Timing comparison for diffeq program in c++, Maple and Maxima

How, given the diffeq below, do you generate a Taylor series in 
Maxima?

diff ( y , x , 1 ) = tan(sqrt(2.0*x + 3.0));or better, the system:
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;
Dennis J. Darland

dennis.darland at yahoo.com

http://dennisdarland.com/

http://dennisdarland.com/dennisdaze/

http://dennisdarland.com/philosophy/

http://sode.sourceforge.net/

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-- Peter Singer _Practical Ethics, Third Edition_, p. 216.

--- On Thu, 8/9/12, Richard Fateman <fateman at eecs.berkeley.edu> wrote:

From: Richard Fateman <fateman at eecs.berkeley.edu>
Subject: Re: [Maxima] Timing comparison for diffeq program in c++, Maple and Maxima
To: maxima at math.utexas.edu
Cc: "Rupert Swarbrick" <rswarbrick at gmail.com>
Date: Thursday, August 9, 2012, 9:09 AM


  

    
  
  
    On 8/9/2012 5:32 AM, Rupert Swarbrick
      wrote:

    
    
      Dennis Darland <dennis.darland at yahoo.com> writes:

      
        I ran a timing test comparison for c++, Maple and Maxima.
All three programs generated by omnisode - a set of Ruby programs.
Set time limit to 1 minute.
Maximum iteration was sufficient to solve entire problem.
Problem was sin.ode for all three.
Output was redirected to file only - none to screen
Results:
c++ solved entire problem in 23 seconds (140001 iterations)
Maple performed 11542 iterations in 60 seconds
Maxima performed 372 iterations in 60 seconds
That amounts to:
c++ 6,087 iterations/second
Maple 192 iterations/second
Maxima 6.2 iterations/second
c++ is almost 32 times faster than Maple which is almost 31 times faster than Maxima.
So c++ is almost 982 times faster than Maxima.

More info on omnisode at:
http://sode.sourceforge.net/

      
      Right, I just tried to look up the Maxima code you're generating and
found things like [1]. Since I'm clearly not going to read through that
carefully, and I presume no-one else is either, can you explain exactly
what you're measuring?

Your code looks to me like a C/FORTRAN program translated to
Maxima. Unsurprisingly, it runs very slowly. What are you actually
trying to do? What capabilities of Maple or Maxima are you using other
than basic arithmetic?

Or should we interpret your message as

  "Writing bare-metal calculations in Maple and running them is
   marginally less slow that writing them in Maxima and running
   them. But it would have been easier to do it in C anyway"

 ?
    
    

    I spent 1 minute looking at the code in [1] ... It seems to me that
    if you are computing Taylor

    series you should use the Taylor series command and not write
    something in what looks

    like C.? Etc.? So you are using these enormously powerful programs
    to simulate very

    low level operations, as Rubert says.? So you should use C.? And if
    you want it to run

    faster, consider generating assembler.

    

    (You can make Maxima run faster by adding declarations and
    compiling, but that will

    probably make it no more than about 100X faster.)

    
      

Rupert

[1] http://sode.sourceforge.net/omniresults/special_cases_007/diffeq.tan_sqrt_lin.mxt.txt

      

      
      

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