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Siginificant speed difference of Integrate between 9.0 and 12.0

Why the Kernel crashes on these integrals in V12?xkcdConvert routines perform slower in Mathematica 9About auto-compiling and performance between Do and FoldWhy is Query so much slower than Part?The efficiency compare between Flatten[#, 1] & and Join @@ # &When is RegionMeasure[ImplicitRegion[…]] faster than (N)Integrate[Boole[…]]?Why does Outer sometimes return a packed array, and sometimes not?CPU timing for matrix rank calculation difference between 10.3 and 10.4 and 11.0Integrate yields no answer and crashes kernel

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4

$begingroup$

I just upgraded from 9.0 to 12.0, and I found some strange difference in timings for the following expressions:

a. Integrate[Exp[-a*x^8],x,-Infinity,Infinity]

b. Integrate[Exp[-a*x^n],x,-Infinity,Infinity]

When I evaluate them in 9.0 and 12.0, the time cost is

9.0+a(~1s)<<12.0+b(~15s)<12.0+a(~20s)<<9.0+b(~75s)

Why is b. faster than a. under version 12.0? And why is a. so much slower under 12.0 than 9.0?

calculus-and-analysis performance-tuning

share|improve this question

edited Oct 16 at 8:33

Alexey Popkov

48.1k44 gold badges118118 silver badges282282 bronze badges

asked Oct 16 at 8:21

HankHank

4111 bronze badge

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  How does Integrate[Exp[-a*x^8], x, -Infinity, Infinity, Assumptions -> a > 0] compare?
  $endgroup$
  – Michael E2
  Oct 16 at 10:08
  

  
  
  
  

add a comment
 | 

4

$begingroup$

I just upgraded from 9.0 to 12.0, and I found some strange difference in timings for the following expressions:

a. Integrate[Exp[-a*x^8],x,-Infinity,Infinity]

b. Integrate[Exp[-a*x^n],x,-Infinity,Infinity]

When I evaluate them in 9.0 and 12.0, the time cost is

9.0+a(~1s)<<12.0+b(~15s)<12.0+a(~20s)<<9.0+b(~75s)

Why is b. faster than a. under version 12.0? And why is a. so much slower under 12.0 than 9.0?

calculus-and-analysis performance-tuning

share|improve this question

edited Oct 16 at 8:33

Alexey Popkov

48.1k44 gold badges118118 silver badges282282 bronze badges

asked Oct 16 at 8:21

HankHank

4111 bronze badge

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  How does Integrate[Exp[-a*x^8], x, -Infinity, Infinity, Assumptions -> a > 0] compare?
  $endgroup$
  – Michael E2
  Oct 16 at 10:08
  

  
  
  
  

add a comment
 | 

$begingroup$

I just upgraded from 9.0 to 12.0, and I found some strange difference in timings for the following expressions:

a. Integrate[Exp[-a*x^8],x,-Infinity,Infinity]

b. Integrate[Exp[-a*x^n],x,-Infinity,Infinity]

When I evaluate them in 9.0 and 12.0, the time cost is

9.0+a(~1s)<<12.0+b(~15s)<12.0+a(~20s)<<9.0+b(~75s)

Why is b. faster than a. under version 12.0? And why is a. so much slower under 12.0 than 9.0?

calculus-and-analysis performance-tuning

share|improve this question

edited Oct 16 at 8:33

Alexey Popkov

48.1k44 gold badges118118 silver badges282282 bronze badges

asked Oct 16 at 8:21

HankHank

4111 bronze badge

$endgroup$

share|improve this question

edited Oct 16 at 8:33

Alexey Popkov

48.1k44 gold badges118118 silver badges282282 bronze badges

asked Oct 16 at 8:21

HankHank

4111 bronze badge

share|improve this question

edited Oct 16 at 8:33

Alexey Popkov

48.1k44 gold badges118118 silver badges282282 bronze badges

asked Oct 16 at 8:21

HankHank

4111 bronze badge

edited Oct 16 at 8:33

Alexey Popkov

48.1k44 gold badges118118 silver badges282282 bronze badges

edited Oct 16 at 8:33

Alexey Popkov

48.1k44 gold badges118118 silver badges282282 bronze badges

asked Oct 16 at 8:21

HankHank

4111 bronze badge

asked Oct 16 at 8:21

HankHank

4111 bronze badge

2 Answers
2

active

oldest

votes

6

$begingroup$

Here are timings obtained with versions 12.0, 11.3 and 8.0.4 on the same machine:

It is apparent that between versions 11.3 and 12.0 we have significant degradation of performance for simple integrals as I recently notices in another answer. I recommend reporting this to the technical support.

share|improve this answer

answered Oct 16 at 8:49

Alexey PopkovAlexey Popkov

48.1k44 gold badges118118 silver badges282282 bronze badges

$endgroup$

add a comment
 | 

6

$begingroup$

I can't comment of the specific integral you have. But on a test suite that contains 14,944 integrals, the following shows the average time (in seconds) used to solve each integral for different Mathematica versions

Version 12 timing is not completed yet. This shows that version 9.0 was fast compared to newer versions.

But this does not necessarily mean something bad happened.

It could be that much more error checking was added to make Integrate more robust, and it could also be that more algorithms were added that Integrate now tries.

And many other such things (additional pre-processing and additional post-processing, etc...). All of this would increase the time used to process each integral on average.

Of course, it could also mean that there is indeed a real issue other than the above which causes this slow down for your specific integrals.

reference: Mathematica report

share|improve this answer

answered Oct 16 at 8:53

NasserNasser

72.3k44 gold badges9494 silver badges219219 bronze badges

$endgroup$

add a comment
 | 

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6

$begingroup$

Here are timings obtained with versions 12.0, 11.3 and 8.0.4 on the same machine:

It is apparent that between versions 11.3 and 12.0 we have significant degradation of performance for simple integrals as I recently notices in another answer. I recommend reporting this to the technical support.

share|improve this answer

answered Oct 16 at 8:49

Alexey PopkovAlexey Popkov

48.1k44 gold badges118118 silver badges282282 bronze badges

$endgroup$

add a comment
 | 

6

$begingroup$

Here are timings obtained with versions 12.0, 11.3 and 8.0.4 on the same machine:

It is apparent that between versions 11.3 and 12.0 we have significant degradation of performance for simple integrals as I recently notices in another answer. I recommend reporting this to the technical support.

share|improve this answer

answered Oct 16 at 8:49

Alexey PopkovAlexey Popkov

48.1k44 gold badges118118 silver badges282282 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

Here are timings obtained with versions 12.0, 11.3 and 8.0.4 on the same machine:

It is apparent that between versions 11.3 and 12.0 we have significant degradation of performance for simple integrals as I recently notices in another answer. I recommend reporting this to the technical support.

share|improve this answer

answered Oct 16 at 8:49

Alexey PopkovAlexey Popkov

48.1k44 gold badges118118 silver badges282282 bronze badges

$endgroup$

share|improve this answer

answered Oct 16 at 8:49

Alexey PopkovAlexey Popkov

48.1k44 gold badges118118 silver badges282282 bronze badges

answered Oct 16 at 8:49

Alexey PopkovAlexey Popkov

48.1k44 gold badges118118 silver badges282282 bronze badges

answered Oct 16 at 8:49

Alexey PopkovAlexey Popkov

48.1k44 gold badges118118 silver badges282282 bronze badges

6

$begingroup$

I can't comment of the specific integral you have. But on a test suite that contains 14,944 integrals, the following shows the average time (in seconds) used to solve each integral for different Mathematica versions

Version 12 timing is not completed yet. This shows that version 9.0 was fast compared to newer versions.

But this does not necessarily mean something bad happened.

It could be that much more error checking was added to make Integrate more robust, and it could also be that more algorithms were added that Integrate now tries.

And many other such things (additional pre-processing and additional post-processing, etc...). All of this would increase the time used to process each integral on average.

Of course, it could also mean that there is indeed a real issue other than the above which causes this slow down for your specific integrals.

reference: Mathematica report

share|improve this answer

answered Oct 16 at 8:53

NasserNasser

72.3k44 gold badges9494 silver badges219219 bronze badges

$endgroup$

add a comment
 | 

6

$begingroup$

I can't comment of the specific integral you have. But on a test suite that contains 14,944 integrals, the following shows the average time (in seconds) used to solve each integral for different Mathematica versions

Version 12 timing is not completed yet. This shows that version 9.0 was fast compared to newer versions.

But this does not necessarily mean something bad happened.

It could be that much more error checking was added to make Integrate more robust, and it could also be that more algorithms were added that Integrate now tries.

And many other such things (additional pre-processing and additional post-processing, etc...). All of this would increase the time used to process each integral on average.

Of course, it could also mean that there is indeed a real issue other than the above which causes this slow down for your specific integrals.

reference: Mathematica report

share|improve this answer

answered Oct 16 at 8:53

NasserNasser

72.3k44 gold badges9494 silver badges219219 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

I can't comment of the specific integral you have. But on a test suite that contains 14,944 integrals, the following shows the average time (in seconds) used to solve each integral for different Mathematica versions

Version 12 timing is not completed yet. This shows that version 9.0 was fast compared to newer versions.

But this does not necessarily mean something bad happened.

It could be that much more error checking was added to make Integrate more robust, and it could also be that more algorithms were added that Integrate now tries.

And many other such things (additional pre-processing and additional post-processing, etc...). All of this would increase the time used to process each integral on average.

Of course, it could also mean that there is indeed a real issue other than the above which causes this slow down for your specific integrals.

reference: Mathematica report

share|improve this answer

answered Oct 16 at 8:53

NasserNasser

72.3k44 gold badges9494 silver badges219219 bronze badges

$endgroup$

share|improve this answer

answered Oct 16 at 8:53

NasserNasser

72.3k44 gold badges9494 silver badges219219 bronze badges

answered Oct 16 at 8:53

NasserNasser

72.3k44 gold badges9494 silver badges219219 bronze badges

answered Oct 16 at 8:53

NasserNasser

72.3k44 gold badges9494 silver badges219219 bronze badges