The random number generator needs to be seeded differently in each node. (The reason for this is easy to understand.)

The random variables generated by Statistics:-RandomVariable need to have different names in each node. This one is mind-boggling to me. Afterall, each node has its own kernel and so its own memory It's as if the names of random variables are stored in a disk file which all kernels access. And also the generator has been seeded differently in each node.

restart
:

Digits:= 15
:

#Specify the size of the computation:
(n1,n2,n3):= (100, 100, 1000):
# n1 = size of each random sample;
# n2 = number of samples in a batch;
# n3 = number of batches.

#
#Procedure to initialize needed globals on each node:
Init:= proc(n::posint)
local node:= Grid:-MyNode();
   #This is wrapped in parse so that it'll act globally. Otherwise, an environment
   #variable would be reset when this procedure ends.
   parse("Digits:= 15;", 'statement');

   randomize(randomize()+node); #Initialize independent RNG for this node.
   #If repeatability of results is desired, remove the inner randomize().

   (:-X,:-Y):= Array(1..n, 'datatype'= 'hfloat') $ 2;

   #Perhaps due to some oversight in the design of Statistics, it seems necessary that
   #r.v.s in different nodes **need different names** in order to be independent:
   N||node:= Statistics:-RandomVariable('Normal'(0,1));
   :-TRS:= (X::rtable)-> Statistics:-Sample(N||node, X);
   #To verify that different names are needed, change N||node to N in both lines.
   #Doing so, each node will generate identical samples!

   #Perform some computation. For the pedagogical purpose of this worksheet, all that
   #matters is that it's some numeric computation on some Arrays of random Samples.
   :-GG:= (X::Array, Y::Array)->
      evalhf(
         proc(X::Array, Y::Array, n::posint)
         local s, k, S:= 0, p:= 2*Pi;
            for k to n do
               s:= sin(p*X[k]);  
               S:= S + X[k]^2*cos(p*Y[k])/sqrt(2-sin(s)) + Y[k]^2*s
            od
         end proc
         (X, Y, n)
      )      
   ;
   #Perform a batch of the above computations, and somehow numerically consolidate the
   #results. Once again, pedagogically it doesn't matter how they're consolidated.  
   :-TRX1:= (n::posint)-> add(GG(TRS(X), TRS(Y)), 1..n);
   
   #It doesn't matter much what's returned. Returning `node` lets us verify that we're
   #actually running this on a grid.
   return node
end proc
:

#
#Time the initialization:
st:= time[real]():
   #Send Init to each node, but don't run it yet:
   Grid:-Set(Init)
   ;
   #Run Init on each node:
   Nodes:= Grid:-Run(Init, [n1], 'wait');
time__init_Grid:= time[real]() - st;

num_nodes:= numelems(Nodes);

#Time the actual execution:
st:= time[real]():
   R1:= [Grid:-Seq['tasksize'= iquo(n3, num_nodes)](TRX1(k), k= [n2 $ n3])]:
time__run_Grid:= time[real]() - st

#Just for comparison, run it sequentially:
st:= time[real]():
   Init(n1):
time__init_noGrid:= time[real]() - st;

st:= time[real]():
   R2:= [seq(TRX1(k), k= [n2 $ n3])]:
time__run_noGrid:= time[real]() - st;

plots:-display(
   Statistics:-Histogram~(
      <R1 | R2>, #side-by-side plots
      'title'=~ <<"With Grid\n"> | <"Without Grid\n">>,
      'gridlines'= false
   )
);

speedup_factor:= time__run_noGrid / time__run_Grid;

efficiency:= speedup_factor / num_nodes;