/\
2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/\
2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + exp(-2^(1/2)*(arctan(1/\
cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*co\
s(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + \
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2\
^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*s\
in(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(\
1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 +\
2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2)))^2)))^2)*(- 2^(1/2) + 2)^(1/2))*exp(1/8*2^(3\
/4)*ln(exp(2*2^(1/2)*(1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(\
1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/\
2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*\
cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) \
+ 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin\
(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
+ 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/\
2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^\
(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*exp(-2^(\
1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) +\
1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*\
(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))^2))) + exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln\
(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2\
)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))*cos\
(2^(1/2)*(- 1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/\
2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(\
1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)\
*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1\
/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1\
/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)))\
+ 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*exp(-2^(1/2)*(arct\
an(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2\
))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/\
2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) \
+ exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2\
*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/\
2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*s\
in(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))^2 + exp(2*2^(\
1/2)*(1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*si\
n(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*ar\
ctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(\
1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))\
)) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2\
) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4\
*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) \
- 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)\
*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*exp(-2^(1/2)*(arctan(1/c\
os(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) \
- 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1\
/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + exp(\
-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/\
2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1\
/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2\
) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))*sin(2^(1/2)*(- 1/2*\
arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln\
(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2\
)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*l\
n(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(\
1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(\
1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))^2)))^2*exp(-2^(1/2)*(arctan(1/cos(ln(2)*(\
1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/\
2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))\
*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + exp(-2^(1/2)*(\
arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/\
2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^\
(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)\
^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2\
*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(\
1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))^2)))^2)))^2)*(2^(1/2) + 2)^(1/2) - 1/4*\
2^(3/4)*arctan(1/cos(2^(1/2)*(- 1/2*arctan(1/cos(2^(1/2)*(1\
/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/\
2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/\
2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arct\
an(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2\
))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/\
2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^\
2*exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2\
*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))^2))) + exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*si\
n(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*ar\
ctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(\
1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))\
)^2)))*sin(2^(1/2)*(- 1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(\
1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/\
2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*\
cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) \
+ 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin\
(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
+ 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/\
2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^\
(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*exp(-2^(\
1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) +\
1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*\
(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))^2))) + exp(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln\
(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2\
)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2))))*(-\
2^(1/2) + 2)^(1/2)))*I:
Spare no bullets. Take no prisoners. Onward!
............................................................. |
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|
| Peter L. Montgomery |
| Posted: Sun Apr 29, 2007 4:11 pm |
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Guest
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In article <1177844064.692576.60700@y80g2000hsf.googlegroups.com>
Vladimir Bondarenko <vb@cybertester.com> writes:
Quote: Oh you brave computer algebra warriors,
Needless to speak that again, neither Maple nor Mathematica
nor MuPAD nor Derive is able to simplify this expression
directly... within a reasonable span of Core 2 duo time...
Is there a simplification field marshal who can come up with
and implement a war scenario, in terms of a CAS commands to
defeat the enemy and savour the victory of the exact answer?
I manually replaced each exp by EXP in the big expression,
going back to exp later. It took 253 seconds
on a 2162 MHz Athlon XP 2700+ for Maple 10
to simplify the expression to 2.
f :=
cos(- 1/4*2^(3/4)*arctan(1/cos(2^(1/2)*(- 1/2*arctan(1/cos(\
2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*\
sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^\
(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 \
+ 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) \
+ 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(\
1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2)\
*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) +\
1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*\
(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))^2)))^2*EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln\
(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2))) + EXP(-2^(1/2)*(arctan(1/cos(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln\
(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)\
^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/\
2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2)\
+ 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(\
2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))^2)))^2)))*sin(2^(1/2)*(- 1/2*arctan(1/cos(2^(1/2)*(1\
/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/\
2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/\
2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arct\
an(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2\
))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/\
2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^\
2*EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2\
*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))^2))) + EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*si\
n(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*ar\
ctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(\
1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))\
)^2))))*(2^(1/2) + 2)^(1/2) - 1/8*2^(3/4)*ln(EXP(2*2^(1/2)*\
(1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1\
/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2\
) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(\
1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/\
2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*\
cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) \
+ 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + \
1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2)))^2*EXP(-2^(1/2)*(arctan(1/cos(ln\
(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(\
1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + EXP(-2^(1\
/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + \
1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(\
1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln\
(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))*cos(2^(1/2)*(- 1/2*arcta\
n(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)\
^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2\
*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(\
1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/\
2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos\
(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
+ 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2)))^2*EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) \
- 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(\
1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + EXP(-2^(1/2)*(arcta\
n(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(\
1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2)\
)*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2\
) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*s\
in(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2\
*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))^2)))^2)))^2 + EXP(2*2^(1/2)*(1/2*arctan(1/co\
s(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*\
2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^\
2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) \
- 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*si\
n(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/\
2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2)\
+ 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(\
2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))^2)))^2*EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*\
ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))^2))) + EXP(-2^(1/2)*(arctan(1/co\
s(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/\
2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(\
1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/\
2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2)))^2)))*sin(2^(1/2)*(- 1/2*arctan(1/cos(2^(1/2)*\
(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + \
1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(\
1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln\
(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*ar\
ctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(\
1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))\
)^2*EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1\
/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/\
2) - 1/2)^(1/2))^2))) + EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*\
sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*\
arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/\
2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^\
(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
)))^2)))^2)*(- 2^(1/2) + 2)^(1/2))*EXP(1/8*2^(3/4)*ln(EXP(2\
*2^(1/2)*(1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2)\
)*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/\
2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(\
1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2\
)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2\
*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) +\
1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*EXP(-2^(1/2)*(arctan\
(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))\
*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2)\
+ 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + \
EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
+ 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)))\
+ 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))*cos(2^(1/2)*(- \
1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/\
2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/\
4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1\
/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2\
) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*c\
os(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) +\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1\
/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/\
2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^\
(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)\
^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))^2)))^2*EXP(-2^(1/2)*(arctan(1/cos(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)\
^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)\
*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + EXP(-2^(1/\
2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)\
*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1\
/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1\
/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(\
2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/\
2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/\
2*2^(1/2) - 1/2)^(1/2))^2)))^2)))^2 + EXP(2*2^(1/2)*(1/2*ar\
ctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/\
2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^\
(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(\
cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/\
2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2\
) - 1/2)^(1/2))^2)))^2*EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/\
2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*s\
in(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + EXP(-2^(1/2)*(ar\
ctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(\
1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))\
)*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(\
1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(\
1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))^2)))^2)))*sin(2^(1/2)*(- 1/2*arctan(1/cos\
(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
+ 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)))\
+ 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2\
)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln\
(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) \
+ 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2\
*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(\
1/2))^2)))^2*EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) \
- 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*l\
n(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(\
1/2*2^(1/2) - 1/2)^(1/2))^2))) + EXP(-2^(1/2)*(arctan(1/cos\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2\
)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1\
/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2\
) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^\
(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)\
^(1/2))^2)))^2)))^2)*(2^(1/2) + 2)^(1/2) - 1/4*2^(3/4)*arct\
an(1/cos(2^(1/2)*(- 1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/\
cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*co\
s(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + \
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2\
^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*s\
in(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(\
1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 +\
2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)\
^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)\
*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*EXP(-2^(1/\
2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)\
*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1\
/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1\
/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))^2))) + EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/\
2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^\
(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))*sin(2\
^(1/2)*(- 1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2)\
)*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/\
2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(\
1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2\
)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2\
*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) +\
1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*EXP(-2^(1/2)*(arctan\
(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))\
*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2)\
+ 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + \
EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
+ 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)))\
+ 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2))))*(- 2^(1/2) + 2\
)^(1/2)) + (sin(- 1/4*2^(3/4)*arctan(1/cos(2^(1/2)*(- 1/2*a\
rctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(\
2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/\
2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/\
2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln\
(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)\
^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln\
(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1\
/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/\
2) - 1/2)^(1/2))^2)))^2*EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*\
sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + EXP(-2^(1/2)*(a\
rctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(\
1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^\
(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)\
))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*\
(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(\
1/2) - 1/2)^(1/2))^2)))^2)))*sin(2^(1/2)*(- 1/2*arctan(1/co\
s(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*\
2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^\
2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) \
- 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*si\
n(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/\
2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2)\
+ 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(\
2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))^2)))^2*EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*\
ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))^2))) + EXP(-2^(1/2)*(arctan(1/co\
s(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/\
2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(\
1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/\
2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2)))^2))))*(2^(1/2) + 2)^(1/2) - 1/8*2^(3/4)*ln(ex\
p(2*2^(1/2)*(1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)\
^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)\
*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*\
(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + \
1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(\
1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*si\
n(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*EXP(-2^(1/2)*(arc\
tan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/\
2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1\
/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))\
+ EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/\
2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2\
) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*\
sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))*cos(2^(1/2)*\
(- 1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) +\
1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arcta\
n(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(\
1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2)\
)*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2\
) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) \
+ 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln\
(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2)))^2*EXP(-2^(1/2)*(arctan(1/cos(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln\
(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)\
^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + EXP(-2^\
(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln\
(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) \
+ 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2\
*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(\
1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*\
ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))^2 + EXP(2*2^(1/2)*(1/2\
*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) \
- 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*l\
n(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(\
1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/co\
s(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(\
ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/\
2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*\
ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*\
(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(\
1/2) - 1/2)^(1/2))^2)))^2*EXP(-2^(1/2)*(arctan(1/cos(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2)\
)*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + EXP(-2^(1/2)*\
(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)\
^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*\
2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^\
2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(\
2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))^2)))^2)))*sin(2^(1/2)*(- 1/2*arctan(1/\
cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/\
2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2\
) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*\
sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(\
1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/\
2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2)))^2*EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/\
2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/\
2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + EXP(-2^(1/2)*(arctan(1/\
cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*co\
s(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + \
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2\
^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*s\
in(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(\
1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 +\
2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2)))^2)))^2)*(- 2^(1/2) + 2)^(1/2))*EXP(1/8*2^(3\
/4)*ln(EXP(2*2^(1/2)*(1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(\
1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/\
2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*\
cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) \
+ 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin\
(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
+ 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/\
2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^\
(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*EXP(-2^(\
1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) +\
1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*\
(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))^2))) + EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln\
(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2\
)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))*cos\
(2^(1/2)*(- 1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2\
)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^\
(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/\
2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(\
1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)\
*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1\
/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1\
/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)))\
+ 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*EXP(-2^(1/2)*(arct\
an(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2\
))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/\
2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) \
+ EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2\
*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/\
2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*s\
in(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))^2 + EXP(2*2^(\
1/2)*(1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*si\
n(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*ar\
ctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(\
1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))\
)) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2\
) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4\
*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) \
- 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)\
*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*EXP(-2^(1/2)*(arctan(1/c\
os(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) \
- 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1\
/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + EXP(\
-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/\
2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1\
/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2\
) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2)))*sin(2^(1/2)*(- 1/2*\
arctan(1/cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln\
(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2\
)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*l\
n(cos(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(\
1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(\
1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1\
/2) - 1/2)^(1/2))^2)))^2*EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(\
1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/\
2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/\
2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))\
*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))) + EXP(-2^(1/2)*(\
arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/\
2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^\
(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)\
^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2\
*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(\
1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))^2)))^2)))^2)*(2^(1/2) + 2)^(1/2) - 1/4*\
2^(3/4)*arctan(1/cos(2^(1/2)*(- 1/2*arctan(1/cos(2^(1/2)*(1\
/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*\
(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/\
2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/\
2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2)\
)^2)))*sin(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2\
^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2\
)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arct\
an(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^\
(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2\
))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/\
2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^\
2*EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2\
))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2\
*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2)\
- 1/2)^(1/2))^2))) + EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2\
*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
) - 1/2*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2\
^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*si\
n(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*ar\
ctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*\
2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1\
/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(\
1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2))\
)^2)))*sin(2^(1/2)*(- 1/2*arctan(1/cos(2^(1/2)*(1/2*arctan(\
1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/\
2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*\
cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) \
+ 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))*sin\
(2^(1/2)*(1/2*arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))\
*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2\
^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2\
+ 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))^2)))) + 1/4*ln(cos(2^(1/2)*(1/2*arctan(1/cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/\
2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^\
(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2*EXP(-2^(\
1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(\
2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln(2^(2*(1/2*2^(1/2) +\
1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*\
(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1\
/2))^2))) + EXP(-2^(1/2)*(arctan(1/cos(ln(2)*(1/2*2^(1/2) -\
1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))) - 1/2*ln\
(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(ln(2)*(1/2*2^(1/2) - 1\
/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*sin(ln(2)*(1\
/2*2^(1/2) - 1/2)^(1/2))^2)))*sin(2^(1/2)*(1/2*arctan(1/cos\
(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - \
1/2)^(1/2))) + 1/4*ln(2^(2*(1/2*2^(1/2) + 1/2)^(1/2))*cos(l\
n(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2 + 2^(2*(1/2*2^(1/2) + 1/2\
)^(1/2))*sin(ln(2)*(1/2*2^(1/2) - 1/2)^(1/2))^2)))^2))))*(-\
2^(1/2) + 2)^(1/2)))*I:
f1 := simplify(f); # Simplify sin(x)^2 + cos(x)^2 and other stuff
f2 := simplify(convert(f1, tan)); # Simplify arctan(sin(x) / cos(x))
f3 := radnormal(eval(f2, EXP=exp));
f4 := simplify(expand(f3));
f5 := simplify(convert(combine(f4), tan)); # 2
--
44 months after Japan attacked Pearl Harbor, Japan surrendered.
49 months after US attacked Iraq, it's time for the US to surrender.
pmontgom@cwi.nl Microsoft Research and CWI Home: Bellevue, WA |
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| Thomas Mautsch |
| Posted: Sun Apr 29, 2007 6:12 pm |
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Guest
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In news:<1177844064.692576.60700@y80g2000hsf.googlegroups.com>
schrieb Vladimir Bondarenko <vb@cybertester.com>:
Quote: Needless to speak that again, neither Maple nor Mathematica
nor MuPAD nor Derive is able to simplify this expression
directly... within a reasonable span of Core 2 duo time...
[ ... 600+ lines formula deleted ... ]
I don't know how much I would trust Maple
with the results of the first two
of the following simplification steps, but at least
the result of the code, which is 2,
agrees with the numerical
print( evalf[50](%) );
combine(%);
convert(%,tan);
simplify(%);
2^simplify(log[2](%)); |
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| CW |
| Posted: Sat May 05, 2007 1:29 am |
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Guest
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It should be noted that this code produces the expression given :
P1 := proc()
local x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15,
x16, x17, x18, x19, x20, x21, x22, x23, x24;
x1 := 2^(1/4);
x2 := x1^2;
x3 := 1/2*x2;
x4 := 1/x3;
x5 := ln(2)*(x3 - 1/2)^(1/2);
x6 := sin(x5);
x7 := cos(x5);
x8 := arctan(x6/x7);
x9 := ln((x7^2 + x6^2)*2^(2*(x3 + 1/2)^(1/2)));
x10 := x4*(1/2*x8 + 1/4*x9);
x11 := cos(x10);
x12 := sin(x10);
x13 := 1/4*ln((x11^2 + x12^2)*exp(- x4*(x8 - 1/2*x9)));
x14 := arctan(x12/x11);
x15 := x4*(- 1/2*x14 + x13);
x16 := cos(x15);
x17 := sin(x15);
x18 := - 1/4*arctan(x17/x16);
x19 := x1*x2;
x20 := (-x4 + 2)^(1/2);
x21 := (x4 + 2)^(1/2);
x22 := ln((x16^2 + x17^2)*exp(2*x4*(1/2*x14 + x13)));
x23 := (x21*x18 - 1/8*x22*x20)*x19;
x24 := (cos(x23) + I*sin(x23))*exp((1/8*x22*x21 + x20*x18)*x19)
end;
P1():
or
P2 := proc()
local x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15,
x16, x17, x18, x19, x20, x21, x22, x23, x24;
x1 := 2^(1/4);
x2 := x1^2;
x3 := 1/2*x2;
x4 := (2 + 2*x2)^(1/2);
x5 := x2 + 1;
x6 := 1/2*ln(2)*(-x4 + 2*x5^(1/2));
x7 := cos(x6);
x8 := sin(x6);
x9 := ln((x7^2 + x8^2)*2^x4);
x10 := arctan(x8/x7);
x11 := 1/4*x2*(2*x10 + x9);
x12 := cos(x11);
x13 := sin(x11);
x14 := 1/2*ln((x13^2 + x12^2)*exp((-2*x10 + x9)*x3));
x15 := arctan(x13/x12);
x16 := (-x15 + x14)*x3;
x17 := cos(x16);
x18 := sin(x16);
x19 := arctan(x18/x17);
x20 := ln((x18^2 + x17^2)*exp(x2*(x15 + x14))) + 2*x19;
x21 := x2*x19;
x22 := 1/8*(-2*x2 + 4)^(1/2)*x1;
x23 := (2*x21 + x20)*x22;
x24 := exp(x5*(-2*x21 + x20)*x22)*(cos(x23) - I*sin(x23))
end:
P2();
Simplify the trigs and arctrigs to obtain :
A:=exp(-1/8*ln(2)*(-2*2^(1/2)+4)^(1/2)*2^(1/4)*(-2*I*2^(1/2)*(2^(1/2)+1)^(1/2)+I*2^(1/2)*(2+2*2^(1/2))^(1/2)-2^(1/2)*(2+2*2^(1/2))^(1/2)-2*(2^(1/2)+1)^(1/2)-2*I*(2^(1/2)+1)^(1/2)+2*I*(2+2*2^(1/2))^(1/2)));
(eval@applyop)(radnormal,1,A);
2
Chris |
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