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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?

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  • $\begingroup$ How does Integrate[Exp[-a*x^8], {x, -Infinity, Infinity}, Assumptions -> a > 0] compare? $\endgroup$ – Michael E2 Oct 16 at 10:08
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Here are timings obtained with versions 12.0, 11.3 and 8.0.4 on the same machine:

version 12.0 screenshot

version 11.3 screenshot

version 8.0.4 screenshot

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.

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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

enter image description here

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

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