*************************************
www.BillHowell.ca,   Wed May  4 11:13:36 2016
Expression being tested : Eq_05 for uh|[,k+1] :=  
(D0*(uh|[,k])) + (A0*f_activn_uk) + (B0*f_activn_uk_lagged) + (KG*((yn|[,k]) - (yh|[,k])))
 
Applying write_parenthesis_aligned to result for uh|[,k+1], depth of 5 : 
(+ 
   (+ 
      (+ 
         (* 
            (D_loww@[0] + D_high@[0]) /2 uh@[0,k] 
         ) 
         (+ 
            (* 
               (A_loww@[0,0] + A_high@[0,0]) /2 (f_activn@0 un@[0,k]) ) 
            (* 
               (A_loww@[0,1] + A_high@[0,1]) /2 (f_activn@1 un@[1,k]) ) 
            (* 
               (A_loww@[0,2] + A_high@[0,2]) /2 (f_activn@2 un@[2,k]) ) 
             
         ) 
          
      ) 
      (+ 
         (* 
            (B_loww@[0,0] + B_high@[0,0]) /2 (f_activn@0 un@[0,k - tau@k]) 
         ) 
         (* 
            (B_loww@[0,1] + B_high@[0,1]) /2 (f_activn@1 un@[1,k - tau@k]) 
         ) 
         (* 
            (B_loww@[0,2] + B_high@[0,2]) /2 (f_activn@2 un@[2,k - tau@k]) 
         ) 
          
      ) 
       
   ) 
   (+ 
      (* 
         KG@[0,0] 
         (- 
            yn@[0,k] yh@[0,k] 
         ) 
          
      ) 
      (* 
         KG@[0,1] 
         (- 
            yn@[1,k] yh@[1,k] 
         ) 
          
      ) 
       
   ) 
    
) 


***********************************************
Manual clean-up of the above expression : 
uh|[,k+1], depth of 5 : 
(+ (+ (+ (* (D_loww@[0] + D_high@[0]) /2 uh@[0,k] ) 
         (+ 
            (* (A_loww@[0,0] + A_high@[0,0]) /2 (f_activn@0 un@[0,k]) ) 
            (* (A_loww@[0,1] + A_high@[0,1]) /2 (f_activn@1 un@[1,k]) ) 
            (* (A_loww@[0,2] + A_high@[0,2]) /2 (f_activn@2 un@[2,k]) ) ) 
      ) 
      (+ (* (B_loww@[0,0] + B_high@[0,0]) /2 (f_activn@0 un@[0,k - tau@k]) ) 
         (* (B_loww@[0,1] + B_high@[0,1]) /2 (f_activn@1 un@[1,k - tau@k]) ) 
         (* (B_loww@[0,2] + B_high@[0,2]) /2 (f_activn@2 un@[2,k - tau@k]) ) 
      ) 
   ) 
   (+ (* KG@[0,0] (- yn@[0,k] yh@[0,k] ) ) 
      (* KG@[0,1] (- yn@[1,k] yh@[1,k] ) ) 
   ) 
)