(****************************************************************)
(*                                                              *)
(*  This file contains expressions for the functions E, Et,     *)
(*  and R6 in the limit that one of the cross ratios is set to  *)
(*  1, through three loops. Since E and Et are symmetric and    *)
(*  antisymmetric, respectively, under the exchange u <-> w,    *)
(*  we provide only the v -> 1 and w -> 1 limits of these       *)
(*  functions. Similarly, we only provide the w -> 1 limit of   *)
(*  R6 due to its total symmetry in u, v, and w. The            *)
(*  conversions to the v -> 1 and w -> 1 limits of V, Vt,       *)
(*  and U are also provided at the end of the file.             *)
(*                                                              *)
(****************************************************************)

E3u1w = -HPL[{1}, 1 - u]^6/384 - (HPL[{1}, 1 - u]^5*HPL[{1}, 1 - w])/64 + 
     (HPL[{1}, 1 - u]^4*HPL[{1}, 1 - w]^2)/128 - 
     (5*HPL[{1}, 1 - u]^3*HPL[{1}, 1 - w]^3)/144 + 
     (HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]^4)/128 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^5)/64 - HPL[{1}, 1 - w]^6/384 - 
     (HPL[{1}, 1 - u]^4*HPL[{0, 1}, 1 - u])/32 - 
     (5*HPL[{1}, 1 - u]^3*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u])/48 + 
     (5*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - u])/32 + 
     (HPL[{1}, 1 - w]^4*HPL[{0, 1}, 1 - u])/16 - 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]^2)/8 - 
     (HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - u]^2)/8 + HPL[{0, 1}, 1 - u]^3/12 + 
     (HPL[{1}, 1 - u]^4*HPL[{0, 1}, 1 - w])/16 + 
     (5*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - w])/32 - 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^3*HPL[{0, 1}, 1 - w])/48 - 
     (HPL[{1}, 1 - w]^4*HPL[{0, 1}, 1 - w])/32 + 
     (5*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - w])/16 - 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*
       HPL[{0, 1}, 1 - w])/8 + (5*HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - u]*
       HPL[{0, 1}, 1 - w])/16 - (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - w]^2)/8 - 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]^2)/8 + 
     HPL[{0, 1}, 1 - w]^3/12 - (HPL[{1}, 1 - u]^3*HPL[{0, 0, 1}, 1 - u])/8 - 
     (HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]*HPL[{0, 0, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^2*HPL[{0, 0, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - w]^3*HPL[{0, 0, 1}, 1 - u])/8 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - u])/8 - 
     (HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - u])/8 + 
     (5*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - w]*HPL[{0, 0, 1}, 1 - u])/8 - 
     (5*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*HPL[{0, 0, 1}, 1 - u])/8 - 
     (3*HPL[{0, 0, 1}, 1 - u]^2)/8 - 
     (HPL[{1}, 1 - u]^3*HPL[{0, 0, 1}, 1 - w])/8 + 
     (HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]*HPL[{0, 0, 1}, 1 - w])/4 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^2*HPL[{0, 0, 1}, 1 - w])/4 - 
     (HPL[{1}, 1 - w]^3*HPL[{0, 0, 1}, 1 - w])/8 - 
     (5*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - w])/8 + 
     (5*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - w])/8 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - w]*HPL[{0, 0, 1}, 1 - w])/8 + 
     (HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*HPL[{0, 0, 1}, 1 - w])/8 - 
     (3*HPL[{0, 0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - w])/4 - 
     (3*HPL[{0, 0, 1}, 1 - w]^2)/8 + 
     (HPL[{1}, 1 - u]^3*HPL[{0, 1, 1}, 1 - u])/8 + 
     (3*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]*HPL[{0, 1, 1}, 1 - u])/8 - 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^2*HPL[{0, 1, 1}, 1 - u])/8 - 
     (HPL[{1}, 1 - w]^3*HPL[{0, 1, 1}, 1 - u])/8 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/8 + 
     (11*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/8 - 
     (5*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - w]*HPL[{0, 1, 1}, 1 - u])/8 + 
     (5*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*HPL[{0, 1, 1}, 1 - u])/8 + 
     (HPL[{0, 0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/2 + 
     (HPL[{0, 0, 1}, 1 - w]*HPL[{0, 1, 1}, 1 - u])/2 - 
     HPL[{0, 1, 1}, 1 - u]^2/8 - (HPL[{1}, 1 - u]^3*HPL[{0, 1, 1}, 1 - w])/
      8 - (3*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]*HPL[{0, 1, 1}, 1 - w])/8 + 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^2*HPL[{0, 1, 1}, 1 - w])/8 + 
     (HPL[{1}, 1 - w]^3*HPL[{0, 1, 1}, 1 - w])/8 + 
     (5*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - w])/8 - 
     (5*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - w])/8 + 
     (11*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - w]*HPL[{0, 1, 1}, 1 - w])/8 + 
     (HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*HPL[{0, 1, 1}, 1 - w])/8 + 
     (HPL[{0, 0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - w])/2 + 
     (HPL[{0, 0, 1}, 1 - w]*HPL[{0, 1, 1}, 1 - w])/2 - 
     (3*HPL[{0, 1, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - w])/4 - 
     HPL[{0, 1, 1}, 1 - w]^2/8 - (3*HPL[{1}, 1 - u]^2*
       HPL[{0, 0, 0, 1}, 1 - u])/8 - (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*
       HPL[{0, 0, 0, 1}, 1 - u])/2 + 
     (3*HPL[{1}, 1 - w]^2*HPL[{0, 0, 0, 1}, 1 - u])/8 + 
     (3*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 0, 1}, 1 - u])/4 + 
     (3*HPL[{0, 1}, 1 - w]*HPL[{0, 0, 0, 1}, 1 - u])/4 + 
     (3*HPL[{1}, 1 - u]^2*HPL[{0, 0, 0, 1}, 1 - w])/8 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 0, 0, 1}, 1 - w])/2 - 
     (3*HPL[{1}, 1 - w]^2*HPL[{0, 0, 0, 1}, 1 - w])/8 + 
     (3*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 0, 1}, 1 - w])/4 + 
     (3*HPL[{0, 1}, 1 - w]*HPL[{0, 0, 0, 1}, 1 - w])/4 + 
     (3*HPL[{1}, 1 - u]^2*HPL[{0, 0, 1, 1}, 1 - u])/8 + 
     2*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 0, 1, 1}, 1 - u] + 
     (3*HPL[{1}, 1 - w]^2*HPL[{0, 0, 1, 1}, 1 - u])/8 - 
     (3*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1, 1}, 1 - u])/2 - 
     (HPL[{0, 1}, 1 - w]*HPL[{0, 0, 1, 1}, 1 - u])/2 + 
     (3*HPL[{1}, 1 - u]^2*HPL[{0, 0, 1, 1}, 1 - w])/8 + 
     2*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 0, 1, 1}, 1 - w] + 
     (3*HPL[{1}, 1 - w]^2*HPL[{0, 0, 1, 1}, 1 - w])/8 - 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1, 1}, 1 - w])/2 - 
     (3*HPL[{0, 1}, 1 - w]*HPL[{0, 0, 1, 1}, 1 - w])/2 - 
     (3*HPL[{1}, 1 - u]^2*HPL[{0, 1, 1, 1}, 1 - u])/8 - 
     HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1, 1, 1}, 1 - u] + 
     (5*HPL[{1}, 1 - w]^2*HPL[{0, 1, 1, 1}, 1 - u])/8 + 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1, 1}, 1 - u])/4 + 
     (3*HPL[{0, 1}, 1 - w]*HPL[{0, 1, 1, 1}, 1 - u])/4 + 
     (5*HPL[{1}, 1 - u]^2*HPL[{0, 1, 1, 1}, 1 - w])/8 - 
     HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1, 1, 1}, 1 - w] - 
     (3*HPL[{1}, 1 - w]^2*HPL[{0, 1, 1, 1}, 1 - w])/8 + 
     (3*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1, 1}, 1 - w])/4 + 
     (HPL[{0, 1}, 1 - w]*HPL[{0, 1, 1, 1}, 1 - w])/4 - 
     (3*HPL[{1}, 1 - u]*HPL[{0, 0, 0, 0, 1}, 1 - u])/4 - 
     (3*HPL[{1}, 1 - w]*HPL[{0, 0, 0, 0, 1}, 1 - u])/4 - 
     (3*HPL[{1}, 1 - u]*HPL[{0, 0, 0, 0, 1}, 1 - w])/4 - 
     (3*HPL[{1}, 1 - w]*HPL[{0, 0, 0, 0, 1}, 1 - w])/4 + 
     HPL[{1}, 1 - w]*HPL[{0, 0, 0, 1, 1}, 1 - u] + 
     HPL[{1}, 1 - u]*HPL[{0, 0, 0, 1, 1}, 1 - w] - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1, 0, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1, 0, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1, 0, 1}, 1 - w])/4 - 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1, 0, 1}, 1 - w])/4 - 
     (3*HPL[{1}, 1 - u]*HPL[{0, 0, 1, 1, 1}, 1 - u])/2 - 
     9*HPL[{1}, 1 - w]*HPL[{0, 0, 1, 1, 1}, 1 - u] - 
     9*HPL[{1}, 1 - u]*HPL[{0, 0, 1, 1, 1}, 1 - w] - 
     (3*HPL[{1}, 1 - w]*HPL[{0, 0, 1, 1, 1}, 1 - w])/2 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 0, 1, 1}, 1 - u])/4 - 
     (11*HPL[{1}, 1 - w]*HPL[{0, 1, 0, 1, 1}, 1 - u])/4 - 
     (11*HPL[{1}, 1 - u]*HPL[{0, 1, 0, 1, 1}, 1 - w])/4 - 
     (HPL[{1}, 1 - w]*HPL[{0, 1, 0, 1, 1}, 1 - w])/4 + 
     (3*HPL[{1}, 1 - u]*HPL[{0, 1, 1, 1, 1}, 1 - u])/4 + 
     (5*HPL[{1}, 1 - w]*HPL[{0, 1, 1, 1, 1}, 1 - u])/4 + 
     (5*HPL[{1}, 1 - u]*HPL[{0, 1, 1, 1, 1}, 1 - w])/4 + 
     (3*HPL[{1}, 1 - w]*HPL[{0, 1, 1, 1, 1}, 1 - w])/4 + 
     6*HPL[{0, 0, 0, 1, 1, 1}, 1 - u] + 6*HPL[{0, 0, 0, 1, 1, 1}, 1 - w] + 
     2*HPL[{0, 0, 1, 0, 1, 1}, 1 - u] + 2*HPL[{0, 0, 1, 0, 1, 1}, 1 - w] + 
     HPL[{0, 0, 1, 1, 1, 1}, 1 - u] + HPL[{0, 0, 1, 1, 1, 1}, 1 - w] - 
     (3*HPL[{1}, 1 - u]^4*\[Zeta][2])/32 - 
     (5*HPL[{1}, 1 - u]^3*HPL[{1}, 1 - w]*\[Zeta][2])/12 - 
     (HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]^2*\[Zeta][2])/8 - 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^3*\[Zeta][2])/12 - 
     (3*HPL[{1}, 1 - w]^4*\[Zeta][2])/32 + 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*\[Zeta][2])/4 + 
     (7*HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - u]*\[Zeta][2])/8 - 
     (HPL[{0, 1}, 1 - u]^2*\[Zeta][2])/2 + 
     (7*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - w]*\[Zeta][2])/8 + 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*\[Zeta][2])/4 + 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - w]*\[Zeta][2])/4 - 
     (HPL[{0, 1}, 1 - w]^2*\[Zeta][2])/2 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - u]*\[Zeta][2])/4 - 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1}, 1 - u]*\[Zeta][2])/4 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - w]*\[Zeta][2])/4 - 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1}, 1 - w]*\[Zeta][2])/4 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - u]*\[Zeta][2])/4 - 
     (11*HPL[{1}, 1 - w]*HPL[{0, 1, 1}, 1 - u]*\[Zeta][2])/4 - 
     (11*HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - w]*\[Zeta][2])/4 - 
     (HPL[{1}, 1 - w]*HPL[{0, 1, 1}, 1 - w]*\[Zeta][2])/4 + 
     (5*HPL[{0, 0, 1, 1}, 1 - u]*\[Zeta][2])/2 + 
     (5*HPL[{0, 0, 1, 1}, 1 - w]*\[Zeta][2])/2 + HPL[{0, 1, 1, 1}, 1 - u]*
      \[Zeta][2] + HPL[{0, 1, 1, 1}, 1 - w]*\[Zeta][2] - 
     (17*HPL[{1}, 1 - u]^2*\[Zeta][2]^2)/10 - 
     (49*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*\[Zeta][2]^2)/10 - 
     (17*HPL[{1}, 1 - w]^2*\[Zeta][2]^2)/10 + 
     (21*HPL[{0, 1}, 1 - u]*\[Zeta][2]^2)/10 + 
     (21*HPL[{0, 1}, 1 - w]*\[Zeta][2]^2)/10 - (188*\[Zeta][2]^3)/21 + 
     \[Zeta][3]^2
     
E3uv1 = -HPL[{1}, 1 - u]^6/384 + (HPL[{1}, 1 - u]^5*HPL[{1}, 1 - v])/64 - 
     (3*HPL[{1}, 1 - u]^4*HPL[{1}, 1 - v]^2)/128 + 
     (5*HPL[{1}, 1 - u]^3*HPL[{1}, 1 - v]^3)/144 - 
     (3*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]^4)/128 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^5)/64 - HPL[{1}, 1 - v]^6/384 - 
     (HPL[{1}, 1 - u]^4*HPL[{0, 1}, 1 - u])/32 + 
     (11*HPL[{1}, 1 - u]^3*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u])/64 + 
     (99*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u])/512 - 
     (83*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^3*HPL[{0, 1}, 1 - u])/768 + 
     (HPL[{1}, 1 - v]^4*HPL[{0, 1}, 1 - u])/32 - 
     (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]^2)/32 + 
     (105*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]^2)/256 - 
     (7*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u]^2)/32 + 
     HPL[{0, 1}, 1 - u]^3/12 - (HPL[{1}, 1 - u]^3*HPL[{1}, 1 - v]*
       HPL[{0, 1}, 1 - v])/8 + (107*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]^2*
       HPL[{0, 1}, 1 - v])/512 - (65*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^3*
       HPL[{0, 1}, 1 - v])/768 - (7*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]*
       HPL[{0, 1}, 1 - v])/64 - (19*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*
       HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v])/64 + 
     (5*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v])/32 - 
     (13*HPL[{0, 1}, 1 - u]^2*HPL[{0, 1}, 1 - v])/128 + 
     (3*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - v]^2)/128 + 
     (33*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]^2)/256 + 
     (31*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v]^2)/128 - 
     (HPL[{1}, 1 - u]^3*HPL[{0, 0, 1}, 1 - u])/8 + 
     (15*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - u])/64 + 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*HPL[{0, 0, 1}, 1 - u])/64 + 
     (HPL[{1}, 1 - v]^3*HPL[{0, 0, 1}, 1 - u])/48 - 
     (9*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 1}, 1 - u])/16 - 
     (3*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - v])/64 - 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*HPL[{0, 0, 1}, 1 - v])/64 + 
     (15*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - v])/32 - 
     (3*HPL[{0, 0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - v])/16 + 
     (HPL[{1}, 1 - u]^3*HPL[{0, 1, 1}, 1 - u])/8 - 
     (3*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - u])/8 + 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*HPL[{0, 1, 1}, 1 - u])/64 + 
     (37*HPL[{1}, 1 - v]^3*HPL[{0, 1, 1}, 1 - u])/384 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/4 - 
     (13*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/8 + 
     (13*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*HPL[{0, 1, 1}, 1 - u])/24 - 
     (9*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*HPL[{0, 1, 1}, 1 - u])/32 + 
     (3*HPL[{0, 0, 1}, 1 - v]*HPL[{0, 1, 1}, 1 - u])/16 + 
     HPL[{0, 1, 1}, 1 - u]^2/4 + (23*HPL[{1}, 1 - u]^3*HPL[{0, 1, 1}, 1 - v])/
      64 - (19*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - v])/64 + 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*HPL[{0, 1, 1}, 1 - v])/32 + 
     (27*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - v])/32 - 
     (7*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - v])/12 - 
     (19*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*HPL[{0, 1, 1}, 1 - v])/16 + 
     (9*HPL[{0, 0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - v])/16 + 
     (3*HPL[{0, 1, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - v])/32 - 
     (3*HPL[{1}, 1 - u]^2*HPL[{0, 0, 0, 1}, 1 - u])/8 + 
     (21*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 0, 0, 1}, 1 - u])/32 - 
     (9*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 0, 1}, 1 - u])/16 - 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 0, 0, 1}, 1 - v])/16 + 
     (3*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 0, 1}, 1 - v])/8 + 
     (HPL[{1}, 1 - u]^2*HPL[{0, 0, 1, 1}, 1 - u])/2 - 
     (59*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 0, 1, 1}, 1 - u])/32 + 
     (93*HPL[{1}, 1 - v]^2*HPL[{0, 0, 1, 1}, 1 - u])/128 - 
     HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1, 1}, 1 - u] + 
     (3*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 1, 1}, 1 - u])/8 + 
     (3*HPL[{1}, 1 - u]^2*HPL[{0, 0, 1, 1}, 1 - v])/128 - 
     (13*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 0, 1, 1}, 1 - v])/32 - 
     (19*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1, 1}, 1 - v])/16 - 
     (3*HPL[{1}, 1 - u]^2*HPL[{0, 1, 1, 1}, 1 - u])/8 + 
     (29*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1, 1, 1}, 1 - u])/32 - 
     (71*HPL[{1}, 1 - v]^2*HPL[{0, 1, 1, 1}, 1 - u])/64 - 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1, 1}, 1 - u])/2 - 
     (9*HPL[{0, 1}, 1 - v]*HPL[{0, 1, 1, 1}, 1 - u])/32 - 
     (39*HPL[{1}, 1 - u]^2*HPL[{0, 1, 1, 1}, 1 - v])/64 - 
     (55*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1, 1, 1}, 1 - v])/64 - 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1, 1}, 1 - v])/2 - 
     (3*HPL[{1}, 1 - u]*HPL[{0, 0, 0, 0, 1}, 1 - u])/4 + 
     (3*HPL[{1}, 1 - v]*HPL[{0, 0, 0, 0, 1}, 1 - u])/4 + 
     (3*HPL[{1}, 1 - u]*HPL[{0, 0, 0, 1, 1}, 1 - u])/4 - 
     (3*HPL[{1}, 1 - v]*HPL[{0, 0, 0, 1, 1}, 1 - u])/4 - 
     (9*HPL[{1}, 1 - u]*HPL[{0, 0, 1, 1, 1}, 1 - u])/4 + 
     (33*HPL[{1}, 1 - v]*HPL[{0, 0, 1, 1, 1}, 1 - u])/4 + 
     6*HPL[{1}, 1 - u]*HPL[{0, 0, 1, 1, 1}, 1 - v] - 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 0, 1, 1}, 1 - u])/2 + 
     (5*HPL[{1}, 1 - v]*HPL[{0, 1, 0, 1, 1}, 1 - u])/2 + 
     2*HPL[{1}, 1 - u]*HPL[{0, 1, 0, 1, 1}, 1 - v] + 
     (3*HPL[{1}, 1 - u]*HPL[{0, 1, 1, 1, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - v]*HPL[{0, 1, 1, 1, 1}, 1 - u])/4 + 
     HPL[{1}, 1 - u]*HPL[{0, 1, 1, 1, 1}, 1 - v] + 
     (3*HPL[{0, 0, 0, 0, 1, 1}, 1 - u])/2 + 
     6*HPL[{0, 0, 0, 1, 1, 1}, 1 - u] + 2*HPL[{0, 0, 1, 0, 1, 1}, 1 - u] + 
     (5*HPL[{0, 0, 1, 1, 1, 1}, 1 - u])/2 - 
     (5*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]*SPw2f1[u, v])/32 - 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw2f1[u, v])/16 - 
     (21*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u]*SPw2f1[u, v])/128 - 
     (25*HPL[{0, 1}, 1 - u]^2*SPw2f1[u, v])/128 - 
     (3*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - v]*SPw2f1[u, v])/64 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw2f1[u, v])/16 - 
     (5*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - v]*SPw2f1[u, v])/128 + 
     (13*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v]*SPw2f1[u, v])/64 - 
     (31*HPL[{0, 1}, 1 - v]^2*SPw2f1[u, v])/128 + 
     (9*HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - u]*SPw2f1[u, v])/32 - 
     (9*HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - u]*SPw2f1[u, v])/32 - 
     (3*HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - v]*SPw2f1[u, v])/32 - 
     (3*HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - v]*SPw2f1[u, v])/32 + 
     (33*HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - u]*SPw2f1[u, v])/64 - 
     (7*HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - u]*SPw2f1[u, v])/64 - 
     (33*HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - v]*SPw2f1[u, v])/64 + 
     (25*HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - v]*SPw2f1[u, v])/64 + 
     (3*HPL[{0, 0, 0, 1}, 1 - u]*SPw2f1[u, v])/16 - 
     (3*HPL[{0, 0, 0, 1}, 1 - v]*SPw2f1[u, v])/8 - 
     (HPL[{0, 0, 1, 1}, 1 - u]*SPw2f1[u, v])/8 + 
     (19*HPL[{0, 0, 1, 1}, 1 - v]*SPw2f1[u, v])/16 - 
     (21*HPL[{0, 1, 1, 1}, 1 - u]*SPw2f1[u, v])/16 - 
     (23*HPL[{0, 1, 1, 1}, 1 - v]*SPw2f1[u, v])/32 + 
     (5*HPL[{0, 1}, 1 - u]*SPw2f1[u, v]^2)/128 - 
     (51*HPL[{0, 1}, 1 - v]*SPw2f1[u, v]^2)/128 - 
     (3*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*SPw3f1[u, v])/64 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*SPw3f1[u, v])/64 - 
     (7*HPL[{1}, 1 - v]^3*SPw3f1[u, v])/32 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f1[u, v])/32 - 
     (7*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw3f1[u, v])/32 + 
     (61*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw3f1[u, v])/64 + 
     (3*HPL[{0, 0, 1}, 1 - v]*SPw3f1[u, v])/8 + 
     (3*HPL[{0, 1, 1}, 1 - u]*SPw3f1[u, v])/16 - 
     (13*HPL[{0, 1, 1}, 1 - v]*SPw3f1[u, v])/16 - 
     (HPL[{1}, 1 - u]*SPw2f1[u, v]*SPw3f1[u, v])/8 - 
     (HPL[{1}, 1 - v]*SPw2f1[u, v]*SPw3f1[u, v])/16 + 
     (23*HPL[{1}, 1 - u]^3*SPw3f1[v, u])/96 - 
     (9*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*SPw3f1[v, u])/64 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*SPw3f1[v, u])/32 + 
     (3*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f1[v, u])/64 - 
     (HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw3f1[v, u])/16 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*SPw3f1[v, u])/32 + 
     (HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw3f1[v, u])/32 - 
     (9*HPL[{0, 0, 1}, 1 - u]*SPw3f1[v, u])/16 - 
     (9*HPL[{0, 0, 1}, 1 - v]*SPw3f1[v, u])/16 - 
     (HPL[{0, 1, 1}, 1 - u]*SPw3f1[v, u])/4 + 
     (11*HPL[{0, 1, 1}, 1 - v]*SPw3f1[v, u])/16 + 
     (HPL[{1}, 1 - u]*SPw2f1[u, v]*SPw3f1[v, u])/8 + 
     (3*SPw3f1[u, v]*SPw3f1[v, u])/16 + (3*SPw3f1[v, u]^2)/32 - 
     (11*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f2[u, v])/128 - 
     (HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw3f2[u, v])/32 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*SPw3f2[u, v])/128 + 
     (HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw3f2[u, v])/32 - 
     (5*HPL[{0, 0, 1}, 1 - u]*SPw3f2[u, v])/32 + 
     (3*HPL[{0, 0, 1}, 1 - v]*SPw3f2[u, v])/32 - 
     (27*HPL[{0, 1, 1}, 1 - u]*SPw3f2[u, v])/64 - 
     (9*HPL[{0, 1, 1}, 1 - v]*SPw3f2[u, v])/64 - 
     (3*SPw3f1[u, v]*SPw3f2[u, v])/32 - (SPw3f1[v, u]*SPw3f2[u, v])/32 - 
     (7*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f2[v, u])/64 + 
     (13*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw3f2[v, u])/128 + 
     (9*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*SPw3f2[v, u])/64 - 
     (97*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw3f2[v, u])/128 - 
     (17*HPL[{0, 0, 1}, 1 - u]*SPw3f2[v, u])/32 + 
     (3*HPL[{0, 0, 1}, 1 - v]*SPw3f2[v, u])/32 - 
     (19*HPL[{0, 1, 1}, 1 - u]*SPw3f2[v, u])/64 + 
     (43*HPL[{0, 1, 1}, 1 - v]*SPw3f2[v, u])/64 + 
     (3*SPw3f1[u, v]*SPw3f2[v, u])/32 - (5*SPw3f1[v, u]*SPw3f2[v, u])/16 - 
     (3*HPL[{1}, 1 - v]^2*SPw4f1[u, v])/16 + 
     (9*HPL[{0, 1}, 1 - v]*SPw4f1[u, v])/8 + 
     (3*HPL[{1}, 1 - u]^2*SPw4f1[v, u])/32 - 
     (9*HPL[{0, 1}, 1 - u]*SPw4f1[v, u])/16 - 
     (13*HPL[{0, 1}, 1 - u]*SPw4f2[u, v])/64 - 
     (17*HPL[{0, 1}, 1 - v]*SPw4f2[u, v])/64 - 
     (HPL[{0, 1}, 1 - u]*SPw4f2[v, u])/16 + 
     (13*HPL[{0, 1}, 1 - v]*SPw4f2[v, u])/32 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f3[u, v])/4 - 
     (23*HPL[{1}, 1 - v]^2*SPw4f3[u, v])/64 + 
     (3*HPL[{0, 1}, 1 - v]*SPw4f3[u, v])/16 + 
     (15*HPL[{1}, 1 - u]^2*SPw4f3[v, u])/64 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f3[v, u])/8 - 
     (9*HPL[{0, 1}, 1 - u]*SPw4f3[v, u])/16 - 
     (17*HPL[{1}, 1 - u]^2*SPw4f4[u, v])/64 + 
     (7*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f4[u, v])/32 + 
     (HPL[{1}, 1 - v]^2*SPw4f4[u, v])/32 + 
     (3*HPL[{0, 1}, 1 - u]*SPw4f4[u, v])/16 + 
     (3*HPL[{0, 1}, 1 - v]*SPw4f4[u, v])/16 + (3*SPw2f1[u, v]*SPw4f4[u, v])/
      16 + (HPL[{1}, 1 - u]^2*SPw4f4[v, u])/32 - 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f4[v, u])/32 + 
     (15*HPL[{1}, 1 - v]^2*SPw4f4[v, u])/64 - 
     (3*HPL[{0, 1}, 1 - v]*SPw4f4[v, u])/8 - (3*SPw2f1[u, v]*SPw4f4[v, u])/
      16 - (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f5[u, v])/16 - 
     (HPL[{1}, 1 - v]^2*SPw4f5[u, v])/32 + 
     (3*HPL[{0, 1}, 1 - u]*SPw4f5[u, v])/16 + 
     (9*HPL[{0, 1}, 1 - v]*SPw4f5[u, v])/16 - (3*SPw2f1[u, v]*SPw4f5[u, v])/
      16 - (HPL[{1}, 1 - u]^2*SPw4f5[v, u])/32 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f5[v, u])/32 + 
     (3*HPL[{0, 1}, 1 - u]*SPw4f5[v, u])/16 + 
     (3*HPL[{0, 1}, 1 - v]*SPw4f5[v, u])/16 + 
     (9*HPL[{0, 1}, 1 - u]*SPw4f6[u, v])/64 + 
     (11*HPL[{0, 1}, 1 - v]*SPw4f6[u, v])/64 - 
     (HPL[{1}, 1 - u]^2*SPw4f7[u, v])/16 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f7[u, v])/32 - 
     (3*HPL[{0, 1}, 1 - u]*SPw4f7[u, v])/16 + (3*SPw2f1[u, v]*SPw4f7[u, v])/
      16 - (3*HPL[{1}, 1 - v]*SPw5f10[u, v])/16 + 
     (3*HPL[{1}, 1 - u]*SPw5f12[u, v])/16 + (3*HPL[{1}, 1 - v]*SPw5f16[v, u])/
      32 - (HPL[{1}, 1 - u]*SPw5f17[u, v])/32 + 
     (HPL[{1}, 1 - v]*SPw5f17[u, v])/32 + (HPL[{1}, 1 - u]*SPw5f19[u, v])/
      32 - (HPL[{1}, 1 - v]*SPw5f19[u, v])/32 + 
     (11*HPL[{1}, 1 - u]*SPw5f4[u, v])/32 - (HPL[{1}, 1 - v]*SPw5f4[u, v])/
      8 + (HPL[{1}, 1 - u]*SPw5f4[v, u])/4 - 
     (15*HPL[{1}, 1 - v]*SPw5f4[v, u])/32 + (5*HPL[{1}, 1 - u]*SPw5f7[u, v])/
      128 - (HPL[{1}, 1 - v]*SPw5f7[u, v])/32 - 
     (HPL[{1}, 1 - u]*SPw5f7[v, u])/32 + (5*HPL[{1}, 1 - v]*SPw5f7[v, u])/
      128 + (HPL[{1}, 1 - u]*SPw5f8[u, v])/16 - 
     (HPL[{1}, 1 - v]*SPw5f8[u, v])/16 - (3*HPL[{1}, 1 - v]*SPw5f9[u, v])/
      16 + (3*HPL[{1}, 1 - u]*SPw5f9[v, u])/16 - SPw6f10[u, v]/128 + 
     (101*SPw6f10[v, u])/128 + SPw6f12[u, v]/2 - SPw6f12[v, u]/4 + 
     SPw6f14[u, v]/4 + (3*SPw6f15[u, v])/16 - (3*SPw6f15[v, u])/16 - 
     (3*SPw6f16[u, v])/16 - (3*SPw6f17[u, v])/16 - SPw6f2[u, v]/2 + 
     (9*SPw6f22[u, v])/16 - (9*SPw6f22[v, u])/16 + (3*SPw6f3[u, v])/8 + 
     (3*SPw6f41[u, v])/16 - (3*SPw6f42[v, u])/8 + (3*SPw6f46[u, v])/32 + 
     SPw6f47[u, v]/128 + (21*SPw6f48[u, v])/16 + (11*SPw6f49[u, v])/128 + 
     (21*SPw6f5[u, v])/16 - (7*SPw6f5[v, u])/16 + (7*SPw6f51[u, v])/32 + 
     (9*SPw6f53[u, v])/16 + (3*SPw6f54[u, v])/16 + (5*SPw6f6[u, v])/8 + 
     (113*SPw6f6[v, u])/128 + (3*SPw6f9[u, v])/16 - 
     (3*HPL[{1}, 1 - u]^4*\[Zeta][2])/32 + 
     (95*HPL[{1}, 1 - u]^3*HPL[{1}, 1 - v]*\[Zeta][2])/192 - 
     (37*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]^2*\[Zeta][2])/64 + 
     (45*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^3*\[Zeta][2])/64 - 
     (5*HPL[{1}, 1 - v]^4*\[Zeta][2])/32 + 
     (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]*\[Zeta][2])/8 - 
     (21*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*\[Zeta][2])/16 + 
     HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u]*\[Zeta][2] - 
     (5*HPL[{0, 1}, 1 - u]^2*\[Zeta][2])/8 - 
     (15*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*\[Zeta][2])/16 - 
     (5*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v]*\[Zeta][2])/8 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - u]*\[Zeta][2])/2 + 
     (5*HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - u]*\[Zeta][2])/2 + 
     (5*HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - v]*\[Zeta][2])/2 + 
     (3*HPL[{0, 0, 0, 1}, 1 - u]*\[Zeta][2])/2 + 4*HPL[{0, 0, 1, 1}, 1 - u]*
      \[Zeta][2] + (5*HPL[{0, 1, 1, 1}, 1 - u]*\[Zeta][2])/2 - 
     (11*HPL[{1}, 1 - u]^2*SPw2f1[u, v]*\[Zeta][2])/32 + 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw2f1[u, v]*\[Zeta][2])/16 - 
     (5*HPL[{1}, 1 - v]^2*SPw2f1[u, v]*\[Zeta][2])/32 - 
     (3*HPL[{0, 1}, 1 - u]*SPw2f1[u, v]*\[Zeta][2])/8 + 
     (5*HPL[{0, 1}, 1 - v]*SPw2f1[u, v]*\[Zeta][2])/8 - 
     (5*HPL[{1}, 1 - v]*SPw3f1[u, v]*\[Zeta][2])/8 + 
     (7*HPL[{1}, 1 - u]*SPw3f1[v, u]*\[Zeta][2])/8 - 
     (HPL[{1}, 1 - v]*SPw3f1[v, u]*\[Zeta][2])/4 + 
     (3*HPL[{1}, 1 - u]*SPw3f2[u, v]*\[Zeta][2])/16 - 
     (5*HPL[{1}, 1 - v]*SPw3f2[u, v]*\[Zeta][2])/16 + 
     (9*HPL[{1}, 1 - u]*SPw3f2[v, u]*\[Zeta][2])/16 - 
     (5*HPL[{1}, 1 - v]*SPw3f2[v, u]*\[Zeta][2])/16 + 
     (3*SPw4f1[v, u]*\[Zeta][2])/2 + (11*SPw4f2[u, v]*\[Zeta][2])/16 - 
     (9*SPw4f2[v, u]*\[Zeta][2])/16 - SPw4f3[v, u]*\[Zeta][2] - 
     (SPw4f4[u, v]*\[Zeta][2])/2 - (7*SPw4f6[u, v]*\[Zeta][2])/16 - 
     (5*SPw4f7[u, v]*\[Zeta][2])/8 - (17*HPL[{1}, 1 - u]^2*\[Zeta][2]^2)/10 + 
     (131*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*\[Zeta][2]^2)/20 - 
     (11*HPL[{1}, 1 - v]^2*\[Zeta][2]^2)/4 + 
     (21*HPL[{0, 1}, 1 - u]*\[Zeta][2]^2)/5 - (21*SPw2f1[u, v]*\[Zeta][2]^2)/
      10 - (188*\[Zeta][2]^3)/21 + \[Zeta][3]^2
 
E2u1w = HPL[{1}, 1 - u]^4/32 + (HPL[{1}, 1 - u]^3*HPL[{1}, 1 - w])/8 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^3)/8 + HPL[{1}, 1 - w]^4/32 + 
     (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u])/8 - 
     (HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - w])/4 + 
     (HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - w])/8 - 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - w])/4 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - w])/4 + 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1}, 1 - w])/4 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - w]*HPL[{0, 1, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - w])/4 - 
     (HPL[{1}, 1 - w]*HPL[{0, 1, 1}, 1 - w])/4 - HPL[{0, 0, 1, 1}, 1 - u]/2 - 
     HPL[{0, 0, 1, 1}, 1 - w]/2 + (HPL[{1}, 1 - u]^2*\[Zeta][2])/2 + 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*\[Zeta][2])/2 + 
     (HPL[{1}, 1 - w]^2*\[Zeta][2])/2 - (HPL[{0, 1}, 1 - u]*\[Zeta][2])/2 - 
     (HPL[{0, 1}, 1 - w]*\[Zeta][2])/2 + (13*\[Zeta][2]^2)/5
 
E2uv1 = HPL[{1}, 1 - u]^4/32 - (HPL[{1}, 1 - u]^3*HPL[{1}, 1 - v])/8 + 
     (HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]^2)/8 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^3)/8 + HPL[{1}, 1 - v]^4/32 + 
     (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u])/8 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u])/16 - 
     (HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u])/8 + HPL[{0, 1}, 1 - u]^2/8 + 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v])/16 + 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v])/8 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - v])/2 - HPL[{0, 0, 1, 1}, 1 - u] - 
     (HPL[{0, 1}, 1 - u]*SPw2f1[u, v])/8 - (HPL[{0, 1}, 1 - v]*SPw2f1[u, v])/
      8 + (HPL[{1}, 1 - v]*SPw3f1[u, v])/8 - (HPL[{1}, 1 - u]*SPw3f1[v, u])/
      8 + SPw4f7[u, v]/8 + (HPL[{1}, 1 - u]^2*\[Zeta][2])/2 - 
     (7*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*\[Zeta][2])/4 + 
     (3*HPL[{1}, 1 - v]^2*\[Zeta][2])/4 - HPL[{0, 1}, 1 - u]*\[Zeta][2] + 
     (SPw2f1[u, v]*\[Zeta][2])/2 + (13*\[Zeta][2]^2)/5
     
E1u1w = -HPL[{1}, 1 - u]^2/4 - (HPL[{1}, 1 - u]*HPL[{1}, 1 - w])/2 - 
     HPL[{1}, 1 - w]^2/4 - \[Zeta][2]
 
E1uv1 = -HPL[{1}, 1 - u]^2/4 + (HPL[{1}, 1 - u]*HPL[{1}, 1 - v])/2 - 
     HPL[{1}, 1 - v]^2/4 - \[Zeta][2]
     
Et3u1w = -(HPL[{1}, 1 - u]^4*HPL[{0, 1}, 1 - u])/32 + 
     (97*HPL[{1}, 1 - u]^3*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u])/768 - 
     (3*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - u])/256 + 
     (205*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^3*HPL[{0, 1}, 1 - u])/2304 - 
     (HPL[{1}, 1 - w]^4*HPL[{0, 1}, 1 - u])/32 + 
     (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]^2)/32 - 
     (9*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]^2)/128 + 
     (23*HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - u]^2)/384 - 
     HPL[{0, 1}, 1 - u]^3/36 - (HPL[{1}, 1 - u]^4*HPL[{0, 1}, 1 - w])/32 + 
     (205*HPL[{1}, 1 - u]^3*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w])/2304 - 
     (3*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - w])/256 + 
     (97*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^3*HPL[{0, 1}, 1 - w])/768 - 
     (HPL[{1}, 1 - w]^4*HPL[{0, 1}, 1 - w])/32 - 
     (37*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - w])/192 + 
     (7*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*
       HPL[{0, 1}, 1 - w])/32 - (37*HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - u]*
       HPL[{0, 1}, 1 - w])/192 + (3*HPL[{0, 1}, 1 - u]^2*HPL[{0, 1}, 1 - w])/
      64 + (23*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - w]^2)/384 - 
     (9*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]^2)/128 + 
     (HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - w]^2)/32 + 
     (3*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - w]^2)/64 - 
     HPL[{0, 1}, 1 - w]^3/36 - (HPL[{1}, 1 - u]^3*HPL[{0, 0, 1}, 1 - u])/8 + 
     (5*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]*HPL[{0, 0, 1}, 1 - u])/16 - 
     (23*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^2*HPL[{0, 0, 1}, 1 - u])/96 + 
     (13*HPL[{1}, 1 - w]^3*HPL[{0, 0, 1}, 1 - u])/144 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - u])/12 - 
     (HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - u])/12 - 
     (25*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - w]*HPL[{0, 0, 1}, 1 - u])/96 + 
     (11*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*HPL[{0, 0, 1}, 1 - u])/48 - 
     HPL[{0, 0, 1}, 1 - u]^2/4 + (13*HPL[{1}, 1 - u]^3*HPL[{0, 0, 1}, 1 - w])/
      144 - (23*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]*HPL[{0, 0, 1}, 1 - w])/96 + 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^2*HPL[{0, 0, 1}, 1 - w])/16 - 
     (HPL[{1}, 1 - w]^3*HPL[{0, 0, 1}, 1 - w])/8 + 
     (11*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - w])/48 - 
     (25*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - w])/96 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - w]*HPL[{0, 0, 1}, 1 - w])/12 + 
     (HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*HPL[{0, 0, 1}, 1 - w])/12 + 
     (3*HPL[{0, 0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - w])/8 - 
     HPL[{0, 0, 1}, 1 - w]^2/4 + (HPL[{1}, 1 - u]^3*HPL[{0, 1, 1}, 1 - u])/
      8 - (13*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]*HPL[{0, 1, 1}, 1 - u])/32 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^2*HPL[{0, 1, 1}, 1 - u])/4 - 
     (113*HPL[{1}, 1 - w]^3*HPL[{0, 1, 1}, 1 - u])/1152 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/6 - 
     (HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/48 + 
     (29*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - w]*HPL[{0, 1, 1}, 1 - u])/72 - 
     (11*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*HPL[{0, 1, 1}, 1 - u])/48 + 
     (HPL[{0, 0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/3 - 
     (HPL[{0, 0, 1}, 1 - w]*HPL[{0, 1, 1}, 1 - u])/12 - 
     HPL[{0, 1, 1}, 1 - u]^2/3 - (113*HPL[{1}, 1 - u]^3*
       HPL[{0, 1, 1}, 1 - w])/1152 + (HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]*
       HPL[{0, 1, 1}, 1 - w])/4 - (13*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^2*
       HPL[{0, 1, 1}, 1 - w])/32 + (HPL[{1}, 1 - w]^3*HPL[{0, 1, 1}, 1 - w])/
      8 - (11*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - w])/48 + 
     (29*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - w])/72 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - w]*HPL[{0, 1, 1}, 1 - w])/48 - 
     (HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*HPL[{0, 1, 1}, 1 - w])/6 - 
     (HPL[{0, 0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - w])/12 + 
     (HPL[{0, 0, 1}, 1 - w]*HPL[{0, 1, 1}, 1 - w])/3 + 
     (9*HPL[{0, 1, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - w])/16 - 
     HPL[{0, 1, 1}, 1 - w]^2/3 - (3*HPL[{1}, 1 - u]^2*
       HPL[{0, 0, 0, 1}, 1 - u])/8 + (21*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*
       HPL[{0, 0, 0, 1}, 1 - u])/32 - 
     (HPL[{1}, 1 - w]^2*HPL[{0, 0, 0, 1}, 1 - u])/4 + 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 0, 0, 1}, 1 - u])/2 - 
     (9*HPL[{0, 1}, 1 - w]*HPL[{0, 0, 0, 1}, 1 - u])/16 - 
     (HPL[{1}, 1 - u]^2*HPL[{0, 0, 0, 1}, 1 - w])/4 + 
     (21*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 0, 0, 1}, 1 - w])/32 - 
     (3*HPL[{1}, 1 - w]^2*HPL[{0, 0, 0, 1}, 1 - w])/8 - 
     (9*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 0, 1}, 1 - w])/16 + 
     (HPL[{0, 1}, 1 - w]*HPL[{0, 0, 0, 1}, 1 - w])/2 + 
     (HPL[{1}, 1 - u]^2*HPL[{0, 0, 1, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 0, 1, 1}, 1 - u])/4 + 
     (HPL[{0, 1}, 1 - w]*HPL[{0, 0, 1, 1}, 1 - u])/16 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 0, 1, 1}, 1 - w])/4 + 
     (HPL[{1}, 1 - w]^2*HPL[{0, 0, 1, 1}, 1 - w])/4 + 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1, 1}, 1 - w])/16 - 
     (3*HPL[{1}, 1 - u]^2*HPL[{0, 1, 1, 1}, 1 - u])/8 + 
     (163*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1, 1, 1}, 1 - u])/192 - 
     (95*HPL[{1}, 1 - w]^2*HPL[{0, 1, 1, 1}, 1 - u])/96 + 
     (2*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1, 1}, 1 - u])/3 - 
     (73*HPL[{0, 1}, 1 - w]*HPL[{0, 1, 1, 1}, 1 - u])/96 - 
     (95*HPL[{1}, 1 - u]^2*HPL[{0, 1, 1, 1}, 1 - w])/96 + 
     (163*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1, 1, 1}, 1 - w])/192 - 
     (3*HPL[{1}, 1 - w]^2*HPL[{0, 1, 1, 1}, 1 - w])/8 - 
     (73*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1, 1}, 1 - w])/96 + 
     (2*HPL[{0, 1}, 1 - w]*HPL[{0, 1, 1, 1}, 1 - w])/3 - 
     (3*HPL[{1}, 1 - u]*HPL[{0, 0, 0, 0, 1}, 1 - u])/4 + 
     (3*HPL[{1}, 1 - w]*HPL[{0, 0, 0, 0, 1}, 1 - u])/4 + 
     (3*HPL[{1}, 1 - u]*HPL[{0, 0, 0, 0, 1}, 1 - w])/4 - 
     (3*HPL[{1}, 1 - w]*HPL[{0, 0, 0, 0, 1}, 1 - w])/4 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 0, 1, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 0, 1, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 0, 1, 1}, 1 - w])/4 + 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 0, 1, 1}, 1 - w])/4 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1, 0, 1}, 1 - u])/6 + 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1, 0, 1}, 1 - u])/6 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1, 0, 1}, 1 - w])/6 - 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1, 0, 1}, 1 - w])/6 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1, 1, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1, 1, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1, 1, 1}, 1 - w])/4 + 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1, 1, 1}, 1 - w])/4 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 0, 1, 1}, 1 - u])/3 - 
     (HPL[{1}, 1 - w]*HPL[{0, 1, 0, 1, 1}, 1 - u])/3 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 0, 1, 1}, 1 - w])/3 + 
     (HPL[{1}, 1 - w]*HPL[{0, 1, 0, 1, 1}, 1 - w])/3 + 
     (3*HPL[{1}, 1 - u]*HPL[{0, 1, 1, 1, 1}, 1 - u])/4 - 
     (3*HPL[{1}, 1 - w]*HPL[{0, 1, 1, 1, 1}, 1 - u])/4 - 
     (3*HPL[{1}, 1 - u]*HPL[{0, 1, 1, 1, 1}, 1 - w])/4 + 
     (3*HPL[{1}, 1 - w]*HPL[{0, 1, 1, 1, 1}, 1 - w])/4 + 
     HPL[{0, 0, 0, 0, 1, 1}, 1 - u]/2 + HPL[{0, 0, 0, 0, 1, 1}, 1 - w]/2 - 
     2*HPL[{0, 0, 0, 1, 1, 1}, 1 - u] - 2*HPL[{0, 0, 0, 1, 1, 1}, 1 - w] - 
     (2*HPL[{0, 0, 1, 0, 1, 1}, 1 - u])/3 - 
     (2*HPL[{0, 0, 1, 0, 1, 1}, 1 - w])/3 + HPL[{0, 0, 1, 1, 1, 1}, 1 - u]/
      6 + HPL[{0, 0, 1, 1, 1, 1}, 1 - w]/6 + 
     (5*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]*SPw2f1[w, u])/128 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*SPw2f1[w, u])/12 + 
     (5*HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - u]*SPw2f1[w, u])/128 - 
     (HPL[{0, 1}, 1 - u]^2*SPw2f1[w, u])/64 - 
     (5*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - w]*SPw2f1[w, u])/128 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*SPw2f1[w, u])/12 - 
     (5*HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - w]*SPw2f1[w, u])/128 + 
     (HPL[{0, 1}, 1 - w]^2*SPw2f1[w, u])/64 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - u]*SPw2f1[w, u])/8 + 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1}, 1 - u]*SPw2f1[w, u])/16 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - w]*SPw2f1[w, u])/16 + 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1}, 1 - w]*SPw2f1[w, u])/8 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - u]*SPw2f1[w, u])/24 - 
     (13*HPL[{1}, 1 - w]*HPL[{0, 1, 1}, 1 - u]*SPw2f1[w, u])/96 + 
     (13*HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - w]*SPw2f1[w, u])/96 + 
     (HPL[{1}, 1 - w]*HPL[{0, 1, 1}, 1 - w]*SPw2f1[w, u])/24 - 
     (3*HPL[{0, 0, 0, 1}, 1 - u]*SPw2f1[w, u])/16 + 
     (3*HPL[{0, 0, 0, 1}, 1 - w]*SPw2f1[w, u])/16 + 
     (7*HPL[{0, 0, 1, 1}, 1 - u]*SPw2f1[w, u])/16 - 
     (7*HPL[{0, 0, 1, 1}, 1 - w]*SPw2f1[w, u])/16 + 
     (19*HPL[{0, 1, 1, 1}, 1 - u]*SPw2f1[w, u])/96 - 
     (19*HPL[{0, 1, 1, 1}, 1 - w]*SPw2f1[w, u])/96 - 
     (23*HPL[{0, 1}, 1 - u]*SPw2f1[w, u]^2)/192 - 
     (23*HPL[{0, 1}, 1 - w]*SPw2f1[w, u]^2)/192 - 
     (HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]*SPw3f1[u, w])/192 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^2*SPw3f1[u, w])/24 + 
     (HPL[{1}, 1 - w]^3*SPw3f1[u, w])/144 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f1[u, w])/48 - 
     (HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*SPw3f1[u, w])/12 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - w]*SPw3f1[u, w])/48 + 
     (HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*SPw3f1[u, w])/3 - 
     (3*HPL[{0, 0, 1}, 1 - u]*SPw3f1[u, w])/16 - 
     (HPL[{0, 0, 1}, 1 - w]*SPw3f1[u, w])/16 + 
     (7*HPL[{0, 1, 1}, 1 - u]*SPw3f1[u, w])/24 - 
     (17*HPL[{0, 1, 1}, 1 - w]*SPw3f1[u, w])/48 + 
     (HPL[{1}, 1 - u]*SPw2f1[w, u]*SPw3f1[u, w])/24 + 
     (HPL[{1}, 1 - w]*SPw2f1[w, u]*SPw3f1[u, w])/16 + SPw3f1[u, w]^2/32 + 
     (HPL[{1}, 1 - u]^3*SPw3f1[w, u])/144 - 
     (HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]*SPw3f1[w, u])/24 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^2*SPw3f1[w, u])/192 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f1[w, u])/3 - 
     (HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*SPw3f1[w, u])/48 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - w]*SPw3f1[w, u])/12 + 
     (HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*SPw3f1[w, u])/48 - 
     (HPL[{0, 0, 1}, 1 - u]*SPw3f1[w, u])/16 - 
     (3*HPL[{0, 0, 1}, 1 - w]*SPw3f1[w, u])/16 - 
     (17*HPL[{0, 1, 1}, 1 - u]*SPw3f1[w, u])/48 + 
     (7*HPL[{0, 1, 1}, 1 - w]*SPw3f1[w, u])/24 - 
     (HPL[{1}, 1 - u]*SPw2f1[w, u]*SPw3f1[w, u])/16 - 
     (HPL[{1}, 1 - w]*SPw2f1[w, u]*SPw3f1[w, u])/24 + 
     (SPw3f1[u, w]*SPw3f1[w, u])/8 + SPw3f1[w, u]^2/32 - 
     (9*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f2[u, w])/32 + 
     (7*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*SPw3f2[u, w])/192 + 
     (7*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - w]*SPw3f2[u, w])/192 - 
     (5*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*SPw3f2[u, w])/192 - 
     (HPL[{0, 0, 1}, 1 - u]*SPw3f2[u, w])/48 - 
     (7*HPL[{0, 0, 1}, 1 - w]*SPw3f2[u, w])/48 + 
     (HPL[{0, 1, 1}, 1 - u]*SPw3f2[u, w])/12 - 
     (7*HPL[{0, 1, 1}, 1 - w]*SPw3f2[u, w])/48 - 
     (13*SPw3f1[u, w]*SPw3f2[u, w])/96 + (SPw3f1[w, u]*SPw3f2[u, w])/48 - 
     (5*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f2[w, u])/192 + 
     (7*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*SPw3f2[w, u])/192 + 
     (7*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - w]*SPw3f2[w, u])/192 - 
     (9*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*SPw3f2[w, u])/32 - 
     (7*HPL[{0, 0, 1}, 1 - u]*SPw3f2[w, u])/48 - 
     (HPL[{0, 0, 1}, 1 - w]*SPw3f2[w, u])/48 - 
     (7*HPL[{0, 1, 1}, 1 - u]*SPw3f2[w, u])/48 + 
     (HPL[{0, 1, 1}, 1 - w]*SPw3f2[w, u])/12 + (SPw3f1[u, w]*SPw3f2[w, u])/
      48 - (13*SPw3f1[w, u]*SPw3f2[w, u])/96 - 
     (HPL[{1}, 1 - w]^2*SPw4f1[u, w])/32 + 
     (3*HPL[{0, 1}, 1 - w]*SPw4f1[u, w])/16 - 
     (HPL[{1}, 1 - u]^2*SPw4f1[w, u])/32 + 
     (3*HPL[{0, 1}, 1 - u]*SPw4f1[w, u])/16 + 
     (13*HPL[{0, 1}, 1 - u]*SPw4f2[u, w])/192 - 
     (7*HPL[{0, 1}, 1 - w]*SPw4f2[u, w])/64 - 
     (7*HPL[{0, 1}, 1 - u]*SPw4f2[w, u])/64 + 
     (13*HPL[{0, 1}, 1 - w]*SPw4f2[w, u])/192 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*SPw4f3[u, w])/24 - 
     (HPL[{1}, 1 - w]^2*SPw4f3[u, w])/24 - (HPL[{0, 1}, 1 - w]*SPw4f3[u, w])/
      8 - (HPL[{1}, 1 - u]^2*SPw4f3[w, u])/24 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*SPw4f3[w, u])/24 - 
     (HPL[{0, 1}, 1 - u]*SPw4f3[w, u])/8 - (HPL[{1}, 1 - u]^2*SPw4f4[u, w])/
      96 + (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*SPw4f4[u, w])/48 + 
     (HPL[{1}, 1 - w]^2*SPw4f4[u, w])/48 - (HPL[{0, 1}, 1 - u]*SPw4f4[u, w])/
      16 + (HPL[{0, 1}, 1 - w]*SPw4f4[u, w])/16 - (SPw2f1[w, u]*SPw4f4[u, w])/
      8 + (HPL[{1}, 1 - u]^2*SPw4f4[w, u])/48 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*SPw4f4[w, u])/48 - 
     (HPL[{1}, 1 - w]^2*SPw4f4[w, u])/96 + (HPL[{0, 1}, 1 - u]*SPw4f4[w, u])/
      16 - (HPL[{0, 1}, 1 - w]*SPw4f4[w, u])/16 + (SPw2f1[w, u]*SPw4f4[w, u])/
      8 - (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*SPw4f5[u, w])/96 - 
     (HPL[{1}, 1 - w]^2*SPw4f5[u, w])/48 + (HPL[{0, 1}, 1 - u]*SPw4f5[u, w])/
      8 + (HPL[{0, 1}, 1 - w]*SPw4f5[u, w])/4 + (SPw2f1[w, u]*SPw4f5[u, w])/
      16 - (HPL[{1}, 1 - u]^2*SPw4f5[w, u])/48 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*SPw4f5[w, u])/96 + 
     (HPL[{0, 1}, 1 - u]*SPw4f5[w, u])/4 + (HPL[{0, 1}, 1 - w]*SPw4f5[w, u])/
      8 - (SPw2f1[w, u]*SPw4f5[w, u])/16 + (HPL[{0, 1}, 1 - u]*SPw4f6[w, u])/
      96 - (HPL[{0, 1}, 1 - w]*SPw4f6[w, u])/96 + 
     (HPL[{1}, 1 - u]^2*SPw4f7[w, u])/48 - (HPL[{1}, 1 - w]^2*SPw4f7[w, u])/
      48 + (HPL[{0, 1}, 1 - u]*SPw4f7[w, u])/16 - 
     (HPL[{0, 1}, 1 - w]*SPw4f7[w, u])/16 + (SPw2f1[w, u]*SPw4f7[w, u])/8 - 
     (HPL[{1}, 1 - w]*SPw5f10[u, w])/16 - (HPL[{1}, 1 - u]*SPw5f10[w, u])/
      16 + (HPL[{1}, 1 - u]*SPw5f12[u, w])/16 + 
     (HPL[{1}, 1 - w]*SPw5f12[w, u])/16 + (HPL[{1}, 1 - u]*SPw5f16[u, w])/
      32 + (HPL[{1}, 1 - w]*SPw5f16[w, u])/32 - 
     (HPL[{1}, 1 - u]*SPw5f19[w, u])/48 + (HPL[{1}, 1 - w]*SPw5f19[w, u])/
      48 - (HPL[{1}, 1 - u]*SPw5f4[u, w])/24 + (HPL[{1}, 1 - w]*SPw5f4[u, w])/
      24 + (HPL[{1}, 1 - u]*SPw5f4[w, u])/24 - (HPL[{1}, 1 - w]*SPw5f4[w, u])/
      24 + (5*HPL[{1}, 1 - u]*SPw5f7[u, w])/192 - 
     (HPL[{1}, 1 - w]*SPw5f7[u, w])/48 - (HPL[{1}, 1 - u]*SPw5f7[w, u])/48 + 
     (5*HPL[{1}, 1 - w]*SPw5f7[w, u])/192 + (HPL[{1}, 1 - u]*SPw5f8[u, w])/
      48 - (HPL[{1}, 1 - w]*SPw5f8[u, w])/48 - (HPL[{1}, 1 - u]*SPw5f8[w, u])/
      48 + (HPL[{1}, 1 - w]*SPw5f8[w, u])/48 + (25*SPw6f10[u, w])/96 + 
     (25*SPw6f10[w, u])/96 + SPw6f12[u, w]/12 + SPw6f12[w, u]/12 + 
     SPw6f14[u, w]/12 + SPw6f14[w, u]/12 - SPw6f16[u, w]/16 - 
     SPw6f16[w, u]/16 - SPw6f17[u, w]/16 - SPw6f17[w, u]/16 - 
     SPw6f2[u, w]/6 - SPw6f2[w, u]/6 + SPw6f3[u, w]/8 + SPw6f3[w, u]/8 + 
     SPw6f41[u, w]/16 + SPw6f41[w, u]/16 - SPw6f42[u, w]/8 - 
     SPw6f42[w, u]/8 + SPw6f46[w, u]/16 + SPw6f47[w, u]/192 + 
     (7*SPw6f5[u, w])/24 + (7*SPw6f5[w, u])/24 + (193*SPw6f6[u, w])/384 + 
     (193*SPw6f6[w, u])/384 + SPw6f9[u, w]/16 + SPw6f9[w, u]/16 + 
     (HPL[{1}, 1 - u]^4*\[Zeta][2])/16 - 
     (61*HPL[{1}, 1 - u]^3*HPL[{1}, 1 - w]*\[Zeta][2])/288 + 
     (9*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - w]^2*\[Zeta][2])/32 - 
     (61*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]^3*\[Zeta][2])/288 + 
     (HPL[{1}, 1 - w]^4*\[Zeta][2])/16 - 
     (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]*\[Zeta][2])/8 + 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u]*\[Zeta][2])/12 - 
     (HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - u]*\[Zeta][2])/4 + 
     (7*HPL[{0, 1}, 1 - u]^2*\[Zeta][2])/24 - 
     (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - w]*\[Zeta][2])/4 + 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w]*\[Zeta][2])/12 - 
     (HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - w]*\[Zeta][2])/8 - 
     (7*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - w]*\[Zeta][2])/12 + 
     (7*HPL[{0, 1}, 1 - w]^2*\[Zeta][2])/24 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - u]*\[Zeta][2])/6 + 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1}, 1 - u]*\[Zeta][2])/6 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - w]*\[Zeta][2])/6 - 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1}, 1 - w]*\[Zeta][2])/6 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - u]*\[Zeta][2])/3 - 
     (HPL[{1}, 1 - w]*HPL[{0, 1, 1}, 1 - u]*\[Zeta][2])/2 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - w]*\[Zeta][2])/2 + 
     (HPL[{1}, 1 - w]*HPL[{0, 1, 1}, 1 - w]*\[Zeta][2])/3 + 
     (HPL[{0, 0, 0, 1}, 1 - u]*\[Zeta][2])/2 + 
     (HPL[{0, 0, 0, 1}, 1 - w]*\[Zeta][2])/2 - 
     (HPL[{0, 0, 1, 1}, 1 - u]*\[Zeta][2])/3 - 
     (HPL[{0, 0, 1, 1}, 1 - w]*\[Zeta][2])/3 + 
     (HPL[{0, 1, 1, 1}, 1 - u]*\[Zeta][2])/6 + 
     (HPL[{0, 1, 1, 1}, 1 - w]*\[Zeta][2])/6 + 
     (HPL[{1}, 1 - u]^2*SPw2f1[w, u]*\[Zeta][2])/16 - 
     (HPL[{1}, 1 - w]^2*SPw2f1[w, u]*\[Zeta][2])/16 + 
     (HPL[{0, 1}, 1 - u]*SPw2f1[w, u]*\[Zeta][2])/3 - 
     (HPL[{0, 1}, 1 - w]*SPw2f1[w, u]*\[Zeta][2])/3 - 
     (HPL[{1}, 1 - u]*SPw3f1[u, w]*\[Zeta][2])/12 + 
     (HPL[{1}, 1 - w]*SPw3f1[u, w]*\[Zeta][2])/12 + 
     (HPL[{1}, 1 - u]*SPw3f1[w, u]*\[Zeta][2])/12 - 
     (HPL[{1}, 1 - w]*SPw3f1[w, u]*\[Zeta][2])/12 - 
     (HPL[{1}, 1 - u]*SPw3f2[u, w]*\[Zeta][2])/24 + 
     (HPL[{1}, 1 - w]*SPw3f2[u, w]*\[Zeta][2])/12 + 
     (HPL[{1}, 1 - u]*SPw3f2[w, u]*\[Zeta][2])/12 - 
     (HPL[{1}, 1 - w]*SPw3f2[w, u]*\[Zeta][2])/24 + 
     (SPw4f1[u, w]*\[Zeta][2])/2 + (SPw4f1[w, u]*\[Zeta][2])/2 + 
     (SPw4f2[u, w]*\[Zeta][2])/24 + (SPw4f2[w, u]*\[Zeta][2])/24 - 
     (SPw4f3[u, w]*\[Zeta][2])/3 - (SPw4f3[w, u]*\[Zeta][2])/3 - 
     (SPw4f4[u, w]*\[Zeta][2])/6 - (SPw4f4[w, u]*\[Zeta][2])/6 + 
     (21*HPL[{1}, 1 - u]^2*\[Zeta][2]^2)/20 - 
     (21*HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*\[Zeta][2]^2)/10 + 
     (21*HPL[{1}, 1 - w]^2*\[Zeta][2]^2)/20
 
Et3uv1 = (HPL[{1}, 1 - u]^4*HPL[{0, 1}, 1 - u])/32 - 
     (49*HPL[{1}, 1 - u]^3*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u])/256 + 
     (7*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u])/512 - 
     (61*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^3*HPL[{0, 1}, 1 - u])/1152 - 
     (27*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]^2)/256 + 
     (35*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u]^2)/384 - 
     HPL[{0, 1}, 1 - u]^3/36 + (HPL[{1}, 1 - u]^4*HPL[{0, 1}, 1 - v])/32 - 
     (83*HPL[{1}, 1 - u]^3*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v])/2304 - 
     (HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - v])/512 + 
     (25*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^3*HPL[{0, 1}, 1 - v])/384 + 
     (11*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v])/48 - 
     (7*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*
       HPL[{0, 1}, 1 - v])/64 - (7*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u]*
       HPL[{0, 1}, 1 - v])/192 + (19*HPL[{0, 1}, 1 - u]^2*HPL[{0, 1}, 1 - v])/
      128 - (29*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - v]^2)/192 + 
     (45*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]^2)/256 - 
     (HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - v]^2)/32 - 
     (25*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v]^2)/128 + 
     HPL[{0, 1}, 1 - v]^3/18 + (HPL[{1}, 1 - u]^3*HPL[{0, 0, 1}, 1 - u])/8 - 
     (19*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - u])/64 + 
     (11*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*HPL[{0, 0, 1}, 1 - u])/192 - 
     (HPL[{1}, 1 - v]^3*HPL[{0, 0, 1}, 1 - u])/18 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - u])/24 + 
     (HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - u])/24 + 
     (35*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 1}, 1 - u])/96 + 
     (HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 1}, 1 - u])/6 + 
     HPL[{0, 0, 1}, 1 - u]^2/8 - (5*HPL[{1}, 1 - u]^3*HPL[{0, 0, 1}, 1 - v])/
      144 + (35*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - v])/
      192 - (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*HPL[{0, 0, 1}, 1 - v])/64 - 
     (19*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - v])/48 - 
     (5*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - v])/48 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 1}, 1 - v])/24 - 
     (HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 1}, 1 - v])/24 - 
     (3*HPL[{0, 0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - v])/16 + 
     HPL[{0, 0, 1}, 1 - v]^2/8 - (HPL[{1}, 1 - u]^3*HPL[{0, 1, 1}, 1 - u])/
      8 + (15*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - u])/32 - 
     (19*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*HPL[{0, 1, 1}, 1 - u])/64 + 
     (13*HPL[{1}, 1 - v]^3*HPL[{0, 1, 1}, 1 - u])/72 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/24 + 
     (11*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/48 - 
     (55*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*HPL[{0, 1, 1}, 1 - u])/72 + 
     (65*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*HPL[{0, 1, 1}, 1 - u])/96 - 
     (HPL[{0, 0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/6 + 
     (11*HPL[{0, 0, 1}, 1 - v]*HPL[{0, 1, 1}, 1 - u])/48 + 
     HPL[{0, 1, 1}, 1 - u]^2/24 - (95*HPL[{1}, 1 - u]^3*
       HPL[{0, 1, 1}, 1 - v])/1152 + (3*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*
       HPL[{0, 1, 1}, 1 - v])/64 - (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*
       HPL[{0, 1, 1}, 1 - v])/16 - (43*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*
       HPL[{0, 1, 1}, 1 - v])/96 + (13*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*
       HPL[{0, 1, 1}, 1 - v])/36 - (5*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*
       HPL[{0, 1, 1}, 1 - v])/24 + (5*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*
       HPL[{0, 1, 1}, 1 - v])/24 - (7*HPL[{0, 0, 1}, 1 - u]*
       HPL[{0, 1, 1}, 1 - v])/48 - (HPL[{0, 0, 1}, 1 - v]*
       HPL[{0, 1, 1}, 1 - v])/6 - (9*HPL[{0, 1, 1}, 1 - u]*
       HPL[{0, 1, 1}, 1 - v])/32 + (7*HPL[{0, 1, 1}, 1 - v]^2)/24 + 
     (3*HPL[{1}, 1 - u]^2*HPL[{0, 0, 0, 1}, 1 - u])/8 - 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 0, 0, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - v]^2*HPL[{0, 0, 0, 1}, 1 - u])/8 - 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 0, 0, 1}, 1 - u])/4 + 
     (3*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 0, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - u]^2*HPL[{0, 0, 0, 1}, 1 - v])/8 + 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 0, 0, 1}, 1 - v])/32 - 
     (3*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 0, 1}, 1 - v])/16 - 
     (HPL[{0, 1}, 1 - v]*HPL[{0, 0, 0, 1}, 1 - v])/4 - 
     (3*HPL[{1}, 1 - u]^2*HPL[{0, 0, 1, 1}, 1 - u])/8 + 
     (27*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 0, 1, 1}, 1 - u])/32 - 
     (45*HPL[{1}, 1 - v]^2*HPL[{0, 0, 1, 1}, 1 - u])/128 + 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1, 1}, 1 - u])/2 - 
     (13*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 1, 1}, 1 - u])/16 + 
     (45*HPL[{1}, 1 - u]^2*HPL[{0, 0, 1, 1}, 1 - v])/128 - 
     (19*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 0, 1, 1}, 1 - v])/32 + 
     (HPL[{1}, 1 - v]^2*HPL[{0, 0, 1, 1}, 1 - v])/8 + 
     (3*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1, 1}, 1 - v])/4 - 
     (HPL[{0, 1}, 1 - v]*HPL[{0, 0, 1, 1}, 1 - v])/2 + 
     (3*HPL[{1}, 1 - u]^2*HPL[{0, 1, 1, 1}, 1 - u])/8 - 
     (251*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1, 1, 1}, 1 - u])/192 + 
     (143*HPL[{1}, 1 - v]^2*HPL[{0, 1, 1, 1}, 1 - u])/192 - 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1, 1}, 1 - u])/12 + 
     (13*HPL[{0, 1}, 1 - v]*HPL[{0, 1, 1, 1}, 1 - u])/48 + 
     (47*HPL[{1}, 1 - u]^2*HPL[{0, 1, 1, 1}, 1 - v])/192 + 
     (11*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1, 1, 1}, 1 - v])/24 + 
     (47*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1, 1}, 1 - v])/96 - 
     (7*HPL[{0, 1}, 1 - v]*HPL[{0, 1, 1, 1}, 1 - v])/12 + 
     (3*HPL[{1}, 1 - u]*HPL[{0, 0, 0, 0, 1}, 1 - u])/4 - 
     (3*HPL[{1}, 1 - v]*HPL[{0, 0, 0, 0, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 0, 1, 1}, 1 - u])/2 + 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 0, 1, 1}, 1 - u])/2 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 0, 1, 1}, 1 - v])/4 + 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 0, 1, 1}, 1 - v])/4 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1, 0, 1}, 1 - u])/12 - 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 1, 0, 1}, 1 - u])/12 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1, 0, 1}, 1 - v])/12 + 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 1, 0, 1}, 1 - v])/12 + 
     HPL[{1}, 1 - u]*HPL[{0, 0, 1, 1, 1}, 1 - u] - 
     HPL[{1}, 1 - v]*HPL[{0, 0, 1, 1, 1}, 1 - u] + 
     (5*HPL[{1}, 1 - u]*HPL[{0, 0, 1, 1, 1}, 1 - v])/4 - 
     (5*HPL[{1}, 1 - v]*HPL[{0, 0, 1, 1, 1}, 1 - v])/4 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 0, 1, 1}, 1 - u])/12 - 
     (HPL[{1}, 1 - v]*HPL[{0, 1, 0, 1, 1}, 1 - u])/12 + 
     (5*HPL[{1}, 1 - u]*HPL[{0, 1, 0, 1, 1}, 1 - v])/12 - 
     (5*HPL[{1}, 1 - v]*HPL[{0, 1, 0, 1, 1}, 1 - v])/12 - 
     (3*HPL[{1}, 1 - u]*HPL[{0, 1, 1, 1, 1}, 1 - u])/4 + 
     (3*HPL[{1}, 1 - v]*HPL[{0, 1, 1, 1, 1}, 1 - u])/4 - 
     HPL[{0, 0, 0, 0, 1, 1}, 1 - u] + HPL[{0, 0, 0, 0, 1, 1}, 1 - v]/2 - 
     2*HPL[{0, 0, 0, 1, 1, 1}, 1 - u] + 4*HPL[{0, 0, 0, 1, 1, 1}, 1 - v] - 
     (2*HPL[{0, 0, 1, 0, 1, 1}, 1 - u])/3 + 
     (4*HPL[{0, 0, 1, 0, 1, 1}, 1 - v])/3 - 
     (4*HPL[{0, 0, 1, 1, 1, 1}, 1 - u])/3 + 
     (7*HPL[{0, 0, 1, 1, 1, 1}, 1 - v])/6 + 
     (15*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]*SPw2f1[u, v])/128 + 
     (11*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw2f1[u, v])/
      48 + (HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u]*SPw2f1[u, v])/8 + 
     (27*HPL[{0, 1}, 1 - u]^2*SPw2f1[u, v])/128 + 
     (11*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - v]*SPw2f1[u, v])/128 + 
     (7*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw2f1[u, v])/48 + 
     (5*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - v]*SPw2f1[u, v])/64 - 
     (13*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v]*SPw2f1[u, v])/64 + 
     (29*HPL[{0, 1}, 1 - v]^2*SPw2f1[u, v])/128 - 
     (5*HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - u]*SPw2f1[u, v])/32 + 
     (7*HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - u]*SPw2f1[u, v])/32 + 
     (5*HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - v]*SPw2f1[u, v])/32 - 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - v]*SPw2f1[u, v])/32 - 
     (91*HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - u]*SPw2f1[u, v])/192 + 
     (47*HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - u]*SPw2f1[u, v])/192 + 
     (73*HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - v]*SPw2f1[u, v])/192 - 
     (83*HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - v]*SPw2f1[u, v])/192 + 
     (3*HPL[{0, 0, 0, 1}, 1 - v]*SPw2f1[u, v])/16 - 
     (5*HPL[{0, 0, 1, 1}, 1 - u]*SPw2f1[u, v])/16 - 
     (3*HPL[{0, 0, 1, 1}, 1 - v]*SPw2f1[u, v])/4 + 
     (107*HPL[{0, 1, 1, 1}, 1 - u]*SPw2f1[u, v])/96 + 
     (11*HPL[{0, 1, 1, 1}, 1 - v]*SPw2f1[u, v])/12 - 
     (61*HPL[{0, 1}, 1 - u]*SPw2f1[u, v]^2)/384 + 
     (107*HPL[{0, 1}, 1 - v]*SPw2f1[u, v]^2)/384 + 
     (HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*SPw3f1[u, v])/24 - 
     (11*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*SPw3f1[u, v])/192 + 
     (65*HPL[{1}, 1 - v]^3*SPw3f1[u, v])/288 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f1[u, v])/96 + 
     (13*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw3f1[u, v])/96 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*SPw3f1[u, v])/48 - 
     (119*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw3f1[u, v])/192 - 
     (3*HPL[{0, 0, 1}, 1 - u]*SPw3f1[u, v])/16 - 
     (7*HPL[{0, 0, 1}, 1 - v]*SPw3f1[u, v])/16 + 
     (5*HPL[{0, 1, 1}, 1 - u]*SPw3f1[u, v])/48 + 
     (11*HPL[{0, 1, 1}, 1 - v]*SPw3f1[u, v])/24 + 
     (HPL[{1}, 1 - u]*SPw2f1[u, v]*SPw3f1[u, v])/12 + SPw3f1[u, v]^2/32 - 
     (67*HPL[{1}, 1 - u]^3*SPw3f1[v, u])/288 + 
     (19*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*SPw3f1[v, u])/192 - 
     (7*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*SPw3f1[v, u])/192 + 
     (55*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f1[v, u])/192 + 
     (HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw3f1[v, u])/24 - 
     (5*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*SPw3f1[v, u])/96 - 
     (HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw3f1[v, u])/96 + 
     (HPL[{0, 0, 1}, 1 - u]*SPw3f1[v, u])/2 + 
     (3*HPL[{0, 0, 1}, 1 - v]*SPw3f1[v, u])/8 - 
     (5*HPL[{0, 1, 1}, 1 - u]*SPw3f1[v, u])/48 - 
     (19*HPL[{0, 1, 1}, 1 - v]*SPw3f1[v, u])/48 - 
     (HPL[{1}, 1 - u]*SPw2f1[u, v]*SPw3f1[v, u])/16 + 
     (HPL[{1}, 1 - v]*SPw2f1[u, v]*SPw3f1[v, u])/24 - 
     (SPw3f1[u, v]*SPw3f1[v, u])/16 - SPw3f1[v, u]^2/16 - 
     (25*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f2[u, v])/128 + 
     (13*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw3f2[u, v])/192 + 
     (11*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*SPw3f2[u, v])/384 - 
     (11*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw3f2[u, v])/192 + 
     (13*HPL[{0, 0, 1}, 1 - u]*SPw3f2[u, v])/96 - 
     (23*HPL[{0, 0, 1}, 1 - v]*SPw3f2[u, v])/96 + 
     (97*HPL[{0, 1, 1}, 1 - u]*SPw3f2[u, v])/192 - 
     (HPL[{0, 1, 1}, 1 - v]*SPw3f2[u, v])/192 - (SPw3f1[u, v]*SPw3f2[u, v])/
      24 + (5*SPw3f1[v, u]*SPw3f2[u, v])/96 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f2[v, u])/12 - 
     (25*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw3f2[v, u])/384 - 
     (5*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*SPw3f2[v, u])/48 + 
     (61*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw3f2[v, u])/128 + 
     (37*HPL[{0, 0, 1}, 1 - u]*SPw3f2[v, u])/96 - 
     (11*HPL[{0, 0, 1}, 1 - v]*SPw3f2[v, u])/96 + 
     (29*HPL[{0, 1, 1}, 1 - u]*SPw3f2[v, u])/192 - 
     (113*HPL[{0, 1, 1}, 1 - v]*SPw3f2[v, u])/192 - 
     (7*SPw3f1[u, v]*SPw3f2[v, u])/96 + (17*SPw3f1[v, u]*SPw3f2[v, u])/96 + 
     (5*HPL[{1}, 1 - v]^2*SPw4f1[u, v])/32 - 
     (15*HPL[{0, 1}, 1 - v]*SPw4f1[u, v])/16 - 
     (HPL[{1}, 1 - u]^2*SPw4f1[v, u])/8 + (3*HPL[{0, 1}, 1 - u]*SPw4f1[v, u])/
      4 + (13*HPL[{0, 1}, 1 - u]*SPw4f2[u, v])/48 + 
     (5*HPL[{0, 1}, 1 - v]*SPw4f2[u, v])/32 - 
     (3*HPL[{0, 1}, 1 - u]*SPw4f2[v, u])/64 - 
     (65*HPL[{0, 1}, 1 - v]*SPw4f2[v, u])/192 - 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f3[u, v])/24 + 
     (61*HPL[{1}, 1 - v]^2*SPw4f3[u, v])/192 - 
     (5*HPL[{0, 1}, 1 - v]*SPw4f3[u, v])/16 - 
     (53*HPL[{1}, 1 - u]^2*SPw4f3[v, u])/192 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f3[v, u])/6 + 
     (7*HPL[{0, 1}, 1 - u]*SPw4f3[v, u])/16 + 
     (49*HPL[{1}, 1 - u]^2*SPw4f4[u, v])/192 - 
     (19*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f4[u, v])/96 - 
     (HPL[{1}, 1 - v]^2*SPw4f4[u, v])/96 - (HPL[{0, 1}, 1 - u]*SPw4f4[u, v])/
      4 - (HPL[{0, 1}, 1 - v]*SPw4f4[u, v])/8 - (SPw2f1[u, v]*SPw4f4[u, v])/
      16 - (HPL[{1}, 1 - u]^2*SPw4f4[v, u])/96 + 
     (17*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f4[v, u])/96 - 
     (47*HPL[{1}, 1 - v]^2*SPw4f4[v, u])/192 + 
     (HPL[{0, 1}, 1 - u]*SPw4f4[v, u])/16 + 
     (5*HPL[{0, 1}, 1 - v]*SPw4f4[v, u])/16 + (SPw2f1[u, v]*SPw4f4[v, u])/
      16 + (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f5[u, v])/96 + 
     (HPL[{1}, 1 - v]^2*SPw4f5[u, v])/96 - (HPL[{0, 1}, 1 - u]*SPw4f5[u, v])/
      16 - (5*HPL[{0, 1}, 1 - v]*SPw4f5[u, v])/16 + 
     (SPw2f1[u, v]*SPw4f5[u, v])/8 + (HPL[{1}, 1 - u]^2*SPw4f5[v, u])/96 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f5[v, u])/24 + 
     (HPL[{0, 1}, 1 - u]*SPw4f5[v, u])/16 - (HPL[{0, 1}, 1 - v]*SPw4f5[v, u])/
      16 + (SPw2f1[u, v]*SPw4f5[v, u])/16 - 
     (29*HPL[{0, 1}, 1 - u]*SPw4f6[u, v])/192 - 
     (31*HPL[{0, 1}, 1 - v]*SPw4f6[u, v])/192 + 
     (HPL[{1}, 1 - u]^2*SPw4f7[u, v])/24 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f7[u, v])/32 + 
     (HPL[{1}, 1 - v]^2*SPw4f7[u, v])/48 + (HPL[{0, 1}, 1 - u]*SPw4f7[u, v])/
      8 + (HPL[{0, 1}, 1 - v]*SPw4f7[u, v])/16 - (SPw2f1[u, v]*SPw4f7[u, v])/
      16 + (HPL[{1}, 1 - v]*SPw5f10[u, v])/8 - 
     (HPL[{1}, 1 - u]*SPw5f10[v, u])/16 - (HPL[{1}, 1 - u]*SPw5f12[u, v])/8 + 
     (HPL[{1}, 1 - v]*SPw5f12[v, u])/16 + (HPL[{1}, 1 - u]*SPw5f16[u, v])/
      32 - (HPL[{1}, 1 - v]*SPw5f16[v, u])/16 + 
     (HPL[{1}, 1 - u]*SPw5f17[u, v])/32 - (HPL[{1}, 1 - v]*SPw5f17[u, v])/
      32 - (HPL[{1}, 1 - u]*SPw5f19[u, v])/96 + 
     (HPL[{1}, 1 - v]*SPw5f19[u, v])/96 - (37*HPL[{1}, 1 - u]*SPw5f4[u, v])/
      96 + (HPL[{1}, 1 - v]*SPw5f4[u, v])/6 - 
     (5*HPL[{1}, 1 - u]*SPw5f4[v, u])/24 + (41*HPL[{1}, 1 - v]*SPw5f4[v, u])/
      96 - (5*HPL[{1}, 1 - u]*SPw5f7[u, v])/384 + 
     (HPL[{1}, 1 - v]*SPw5f7[u, v])/96 + (HPL[{1}, 1 - u]*SPw5f7[v, u])/96 - 
     (5*HPL[{1}, 1 - v]*SPw5f7[v, u])/384 - (HPL[{1}, 1 - u]*SPw5f8[u, v])/
      24 + (HPL[{1}, 1 - v]*SPw5f8[u, v])/24 - (HPL[{1}, 1 - u]*SPw5f8[v, u])/
      48 + (HPL[{1}, 1 - v]*SPw5f8[v, u])/48 + 
     (3*HPL[{1}, 1 - v]*SPw5f9[u, v])/16 - (3*HPL[{1}, 1 - u]*SPw5f9[v, u])/
      16 + (103*SPw6f10[u, v])/384 - (203*SPw6f10[v, u])/384 - 
     (5*SPw6f12[u, v])/12 + SPw6f12[v, u]/3 - SPw6f14[u, v]/6 + 
     SPw6f14[v, u]/12 - (3*SPw6f15[u, v])/16 + (3*SPw6f15[v, u])/16 + 
     SPw6f16[u, v]/8 - SPw6f16[v, u]/16 + SPw6f17[u, v]/8 - 
     SPw6f17[v, u]/16 + SPw6f2[u, v]/3 - SPw6f2[v, u]/6 - 
     (9*SPw6f22[u, v])/16 + (9*SPw6f22[v, u])/16 - SPw6f3[u, v]/4 + 
     SPw6f3[v, u]/8 - SPw6f41[u, v]/8 + SPw6f41[v, u]/16 - SPw6f42[u, v]/8 + 
     SPw6f42[v, u]/4 - SPw6f46[u, v]/32 - SPw6f47[u, v]/384 - 
     (21*SPw6f48[u, v])/16 - (11*SPw6f49[u, v])/128 - (49*SPw6f5[u, v])/48 + 
     (35*SPw6f5[v, u])/48 - (7*SPw6f51[u, v])/32 - (9*SPw6f53[u, v])/16 - 
     (3*SPw6f54[u, v])/16 - (47*SPw6f6[u, v])/384 - (73*SPw6f6[v, u])/192 - 
     SPw6f9[u, v]/8 + SPw6f9[v, u]/16 - (HPL[{1}, 1 - u]^4*\[Zeta][2])/16 + 
     (121*HPL[{1}, 1 - u]^3*HPL[{1}, 1 - v]*\[Zeta][2])/576 - 
     (9*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]^2*\[Zeta][2])/64 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^3*\[Zeta][2])/576 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*\[Zeta][2])/48 - 
     (3*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u]*\[Zeta][2])/8 + 
     (HPL[{0, 1}, 1 - u]^2*\[Zeta][2])/6 + 
     (5*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - v]*\[Zeta][2])/8 - 
     (19*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*\[Zeta][2])/48 + 
     (HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - v]*\[Zeta][2])/8 + 
     (7*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v]*\[Zeta][2])/24 - 
     (11*HPL[{0, 1}, 1 - v]^2*\[Zeta][2])/24 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - u]*\[Zeta][2])/12 - 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - u]*\[Zeta][2])/12 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - v]*\[Zeta][2])/12 + 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - v]*\[Zeta][2])/12 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - u]*\[Zeta][2])/12 + 
     (HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - u]*\[Zeta][2])/4 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - v]*\[Zeta][2])/4 - 
     (5*HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - v]*\[Zeta][2])/12 - 
     HPL[{0, 0, 0, 1}, 1 - u]*\[Zeta][2] + 
     (HPL[{0, 0, 0, 1}, 1 - v]*\[Zeta][2])/2 - 
     (11*HPL[{0, 0, 1, 1}, 1 - u]*\[Zeta][2])/6 + 
     (13*HPL[{0, 0, 1, 1}, 1 - v]*\[Zeta][2])/6 - 
     (4*HPL[{0, 1, 1, 1}, 1 - u]*\[Zeta][2])/3 + 
     (7*HPL[{0, 1, 1, 1}, 1 - v]*\[Zeta][2])/6 + 
     (9*HPL[{1}, 1 - u]^2*SPw2f1[u, v]*\[Zeta][2])/32 - 
     (5*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw2f1[u, v]*\[Zeta][2])/16 + 
     (7*HPL[{1}, 1 - v]^2*SPw2f1[u, v]*\[Zeta][2])/32 + 
     (HPL[{0, 1}, 1 - u]*SPw2f1[u, v]*\[Zeta][2])/24 - 
     (7*HPL[{0, 1}, 1 - v]*SPw2f1[u, v]*\[Zeta][2])/24 - 
     (HPL[{1}, 1 - u]*SPw3f1[u, v]*\[Zeta][2])/12 + 
     (17*HPL[{1}, 1 - v]*SPw3f1[u, v]*\[Zeta][2])/24 - 
     (19*HPL[{1}, 1 - u]*SPw3f1[v, u]*\[Zeta][2])/24 + 
     (HPL[{1}, 1 - v]*SPw3f1[v, u]*\[Zeta][2])/6 - 
     (11*HPL[{1}, 1 - u]*SPw3f2[u, v]*\[Zeta][2])/48 + 
     (19*HPL[{1}, 1 - v]*SPw3f2[u, v]*\[Zeta][2])/48 - 
     (23*HPL[{1}, 1 - u]*SPw3f2[v, u]*\[Zeta][2])/48 + 
     (13*HPL[{1}, 1 - v]*SPw3f2[v, u]*\[Zeta][2])/48 + 
     (SPw4f1[u, v]*\[Zeta][2])/2 - SPw4f1[v, u]*\[Zeta][2] - 
     (31*SPw4f2[u, v]*\[Zeta][2])/48 + (29*SPw4f2[v, u]*\[Zeta][2])/48 - 
     (SPw4f3[u, v]*\[Zeta][2])/3 + (2*SPw4f3[v, u]*\[Zeta][2])/3 + 
     (SPw4f4[u, v]*\[Zeta][2])/3 - (SPw4f4[v, u]*\[Zeta][2])/6 + 
     (7*SPw4f6[u, v]*\[Zeta][2])/16 + (5*SPw4f7[u, v]*\[Zeta][2])/8 - 
     (21*HPL[{1}, 1 - u]^2*\[Zeta][2]^2)/20 + 
     (21*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*\[Zeta][2]^2)/20 - 
     (21*HPL[{0, 1}, 1 - u]*\[Zeta][2]^2)/10 + 
     (21*HPL[{0, 1}, 1 - v]*\[Zeta][2]^2)/10 + (21*SPw2f1[u, v]*\[Zeta][2]^2)/
      10
 
Et2u1w = (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u])/8 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - u])/8 - HPL[{0, 1}, 1 - u]^2/8 + 
     (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - w])/8 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*HPL[{0, 1}, 1 - w])/4 + 
     (HPL[{1}, 1 - w]^2*HPL[{0, 1}, 1 - w])/8 + 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - w])/4 - HPL[{0, 1}, 1 - w]^2/8 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - w])/4 + 
     (HPL[{1}, 1 - w]*HPL[{0, 0, 1}, 1 - w])/4 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - w]*HPL[{0, 1, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - w])/4 - 
     (HPL[{1}, 1 - w]*HPL[{0, 1, 1}, 1 - w])/4 - 
     (HPL[{1}, 1 - u]^2*\[Zeta][2])/4 + (HPL[{1}, 1 - u]*HPL[{1}, 1 - w]*
       \[Zeta][2])/2 - (HPL[{1}, 1 - w]^2*\[Zeta][2])/4

Et2uv1 = -(HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u])/8 + 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u])/16 - 
     (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - v])/8 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v])/16 - 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v])/8 + HPL[{0, 1}, 1 - v]^2/8 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - u])/4 + HPL[{0, 0, 1, 1}, 1 - u]/2 - 
     HPL[{0, 0, 1, 1}, 1 - v]/2 + (HPL[{0, 1}, 1 - u]*SPw2f1[u, v])/8 + 
     (HPL[{0, 1}, 1 - v]*SPw2f1[u, v])/8 - (HPL[{1}, 1 - v]*SPw3f1[u, v])/8 + 
     (HPL[{1}, 1 - u]*SPw3f1[v, u])/8 - SPw4f7[u, v]/8 + 
     (HPL[{1}, 1 - u]^2*\[Zeta][2])/4 - (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*
       \[Zeta][2])/4 + (HPL[{0, 1}, 1 - u]*\[Zeta][2])/2 - 
     (HPL[{0, 1}, 1 - v]*\[Zeta][2])/2 - (SPw2f1[u, v]*\[Zeta][2])/2

R63uv1 = (-79*HPL[{1}, 1 - u]^3*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u])/1536 + 
     (25*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u])/512 - 
     (7*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^3*HPL[{0, 1}, 1 - u])/512 + 
     (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]^2)/8 - 
     (65*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]^2)/256 + 
     (13*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u]^2)/256 - 
     HPL[{0, 1}, 1 - u]^3/16 - (7*HPL[{1}, 1 - u]^3*HPL[{1}, 1 - v]*
       HPL[{0, 1}, 1 - v])/512 + (25*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]^2*
       HPL[{0, 1}, 1 - v])/512 - (79*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^3*
       HPL[{0, 1}, 1 - v])/1536 + (17*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]*
       HPL[{0, 1}, 1 - v])/128 - (9*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*
       HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v])/64 + 
     (17*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v])/128 - 
     (13*HPL[{0, 1}, 1 - u]^2*HPL[{0, 1}, 1 - v])/128 + 
     (13*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - v]^2)/256 - 
     (65*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]^2)/256 + 
     (HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - v]^2)/8 - 
     (13*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v]^2)/128 - 
     HPL[{0, 1}, 1 - v]^3/16 - (HPL[{1}, 1 - u]^3*HPL[{0, 0, 1}, 1 - u])/8 + 
     (3*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - u])/32 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*HPL[{0, 0, 1}, 1 - u])/64 + 
     (3*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - u])/8 - 
     (HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - u])/8 + 
     (21*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 1}, 1 - u])/64 - 
     (3*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 1}, 1 - u])/32 - 
     HPL[{0, 0, 1}, 1 - u]^2/16 + (HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*
       HPL[{0, 0, 1}, 1 - v])/64 + (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*
       HPL[{0, 0, 1}, 1 - v])/32 - (HPL[{1}, 1 - v]^3*HPL[{0, 0, 1}, 1 - v])/
      8 - (3*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - v])/32 + 
     (21*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - v])/64 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 1}, 1 - v])/8 + 
     (3*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 1}, 1 - v])/8 - 
     (3*HPL[{0, 0, 1}, 1 - u]*HPL[{0, 0, 1}, 1 - v])/16 - 
     HPL[{0, 0, 1}, 1 - v]^2/16 + (HPL[{1}, 1 - u]^3*HPL[{0, 1, 1}, 1 - u])/
      8 - (9*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - u])/64 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*HPL[{0, 1, 1}, 1 - u])/16 - 
     (23*HPL[{1}, 1 - v]^3*HPL[{0, 1, 1}, 1 - u])/768 - 
     (3*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/8 + 
     (17*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/32 - 
     (37*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*HPL[{0, 1, 1}, 1 - u])/96 + 
     (3*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*HPL[{0, 1, 1}, 1 - u])/16 - 
     (HPL[{0, 0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - u])/8 + 
     (3*HPL[{0, 1, 1}, 1 - u]^2)/16 - 
     (23*HPL[{1}, 1 - u]^3*HPL[{0, 1, 1}, 1 - v])/768 - 
     (HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - v])/16 - 
     (9*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*HPL[{0, 1, 1}, 1 - v])/64 + 
     (HPL[{1}, 1 - v]^3*HPL[{0, 1, 1}, 1 - v])/8 + 
     (3*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - v])/16 - 
     (37*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - v])/96 + 
     (17*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*HPL[{0, 1, 1}, 1 - v])/32 - 
     (3*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*HPL[{0, 1, 1}, 1 - v])/8 - 
     (HPL[{0, 0, 1}, 1 - v]*HPL[{0, 1, 1}, 1 - v])/8 - 
     (3*HPL[{0, 1, 1}, 1 - u]*HPL[{0, 1, 1}, 1 - v])/32 + 
     (3*HPL[{0, 1, 1}, 1 - v]^2)/16 - 
     (5*HPL[{1}, 1 - u]^2*HPL[{0, 0, 0, 1}, 1 - u])/8 + 
     (13*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 0, 0, 1}, 1 - u])/64 + 
     (HPL[{1}, 1 - v]^2*HPL[{0, 0, 0, 1}, 1 - u])/16 + 
     (3*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 0, 1}, 1 - u])/8 + 
     (11*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 0, 1}, 1 - u])/32 + 
     (HPL[{1}, 1 - u]^2*HPL[{0, 0, 0, 1}, 1 - v])/16 + 
     (13*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 0, 0, 1}, 1 - v])/64 - 
     (5*HPL[{1}, 1 - v]^2*HPL[{0, 0, 0, 1}, 1 - v])/8 + 
     (11*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 0, 1}, 1 - v])/32 + 
     (3*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 0, 1}, 1 - v])/8 + 
     (5*HPL[{1}, 1 - u]^2*HPL[{0, 0, 1, 1}, 1 - u])/8 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 0, 1, 1}, 1 - u])/16 - 
     (HPL[{1}, 1 - v]^2*HPL[{0, 0, 1, 1}, 1 - u])/16 + 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1, 1}, 1 - u])/8 + 
     (5*HPL[{0, 1}, 1 - v]*HPL[{0, 0, 1, 1}, 1 - u])/32 - 
     (HPL[{1}, 1 - u]^2*HPL[{0, 0, 1, 1}, 1 - v])/16 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 0, 1, 1}, 1 - v])/16 + 
     (5*HPL[{1}, 1 - v]^2*HPL[{0, 0, 1, 1}, 1 - v])/8 + 
     (5*HPL[{0, 1}, 1 - u]*HPL[{0, 0, 1, 1}, 1 - v])/32 + 
     (HPL[{0, 1}, 1 - v]*HPL[{0, 0, 1, 1}, 1 - v])/8 - 
     (9*HPL[{1}, 1 - u]^2*HPL[{0, 1, 1, 1}, 1 - u])/8 + 
     (129*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1, 1, 1}, 1 - u])/128 - 
     (33*HPL[{1}, 1 - v]^2*HPL[{0, 1, 1, 1}, 1 - u])/64 + 
     (3*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1, 1}, 1 - u])/8 + 
     (21*HPL[{0, 1}, 1 - v]*HPL[{0, 1, 1, 1}, 1 - u])/64 - 
     (33*HPL[{1}, 1 - u]^2*HPL[{0, 1, 1, 1}, 1 - v])/64 + 
     (129*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1, 1, 1}, 1 - v])/128 - 
     (9*HPL[{1}, 1 - v]^2*HPL[{0, 1, 1, 1}, 1 - v])/8 + 
     (21*HPL[{0, 1}, 1 - u]*HPL[{0, 1, 1, 1}, 1 - v])/64 + 
     (3*HPL[{0, 1}, 1 - v]*HPL[{0, 1, 1, 1}, 1 - v])/8 - 
     (3*HPL[{1}, 1 - u]*HPL[{0, 0, 0, 0, 1}, 1 - u])/2 - 
     (3*HPL[{1}, 1 - v]*HPL[{0, 0, 0, 0, 1}, 1 - v])/2 + 
     (3*HPL[{1}, 1 - u]*HPL[{0, 0, 0, 1, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 0, 1, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 0, 1, 1}, 1 - v])/4 + 
     (3*HPL[{1}, 1 - v]*HPL[{0, 0, 0, 1, 1}, 1 - v])/4 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1, 0, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 1, 0, 1}, 1 - u])/4 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1, 0, 1}, 1 - v])/4 - 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 1, 0, 1}, 1 - v])/4 - 
     (9*HPL[{1}, 1 - u]*HPL[{0, 0, 1, 1, 1}, 1 - u])/4 - 
     (9*HPL[{1}, 1 - v]*HPL[{0, 0, 1, 1, 1}, 1 - u])/4 - 
     (9*HPL[{1}, 1 - u]*HPL[{0, 0, 1, 1, 1}, 1 - v])/4 - 
     (9*HPL[{1}, 1 - v]*HPL[{0, 0, 1, 1, 1}, 1 - v])/4 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 0, 1, 1}, 1 - u])/4 - 
     (3*HPL[{1}, 1 - v]*HPL[{0, 1, 0, 1, 1}, 1 - u])/4 - 
     (3*HPL[{1}, 1 - u]*HPL[{0, 1, 0, 1, 1}, 1 - v])/4 - 
     (HPL[{1}, 1 - v]*HPL[{0, 1, 0, 1, 1}, 1 - v])/4 + 
     (9*HPL[{1}, 1 - u]*HPL[{0, 1, 1, 1, 1}, 1 - u])/2 - 
     (3*HPL[{1}, 1 - v]*HPL[{0, 1, 1, 1, 1}, 1 - u])/2 - 
     (3*HPL[{1}, 1 - u]*HPL[{0, 1, 1, 1, 1}, 1 - v])/2 + 
     (9*HPL[{1}, 1 - v]*HPL[{0, 1, 1, 1, 1}, 1 - v])/2 - 
     (3*HPL[{0, 0, 0, 0, 0, 1}, 1 - u])/2 - 
     (3*HPL[{0, 0, 0, 0, 0, 1}, 1 - v])/2 + 
     (5*HPL[{0, 0, 0, 0, 1, 1}, 1 - u])/4 + 
     (5*HPL[{0, 0, 0, 0, 1, 1}, 1 - v])/4 - 
     3*HPL[{0, 0, 0, 1, 1, 1}, 1 - u] - 3*HPL[{0, 0, 0, 1, 1, 1}, 1 - v] - 
     HPL[{0, 0, 1, 0, 1, 1}, 1 - u]/2 - HPL[{0, 0, 1, 0, 1, 1}, 1 - v]/2 + 
     (9*HPL[{0, 0, 1, 1, 1, 1}, 1 - u])/4 + 
     (9*HPL[{0, 0, 1, 1, 1, 1}, 1 - v])/4 - 
     (15*HPL[{0, 1, 1, 1, 1, 1}, 1 - u])/2 - 
     (15*HPL[{0, 1, 1, 1, 1, 1}, 1 - v])/2 + 
     (35*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]*SPw2f1[u, v])/256 - 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw2f1[u, v])/32 - 
     (5*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - u]*SPw2f1[u, v])/256 + 
     (HPL[{0, 1}, 1 - u]^2*SPw2f1[u, v])/128 + 
     (5*HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - v]*SPw2f1[u, v])/256 + 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw2f1[u, v])/32 - 
     (35*HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - v]*SPw2f1[u, v])/256 - 
     (HPL[{0, 1}, 1 - v]^2*SPw2f1[u, v])/128 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - u]*SPw2f1[u, v])/16 - 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - u]*SPw2f1[u, v])/32 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - v]*SPw2f1[u, v])/32 - 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - v]*SPw2f1[u, v])/16 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - u]*SPw2f1[u, v])/32 + 
     (21*HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - u]*SPw2f1[u, v])/64 - 
     (21*HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - v]*SPw2f1[u, v])/64 + 
     (HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - v]*SPw2f1[u, v])/32 + 
     (3*HPL[{0, 0, 0, 1}, 1 - u]*SPw2f1[u, v])/32 - 
     (3*HPL[{0, 0, 0, 1}, 1 - v]*SPw2f1[u, v])/32 + 
     (13*HPL[{0, 0, 1, 1}, 1 - u]*SPw2f1[u, v])/32 - 
     (13*HPL[{0, 0, 1, 1}, 1 - v]*SPw2f1[u, v])/32 - 
     (33*HPL[{0, 1, 1, 1}, 1 - u]*SPw2f1[u, v])/64 + 
     (33*HPL[{0, 1, 1, 1}, 1 - v]*SPw2f1[u, v])/64 - 
     (HPL[{0, 1}, 1 - u]*SPw2f1[u, v]^2)/128 - 
     (HPL[{0, 1}, 1 - v]*SPw2f1[u, v]^2)/128 + 
     (3*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*SPw3f1[u, v])/128 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*SPw3f1[u, v])/32 - 
     (HPL[{1}, 1 - v]^3*SPw3f1[u, v])/192 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f1[u, v])/16 - 
     (3*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw3f1[u, v])/32 - 
     (HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*SPw3f1[u, v])/16 + 
     (7*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw3f1[u, v])/32 - 
     (3*HPL[{0, 0, 1}, 1 - u]*SPw3f1[u, v])/32 - 
     (HPL[{0, 0, 1}, 1 - v]*SPw3f1[u, v])/32 + 
     (9*HPL[{0, 1, 1}, 1 - u]*SPw3f1[u, v])/16 + 
     (HPL[{0, 1, 1}, 1 - v]*SPw3f1[u, v])/32 + 
     (HPL[{1}, 1 - u]*SPw2f1[u, v]*SPw3f1[u, v])/32 + 
     (HPL[{1}, 1 - v]*SPw2f1[u, v]*SPw3f1[u, v])/8 + SPw3f1[u, v]^2/64 - 
     (HPL[{1}, 1 - u]^3*SPw3f1[v, u])/192 + 
     (HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]*SPw3f1[v, u])/32 + 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^2*SPw3f1[v, u])/128 + 
     (7*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f1[v, u])/32 - 
     (HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw3f1[v, u])/16 - 
     (3*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*SPw3f1[v, u])/32 + 
     (HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw3f1[v, u])/16 - 
     (HPL[{0, 0, 1}, 1 - u]*SPw3f1[v, u])/32 - 
     (3*HPL[{0, 0, 1}, 1 - v]*SPw3f1[v, u])/32 + 
     (HPL[{0, 1, 1}, 1 - u]*SPw3f1[v, u])/32 + 
     (9*HPL[{0, 1, 1}, 1 - v]*SPw3f1[v, u])/16 - 
     (HPL[{1}, 1 - u]*SPw2f1[u, v]*SPw3f1[v, u])/8 - 
     (HPL[{1}, 1 - v]*SPw2f1[u, v]*SPw3f1[v, u])/32 + 
     (SPw3f1[u, v]*SPw3f1[v, u])/16 + SPw3f1[v, u]^2/64 - 
     (7*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f2[u, v])/32 + 
     (19*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw3f2[u, v])/128 + 
     (19*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*SPw3f2[u, v])/128 - 
     (25*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw3f2[u, v])/128 + 
     (3*HPL[{0, 0, 1}, 1 - u]*SPw3f2[u, v])/32 + 
     (HPL[{0, 0, 1}, 1 - v]*SPw3f2[u, v])/32 + 
     (HPL[{0, 1, 1}, 1 - u]*SPw3f2[u, v])/4 - 
     (9*HPL[{0, 1, 1}, 1 - v]*SPw3f2[u, v])/32 - 
     (11*SPw3f1[u, v]*SPw3f2[u, v])/64 - (3*SPw3f1[v, u]*SPw3f2[u, v])/32 - 
     (25*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - u]*SPw3f2[v, u])/128 + 
     (19*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*SPw3f2[v, u])/128 + 
     (19*HPL[{1}, 1 - u]*HPL[{0, 1}, 1 - v]*SPw3f2[v, u])/128 - 
     (7*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*SPw3f2[v, u])/32 + 
     (HPL[{0, 0, 1}, 1 - u]*SPw3f2[v, u])/32 + 
     (3*HPL[{0, 0, 1}, 1 - v]*SPw3f2[v, u])/32 - 
     (9*HPL[{0, 1, 1}, 1 - u]*SPw3f2[v, u])/32 + 
     (HPL[{0, 1, 1}, 1 - v]*SPw3f2[v, u])/4 - (3*SPw3f1[u, v]*SPw3f2[v, u])/
      32 - (11*SPw3f1[v, u]*SPw3f2[v, u])/64 - 
     (HPL[{1}, 1 - v]^2*SPw4f1[u, v])/64 + 
     (3*HPL[{0, 1}, 1 - v]*SPw4f1[u, v])/32 - 
     (HPL[{1}, 1 - u]^2*SPw4f1[v, u])/64 + 
     (3*HPL[{0, 1}, 1 - u]*SPw4f1[v, u])/32 + 
     (11*HPL[{0, 1}, 1 - u]*SPw4f2[u, v])/128 + 
     (13*HPL[{0, 1}, 1 - v]*SPw4f2[u, v])/128 + 
     (13*HPL[{0, 1}, 1 - u]*SPw4f2[v, u])/128 + 
     (11*HPL[{0, 1}, 1 - v]*SPw4f2[v, u])/128 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f3[u, v])/8 - 
     (HPL[{1}, 1 - v]^2*SPw4f3[u, v])/8 - (HPL[{0, 1}, 1 - v]*SPw4f3[u, v])/
      16 - (HPL[{1}, 1 - u]^2*SPw4f3[v, u])/8 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f3[v, u])/8 - 
     (HPL[{0, 1}, 1 - u]*SPw4f3[v, u])/16 + 
     (3*HPL[{1}, 1 - u]^2*SPw4f4[u, v])/64 - 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f4[u, v])/32 + 
     (HPL[{1}, 1 - v]^2*SPw4f4[u, v])/16 - (HPL[{0, 1}, 1 - u]*SPw4f4[u, v])/
      32 + (HPL[{0, 1}, 1 - v]*SPw4f4[u, v])/32 + (SPw2f1[u, v]*SPw4f4[u, v])/
      16 + (HPL[{1}, 1 - u]^2*SPw4f4[v, u])/16 - 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f4[v, u])/32 + 
     (3*HPL[{1}, 1 - v]^2*SPw4f4[v, u])/64 + 
     (HPL[{0, 1}, 1 - u]*SPw4f4[v, u])/32 - (HPL[{0, 1}, 1 - v]*SPw4f4[v, u])/
      32 - (SPw2f1[u, v]*SPw4f4[v, u])/16 + 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f5[u, v])/64 - 
     (HPL[{1}, 1 - v]^2*SPw4f5[u, v])/16 + (HPL[{0, 1}, 1 - u]*SPw4f5[u, v])/
      16 + (HPL[{0, 1}, 1 - v]*SPw4f5[u, v])/8 - (SPw2f1[u, v]*SPw4f5[u, v])/
      32 - (HPL[{1}, 1 - u]^2*SPw4f5[v, u])/16 + 
     (3*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*SPw4f5[v, u])/64 + 
     (HPL[{0, 1}, 1 - u]*SPw4f5[v, u])/8 + (HPL[{0, 1}, 1 - v]*SPw4f5[v, u])/
      16 + (SPw2f1[u, v]*SPw4f5[v, u])/32 + 
     (3*HPL[{0, 1}, 1 - u]*SPw4f6[u, v])/64 - 
     (3*HPL[{0, 1}, 1 - v]*SPw4f6[u, v])/64 - 
     (HPL[{1}, 1 - u]^2*SPw4f7[u, v])/16 + (HPL[{1}, 1 - v]^2*SPw4f7[u, v])/
      16 - (HPL[{0, 1}, 1 - u]*SPw4f7[u, v])/32 + 
     (HPL[{0, 1}, 1 - v]*SPw4f7[u, v])/32 + (SPw2f1[u, v]*SPw4f7[u, v])/16 - 
     (HPL[{1}, 1 - v]*SPw5f10[u, v])/32 - (HPL[{1}, 1 - u]*SPw5f10[v, u])/
      32 + (HPL[{1}, 1 - u]*SPw5f12[u, v])/32 + 
     (HPL[{1}, 1 - v]*SPw5f12[v, u])/32 + (HPL[{1}, 1 - u]*SPw5f16[u, v])/
      64 + (HPL[{1}, 1 - v]*SPw5f16[v, u])/64 + 
     (HPL[{1}, 1 - u]*SPw5f19[u, v])/16 - (HPL[{1}, 1 - v]*SPw5f19[u, v])/
      16 - (HPL[{1}, 1 - u]*SPw5f4[u, v])/8 + (HPL[{1}, 1 - v]*SPw5f4[u, v])/
      8 + (HPL[{1}, 1 - u]*SPw5f4[v, u])/8 - (HPL[{1}, 1 - v]*SPw5f4[v, u])/
      8 - (5*HPL[{1}, 1 - u]*SPw5f7[u, v])/128 - 
     (HPL[{1}, 1 - v]*SPw5f7[u, v])/16 - (HPL[{1}, 1 - u]*SPw5f7[v, u])/16 - 
     (5*HPL[{1}, 1 - v]*SPw5f7[v, u])/128 + (HPL[{1}, 1 - u]*SPw5f8[u, v])/
      16 - (HPL[{1}, 1 - v]*SPw5f8[u, v])/16 - (HPL[{1}, 1 - u]*SPw5f8[v, u])/
      16 + (HPL[{1}, 1 - v]*SPw5f8[v, u])/16 + (5*SPw6f10[u, v])/64 + 
     (5*SPw6f10[v, u])/64 - (3*SPw6f12[u, v])/8 - (3*SPw6f12[v, u])/8 + 
     SPw6f14[u, v]/4 + SPw6f14[v, u]/4 - SPw6f16[u, v]/32 - 
     SPw6f16[v, u]/32 - SPw6f17[u, v]/32 - SPw6f17[v, u]/32 + 
     SPw6f2[u, v]/8 + SPw6f2[v, u]/8 + SPw6f3[u, v]/16 + SPw6f3[v, u]/16 + 
     SPw6f41[u, v]/32 + SPw6f41[v, u]/32 - SPw6f42[u, v]/16 - 
     SPw6f42[v, u]/16 + SPw6f46[u, v]/32 - (13*SPw6f47[u, v])/128 - 
     SPw6f5[u, v]/16 - SPw6f5[v, u]/16 + (51*SPw6f6[u, v])/256 + 
     (51*SPw6f6[v, u])/256 + SPw6f9[u, v]/32 + SPw6f9[v, u]/32 - 
     (HPL[{1}, 1 - u]^3*HPL[{1}, 1 - v]*\[Zeta][2])/64 + 
     (7*HPL[{1}, 1 - u]^2*HPL[{1}, 1 - v]^2*\[Zeta][2])/64 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]^3*\[Zeta][2])/64 - 
     (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u]*\[Zeta][2])/4 + 
     (7*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u]*\[Zeta][2])/8 + 
     (3*HPL[{0, 1}, 1 - u]^2*\[Zeta][2])/8 + 
     (7*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - v]*\[Zeta][2])/8 - 
     (HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - v]*\[Zeta][2])/4 + 
     (3*HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v]*\[Zeta][2])/4 + 
     (3*HPL[{0, 1}, 1 - v]^2*\[Zeta][2])/8 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - u]*\[Zeta][2])/4 - 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - u]*\[Zeta][2])/4 - 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - v]*\[Zeta][2])/4 - 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - v]*\[Zeta][2])/4 + 
     (5*HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - u]*\[Zeta][2])/4 - 
     (13*HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - u]*\[Zeta][2])/8 - 
     (13*HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - v]*\[Zeta][2])/8 + 
     (5*HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - v]*\[Zeta][2])/4 - 
     (HPL[{0, 0, 0, 1}, 1 - u]*\[Zeta][2])/4 - 
     (HPL[{0, 0, 0, 1}, 1 - v]*\[Zeta][2])/4 - 
     (HPL[{0, 0, 1, 1}, 1 - u]*\[Zeta][2])/4 - 
     (HPL[{0, 0, 1, 1}, 1 - v]*\[Zeta][2])/4 - 
     (9*HPL[{0, 1, 1, 1}, 1 - u]*\[Zeta][2])/4 - 
     (9*HPL[{0, 1, 1, 1}, 1 - v]*\[Zeta][2])/4 - 
     (HPL[{1}, 1 - u]^2*SPw2f1[u, v]*\[Zeta][2])/32 + 
     (HPL[{1}, 1 - v]^2*SPw2f1[u, v]*\[Zeta][2])/32 + 
     (HPL[{0, 1}, 1 - u]*SPw2f1[u, v]*\[Zeta][2])/4 - 
     (HPL[{0, 1}, 1 - v]*SPw2f1[u, v]*\[Zeta][2])/4 - 
     (HPL[{1}, 1 - u]*SPw3f1[u, v]*\[Zeta][2])/4 + 
     (HPL[{1}, 1 - v]*SPw3f1[u, v]*\[Zeta][2])/4 + 
     (HPL[{1}, 1 - u]*SPw3f1[v, u]*\[Zeta][2])/4 - 
     (HPL[{1}, 1 - v]*SPw3f1[v, u]*\[Zeta][2])/4 - 
     (HPL[{1}, 1 - u]*SPw3f2[u, v]*\[Zeta][2])/8 - 
     (HPL[{1}, 1 - v]*SPw3f2[u, v]*\[Zeta][2])/16 - 
     (HPL[{1}, 1 - u]*SPw3f2[v, u]*\[Zeta][2])/16 - 
     (HPL[{1}, 1 - v]*SPw3f2[v, u]*\[Zeta][2])/8 + (SPw4f1[u, v]*\[Zeta][2])/
      4 + (SPw4f1[v, u]*\[Zeta][2])/4 - (3*SPw4f2[u, v]*\[Zeta][2])/16 - 
     (3*SPw4f2[v, u]*\[Zeta][2])/16 + (SPw4f3[u, v]*\[Zeta][2])/4 + 
     (SPw4f3[v, u]*\[Zeta][2])/4 - (SPw4f4[u, v]*\[Zeta][2])/2 - 
     (SPw4f4[v, u]*\[Zeta][2])/2 + (17*HPL[{1}, 1 - u]^2*\[Zeta][2]^2)/20 - 
     (21*HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*\[Zeta][2]^2)/10 + 
     (17*HPL[{1}, 1 - v]^2*\[Zeta][2]^2)/20 - 
     (2*HPL[{0, 1}, 1 - u]*\[Zeta][2]^2)/5 - 
     (2*HPL[{0, 1}, 1 - v]*\[Zeta][2]^2)/5 + (59*\[Zeta][2]^3)/15 + 
     \[Zeta][3]^2
     
R63u1w = R63uv1/.{v->w}
 
R62uv1 = (HPL[{1}, 1 - u]^2*HPL[{0, 1}, 1 - u])/4 - 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*HPL[{0, 1}, 1 - u])/4 - 
     HPL[{0, 1}, 1 - u]^2/8 - (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*
       HPL[{0, 1}, 1 - v])/4 + (HPL[{1}, 1 - v]^2*HPL[{0, 1}, 1 - v])/4 - 
     (HPL[{0, 1}, 1 - u]*HPL[{0, 1}, 1 - v])/4 - HPL[{0, 1}, 1 - v]^2/8 + 
     (HPL[{1}, 1 - u]*HPL[{0, 0, 1}, 1 - u])/2 + 
     (HPL[{1}, 1 - v]*HPL[{0, 0, 1}, 1 - v])/2 - 
     HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - u] + 
     (HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - u])/2 + 
     (HPL[{1}, 1 - u]*HPL[{0, 1, 1}, 1 - v])/2 - 
     HPL[{1}, 1 - v]*HPL[{0, 1, 1}, 1 - v] + HPL[{0, 0, 0, 1}, 1 - u]/2 + 
     HPL[{0, 0, 0, 1}, 1 - v]/2 - HPL[{0, 0, 1, 1}, 1 - u]/2 - 
     HPL[{0, 0, 1, 1}, 1 - v]/2 + (3*HPL[{0, 1, 1, 1}, 1 - u])/2 + 
     (3*HPL[{0, 1, 1, 1}, 1 - v])/2 - (HPL[{1}, 1 - u]^2*\[Zeta][2])/4 + 
     (HPL[{1}, 1 - u]*HPL[{1}, 1 - v]*\[Zeta][2])/2 - 
     (HPL[{1}, 1 - v]^2*\[Zeta][2])/4 - \[Zeta][2]^2
     
R62u1w = R62uv1/.{v->w}
 
V3u1w = E3u1w - E1u1w*R62u1w - R63u1w + (E2u1w*Yu1w)/2 - (R62u1w*Yu1w)/2 + (E1u1w*Yu1w^2)/8 + Yu1w^3/48 - 
     (E1u1w*Yu1w*\[Zeta][2])/2 - (Yu1w^2*\[Zeta][2])/4 + (11*Yu1w*\[Zeta][2]^2)/10

V3uv1 = E3uv1 - E1uv1*R62uv1 - R63uv1 + (E2uv1*Yuv1)/2 - (R62uv1*Yuv1)/2 + (E1uv1*Yuv1^2)/8 + Yuv1^3/48 - 
     (E1uv1*Yuv1*\[Zeta][2])/2 - (Yuv1^2*\[Zeta][2])/4 + (11*Yuv1*\[Zeta][2]^2)/10
 
V2u1w = E2u1w - R62u1w + (E1u1w*Yu1w)/2 + Yu1w^2/8 - (Yu1w*\[Zeta][2])/2

V2uv1 = E2uv1 - R62uv1 + (E1uv1*Yuv1)/2 + Yuv1^2/8 - (Yuv1*\[Zeta][2])/2
 
V1u1w = E1u1w + Yu1w/2

V1uv1 = E1uv1 + Yuv1/2

Vt3u1w = Et3u1w + (Et2u1w*Yu1w)/2

Vt3uv1 = Et3uv1 + (Et2uv1*Yuv1)/2
 
Vt2u1w = Et2u1w

Vt2uv1 = Et2uv1

U3u1w = E1u1w^3/3 - E1u1w*E2u1w + E3u1w

U3uv1 = E1uv1^3/3 - E1uv1*E2uv1 + E3uv1

U2u1w = -E1u1w^2/2 + E2u1w

U2uv1 = -E1uv1^2/2 + E2uv1

U1u1w = E1u1w

U1uv1 = E1uv1

Yu1w = HPL[{1}, 1 - u]^2/2 + HPL[{1}, 1 - w]^2/2 + HPL[{0, 1}, 1 - u] + 
     HPL[{0, 1}, 1 - w]
     
Yuv1 = HPL[{1}, 1 - u]^2/2 + HPL[{1}, 1 - v]^2/2 + HPL[{0, 1}, 1 - u] + 
     HPL[{0, 1}, 1 - v]