OK, this solution works for now well... !!!

OK, my final observations are as follows:

1. Without MTC 4.8.6 Build 14636 at the PATH commands eps('like',y) and eps("like",y) works both identically and well on R2022a
2. With MTC 4.8.6 Build 14636 at the PATH works only eps("like",y), the eps('like', y) produce above mentioned error on R2022a

3. R2021b used eps(class(y)) instead of R2022a, which is using esp('like',y) at nthroot.m

R2021b ... function eps does not support two arguments call 
R2022a ... function eps support two arguments call (!!!), but presence of MTC at PATH introduce some problem with single quote argument used at ntroot.m  

From my point of view, the current problem with R2022a is introduced by MTC 

I tried to investigate this problem more deeply, too. Two arguments call to 'eps' is still fully supported at R2022a!!! The only change is the double quote strings instead of single.

But!!! TMW made a mistake and use in version R2022a some outdated version of 'nthroot' function with single quote at line 35 (nthroot.m) :)

That is all ...

Moreover:
1. R2021b: nthroot.m line 35: m = x ~= 0 & (abs(x) < (1/eps(class(y)))) & isfinite(n);
2. R2022a: nthroot.m line 35: m = x ~= 0 & (abs(x) < 1./eps('like',y)) & isfinite(n);

Thank you for very interesting FFT benchmarks. Especially the MTC parallel scaling is very impressive.

MTC is permanently the best available high-level language solution for multi precision computing. 

I gave up this activity, because I asked for help the Maplesoft and Wolfram support few times to solve some benchmark Maple and Mathematica scripts problems (optimization of the benchmark code to avoid bad programming habits) and the response was very vague or directly unfriendly.

So, sorry for premature promises...:)

OK ... so do you recommend to use your currently available scripts? Can you send me the whole package of all available scripts so that we don't miss anything important?

I am using 8-Core Intel Core i9-9900 with 64GB RAM (Windows 10 Pro).

Pavel, let me know if it is a good idea from your point of view.

Sorry, wrong formulation of my question. I am asking for what precision are presented CPU times?

Of course Pavel, any additional speed up of expm for quadruple precision would be great, especially for me :). I just trying to effectively solve the stiff system of 1st order linear ODEs (constants differ by magnitudes of order), so expm plays crucial role.

The link on new version of MCT does not work. 

403. That’s an error.

We're sorry, but you do not have access to this page. That’s all we know.

I came across YALMIP project (MATLAB optimization environment), and there is REFINER: Built-in layer for arbitrary precision linear programming (https://yalmip.github.io/solver/refiner/), which is based on GEM library (https://github.com/jdbancal/gem), which is of course not so sophisticated as MCT.

Could be possible to create modified version of REFINER based on MCT???