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Did you use a plotting utility to look at the shape of the function?
Did you use a grid search to find candidate staring points?
Did you refine your grid search to get a set of four adjacent
minimum values?
(Refine means closing in on xmin, xmax, ymin, ymax as well as
reducing the step size.)
Given a good candidate staring point, use an available minimization
to find the global minimum value.
To get high accuracy, 100 digits, requires that the function be
evaluated using multiple precision, covered in an earlier lecture.
Typically, if 100 digit accuracy is desired, then all computation
would be performed at 110 digit accuracy. This is slow yet not
difficult for sin(x) and exp(x) for small values of x.
exp(x)=1 + x + x^2/2! + x^3/3! + x^4/4! + ...
For |x|<1 you need the nth term where n! > 10^110
Similarly for sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ...
Obviously, you find a good staring point and find a reasonable
optimization method before going to multiple precision computation.
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