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M9 performance regression for Fold?

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Hello,

I noticed an over 10x performance drop on Mathematica v9.0.1 compared with v7.01 for this code:

SetSystemOptions["CatchMachineUnderflow" -> False];
AbsoluteTiming@
 Fold[{(#[[1]] Sin[10.5])/(#2 + 1), #[[2]] + Tan[#[[1]]]} &, {Sin[
    10.5], 1.0}, N@Range[10^6]]

I got {0.184287, {0., 0.105747}} on v7, but got {2.311755, {0., 0.105747}} on v9. Note that the Do[...] version of above code needs about 2 seconds. Thus I suspect that on v9 the Fold code is not properly auto-compiled.

Is this a regression? (Also is there a way to see if auto-compile worked or not?)

Thanks!
Yi

PS: To compare, I also tried the following code, where the performance on v7 and v9 are roughly the same (v9 is on average 5% more slowly though).

AbsoluteTiming@Fold[# + Sin[#2] &, 1.0, Range[10^6]]

A difference is that here the first argument of function in Fold is a number, and in the problematic example, the first argument is a list.

PS: I noticed this issuee during a discussion at http://mathematica.stackexchange.com/questions/41103/about-auto-compiling-and-performance-between-do-and-fold

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M9 performance regression for Fold? Yi Wang <tririverwangyi@gmail.com> - 2014-01-28 11:08 +0000

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