How to combine two different tables in the following way?

Question

Consider the following two grids:

grid1 = RandomReal[{0, 1}, {3, 2}];
grid2 = Flatten[Thread[{#[[1]], #[[2]], Range[3]}] & /@ grid1, 1];

Therefore, grid2 is grid1 but with additional coordinate.

Next, consider the tables of values of two functions func1, func2 on grid1, grid2:

func1[x_,y_]=Exp[-x]*Cos[y];
func2[x_,y_,z_]=Exp[-x^2]Sin[y]/z;
vals1 = Join[grid1, {func1[#[[1]],#[[2]]]} & /@ grid1, 2];
vals2 = Join[grid2, {func2[#[[1]],#[[2]],#[[3]]]} & /@ grid2, 
   2];

I want to obtain the table

table=Join[grid2,{func1[#[[1]],#[[2]]]*func2[#[[1]],#[[2]],#[[3]]]}&/@grid2,2]

assuming that I do not know func1, func2, i.e., having pre-computed vals1, vals2.

Could you please tell me how to do this quickly (in reality, vals1, vals2 are large multi-dimensional datasets)?

Answer 1

Join[grid2, 
 List /@ Flatten[vals1[[All, -1]] Partition[vals2[[All, -1]], 3]], 2]

% == table

True