parallelization during parallelization in recursive function

Everyone good time of day!

Not so long ago, I began to deal with parallel computing toolbox. I wrote a rather large program, which I will not bring here, which, in fact, is sorting out options for meanings. Since there can be a lot and a lot of options, I decided not to keep a list of options, but just compare a couple of options on each iteration. This is complicated, so I found a way out in double recursion - one recursive function is called, which calls itself up to some point, after which it calls a second recursive function, which, in turn, also refers to itself several times. Within the body of each recursive function there are two for loops.

Forgive me my English (I do not know him well), but I will continue :D

This algorithm works for quite some time, but I managed to get acceleration almost 10 times compared to the original version with sorting the entire list. Nevertheless, I would like to learn to take advantage of some of the advantages of modern processors, such as multi-core.

I introduced one parfor cycle into the "upper recursion" body instead of the usual for, which accelerated the program three times. However, for 60% of the program time, only one out of six core is occupied, which, obviously, cannot but be depressed. I noticed that despite the fact that the recursive function is called several times, and the new parfor cycle is inside another parfor cycle, internal parfor cycles do not lead to the inclusion of new processor cores.

The essence of my question is how you can organize "parallelization during another parallelization."

parfor inside another parfor within the same function turns out to be an incorrect syntax, and if you transfer the internal cycle to a separate function, then it simply ceases to work as parfor and is replaced by the usual for.

I tried to put the whole body of the recursive function ("upper") in the cycle "spmd ... end "(without any parfor), however, this leads to an incredibly large busy amount of RAM (MatLab closes without finishing work, since there is not enough memory).

I also tried to call a recursive function using parfevalOnAll, but the program just works indefinitely, although the processor is fully loaded and the program should complete in a minute or two (I think).

I ask for help with understanding not only how to properly organize parallelization, but also what mistakes I make (from the description of what I am doing). Unfortunately, the documentation describes everything rather vaguely. I will be immensely grateful for any help!

Below I will give the basic template of my algorithm, which I am trying to parallel as much as possible.

% enter all x

variant = PEREBOR(x1, x2, .., xN);

function [variant] = PEREBOR(x1, x2, .., xN)

    % some preliminary one-time calculations

    for k = left:1:k_right
        
        variants = nchoosek(..);
        
        if isempty(variants) ~= 1

            for i = 1:1:size(variants,1)
                if recursion_depth > 1
                    [variant] = PEREBOR(x1, x2, .., xN);
                else
                    [variant] = PEREBOR_2(x2, x4, x7);
                end
            end
            
        else

            if recursion_depth > 1
                [variant] = PEREBOR(x1, x2, .., xN);
            else
                [variant] = PEREBOR_2(x2, x4, x7);
            end
            
        end
        
    end



function [variant] = PEREBOR_2(x2, x4, x7)
    
    % some preliminary one-time calculations
    
    for k = left:1:k_right
        
        variants = nchoosek(..);
        
        if isempty(variants) ~= 1
            
            for i = 1:1:size(variants,1)

                if recursion_depth > 1
                    [variant] = PEREBOR_2(x2, x4, x7);
                else
                    if ...
                        variant = something...
                    else
                        variant = [];
                        continue
                    end
                end
                
            end
            
        else
            
            if recursion_depth > 1
                [variant] = PEREBOR_2(x2, x4, x7);
            else
                if ...
                    variant = something...
                else
                    variant = [];
                    continue
                end
            end
            
        end
        
    end