       Why is Timing so irregular? How should I measure efficiency?

• To: mathgroup at smc.vnet.net
• Subject: [mg23364] Why is Timing so irregular? How should I measure efficiency?
• From: Wijnand Schepens <Wijnand.Schepens at rug.ac.be>
• Date: Thu, 4 May 2000 02:59:31 -0400 (EDT)
• Organization: RUG
• Sender: owner-wri-mathgroup at wolfram.com

```Hi everybody,

If I want to compare some functions (or procedures, or programming
constructs, whatever) (which do the same thing) to find out which one is
the fastest, I use Timing.
But if I repeat Timing of the same expression, I get a (totally)
different time (usually much less). Subsequent timing experiments
normally yield the same (low) duration (asumptotic behaviour), but
sometimes the timings are irregular and jumpy.

Why is this?
Are some initialisations necessary?
Is it because Mathematica tries to compile? If so, does Mathematica
remember the compiled form and try it if you redo the same thing?
Does Mathematica store intermediate results?
Has it got to do with memory (page swapping...)?
If I do other things in Windows at the same time, does that affect the
timing?

What is the real duration of some calculation? The one returned by the
first Timing? Or the asymptotic value of multiple timings? Or the mean
value of a few timings excluding the first one?

I see that most people on the newsgroup who want to compare efficiency
of alternative functions do just 1 Timing. Is that the correct thing to
do?
What is the best way of determining the efficiency of a calculation?

Example:

In:=
divpairs2[lst_List] :=
Table[Sequence @@  Table[lst [[{j, i}]], {j, 1, i - 1}], {i, 2,
Length[lst]}]

In:=
testeff[f_, n_] :=
Table[{Timing[f;] // First}, {n}]; SetAttributes[testeff, HoldAll];

In:=
n = 200; t = Table[Random[], {n}];

In:=
testeff[divpairs2[t], 10]

Out=
{{40.92 Second}, {3.84 Second}, {0.82 Second}, {0.88 Second}, {0.83
Second}, \
{0.82 Second}, {0.88 Second}, {0.82 Second}, {0.83 Second}, {0.88
Second}}

The first duration is very long, the second less, and then it drops to a
low value

These are some durations I got on another calculation (10 times the same
calculation!!):
{{9.01 Second}, {111.77 Second}, {76.12 Second}, {62.17 Second}, {38.06
\
Second}, {10.99 Second}, {8.95 Second}, {4.34 Second}, {4.62 Second},
{3.9 \
Second}}
Very strange. Maybe this is due to the fact that this calculation took a
lot of memory and there was a lot of memory-swapping. I don't know.

```

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