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I was reading a useful post at WRI blog on improving speed of code , and I need help in understanding this one. Compare these speeds Timing[ tbl = Table[i + j, {i, 1, 1000}, {j, 1, 1000}]; ] {0.031, Null} and Timing[ a = 1000; tbl = Table[i + j, {i, 1, a}, {j, 1, a}]; ] {0.422, Null} So it is much faster when putting the actual value for the limit inside the table itself vs outside. The explanation for this, which I am sure it is correct, but I need help in understanding, is that Table is compiled if its limit are numeric vs. not, this is because its Attributes is HoldAll . But my question is: How would the above actually work, because the limits to Table must, at one point, become numeric anyway? I can't write Clear[a] tbl = Table[i + j, {i, 1, a}, {j, 1, a}] The above gives an error. So, for me, writing a=1000 outside Table vs. inside, should have made no difference, since without a having a numerical value, Table[] can't do anything. So the replacing of a by the number 1000 must occur at one point of time by evaluator before Table[] can do anything useful, would it not? In other words, what Table should see, eventually, is {i, 1, 1000}, {j, 1, 1000} in both cases. So, the way I thought this would happen is this: Evaluator replaces a by 1000 in the arguments of table Evaluator calls Table with the result, which is now all numeric. Table Compiles, and runs faster now. But what seems to happen is something else. (due to HoldAll ?) Table takes its arguments, a

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