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Pure functions vs rule based functions inside NIntegrate


Hello,

As I was told, only pure functions can be compiled. Also, NIntegrate or NDSolve first compiles a function before doing numerical operations. Thus, I would have expected that using pure functions in NIntegrate or NDSolve could be faster than rule based functions.

However, in tests I didn't find such a difference. For example,

f1[x_, y_] := Sin[Sin[x Sin[y]]];
AbsoluteTiming@NIntegrate[f1[x, y], {x, 0, 100}, {y, 0, 100}]

and

f2 = Sin[Sin[#1 Sin[#2]]] &
AbsoluteTiming@NIntegrate[f2[x, y], {x, 0, 100}, {y, 0, 100}]

takes about the same time. How can I tell if both are compiled, or neither, and why?

Thanks!
Yi



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