Re: computing times and output display
- To: mathgroup at smc.vnet.net
- Subject: [mg66955] Re: [mg66923] computing times and output display
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Mon, 5 Jun 2006 03:48:01 -0400 (EDT)
- References: <200606040509.BAA13008@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Steven Shippee wrote:
> Running Mathematica version 5.2 on Windows XP Professional with an older
> Pentium III 833MHz processor and 512 GB of RAM.
>
> Anyone know why 8^8^8 (or 9^9^9) takes several minutes to "compute" and
> display results, but in a new fresh kernel/environment 9^9^9. (decimal after
> the last number 9) one gets an almost instantaneous response? Is this
> merely the difference in preparing for the output of the computation to the
> screen ...
>
> Thanks in advance,
>
> Steven Shippee
>
Yes and no, respectively.
8^8^8, being a power of 2, is computed quite fast.
In[1]:= Timing[a=8^8^8;]
Out[1]= {0.004, Null}
Formatting suitable for output involves a hex-to-decimal conversion. One
can see this by writing it to a string.
In[7]:= Timing[as = ToString[a,InputForm];]
Out[7]= {55.6395, Null}
The case of 9^9^9 is slow in both directions. More so for output
preparation because that involves division rather than multiplication by
large numbers.
Working with a numeric approximation is going to be very fast, among
other reasons, because only a few significant digits are maintained.
Daniel Lichtblau
Wolfram Research
- References:
- computing times and output display
- From: "Steven Shippee" <droukas@comcast.net>
- computing times and output display