Timeline for Why are numeric division and subtraction not handled better in Mathematica?
Current License: CC BY-SA 3.0
42 events
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| Aug 6 at 19:40 | comment | added | Felipe |
@Mr.Wizard This seems to work: MakeExpression[FractionBox[x_, y_], StandardForm] := MakeExpression[ RowBox[{ "Divide", "[" , x, "," , y, "]" }], StandardForm ] However only if you use SetDelayed in your definitions. It is not perfect but it makes typing expressions less inconvenient as one can write normal fractions.
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| Feb 17 at 18:54 | comment | added | Mr.Wizard | @Felipe A better approach is probably to provide your own Head for the divide operation that only evaluates to Divide when arguments are numeric. If that doesn't make sense to you let me know and I'll explain further. | |
| Feb 17 at 18:47 | comment | added | Mr.Wizard |
@Felipe It is possible but not convenient, as you have to Hold and HoldRelease or Inactive and Activate the expression to keep the auto-conversion from taking place. For example: expr = Hold[a/b] /. (x_/y_) :> Divide[x, y] and then Do[ReleaseHold@expr, {50}] // Timing // First using the example above.
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| Feb 13 at 19:53 | comment | added | Felipe | Has someone found a way to get around that, I mean convert Times[x, Power[y,-1]] to Divide[x,y]? I am on mathematica 14 and it still has this problem. I work with mcmc sampling, where you calculate a function many many times, in which case this effect may accumulate. I tried Times[x, Power[y,-1]]//.Times[a_, Power[b_,-1]]->Divide[a,b] but it returned the same thing. | |
| Apr 13, 2017 at 12:55 | history | edited | CommunityBot |
replaced http://mathematica.stackexchange.com/ with https://mathematica.stackexchange.com/
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| Dec 30, 2016 at 21:05 | comment | added | b3m2a1 |
@Mr.Wizard could the differences in implementation be for symbolic reasons? i.e., a - b becoming a + (- b) is the way it would be handled by Mathematicians symbolically / algebraically (and decreases the number of cases WRI needs to code in for a bunch of things). And so WRI performs that conversion so they can simplify how they handle things like Solve?
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| Apr 15, 2015 at 17:48 | history | edited | Mr.Wizard | CC BY-SA 3.0 |
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| Apr 3, 2014 at 21:25 | answer | added | Ymareth | timeline score: 15 | |
| Apr 3, 2014 at 20:21 | history | edited | Mr.Wizard | CC BY-SA 3.0 |
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| Mar 21, 2014 at 19:30 | comment | added | murray | I don't see what the timings have to do with the original question. Surely when the documentation says the various forms of division are the same, it means that the output is the same. I would expect variation in what happens to convert each form into the form that actually gets executed to perform the division. | |
| Mar 14, 2014 at 0:30 | comment | added | GeofAndron | One solution might be to build into Mathca an (ever growing) list of functions which are alternatives and faster compared to other functions. Of course calling such an option might totally change the FullForm of our code. For example, I may not be aware that treating my data as matrices might vastly accelerate computation, but Mathca might "know" that... | |
| Mar 14, 2014 at 0:22 | comment | added | GeofAndron | Part of me is relieved it's slower to use non FullForm language. I'm new, but isn't FullForm what's sent to the calculator (the Kernal)? Yet there certainly seems to be a bug in the front end: It does seem crazy to translate x/y into Times[x, Power[y,-1] instead of into Divide[x,y]. By the way, when I wrap Divide[x,y] in Simplify it gives back x/y, which I also find goofy. It should give back Divide[x,y]. Maybe the front end should have an option for the FullForm command which if invoked would substitute faster FullForms like Divide[x,y] for equivalent slower ones like Times[x, Power[y,-1]! | |
| Feb 21, 2014 at 22:33 | comment | added | Mr.Wizard | @tchronis I have no general solution. I asked this question hoping that someone else already had implemented one (or to learn that it was fixed in a later version), and to spread awareness of the issue. I have a few ideas that if successful would improve this for a number of cases, but many would be left out, and I think an incomplete fix is worse than none is some ways. Don't spend your reputation on a bounty; if this is still unanswered in a few weeks I'll either post an (incomplete) answer myself and/or start a bounty. | |
| Feb 21, 2014 at 11:50 | comment | added | tchronis | @Mr.Wizard Is there a remedy for this efficiency problems? Perhaps a set of substituting rules that apply to FullForms? Could I start a bounty for a complete answer on your question ? - I think this should be fully answered. | |
| Feb 6, 2014 at 2:35 | comment | added | Bob R | The Attributes of Power, Times, Plus, are more detailed than the Attributes of Subtract and Divide, which likely means that they carry more overhead in terms of checking. Using //FullForm to check how things are entered in the interpreter, Divide and Subtract seem to be used only if they are entered explicitly. When entered in the short forms the longer constructions seem to be taken by the interpreter. Clearly this could be improved. This difference can be seen with Divide[#1,#2]&//FullForm and #1/#2&//FullForm. | |
| Jan 23, 2014 at 13:31 | comment | added | Rojo |
If there are symbols around, it will still end up unevaluated as slow form, but we don't have a SimplifyForPerformance function anyway (we should). I also would change the makeboxing of Power[_, _?Negative] so that it is visually evident when the slow forms are used
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| Jan 23, 2014 at 13:29 | comment | added | Rojo |
I think it would help you a lot to fix the parsing, so the short forms are converted to Subtract and Divide. I actually do that (for Divide only and for a different purpuse)
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| Jan 22, 2014 at 21:55 | comment | added | Sjoerd C. de Vries | And I'm running a single kernel too. Confused threads and kernels. | |
| Jan 22, 2014 at 21:48 | comment | added | Sjoerd C. de Vries | I get 11.544074, 11.715675, 11.419273, 1.840812. Obviously, your computer is much faster than mine, but the timing ratios are similar. I can confirm Ymareth's and Simon's results about peak loads. | |
| Jan 22, 2014 at 21:37 | comment | added | Simon Woods |
I see similar results to Ymareth on an i5 processor (win7, MMA 9.0.1) - all methods use all 4 cores roughly equally but the multiplication versions run at about 40% CPU with Divide at about 70%
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| Jan 22, 2014 at 21:28 | comment | added | Ymareth | Running on a somewhat elderly 8 core intel xeon machine (win7 / M9.0.1). I see two oddities. The a/b variant uses ~10Mb more memory at peak than the Divide[a,b] case. The a/b variant also engages only ~40% of the machine's aggregate compute capacity (in task manager). The Divide[a, b] peaks at 66%. This suggests something down in the library calls made. Would be interesting to see the same under linux. | |
| Jan 22, 2014 at 21:28 | comment | added | Ajasja | @Mr.Wizard I see activity on ~3 of the four cores (the cpu usage is not 100%). My timings have similar ratios as your. Are you sure you're running this on only one core. (Oh I use MMA 9.01 and win7x64) | |
| Jan 22, 2014 at 21:13 | comment | added | Mr.Wizard | @Sjoerd I am running the code in a single Kernel. The parallelism is taking place in the Intel MKL I believe. How do your timing ratios compare to the ones in my question? | |
| Jan 22, 2014 at 21:07 | comment | added | Sjoerd C. de Vries | No, that's not what I'm seeing. I can see activity on six cores for each of the variants, though my license allows only 4. Maybe hyperthreading has to do with that. Or windows is splitting up each of the kernels over more than one core. | |
| Jan 22, 2014 at 20:33 | comment | added | Mr.Wizard |
@Ajasja Interesting! Each multiplication method appears to use a single core, while Divide[a, b] uses multiple cores. Is that the behavior you are seeing as well?
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| Jan 22, 2014 at 20:18 | comment | added | Ajasja |
Something funny is going on. The results for power are all slower than the Divide. Do[a*b, {50}] // Timing // First Do[Times[a, b], {50}] // Timing // First Do[a b, {50}] // Timing // First. Also, while running this, more than one core is used.
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| Jan 22, 2014 at 19:24 | comment | added | ybeltukov | Nice question! This is true even for compiled expressions. | |
| Jan 22, 2014 at 19:13 | comment | added | Peltio |
To clarify: a/b require parsing time to be converted to Time[a,b^-1] (or Times[a,1/b], I don't remember) and this form requires more computations then Divide[a,b]. But the infix form of this latter procedure also require parsing time to be transformed into a call to Divide. When the operation is fast, parsing time could make the difference. Just guessing, eh...
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| Jan 22, 2014 at 19:12 | history | tweeted | twitter.com/#!/StackMma/status/426069926416482305 | ||
| Jan 22, 2014 at 18:56 | comment | added | Peltio |
I was speaking in general. Your trace seems to show that a-b is treated as a + (-b), hence the additional operations (despite the expressions be mathematically equivalent). But by parsing times I was thinking at the time needed to convert an infix operator into the call to the corresponding compiled function (which should be automatic in case you call it directly in the code). Mine was just a guess.
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| Jan 22, 2014 at 18:41 | comment | added | Mr.Wizard |
@Peltio To whom are you speaking? I am fairly certain this is not a superficial difference as I attempted to show with Trace.
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| Jan 22, 2014 at 18:39 | history | edited | Mr.Wizard |
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| Jan 22, 2014 at 18:39 | comment | added | Peltio | Could it be you are timing parsing times? | |
| Jan 22, 2014 at 18:27 | history | edited | Mr.Wizard | CC BY-SA 3.0 |
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| Jan 22, 2014 at 18:09 | comment | added | RunnyKine | I agree. Thanks for this question, didn't realize such a huge difference existed between these forms | |
| Jan 22, 2014 at 18:08 | comment | added | Mr.Wizard | @RunnyKine That's even more aggravating. Imagine all the numeric performance you may be losing due to the lack of proper optimizations. :-/ | |
| Jan 22, 2014 at 18:07 | comment | added | RunnyKine | Something about the timing is interesting. On my PC which runs at 3.8 GHz (base is 3.2 GHz, Intel i7-3930K, MMA V. 9.0.1), The short form timing for subtraction is 4.59375 seconds whereas the long form is an astonishing 0.125 seconds (an order of magnitude faster than yours). | |
| Jan 22, 2014 at 18:06 | history | edited | Mr.Wizard | CC BY-SA 3.0 |
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| Jan 22, 2014 at 17:59 | comment | added | Mr.Wizard | @Stefan I've gotten that comment a number of times; I believe there are two factors: version 7 is faster in a number of simple cases, and Mathematica performance seems to correlate quite strongly to clock speed. I use an Intel i5-2500K at 4.6 GHz. It is not the newest chip (released January 2011) but I doubt the recent Haswell chips (e.g. i5-4670K) are significantly better for Mathematica as they don't run faster. | |
| Jan 22, 2014 at 17:46 | comment | added | Mark Adler | Related question: mathematica.stackexchange.com/questions/39200/… | |
| Jan 22, 2014 at 17:41 | comment | added | Stefan | finally you're asking a question i was wondering constantly. maybe someone from WRI can shed some light on that dark matter, but i doubt it, as it is often the case if it is not covered by their marketing allowance... +1 | |
| Jan 22, 2014 at 17:34 | history | asked | Mr.Wizard | CC BY-SA 3.0 |