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Re: How fast does & perform?

  • To: mathgroup at
  • Subject: [mg107329] Re: How fast does & perform?
  • From: David Bailey <dave at>
  • Date: Tue, 9 Feb 2010 02:46:24 -0500 (EST)
  • References: <hkoic7$t30$>

Canopus56 wrote:
> Setting aside the syntax question of the thread "What does & mean?", there appears to be a performance difference between the two syntax forms. Looks like the := form is faster: 
> data = Table[x, {x, (\[Pi]/8), \[Pi], (\[Pi]/512)}]
> g[x_] := x*Sin[x]
> Timing[Table[g[data[[k]]], {k, 1, Length[data]}]]
> 2.71051*10^-17 seconds
> Timing[Map[g, data]]
> 0. seconds
> Timing[Map[g[#] &, data]] 
> 0.016 seconds
> Timing[Map[#*Sin[#] &, data]]
> 0.031 seconds
> Timing[#*Sin[#] & /@ data]
> 0.032 seconds
> - Kurt 
First, I would say that to do sensible timings, you should choose an 
example that will run for at least 5 seconds.

However, clearly using a pure function is less efficient than one might 
expect. Pure functions are perhaps best thought of as a convenience feature.

Unless a Mathematica program consumes a lot of time, it is usually best 
to use the syntax that best describes what you want to do.

Furthermore, if you do need to improve the performance of your code, it 
is important first to establish which part of a program is in fact 
consuming most of the time - usually only a small part. What I am 
saying, is don't just deprecate one way of doing something in 
Mathematica just because it is not the fastest, because in most 
situations it will not matter.

David Bailey

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