[Jprogramming] arithmetic sequence

[Bo Jacoby]

Hi Skip Cave

Note that the closed form solution doesn't have to compute the intermediate values.

    ts=: (6!:2),7!:2
    ts '((0 3+*&5)^:5000)1 0x' NB. brute force solution
0.244886 38848
    ts '(,.3*4%~1-~])5^5000x' NB. closed form solution
0.0174891 27712


Here the closed form solution was 14 times faster and used 29 per cent less space.

    0.244886 38848%0.0174891 27712
14.0022 1.40185

    %0.244886 38848%0.0174891 27712
0.0714173 0.713344


- Bo



>________________________________
> Fra: Skip Cave <skip at caveconsulting.com>
>Til: programming at jsoftware.com 
>Sendt: 22:16 lørdag den 22. december 2012
>Emne: Re: [Jprogramming] arithmetic sequence
> 
>> Is Skip Cave saying that the closed form solution is inferior?
>> Bo
>>
>
>No. What I am saying is:
>
>The brute force solution is the fastest by several orders of magnitude,
>but uses lots of space:
>
>   ts '((0 3+*&5)^:(i.5000))1 0x'
>0.0714665 2.59842e7
>
>The closed form solution is slow AND uses lots of space:
>
>   ts '(,.3*4%~1-~])5^(i.5000x)'
>7.70079 4.99247e7
>
>The looping solution is slow, but not as slow as the closed form. However
>it uses many orders of magnitude less space.
>
>   ts 'acx 5000'
>2.51865 107264
>
>So if your criteria is time and space usage, then the closed form is the
>worst of the lot. There may be other criteria that would result in a
>different conclusion. As I have mentioned before, processing time and space
>is still much less costly than human programming time, so the large
>differences in time and space usage are still miniscule when compared with
>the time it took to develop these verbs.
>
>Skip
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