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Re: computing times and output display

  • To: mathgroup at
  • Subject: [mg66955] Re: [mg66923] computing times and output display
  • From: Daniel Lichtblau <danl at>
  • Date: Mon, 5 Jun 2006 03:48:01 -0400 (EDT)
  • References: <>
  • Sender: owner-wri-mathgroup at

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

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