Why is there a huge performance gap using Map with more than 100 List entries

Question

im using Map on a List like this:

cube= {{1, 1, 1}, {1, 1, 2}, {1, 1, 3}, {1, 1, 4}, ... , {5, 5, 4}, {5, 5, 5}}

Mapping the whole List with 125 entries takes like 2.5s.

AbsoluteTiming[
 Map[Apply[d[[#1, #2, #3]] &, #] &, cube];
 ]

{2.552146, Null}

Mapping in two sublists with less than 100 entries the whole thing takes nearly no time.

 AbsoluteTiming[
     Join[
       Map[Apply[d[[#1, #2, #3]] &, #] &, cube[[1 ;; 99]]],
       Map[Apply[d[[#1, #2, #3]] &, #] &, cube[[100 ;; 125]]]
       ];

 ]

{0., Null}

Why is there a huge performance gap? An how do I avoid it except splitting my list?

Answer 1

If you look at SystemOptions[], like so,

Column[
 OpenerView /@
  (Replace[SystemOptions[], Rule[x_, y_] -> List[x, y],
     1])
 ]

you see that under CompileOptions, if you click on the triangle to open it,

there is an option "MapCompileLength" -> 100. Set it to eg 10 and see it it helps (do SetSystemOptions["CompileOptions" -> {"MapCompileLength" -> 10}]).

This option determines the length of the list above which Mathematica (tries to) compile the function to be mapped.

EDIT: Example:

Here's some data:

Length[cube = Tuples[Range[10], 4]]

And here's a function which is a) inefficient on purpose, b) designed to be compilable as-is (that's why I localise s, so that Compile will work).

d = (Module[{s = 0}, Do[s = s + #[[i]]^2, {i, Length@#}];s] &)

Now, set the auto-compilation length for Map to 100 (the default):

SetSystemOptions["CompileOptions" -> {"MapCompileLength" -> 100}]

and now test:

Needs["GeneralUtilities`"]
Quiet@BenchmarkPlot[d /@ # &, cube[[1 ;; #]] &, Range[90, 110]]