Print cos(2π/17) exactly One way to construct a regular heptadecagon starts with drawing a horizontal line of length 1 from the center to a vertex. Then the distance along that line from the center to the second vertex is cos(2π/17). All other vertices are easy to get.

The goal of this challenge is to print (or produce in any other conventional way) an ASCII math expression involving the operations +, -, *, /, sqrt() and the natural numbers, which gives cos(2π/17) when evaluated. The power operator is not allowed: e.g. sqrt(17) cannot be written as 17^(1/2).

For example (formula taken from Wikipedia):

1/16*(
    -1+
    sqrt(17)+
    sqrt(34-2*sqrt(17))+
    2*sqrt(
        17+
        3*sqrt(17)-
        sqrt(34-2*sqrt(17))-
        2*sqrt(34+2*sqrt(17))
    )
)


Whitespace doesn't matter. The length and complexity of the expression doesn't matter, as long as it's syntactically correct (as defined above) and numerically equivalent to cos(2π/17).

Built-in functions are allowed.
CJam (60 bytes)

1-4{"(- +sqrt( * -4*
))/2"S/@a*N/\a*}:F~'-\+WF'-\+W-4FWFF'/2


Online demo

Output (with added newlines to avoid wrapping):

(--(--(-1+sqrt(1*1-4*-4))/2+sqrt(-(-1+sqrt(1*1-4*-4))/2*-(-1+sqrt(1*1-4*-4))/2-4*-1)
)/2+sqrt(-(--(-1+sqrt(1*1-4*-4))/2+sqrt(-(-1+sqrt(1*1-4*-4))/2*-(-1+sqrt(1*1-4*-4))/
2-4*-1))/2*-(--(-1+sqrt(1*1-4*-4))/2+sqrt(-(-1+sqrt(1*1-4*-4))/2*-(-1+sqrt(1*1-4*-4)
)/2-4*-1))/2-4*(-(--1+sqrt(-1*-1-4*-4))/2+sqrt((--1+sqrt(-1*-1-4*-4))/2*(--1+sqrt(-1
*-1-4*-4))/2-4*-1))/2))/2/2


I suspect this is the kind of answer OP was secretly hoping for. Rather than apply general-purpose compression to a string, it uses the field structure which Gauss first exploited to present this value in surds, in his Disquisitiones Arithmeticae.

I worked from this presentation (pages 18 and 19) but adapted it slightly in order to only ever require the positive root of a quadratic. Unrolled and in pseudo-code, the expression breaks down as

# Positive root of x^2 + bx + c = 0
F(b, c) = (-b + sqrt(b*b - 4*c))/2
# (8,1)
p = F(1, -4)
# (4,1)
q = F(-p, -1)
# -(8,3)
r = F(-1, -4)
# (4,3)
s = F(r, -1)
# Result
F(-q, s)/2