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Question: Why is this function evaluation so slow?

Question:Why is this function evaluation so slow?

steweb 35 Maple
performance
August 28 2011
2

Consider a function f depending on a parameter k and a variable y

f:=(k,y)->k*s(y);

where s:=y->add(sin(1/y^i),i=1..1000000) is just some nasty function.

Now, why does it take a long time to evaluate f(0,y)? And how could I speed this up?

 

More generally, I would like to plug (varying) parameters into a function, simplify and then do analysis on the resulting function. How could I do that?
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