I am trying to simplify a complicated integration result containing both error functions and MeijerG – I give the full expression below. A simple FullSimplify(expression,{x>0,y>0,z>0}) would run for about one day and then simply crash the kernel without returning any result. I have been trying to play around with the TimeConstraint parameter. I started multiple runs at the same time, with TimeConstraint->{10000*n,10000*n} for n=1,5,9.

Weirdly, the one for n=9 which should have run the longest already finished after just a few minutes without significant simplification and the warning message (note the negative sign!)

“FullSimplify::time: Time spent on a transformation exceeded -2.95596

10^12 seconds, and the transformation was aborted. Increasing the

value of TimeConstraint option may improve the result of

simplification.”

The one for n=1 crashed after a few minutes without result. The one for n=5 is still running.

Any guesses what causes this erratic behavior? What is the best way to use TimeConstraint (specifically, what is the best ration between the local and total time parameter)?

And what is the best strategy to find out if a result like this can be further simplified?

I did a regular Simplify first, of course. I guess I could split the expression into separate terms, but my suspicion is that some of them only yield a simpler expression when taken together with the other terms.

Would be happy for any ideas.

Here is the function (where I know that x, y, z are positive reals):

```
((x*Erf(2*x*z - y*z)*((2*Pi*(x - y)*(E^(2*x^2)*(-1 + Sqrt(2*Pi)*x)*(3*x - y)
+ Pi*x*(1 - 6*x^2 + 2*x*y)*Erfi(Sqrt(2)*x)
+ x*(-1 + 6*x^2 - 2*x*y)*ExpIntegralEi(2*x^2)))/E^(2*x^2)
- MeijerG({{0, 1/2}, {}}, {{1/2, 1, 1}, {}}, 2*x^2)
+ 2*((x - y)^2*MeijerG({{0, 1/2, 1}, {}}, {{1/2, 1}, {}}, -(1/(Sqrt(2)*x)), 1/2)
+ x*(-2*(x - y)*MeijerG({{1/2, 1, 1}, {}}, {{1, 3/2}, {}}, -(1/(Sqrt(2)*x)), 1/2)
+ x*MeijerG({{1, 1, 3/2}, {}}, {{3/2, 2}, {}}, -(1/(Sqrt(2)*x)), 1/2)))))/E^(2*(x - y)^2)
- (x*Erf((2*x + y)*z)*((2*Pi*(x + y)*(E^(2*x^2)*(-1 + Sqrt(2*Pi)*x)*(3*x + y)
+ Pi*x*(1 - 6*x^2 - 2*x*y)*Erfi(Sqrt(2)*x)
+ x*(-1 + 6*x^2 + 2*x*y)*ExpIntegralEi(2*x^2)))/E^(2*x^2)
- MeijerG({{0, 1/2}, {}}, {{1/2, 1, 1}, {}}, 2*x^2)
+ 2*((x + y)^2*MeijerG({{0, 1/2, 1}, {}}, {{1/2, 1}, {}}, -(1/(Sqrt(2)*x)), 1/2)
+ x*(-2*(x + y)*MeijerG({{1/2, 1, 1}, {}}, {{1, 3/2}, {}}, -(1/(Sqrt(2)*x)), 1/2)
+ x*MeijerG({{1, 1, 3/2}, {}}, {{3/2, 2}, {}}, -(1/(Sqrt(2)*x)), 1/2)))))/E^(2*(x + y)^2))/(2*Pi*x^2)
```