Point<2>
barycenter(const TriaAccessor<2, 2, 2> &accessor)
{
- // the evaluation of the formulae
- // is a bit tricky when done dimension
- // independently, so we write this function
- // for 2D and 3D separately
- /*
- Get the computation of the barycenter by this little Maple script. We
- use the bilinear mapping of the unit quad to the real quad. However,
- every transformation mapping the unit faces to straight lines should
- do.
-
- Remember that the area of the quad is given by
- |K| = \int_K 1 dx dy = \int_{\hat K} |det J| d(xi) d(eta)
- and that the barycenter is given by
- \vec x_s = 1/|K| \int_K \vec x dx dy
- = 1/|K| \int_{\hat K} \vec x(xi,eta) |det J| d(xi) d(eta)
-
- # x and y are arrays holding the x- and y-values of the four vertices
- # of this cell in real space.
- x := array(0..3);
- y := array(0..3);
- tphi[0] := (1-xi)*(1-eta):
- tphi[1] := xi*(1-eta):
- tphi[2] := (1-xi)*eta:
- tphi[3] := xi*eta:
- x_real := sum(x[s]*tphi[s], s=0..3):
- y_real := sum(y[s]*tphi[s], s=0..3):
- detJ := diff(x_real,xi)*diff(y_real,eta) -
- diff(x_real,eta)*diff(y_real,xi):
-
- measure := simplify ( int ( int (detJ, xi=0..1), eta=0..1)):
-
- xs := simplify (1/measure * int ( int (x_real * detJ, xi=0..1),
- eta=0..1)): ys := simplify (1/measure * int ( int (y_real * detJ,
- xi=0..1), eta=0..1)): readlib(C):
-
- C(array(1..2, [xs, ys]), optimized);
- */
-
- const double x[4] = {accessor.vertex(0)(0),
- accessor.vertex(1)(0),
- accessor.vertex(2)(0),
- accessor.vertex(3)(0)};
- const double y[4] = {accessor.vertex(0)(1),
- accessor.vertex(1)(1),
- accessor.vertex(2)(1),
- accessor.vertex(3)(1)};
- const double t1 = x[0] * x[1];
- const double t3 = x[0] * x[0];
- const double t5 = x[1] * x[1];
- const double t9 = y[0] * x[0];
- const double t11 = y[1] * x[1];
- const double t14 = x[2] * x[2];
- const double t16 = x[3] * x[3];
- const double t20 = x[2] * x[3];
- const double t27 = t1 * y[1] + t3 * y[1] - t5 * y[0] - t3 * y[2] +
- t5 * y[3] + t9 * x[2] - t11 * x[3] - t1 * y[0] -
- t14 * y[3] + t16 * y[2] - t16 * y[1] + t14 * y[0] -
- t20 * y[3] - x[0] * x[2] * y[2] + x[1] * x[3] * y[3] +
- t20 * y[2];
- const double t37 =
- 1 / (-x[1] * y[0] + x[1] * y[3] + y[0] * x[2] + x[0] * y[1] -
- x[0] * y[2] - y[1] * x[3] - x[2] * y[3] + x[3] * y[2]);
- const double t39 = y[2] * y[2];
- const double t51 = y[0] * y[0];
- const double t53 = y[1] * y[1];
- const double t59 = y[3] * y[3];
- const double t63 = t39 * x[3] + y[2] * y[0] * x[2] + y[3] * x[3] * y[2] -
- y[2] * x[2] * y[3] - y[3] * y[1] * x[3] - t9 * y[2] +
- t11 * y[3] + t51 * x[2] - t53 * x[3] - x[1] * t51 +
- t9 * y[1] - t11 * y[0] + x[0] * t53 - t59 * x[2] +
- t59 * x[1] - t39 * x[0];
-
- return {t27 * t37 / 3, t63 * t37 / 3};
+ if (accessor.reference_cell() == ReferenceCells::Triangle)
+ {
+ // We define the center in the same way as a simplex barycenter
+ return accessor.center();
+ }
+ else if (accessor.reference_cell() == ReferenceCells::Quadrilateral)
+ {
+ // the evaluation of the formulae
+ // is a bit tricky when done dimension
+ // independently, so we write this function
+ // for 2D and 3D separately
+ /*
+ Get the computation of the barycenter by this little Maple script. We
+ use the bilinear mapping of the unit quad to the real quad. However,
+ every transformation mapping the unit faces to straight lines should
+ do.
+
+ Remember that the area of the quad is given by
+ |K| = \int_K 1 dx dy = \int_{\hat K} |det J| d(xi) d(eta)
+ and that the barycenter is given by
+ \vec x_s = 1/|K| \int_K \vec x dx dy
+ = 1/|K| \int_{\hat K} \vec x(xi,eta) |det J| d(xi) d(eta)
+
+ # x and y are arrays holding the x- and y-values of the four vertices
+ # of this cell in real space.
+ x := array(0..3);
+ y := array(0..3);
+ tphi[0] := (1-xi)*(1-eta):
+ tphi[1] := xi*(1-eta):
+ tphi[2] := (1-xi)*eta:
+ tphi[3] := xi*eta:
+ x_real := sum(x[s]*tphi[s], s=0..3):
+ y_real := sum(y[s]*tphi[s], s=0..3):
+ detJ := diff(x_real,xi)*diff(y_real,eta) -
+ diff(x_real,eta)*diff(y_real,xi):
+
+ measure := simplify ( int ( int (detJ, xi=0..1), eta=0..1)):
+
+ xs := simplify (1/measure * int ( int (x_real * detJ, xi=0..1),
+ eta=0..1)): ys := simplify (1/measure * int ( int (y_real * detJ,
+ xi=0..1), eta=0..1)): readlib(C):
+
+ C(array(1..2, [xs, ys]), optimized);
+ */
+
+ const double x[4] = {accessor.vertex(0)(0),
+ accessor.vertex(1)(0),
+ accessor.vertex(2)(0),
+ accessor.vertex(3)(0)};
+ const double y[4] = {accessor.vertex(0)(1),
+ accessor.vertex(1)(1),
+ accessor.vertex(2)(1),
+ accessor.vertex(3)(1)};
+ const double t1 = x[0] * x[1];
+ const double t3 = x[0] * x[0];
+ const double t5 = x[1] * x[1];
+ const double t9 = y[0] * x[0];
+ const double t11 = y[1] * x[1];
+ const double t14 = x[2] * x[2];
+ const double t16 = x[3] * x[3];
+ const double t20 = x[2] * x[3];
+ const double t27 = t1 * y[1] + t3 * y[1] - t5 * y[0] - t3 * y[2] +
+ t5 * y[3] + t9 * x[2] - t11 * x[3] - t1 * y[0] -
+ t14 * y[3] + t16 * y[2] - t16 * y[1] + t14 * y[0] -
+ t20 * y[3] - x[0] * x[2] * y[2] +
+ x[1] * x[3] * y[3] + t20 * y[2];
+ const double t37 =
+ 1 / (-x[1] * y[0] + x[1] * y[3] + y[0] * x[2] + x[0] * y[1] -
+ x[0] * y[2] - y[1] * x[3] - x[2] * y[3] + x[3] * y[2]);
+ const double t39 = y[2] * y[2];
+ const double t51 = y[0] * y[0];
+ const double t53 = y[1] * y[1];
+ const double t59 = y[3] * y[3];
+ const double t63 =
+ t39 * x[3] + y[2] * y[0] * x[2] + y[3] * x[3] * y[2] -
+ y[2] * x[2] * y[3] - y[3] * y[1] * x[3] - t9 * y[2] + t11 * y[3] +
+ t51 * x[2] - t53 * x[3] - x[1] * t51 + t9 * y[1] - t11 * y[0] +
+ x[0] * t53 - t59 * x[2] + t59 * x[1] - t39 * x[0];
+
+ return {t27 * t37 / 3, t63 * t37 / 3};
+ }
+ else
+ {
+ Assert(false, ExcInternalError());
+ return {};
+ }
}
Point<3>
barycenter(const TriaAccessor<3, 3, 3> &accessor)
{
- /*
- Get the computation of the barycenter by this little Maple script. We
- use the trilinear mapping of the unit hex to the real hex.
-
- Remember that the area of the hex is given by
- |K| = \int_K 1 dx dy dz = \int_{\hat K} |det J| d(xi) d(eta) d(zeta)
- and that the barycenter is given by
- \vec x_s = 1/|K| \int_K \vec x dx dy dz
- = 1/|K| \int_{\hat K} \vec x(xi,eta,zeta) |det J| d(xi) d(eta) d(zeta)
-
- Note, that in the ordering of the shape functions tphi[0]-tphi[7]
- below, eta and zeta have been exchanged (zeta belongs to the y, and
- eta to the z direction). However, the resulting Jacobian determinant
- detJ should be the same, as a matrix and the matrix created from it
- by exchanging two consecutive lines and two neighboring columns have
- the same determinant.
-
- # x, y and z are arrays holding the x-, y- and z-values of the four
- vertices # of this cell in real space. x := array(0..7): y := array(0..7):
- z := array(0..7):
- tphi[0] := (1-xi)*(1-eta)*(1-zeta):
- tphi[1] := xi*(1-eta)*(1-zeta):
- tphi[2] := xi*eta*(1-zeta):
- tphi[3] := (1-xi)*eta*(1-zeta):
- tphi[4] := (1-xi)*(1-eta)*zeta:
- tphi[5] := xi*(1-eta)*zeta:
- tphi[6] := xi*eta*zeta:
- tphi[7] := (1-xi)*eta*zeta:
- x_real := sum(x[s]*tphi[s], s=0..7):
- y_real := sum(y[s]*tphi[s], s=0..7):
- z_real := sum(z[s]*tphi[s], s=0..7):
- with (linalg):
- J := matrix(3,3, [[diff(x_real, xi), diff(x_real, eta), diff(x_real,
- zeta)], [diff(y_real, xi), diff(y_real, eta), diff(y_real, zeta)],
- [diff(z_real, xi), diff(z_real, eta), diff(z_real, zeta)]]):
- detJ := det (J):
-
- measure := simplify ( int ( int ( int (detJ, xi=0..1), eta=0..1),
- zeta=0..1)):
-
- xs := simplify (1/measure * int ( int ( int (x_real * detJ, xi=0..1),
- eta=0..1), zeta=0..1)): ys := simplify (1/measure * int ( int ( int
- (y_real * detJ, xi=0..1), eta=0..1), zeta=0..1)): zs := simplify
- (1/measure * int ( int ( int (z_real * detJ, xi=0..1), eta=0..1),
- zeta=0..1)):
-
- readlib(C):
-
- C(array(1..3, [xs, ys, zs]));
-
-
- This script takes more than several hours when using an old version
- of maple on an old and slow computer. Therefore, when changing to
- the new deal.II numbering scheme (lexicographic numbering) the code
- lines below have not been reproduced with maple but only the
- ordering of points in the definitions of x[], y[] and z[] have been
- changed.
-
- For the case, someone is willing to rerun the maple script, he/she
- should use following ordering of shape functions:
-
- tphi[0] := (1-xi)*(1-eta)*(1-zeta):
- tphi[1] := xi*(1-eta)*(1-zeta):
- tphi[2] := (1-xi)* eta*(1-zeta):
- tphi[3] := xi* eta*(1-zeta):
- tphi[4] := (1-xi)*(1-eta)*zeta:
- tphi[5] := xi*(1-eta)*zeta:
- tphi[6] := (1-xi)* eta*zeta:
- tphi[7] := xi* eta*zeta:
-
- and change the ordering of points in the definitions of x[], y[] and
- z[] back to the standard ordering.
- */
-
- const double x[8] = {accessor.vertex(0)(0),
- accessor.vertex(1)(0),
- accessor.vertex(5)(0),
- accessor.vertex(4)(0),
- accessor.vertex(2)(0),
- accessor.vertex(3)(0),
- accessor.vertex(7)(0),
- accessor.vertex(6)(0)};
- const double y[8] = {accessor.vertex(0)(1),
- accessor.vertex(1)(1),
- accessor.vertex(5)(1),
- accessor.vertex(4)(1),
- accessor.vertex(2)(1),
- accessor.vertex(3)(1),
- accessor.vertex(7)(1),
- accessor.vertex(6)(1)};
- const double z[8] = {accessor.vertex(0)(2),
- accessor.vertex(1)(2),
- accessor.vertex(5)(2),
- accessor.vertex(4)(2),
- accessor.vertex(2)(2),
- accessor.vertex(3)(2),
- accessor.vertex(7)(2),
- accessor.vertex(6)(2)};
-
- double s1, s2, s3, s4, s5, s6, s7, s8;
-
- s1 = 1.0 / 6.0;
- s8 = -x[2] * x[2] * y[0] * z[3] - 2.0 * z[6] * x[7] * x[7] * y[4] -
- z[5] * x[7] * x[7] * y[4] - z[6] * x[7] * x[7] * y[5] +
- 2.0 * y[6] * x[7] * x[7] * z[4] - z[5] * x[6] * x[6] * y[4] +
- x[6] * x[6] * y[4] * z[7] - z[1] * x[0] * x[0] * y[2] -
- x[6] * x[6] * y[7] * z[4] + 2.0 * x[6] * x[6] * y[5] * z[7] -
- 2.0 * x[6] * x[6] * y[7] * z[5] + y[5] * x[6] * x[6] * z[4] +
- 2.0 * x[5] * x[5] * y[4] * z[6] + x[0] * x[0] * y[7] * z[4] -
- 2.0 * x[5] * x[5] * y[6] * z[4];
- s7 = s8 - y[6] * x[5] * x[5] * z[7] + z[6] * x[5] * x[5] * y[7] -
- y[1] * x[0] * x[0] * z[5] + x[7] * z[5] * x[4] * y[7] -
- x[7] * y[6] * x[5] * z[7] - 2.0 * x[7] * x[6] * y[7] * z[4] +
- 2.0 * x[7] * x[6] * y[4] * z[7] - x[7] * x[5] * y[7] * z[4] -
- 2.0 * x[7] * y[6] * x[4] * z[7] - x[7] * y[5] * x[4] * z[7] +
- x[2] * x[2] * y[3] * z[0] - x[7] * x[6] * y[7] * z[5] +
- x[7] * x[6] * y[5] * z[7] + 2.0 * x[1] * x[1] * y[0] * z[5] +
- x[7] * z[6] * x[5] * y[7];
- s8 = -2.0 * x[1] * x[1] * y[5] * z[0] + z[1] * x[0] * x[0] * y[5] +
- 2.0 * x[2] * x[2] * y[3] * z[1] - z[5] * x[4] * x[4] * y[1] +
- y[5] * x[4] * x[4] * z[1] - 2.0 * x[5] * x[5] * y[4] * z[1] +
- 2.0 * x[5] * x[5] * y[1] * z[4] - 2.0 * x[2] * x[2] * y[1] * z[3] -
- y[1] * x[2] * x[2] * z[0] + x[7] * y[2] * x[3] * z[7] +
- x[7] * z[2] * x[6] * y[3] + 2.0 * x[7] * z[6] * x[4] * y[7] +
- z[5] * x[1] * x[1] * y[4] + z[1] * x[2] * x[2] * y[0] -
- 2.0 * y[0] * x[3] * x[3] * z[7];
- s6 = s8 + 2.0 * z[0] * x[3] * x[3] * y[7] - x[7] * x[2] * y[3] * z[7] -
- x[7] * z[2] * x[3] * y[7] + x[7] * x[2] * y[7] * z[3] -
- x[7] * y[2] * x[6] * z[3] + x[4] * x[5] * y[1] * z[4] -
- x[4] * x[5] * y[4] * z[1] + x[4] * z[5] * x[1] * y[4] -
- x[4] * y[5] * x[1] * z[4] - 2.0 * x[5] * z[5] * x[4] * y[1] -
- 2.0 * x[5] * y[5] * x[1] * z[4] + 2.0 * x[5] * z[5] * x[1] * y[4] +
- 2.0 * x[5] * y[5] * x[4] * z[1] - x[6] * z[5] * x[7] * y[4] -
- z[2] * x[3] * x[3] * y[6] + s7;
- s8 = -2.0 * x[6] * z[6] * x[7] * y[5] - x[6] * y[6] * x[4] * z[7] +
- y[2] * x[3] * x[3] * z[6] + x[6] * y[6] * x[7] * z[4] +
- 2.0 * y[2] * x[3] * x[3] * z[7] + x[0] * x[1] * y[0] * z[5] +
- x[0] * y[1] * x[5] * z[0] - x[0] * z[1] * x[5] * y[0] -
- 2.0 * z[2] * x[3] * x[3] * y[7] + 2.0 * x[6] * z[6] * x[5] * y[7] -
- x[0] * x[1] * y[5] * z[0] - x[6] * y[5] * x[4] * z[6] -
- 2.0 * x[3] * z[0] * x[7] * y[3] - x[6] * z[6] * x[7] * y[4] -
- 2.0 * x[1] * z[1] * x[5] * y[0];
- s7 = s8 + 2.0 * x[1] * y[1] * x[5] * z[0] +
- 2.0 * x[1] * z[1] * x[0] * y[5] + 2.0 * x[3] * y[0] * x[7] * z[3] +
- 2.0 * x[3] * x[0] * y[3] * z[7] - 2.0 * x[3] * x[0] * y[7] * z[3] -
- 2.0 * x[1] * y[1] * x[0] * z[5] - 2.0 * x[6] * y[6] * x[5] * z[7] +
- s6 - y[5] * x[1] * x[1] * z[4] + x[6] * z[6] * x[4] * y[7] -
- 2.0 * x[2] * y[2] * x[3] * z[1] + x[6] * z[5] * x[4] * y[6] +
- x[6] * x[5] * y[4] * z[6] - y[6] * x[7] * x[7] * z[2] -
- x[6] * x[5] * y[6] * z[4];
- s8 = x[3] * x[3] * y[7] * z[4] - 2.0 * y[6] * x[7] * x[7] * z[3] +
- z[6] * x[7] * x[7] * y[2] + 2.0 * z[6] * x[7] * x[7] * y[3] +
- 2.0 * y[1] * x[0] * x[0] * z[3] + 2.0 * x[0] * x[1] * y[3] * z[0] -
- 2.0 * x[0] * y[0] * x[3] * z[4] - 2.0 * x[0] * z[1] * x[4] * y[0] -
- 2.0 * x[0] * y[1] * x[3] * z[0] + 2.0 * x[0] * y[0] * x[4] * z[3] -
- 2.0 * x[0] * z[0] * x[4] * y[3] + 2.0 * x[0] * x[1] * y[0] * z[4] +
- 2.0 * x[0] * z[1] * x[3] * y[0] - 2.0 * x[0] * x[1] * y[0] * z[3] -
- 2.0 * x[0] * x[1] * y[4] * z[0] + 2.0 * x[0] * y[1] * x[4] * z[0];
- s5 = s8 + 2.0 * x[0] * z[0] * x[3] * y[4] + x[1] * y[1] * x[0] * z[3] -
- x[1] * z[1] * x[4] * y[0] - x[1] * y[1] * x[0] * z[4] +
- x[1] * z[1] * x[0] * y[4] - x[1] * y[1] * x[3] * z[0] -
- x[1] * z[1] * x[0] * y[3] - x[0] * z[5] * x[4] * y[1] +
- x[0] * y[5] * x[4] * z[1] - 2.0 * x[4] * x[0] * y[4] * z[7] -
- 2.0 * x[4] * y[5] * x[0] * z[4] + 2.0 * x[4] * z[5] * x[0] * y[4] -
- 2.0 * x[4] * x[5] * y[4] * z[0] - 2.0 * x[4] * y[0] * x[7] * z[4] -
- x[5] * y[5] * x[0] * z[4] + s7;
- s8 = x[5] * z[5] * x[0] * y[4] - x[5] * z[5] * x[4] * y[0] +
- x[1] * z[5] * x[0] * y[4] + x[5] * y[5] * x[4] * z[0] -
- x[0] * y[0] * x[7] * z[4] - x[0] * z[5] * x[4] * y[0] -
- x[1] * y[5] * x[0] * z[4] + x[0] * z[0] * x[7] * y[4] +
- x[0] * y[5] * x[4] * z[0] - x[0] * z[0] * x[4] * y[7] +
- x[0] * x[5] * y[0] * z[4] + x[0] * y[0] * x[4] * z[7] -
- x[0] * x[5] * y[4] * z[0] - x[3] * x[3] * y[4] * z[7] +
- 2.0 * x[2] * z[2] * x[3] * y[1];
- s7 = s8 - x[5] * x[5] * y[4] * z[0] + 2.0 * y[5] * x[4] * x[4] * z[0] -
- 2.0 * z[0] * x[4] * x[4] * y[7] + 2.0 * y[0] * x[4] * x[4] * z[7] -
- 2.0 * z[5] * x[4] * x[4] * y[0] + x[5] * x[5] * y[4] * z[7] -
- x[5] * x[5] * y[7] * z[4] - 2.0 * y[5] * x[4] * x[4] * z[7] +
- 2.0 * z[5] * x[4] * x[4] * y[7] - x[0] * x[0] * y[7] * z[3] +
- y[2] * x[0] * x[0] * z[3] + x[0] * x[0] * y[3] * z[7] -
- x[5] * x[1] * y[4] * z[0] + x[5] * y[1] * x[4] * z[0] -
- x[4] * y[0] * x[3] * z[4];
- s8 = -x[4] * y[1] * x[0] * z[4] + x[4] * z[1] * x[0] * y[4] +
- x[4] * x[0] * y[3] * z[4] - x[4] * x[0] * y[4] * z[3] +
- x[4] * x[1] * y[0] * z[4] - x[4] * x[1] * y[4] * z[0] +
- x[4] * z[0] * x[3] * y[4] + x[5] * x[1] * y[0] * z[4] +
- x[1] * z[1] * x[3] * y[0] + x[1] * y[1] * x[4] * z[0] -
- x[5] * z[1] * x[4] * y[0] - 2.0 * y[1] * x[0] * x[0] * z[4] +
- 2.0 * z[1] * x[0] * x[0] * y[4] + 2.0 * x[0] * x[0] * y[3] * z[4] -
- 2.0 * z[1] * x[0] * x[0] * y[3];
- s6 = s8 - 2.0 * x[0] * x[0] * y[4] * z[3] + x[1] * x[1] * y[3] * z[0] +
- x[1] * x[1] * y[0] * z[4] - x[1] * x[1] * y[0] * z[3] -
- x[1] * x[1] * y[4] * z[0] - z[1] * x[4] * x[4] * y[0] +
- y[0] * x[4] * x[4] * z[3] - z[0] * x[4] * x[4] * y[3] +
- y[1] * x[4] * x[4] * z[0] - x[0] * x[0] * y[4] * z[7] -
- y[5] * x[0] * x[0] * z[4] + z[5] * x[0] * x[0] * y[4] +
- x[5] * x[5] * y[0] * z[4] - x[0] * y[0] * x[3] * z[7] +
- x[0] * z[0] * x[3] * y[7] + s7;
- s8 = s6 + x[0] * x[2] * y[3] * z[0] - x[0] * x[2] * y[0] * z[3] +
- x[0] * y[0] * x[7] * z[3] - x[0] * y[2] * x[3] * z[0] +
- x[0] * z[2] * x[3] * y[0] - x[0] * z[0] * x[7] * y[3] +
- x[1] * x[2] * y[3] * z[0] - z[2] * x[0] * x[0] * y[3] +
- x[3] * z[2] * x[6] * y[3] - x[3] * x[2] * y[3] * z[6] +
- x[3] * x[2] * y[6] * z[3] - x[3] * y[2] * x[6] * z[3] -
- 2.0 * x[3] * y[2] * x[7] * z[3] + 2.0 * x[3] * z[2] * x[7] * y[3];
- s7 = s8 + 2.0 * x[4] * y[5] * x[7] * z[4] +
- 2.0 * x[4] * x[5] * y[4] * z[7] - 2.0 * x[4] * z[5] * x[7] * y[4] -
- 2.0 * x[4] * x[5] * y[7] * z[4] + x[5] * y[5] * x[7] * z[4] -
- x[5] * z[5] * x[7] * y[4] - x[5] * y[5] * x[4] * z[7] +
- x[5] * z[5] * x[4] * y[7] + 2.0 * x[3] * x[2] * y[7] * z[3] -
- 2.0 * x[2] * z[2] * x[1] * y[3] + 2.0 * x[4] * z[0] * x[7] * y[4] +
- 2.0 * x[4] * x[0] * y[7] * z[4] + 2.0 * x[4] * x[5] * y[0] * z[4] -
- x[7] * x[6] * y[2] * z[7] - 2.0 * x[3] * x[2] * y[3] * z[7] -
- x[0] * x[4] * y[7] * z[3];
- s8 = x[0] * x[3] * y[7] * z[4] - x[0] * x[3] * y[4] * z[7] +
- x[0] * x[4] * y[3] * z[7] - 2.0 * x[7] * z[6] * x[3] * y[7] +
- x[3] * x[7] * y[4] * z[3] - x[3] * x[4] * y[7] * z[3] -
- x[3] * x[7] * y[3] * z[4] + x[3] * x[4] * y[3] * z[7] +
- 2.0 * x[2] * y[2] * x[1] * z[3] + y[6] * x[3] * x[3] * z[7] -
- z[6] * x[3] * x[3] * y[7] - x[1] * z[5] * x[4] * y[1] -
- x[1] * x[5] * y[4] * z[1] - x[1] * z[2] * x[0] * y[3] -
- x[1] * x[2] * y[0] * z[3] + x[1] * y[2] * x[0] * z[3];
- s4 = s8 + x[1] * x[5] * y[1] * z[4] + x[1] * y[5] * x[4] * z[1] +
- x[4] * y[0] * x[7] * z[3] - x[4] * z[0] * x[7] * y[3] -
- x[4] * x[4] * y[7] * z[3] + x[4] * x[4] * y[3] * z[7] +
- x[3] * z[6] * x[7] * y[3] - x[3] * x[6] * y[3] * z[7] +
- x[3] * x[6] * y[7] * z[3] - x[3] * z[6] * x[2] * y[7] -
- x[3] * y[6] * x[7] * z[3] + x[3] * z[6] * x[7] * y[2] +
- x[3] * y[6] * x[2] * z[7] + 2.0 * x[5] * z[5] * x[4] * y[6] + s5 + s7;
- s8 = s4 - 2.0 * x[5] * z[5] * x[6] * y[4] - x[5] * z[6] * x[7] * y[5] +
- x[5] * x[6] * y[5] * z[7] - x[5] * x[6] * y[7] * z[5] -
- 2.0 * x[5] * y[5] * x[4] * z[6] + 2.0 * x[5] * y[5] * x[6] * z[4] -
- x[3] * y[6] * x[7] * z[2] + x[4] * x[7] * y[4] * z[3] +
- x[4] * x[3] * y[7] * z[4] - x[4] * x[7] * y[3] * z[4] -
- x[4] * x[3] * y[4] * z[7] - z[1] * x[5] * x[5] * y[0] +
- y[1] * x[5] * x[5] * z[0] + x[4] * y[6] * x[7] * z[4];
- s7 = s8 - x[4] * x[6] * y[7] * z[4] + x[4] * x[6] * y[4] * z[7] -
- x[4] * z[6] * x[7] * y[4] - x[5] * y[6] * x[4] * z[7] -
- x[5] * x[6] * y[7] * z[4] + x[5] * x[6] * y[4] * z[7] +
- x[5] * z[6] * x[4] * y[7] - y[6] * x[4] * x[4] * z[7] +
- z[6] * x[4] * x[4] * y[7] + x[7] * x[5] * y[4] * z[7] -
- y[2] * x[7] * x[7] * z[3] + z[2] * x[7] * x[7] * y[3] -
- y[0] * x[3] * x[3] * z[4] - y[1] * x[3] * x[3] * z[0] +
- z[1] * x[3] * x[3] * y[0];
- s8 = z[0] * x[3] * x[3] * y[4] - x[2] * y[1] * x[3] * z[0] +
- x[2] * z[1] * x[3] * y[0] + x[3] * y[1] * x[0] * z[3] +
- x[3] * x[1] * y[3] * z[0] + x[3] * x[0] * y[3] * z[4] -
- x[3] * z[1] * x[0] * y[3] - x[3] * x[0] * y[4] * z[3] +
- x[3] * y[0] * x[4] * z[3] - x[3] * z[0] * x[4] * y[3] -
- x[3] * x[1] * y[0] * z[3] + x[3] * z[0] * x[7] * y[4] -
- x[3] * y[0] * x[7] * z[4] + z[0] * x[7] * x[7] * y[4] -
- y[0] * x[7] * x[7] * z[4];
- s6 = s8 + y[1] * x[0] * x[0] * z[2] - 2.0 * y[2] * x[3] * x[3] * z[0] +
- 2.0 * z[2] * x[3] * x[3] * y[0] - 2.0 * x[1] * x[1] * y[0] * z[2] +
- 2.0 * x[1] * x[1] * y[2] * z[0] - y[2] * x[3] * x[3] * z[1] +
- z[2] * x[3] * x[3] * y[1] - y[5] * x[4] * x[4] * z[6] +
- z[5] * x[4] * x[4] * y[6] + x[7] * x[0] * y[7] * z[4] -
- x[7] * z[0] * x[4] * y[7] - x[7] * x[0] * y[4] * z[7] +
- x[7] * y[0] * x[4] * z[7] - x[0] * x[1] * y[0] * z[2] +
- x[0] * z[1] * x[2] * y[0] + s7;
- s8 = s6 + x[0] * x[1] * y[2] * z[0] - x[0] * y[1] * x[2] * z[0] -
- x[3] * z[1] * x[0] * y[2] + 2.0 * x[3] * x[2] * y[3] * z[0] +
- y[0] * x[7] * x[7] * z[3] - z[0] * x[7] * x[7] * y[3] -
- 2.0 * x[3] * z[2] * x[0] * y[3] - 2.0 * x[3] * x[2] * y[0] * z[3] +
- 2.0 * x[3] * y[2] * x[0] * z[3] + x[3] * x[2] * y[3] * z[1] -
- x[3] * x[2] * y[1] * z[3] - x[5] * y[1] * x[0] * z[5] +
- x[3] * y[1] * x[0] * z[2] + x[4] * y[6] * x[7] * z[5];
- s7 = s8 - x[5] * x[1] * y[5] * z[0] + 2.0 * x[1] * z[1] * x[2] * y[0] -
- 2.0 * x[1] * z[1] * x[0] * y[2] + x[1] * x[2] * y[3] * z[1] -
- x[1] * x[2] * y[1] * z[3] + 2.0 * x[1] * y[1] * x[0] * z[2] -
- 2.0 * x[1] * y[1] * x[2] * z[0] - z[2] * x[1] * x[1] * y[3] +
- y[2] * x[1] * x[1] * z[3] + y[5] * x[7] * x[7] * z[4] +
- y[6] * x[7] * x[7] * z[5] + x[7] * x[6] * y[7] * z[2] +
- x[7] * y[6] * x[2] * z[7] - x[7] * z[6] * x[2] * y[7] -
- 2.0 * x[7] * x[6] * y[3] * z[7];
- s8 = s7 + 2.0 * x[7] * x[6] * y[7] * z[3] +
- 2.0 * x[7] * y[6] * x[3] * z[7] - x[3] * z[2] * x[1] * y[3] +
- x[3] * y[2] * x[1] * z[3] + x[5] * x[1] * y[0] * z[5] +
- x[4] * y[5] * x[6] * z[4] + x[5] * z[1] * x[0] * y[5] -
- x[4] * z[6] * x[7] * y[5] - x[4] * x[5] * y[6] * z[4] +
- x[4] * x[5] * y[4] * z[6] - x[4] * z[5] * x[6] * y[4] -
- x[1] * y[2] * x[3] * z[1] + x[1] * z[2] * x[3] * y[1] -
- x[2] * x[1] * y[0] * z[2] - x[2] * z[1] * x[0] * y[2];
- s5 = s8 + x[2] * x[1] * y[2] * z[0] - x[2] * z[2] * x[0] * y[3] +
- x[2] * y[2] * x[0] * z[3] - x[2] * y[2] * x[3] * z[0] +
- x[2] * z[2] * x[3] * y[0] + x[2] * y[1] * x[0] * z[2] +
- x[5] * y[6] * x[7] * z[5] + x[6] * y[5] * x[7] * z[4] +
- 2.0 * x[6] * y[6] * x[7] * z[5] - x[7] * y[0] * x[3] * z[7] +
- x[7] * z[0] * x[3] * y[7] - x[7] * x[0] * y[7] * z[3] +
- x[7] * x[0] * y[3] * z[7] + 2.0 * x[7] * x[7] * y[4] * z[3] -
- 2.0 * x[7] * x[7] * y[3] * z[4] - 2.0 * x[1] * x[1] * y[2] * z[5];
- s8 = s5 - 2.0 * x[7] * x[4] * y[7] * z[3] +
- 2.0 * x[7] * x[3] * y[7] * z[4] - 2.0 * x[7] * x[3] * y[4] * z[7] +
- 2.0 * x[7] * x[4] * y[3] * z[7] + 2.0 * x[1] * x[1] * y[5] * z[2] -
- x[1] * x[1] * y[2] * z[6] + x[1] * x[1] * y[6] * z[2] +
- z[1] * x[5] * x[5] * y[2] - y[1] * x[5] * x[5] * z[2] -
- x[1] * x[1] * y[6] * z[5] + x[1] * x[1] * y[5] * z[6] +
- x[5] * x[5] * y[6] * z[2] - x[5] * x[5] * y[2] * z[6] -
- 2.0 * y[1] * x[5] * x[5] * z[6];
- s7 = s8 + 2.0 * z[1] * x[5] * x[5] * y[6] +
- 2.0 * x[1] * z[1] * x[5] * y[2] + 2.0 * x[1] * y[1] * x[2] * z[5] -
- 2.0 * x[1] * z[1] * x[2] * y[5] - 2.0 * x[1] * y[1] * x[5] * z[2] -
- x[1] * y[1] * x[6] * z[2] - x[1] * z[1] * x[2] * y[6] +
- x[1] * z[1] * x[6] * y[2] + x[1] * y[1] * x[2] * z[6] -
- x[5] * x[1] * y[2] * z[5] + x[5] * y[1] * x[2] * z[5] -
- x[5] * z[1] * x[2] * y[5] + x[5] * x[1] * y[5] * z[2] -
- x[5] * y[1] * x[6] * z[2] - x[5] * x[1] * y[2] * z[6];
- s8 = s7 + x[5] * x[1] * y[6] * z[2] + x[5] * z[1] * x[6] * y[2] +
- x[1] * x[2] * y[5] * z[6] - x[1] * x[2] * y[6] * z[5] -
- x[1] * z[1] * x[6] * y[5] - x[1] * y[1] * x[5] * z[6] +
- x[1] * z[1] * x[5] * y[6] + x[1] * y[1] * x[6] * z[5] -
- x[5] * x[6] * y[5] * z[2] + x[5] * x[2] * y[5] * z[6] -
- x[5] * x[2] * y[6] * z[5] + x[5] * x[6] * y[2] * z[5] -
- 2.0 * x[5] * z[1] * x[6] * y[5] - 2.0 * x[5] * x[1] * y[6] * z[5] +
- 2.0 * x[5] * x[1] * y[5] * z[6];
- s6 = s8 + 2.0 * x[5] * y[1] * x[6] * z[5] +
- 2.0 * x[2] * x[1] * y[6] * z[2] + 2.0 * x[2] * z[1] * x[6] * y[2] -
- 2.0 * x[2] * x[1] * y[2] * z[6] + x[2] * x[5] * y[6] * z[2] +
- x[2] * x[6] * y[2] * z[5] - x[2] * x[5] * y[2] * z[6] +
- y[1] * x[2] * x[2] * z[5] - z[1] * x[2] * x[2] * y[5] -
- 2.0 * x[2] * y[1] * x[6] * z[2] - x[2] * x[6] * y[5] * z[2] -
- 2.0 * z[1] * x[2] * x[2] * y[6] + x[2] * x[2] * y[5] * z[6] -
- x[2] * x[2] * y[6] * z[5] + 2.0 * y[1] * x[2] * x[2] * z[6] +
- x[2] * z[1] * x[5] * y[2];
- s8 = s6 - x[2] * x[1] * y[2] * z[5] + x[2] * x[1] * y[5] * z[2] -
- x[2] * y[1] * x[5] * z[2] + x[6] * y[1] * x[2] * z[5] -
- x[6] * z[1] * x[2] * y[5] - z[1] * x[6] * x[6] * y[5] +
- y[1] * x[6] * x[6] * z[5] - y[1] * x[6] * x[6] * z[2] -
- 2.0 * x[6] * x[6] * y[5] * z[2] + 2.0 * x[6] * x[6] * y[2] * z[5] +
- z[1] * x[6] * x[6] * y[2] - x[6] * x[1] * y[6] * z[5] -
- x[6] * y[1] * x[5] * z[6] + x[6] * x[1] * y[5] * z[6];
- s7 = s8 + x[6] * z[1] * x[5] * y[6] - x[6] * z[1] * x[2] * y[6] -
- x[6] * x[1] * y[2] * z[6] + 2.0 * x[6] * x[5] * y[6] * z[2] +
- 2.0 * x[6] * x[2] * y[5] * z[6] - 2.0 * x[6] * x[2] * y[6] * z[5] -
- 2.0 * x[6] * x[5] * y[2] * z[6] + x[6] * x[1] * y[6] * z[2] +
- x[6] * y[1] * x[2] * z[6] - x[2] * x[2] * y[3] * z[7] +
- x[2] * x[2] * y[7] * z[3] - x[2] * z[2] * x[3] * y[7] -
- x[2] * y[2] * x[7] * z[3] + x[2] * z[2] * x[7] * y[3] +
- x[2] * y[2] * x[3] * z[7] - x[6] * x[6] * y[3] * z[7];
- s8 = s7 + x[6] * x[6] * y[7] * z[3] - x[6] * x[2] * y[3] * z[7] +
- x[6] * x[2] * y[7] * z[3] - x[6] * y[6] * x[7] * z[3] +
- x[6] * y[6] * x[3] * z[7] - x[6] * z[6] * x[3] * y[7] +
- x[6] * z[6] * x[7] * y[3] + y[6] * x[2] * x[2] * z[7] -
- z[6] * x[2] * x[2] * y[7] + 2.0 * x[2] * x[2] * y[6] * z[3] -
- x[2] * y[6] * x[7] * z[2] - 2.0 * x[2] * y[2] * x[6] * z[3] -
- 2.0 * x[2] * x[2] * y[3] * z[6] + 2.0 * x[2] * y[2] * x[3] * z[6] -
- x[2] * x[6] * y[2] * z[7];
- s3 = s8 + x[2] * x[6] * y[7] * z[2] + x[2] * z[6] * x[7] * y[2] +
- 2.0 * x[2] * z[2] * x[6] * y[3] - 2.0 * x[2] * z[2] * x[3] * y[6] -
- y[2] * x[6] * x[6] * z[3] - 2.0 * x[6] * x[6] * y[2] * z[7] +
- 2.0 * x[6] * x[6] * y[7] * z[2] + z[2] * x[6] * x[6] * y[3] -
- 2.0 * x[6] * y[6] * x[7] * z[2] + x[6] * y[2] * x[3] * z[6] -
- x[6] * x[2] * y[3] * z[6] + 2.0 * x[6] * z[6] * x[7] * y[2] +
- 2.0 * x[6] * y[6] * x[2] * z[7] - 2.0 * x[6] * z[6] * x[2] * y[7] +
- x[6] * x[2] * y[6] * z[3] - x[6] * z[2] * x[3] * y[6];
- s8 = y[1] * x[0] * z[3] + x[1] * y[3] * z[0] - y[0] * x[3] * z[7] -
- x[1] * y[5] * z[0] - y[0] * x[3] * z[4] - x[1] * y[0] * z[2] +
- z[1] * x[2] * y[0] - y[1] * x[0] * z[5] - z[1] * x[0] * y[2] -
- y[1] * x[0] * z[4] + z[1] * x[5] * y[2] + z[0] * x[7] * y[4] +
- z[0] * x[3] * y[7] + z[1] * x[0] * y[4] - x[1] * y[2] * z[5] +
- x[2] * y[3] * z[0] + y[1] * x[2] * z[5] - x[2] * y[3] * z[7];
- s7 = s8 - z[1] * x[2] * y[5] - y[1] * x[3] * z[0] - x[0] * y[7] * z[3] -
- z[1] * x[0] * y[3] + y[5] * x[4] * z[0] - x[0] * y[4] * z[3] +
- y[5] * x[7] * z[4] - z[0] * x[4] * y[3] + x[1] * y[0] * z[4] -
- z[2] * x[3] * y[7] - y[6] * x[7] * z[2] + x[1] * y[5] * z[2] +
- y[6] * x[7] * z[5] + x[0] * y[7] * z[4] + x[1] * y[2] * z[0] -
- z[1] * x[4] * y[0] - z[0] * x[4] * y[7] - z[2] * x[0] * y[3];
- s8 = x[5] * y[0] * z[4] + z[1] * x[0] * y[5] - x[2] * y[0] * z[3] -
- z[1] * x[5] * y[0] + y[1] * x[5] * z[0] - x[1] * y[0] * z[3] -
- x[1] * y[4] * z[0] - y[1] * x[5] * z[2] + x[2] * y[7] * z[3] +
- y[0] * x[4] * z[3] - x[0] * y[4] * z[7] + x[1] * y[0] * z[5] -
- y[1] * x[6] * z[2] - y[2] * x[6] * z[3] + y[0] * x[7] * z[3] -
- y[2] * x[7] * z[3] + z[2] * x[7] * y[3] + y[2] * x[0] * z[3];
- s6 = s8 + y[2] * x[3] * z[7] - y[2] * x[3] * z[0] - x[6] * y[5] * z[2] -
- y[5] * x[0] * z[4] + z[2] * x[3] * y[0] + x[2] * y[3] * z[1] +
- x[0] * y[3] * z[7] - x[2] * y[1] * z[3] + y[1] * x[4] * z[0] +
- y[1] * x[0] * z[2] - z[1] * x[2] * y[6] + y[2] * x[3] * z[6] -
- y[1] * x[2] * z[0] + z[1] * x[3] * y[0] - x[1] * y[2] * z[6] -
- x[2] * y[3] * z[6] + x[0] * y[3] * z[4] + z[0] * x[3] * y[4] + s7;
- s8 = x[5] * y[4] * z[7] + s6 + y[5] * x[6] * z[4] - y[5] * x[4] * z[6] +
- z[6] * x[5] * y[7] - x[6] * y[2] * z[7] - x[6] * y[7] * z[5] +
- x[5] * y[6] * z[2] + x[6] * y[5] * z[7] + x[6] * y[7] * z[2] +
- y[6] * x[7] * z[4] - y[6] * x[4] * z[7] - y[6] * x[7] * z[3] +
- z[6] * x[7] * y[2] + x[2] * y[5] * z[6] - x[2] * y[6] * z[5] +
- y[6] * x[2] * z[7] + x[6] * y[2] * z[5];
- s7 = s8 - x[5] * y[2] * z[6] - z[6] * x[7] * y[5] - z[5] * x[7] * y[4] +
- z[5] * x[0] * y[4] - y[5] * x[4] * z[7] + y[0] * x[4] * z[7] -
- z[6] * x[2] * y[7] - x[5] * y[4] * z[0] - x[5] * y[7] * z[4] -
- y[0] * x[7] * z[4] + y[5] * x[4] * z[1] - x[6] * y[7] * z[4] +
- x[7] * y[4] * z[3] - x[4] * y[7] * z[3] + x[3] * y[7] * z[4] -
- x[7] * y[3] * z[4] - x[6] * y[3] * z[7] + x[6] * y[4] * z[7];
- s8 = -x[3] * y[4] * z[7] + x[4] * y[3] * z[7] - z[6] * x[7] * y[4] -
- z[1] * x[6] * y[5] + x[6] * y[7] * z[3] - x[1] * y[6] * z[5] -
- y[1] * x[5] * z[6] + z[5] * x[4] * y[7] - z[5] * x[4] * y[0] +
- x[1] * y[5] * z[6] - y[6] * x[5] * z[7] - y[2] * x[3] * z[1] +
- z[1] * x[5] * y[6] - y[5] * x[1] * z[4] + z[6] * x[4] * y[7] +
- x[5] * y[1] * z[4] - x[5] * y[6] * z[4] + y[6] * x[3] * z[7] -
- x[5] * y[4] * z[1];
- s5 = s8 + x[5] * y[4] * z[6] + z[5] * x[1] * y[4] + y[1] * x[6] * z[5] -
- z[6] * x[3] * y[7] + z[6] * x[7] * y[3] - z[5] * x[6] * y[4] -
- z[5] * x[4] * y[1] + z[5] * x[4] * y[6] + x[1] * y[6] * z[2] +
- x[2] * y[6] * z[3] + z[2] * x[6] * y[3] + z[1] * x[6] * y[2] +
- z[2] * x[3] * y[1] - z[2] * x[1] * y[3] - z[2] * x[3] * y[6] +
- y[2] * x[1] * z[3] + y[1] * x[2] * z[6] - z[0] * x[7] * y[3] + s7;
- s4 = 1 / s5;
- s2 = s3 * s4;
- const double unknown0 = s1 * s2;
- s1 = 1.0 / 6.0;
- s8 = 2.0 * x[1] * y[0] * y[0] * z[4] + x[5] * y[0] * y[0] * z[4] -
- x[1] * y[4] * y[4] * z[0] + z[1] * x[0] * y[4] * y[4] +
- x[1] * y[0] * y[0] * z[5] - z[1] * x[5] * y[0] * y[0] -
- 2.0 * z[1] * x[4] * y[0] * y[0] + 2.0 * z[1] * x[3] * y[0] * y[0] +
- z[2] * x[3] * y[0] * y[0] + y[0] * y[0] * x[7] * z[3] +
- 2.0 * y[0] * y[0] * x[4] * z[3] - 2.0 * x[1] * y[0] * y[0] * z[3] -
- 2.0 * x[5] * y[4] * y[4] * z[0] + 2.0 * z[5] * x[0] * y[4] * y[4] +
- 2.0 * y[4] * y[5] * x[7] * z[4];
- s7 = s8 - x[3] * y[4] * y[4] * z[7] + x[7] * y[4] * y[4] * z[3] +
- z[0] * x[3] * y[4] * y[4] - 2.0 * x[0] * y[4] * y[4] * z[7] -
- y[1] * x[1] * y[4] * z[0] - x[0] * y[4] * y[4] * z[3] +
- 2.0 * z[0] * x[7] * y[4] * y[4] + y[4] * z[6] * x[4] * y[7] -
- y[0] * y[0] * x[7] * z[4] + y[0] * y[0] * x[4] * z[7] +
- 2.0 * y[4] * z[5] * x[4] * y[7] - 2.0 * y[4] * x[5] * y[7] * z[4] -
- y[4] * x[6] * y[7] * z[4] - y[4] * y[6] * x[4] * z[7] -
- 2.0 * y[4] * y[5] * x[4] * z[7];
- s8 = y[4] * y[6] * x[7] * z[4] - y[7] * y[2] * x[7] * z[3] +
- y[7] * z[2] * x[7] * y[3] + y[7] * y[2] * x[3] * z[7] +
- 2.0 * x[5] * y[4] * y[4] * z[7] - y[7] * x[2] * y[3] * z[7] -
- y[0] * z[0] * x[4] * y[7] + z[6] * x[7] * y[3] * y[3] -
- y[0] * x[0] * y[4] * z[7] + y[0] * x[0] * y[7] * z[4] -
- 2.0 * x[2] * y[3] * y[3] * z[7] - z[5] * x[4] * y[0] * y[0] +
- y[0] * z[0] * x[7] * y[4] - 2.0 * z[6] * x[3] * y[7] * y[7] +
- z[1] * x[2] * y[0] * y[0];
- s6 = s8 + y[4] * y[0] * x[4] * z[3] - 2.0 * y[4] * z[0] * x[4] * y[7] +
- 2.0 * y[4] * x[0] * y[7] * z[4] - y[4] * z[0] * x[4] * y[3] -
- y[4] * x[0] * y[7] * z[3] + y[4] * z[0] * x[3] * y[7] -
- y[4] * y[0] * x[3] * z[4] + y[0] * x[4] * y[3] * z[7] -
- y[0] * x[7] * y[3] * z[4] - y[0] * x[3] * y[4] * z[7] +
- y[0] * x[7] * y[4] * z[3] + x[2] * y[7] * y[7] * z[3] -
- z[2] * x[3] * y[7] * y[7] - 2.0 * z[2] * x[0] * y[3] * y[3] +
- 2.0 * y[0] * z[1] * x[0] * y[4] + s7;
- s8 = -2.0 * y[0] * y[1] * x[0] * z[4] - y[0] * y[1] * x[0] * z[5] -
- y[0] * y[0] * x[3] * z[7] - z[1] * x[0] * y[3] * y[3] -
- y[0] * x[1] * y[5] * z[0] - 2.0 * z[0] * x[7] * y[3] * y[3] +
- x[0] * y[3] * y[3] * z[4] + 2.0 * x[0] * y[3] * y[3] * z[7] -
- z[0] * x[4] * y[3] * y[3] + 2.0 * x[2] * y[3] * y[3] * z[0] +
- x[1] * y[3] * y[3] * z[0] + 2.0 * y[7] * z[6] * x[7] * y[3] +
- 2.0 * y[7] * y[6] * x[3] * z[7] - 2.0 * y[7] * y[6] * x[7] * z[3] -
- 2.0 * y[7] * x[6] * y[3] * z[7];
- s7 = s8 + y[4] * x[4] * y[3] * z[7] - y[4] * x[4] * y[7] * z[3] +
- y[4] * x[3] * y[7] * z[4] - y[4] * x[7] * y[3] * z[4] +
- 2.0 * y[4] * y[0] * x[4] * z[7] - 2.0 * y[4] * y[0] * x[7] * z[4] +
- 2.0 * x[6] * y[7] * y[7] * z[3] + y[4] * x[0] * y[3] * z[4] +
- y[0] * y[1] * x[5] * z[0] + y[0] * z[1] * x[0] * y[5] -
- x[2] * y[0] * y[0] * z[3] + x[4] * y[3] * y[3] * z[7] -
- x[7] * y[3] * y[3] * z[4] - x[5] * y[4] * y[4] * z[1] +
- y[3] * z[0] * x[3] * y[4];
- s8 = y[3] * y[0] * x[4] * z[3] + 2.0 * y[3] * y[0] * x[7] * z[3] +
- 2.0 * y[3] * y[2] * x[0] * z[3] - 2.0 * y[3] * y[2] * x[3] * z[0] +
- 2.0 * y[3] * z[2] * x[3] * y[0] + y[3] * z[1] * x[3] * y[0] -
- 2.0 * y[3] * x[2] * y[0] * z[3] - y[3] * x[1] * y[0] * z[3] -
- y[3] * y[1] * x[3] * z[0] - 2.0 * y[3] * x[0] * y[7] * z[3] -
- y[3] * x[0] * y[4] * z[3] - 2.0 * y[3] * y[0] * x[3] * z[7] -
- y[3] * y[0] * x[3] * z[4] + 2.0 * y[3] * z[0] * x[3] * y[7] +
- y[3] * y[1] * x[0] * z[3] + z[5] * x[1] * y[4] * y[4];
- s5 = s8 - 2.0 * y[0] * y[0] * x[3] * z[4] -
- 2.0 * y[0] * x[1] * y[4] * z[0] + y[3] * x[7] * y[4] * z[3] -
- y[3] * x[4] * y[7] * z[3] + y[3] * x[3] * y[7] * z[4] -
- y[3] * x[3] * y[4] * z[7] + y[3] * x[0] * y[7] * z[4] -
- y[3] * z[0] * x[4] * y[7] - 2.0 * y[4] * y[5] * x[0] * z[4] + s6 +
- y[7] * x[0] * y[3] * z[7] - y[7] * z[0] * x[7] * y[3] +
- y[7] * y[0] * x[7] * z[3] - y[7] * y[0] * x[3] * z[7] +
- 2.0 * y[0] * y[1] * x[4] * z[0] + s7;
- s8 = -2.0 * y[7] * x[7] * y[3] * z[4] - 2.0 * y[7] * x[3] * y[4] * z[7] +
- 2.0 * y[7] * x[4] * y[3] * z[7] + y[7] * y[0] * x[4] * z[7] -
- y[7] * y[0] * x[7] * z[4] + 2.0 * y[7] * x[7] * y[4] * z[3] -
- y[7] * x[0] * y[4] * z[7] + y[7] * z[0] * x[7] * y[4] +
- z[5] * x[4] * y[7] * y[7] + 2.0 * z[6] * x[4] * y[7] * y[7] -
- x[5] * y[7] * y[7] * z[4] - 2.0 * x[6] * y[7] * y[7] * z[4] +
- 2.0 * y[7] * x[6] * y[4] * z[7] - 2.0 * y[7] * z[6] * x[7] * y[4] +
- 2.0 * y[7] * y[6] * x[7] * z[4];
- s7 = s8 - 2.0 * y[7] * y[6] * x[4] * z[7] - y[7] * z[5] * x[7] * y[4] -
- y[7] * y[5] * x[4] * z[7] - x[0] * y[7] * y[7] * z[3] +
- z[0] * x[3] * y[7] * y[7] + y[7] * x[5] * y[4] * z[7] +
- y[7] * y[5] * x[7] * z[4] - y[4] * x[1] * y[5] * z[0] -
- x[1] * y[0] * y[0] * z[2] - y[4] * y[5] * x[1] * z[4] -
- 2.0 * y[4] * z[5] * x[4] * y[0] - y[4] * y[1] * x[0] * z[4] +
- y[4] * y[5] * x[4] * z[1] + y[0] * z[0] * x[3] * y[7] -
- y[0] * z[1] * x[0] * y[2];
- s8 = 2.0 * y[0] * x[1] * y[3] * z[0] + y[4] * y[1] * x[4] * z[0] +
- 2.0 * y[0] * y[1] * x[0] * z[3] + y[4] * x[1] * y[0] * z[5] -
- y[4] * z[1] * x[5] * y[0] + y[4] * z[1] * x[0] * y[5] -
- y[4] * z[1] * x[4] * y[0] + y[4] * x[1] * y[0] * z[4] -
- y[4] * z[5] * x[4] * y[1] + x[5] * y[4] * y[4] * z[6] -
- z[5] * x[6] * y[4] * y[4] + y[4] * x[5] * y[1] * z[4] -
- y[0] * z[2] * x[0] * y[3] + y[0] * y[5] * x[4] * z[0] +
- y[0] * x[1] * y[2] * z[0];
- s6 = s8 - 2.0 * y[0] * z[0] * x[4] * y[3] -
- 2.0 * y[0] * x[0] * y[4] * z[3] - 2.0 * y[0] * z[1] * x[0] * y[3] -
- y[0] * x[0] * y[7] * z[3] - 2.0 * y[0] * y[1] * x[3] * z[0] +
- y[0] * x[2] * y[3] * z[0] - y[0] * y[1] * x[2] * z[0] +
- y[0] * y[1] * x[0] * z[2] - y[0] * x[2] * y[1] * z[3] +
- y[0] * x[0] * y[3] * z[7] + y[0] * x[2] * y[3] * z[1] -
- y[0] * y[2] * x[3] * z[0] + y[0] * y[2] * x[0] * z[3] -
- y[0] * y[5] * x[0] * z[4] - y[4] * y[5] * x[4] * z[6] + s7;
- s8 = s6 + y[4] * z[6] * x[5] * y[7] - y[4] * x[6] * y[7] * z[5] +
- y[4] * x[6] * y[5] * z[7] - y[4] * z[6] * x[7] * y[5] -
- y[4] * x[5] * y[6] * z[4] + y[4] * z[5] * x[4] * y[6] +
- y[4] * y[5] * x[6] * z[4] - 2.0 * y[1] * y[1] * x[0] * z[5] +
- 2.0 * y[1] * y[1] * x[5] * z[0] - 2.0 * y[2] * y[2] * x[6] * z[3] +
- x[5] * y[1] * y[1] * z[4] - z[5] * x[4] * y[1] * y[1] -
- x[6] * y[2] * y[2] * z[7] + z[6] * x[7] * y[2] * y[2];
- s7 = s8 - x[1] * y[5] * y[5] * z[0] + z[1] * x[0] * y[5] * y[5] +
- y[1] * y[5] * x[4] * z[1] - y[1] * y[5] * x[1] * z[4] -
- 2.0 * y[2] * z[2] * x[3] * y[6] + 2.0 * y[1] * z[1] * x[0] * y[5] -
- 2.0 * y[1] * z[1] * x[5] * y[0] + 2.0 * y[1] * x[1] * y[0] * z[5] -
- y[2] * x[2] * y[3] * z[7] - y[2] * z[2] * x[3] * y[7] +
- y[2] * x[2] * y[7] * z[3] + y[2] * z[2] * x[7] * y[3] -
- 2.0 * y[2] * x[2] * y[3] * z[6] + 2.0 * y[2] * x[2] * y[6] * z[3] +
- 2.0 * y[2] * z[2] * x[6] * y[3] - y[3] * y[2] * x[6] * z[3];
- s8 = y[3] * y[2] * x[3] * z[6] + y[3] * x[2] * y[6] * z[3] -
- y[3] * z[2] * x[3] * y[6] - y[2] * y[2] * x[7] * z[3] +
- 2.0 * y[2] * y[2] * x[3] * z[6] + y[2] * y[2] * x[3] * z[7] -
- 2.0 * y[1] * x[1] * y[5] * z[0] - x[2] * y[3] * y[3] * z[6] +
- z[2] * x[6] * y[3] * y[3] + 2.0 * y[6] * x[2] * y[5] * z[6] +
- 2.0 * y[6] * x[6] * y[2] * z[5] - 2.0 * y[6] * x[5] * y[2] * z[6] +
- 2.0 * y[3] * x[2] * y[7] * z[3] - 2.0 * y[3] * z[2] * x[3] * y[7] -
- y[0] * z[0] * x[7] * y[3] - y[0] * z[2] * x[1] * y[3];
- s4 = s8 - y[2] * y[6] * x[7] * z[2] + y[0] * z[2] * x[3] * y[1] +
- y[1] * z[5] * x[1] * y[4] - y[1] * x[5] * y[4] * z[1] +
- 2.0 * y[0] * z[0] * x[3] * y[4] + 2.0 * y[0] * x[0] * y[3] * z[4] +
- 2.0 * z[2] * x[7] * y[3] * y[3] - 2.0 * z[5] * x[7] * y[4] * y[4] +
- x[6] * y[4] * y[4] * z[7] - z[6] * x[7] * y[4] * y[4] +
- y[1] * y[1] * x[0] * z[3] + y[3] * x[6] * y[7] * z[2] -
- y[3] * z[6] * x[2] * y[7] + 2.0 * y[3] * y[2] * x[3] * z[7] + s5 + s7;
- s8 = s4 + y[2] * x[6] * y[7] * z[2] - y[2] * y[6] * x[7] * z[3] +
- y[2] * y[6] * x[2] * z[7] - y[2] * z[6] * x[2] * y[7] -
- y[2] * x[6] * y[3] * z[7] + y[2] * y[6] * x[3] * z[7] +
- y[2] * z[6] * x[7] * y[3] - 2.0 * y[3] * y[2] * x[7] * z[3] -
- x[6] * y[3] * y[3] * z[7] + y[1] * y[1] * x[4] * z[0] -
- y[1] * y[1] * x[3] * z[0] + x[2] * y[6] * y[6] * z[3] -
- z[2] * x[3] * y[6] * y[6] - y[1] * y[1] * x[0] * z[4];
- s7 = s8 + y[5] * x[1] * y[0] * z[5] + y[6] * x[2] * y[7] * z[3] -
- y[6] * y[2] * x[6] * z[3] + y[6] * y[2] * x[3] * z[6] -
- y[6] * x[2] * y[3] * z[6] + y[6] * z[2] * x[6] * y[3] -
- y[5] * y[1] * x[0] * z[5] - y[5] * z[1] * x[5] * y[0] +
- y[5] * y[1] * x[5] * z[0] - y[6] * z[2] * x[3] * y[7] -
- y[7] * y[6] * x[7] * z[2] + 2.0 * y[6] * y[6] * x[2] * z[7] +
- y[6] * y[6] * x[3] * z[7] + x[6] * y[7] * y[7] * z[2] -
- z[6] * x[2] * y[7] * y[7];
- s8 = -x[2] * y[1] * y[1] * z[3] + 2.0 * y[1] * y[1] * x[0] * z[2] -
- 2.0 * y[1] * y[1] * x[2] * z[0] + z[2] * x[3] * y[1] * y[1] -
- z[1] * x[0] * y[2] * y[2] + x[1] * y[2] * y[2] * z[0] +
- y[2] * y[2] * x[0] * z[3] - y[2] * y[2] * x[3] * z[0] -
- 2.0 * y[2] * y[2] * x[3] * z[1] + y[1] * x[1] * y[3] * z[0] -
- 2.0 * y[6] * y[6] * x[7] * z[2] + 2.0 * y[5] * y[5] * x[4] * z[1] -
- 2.0 * y[5] * y[5] * x[1] * z[4] - y[6] * y[6] * x[7] * z[3] -
- 2.0 * y[1] * x[1] * y[0] * z[2];
- s6 = s8 + 2.0 * y[1] * z[1] * x[2] * y[0] -
- 2.0 * y[1] * z[1] * x[0] * y[2] + 2.0 * y[1] * x[1] * y[2] * z[0] +
- y[1] * x[2] * y[3] * z[1] - y[1] * y[2] * x[3] * z[1] -
- y[1] * z[2] * x[1] * y[3] + y[1] * y[2] * x[1] * z[3] -
- y[2] * x[1] * y[0] * z[2] + y[2] * z[1] * x[2] * y[0] +
- y[2] * x[2] * y[3] * z[0] - y[7] * x[6] * y[2] * z[7] +
- y[7] * z[6] * x[7] * y[2] + y[7] * y[6] * x[2] * z[7] -
- y[6] * x[6] * y[3] * z[7] + y[6] * x[6] * y[7] * z[3] + s7;
- s8 = s6 - y[6] * z[6] * x[3] * y[7] + y[6] * z[6] * x[7] * y[3] +
- 2.0 * y[2] * y[2] * x[1] * z[3] + x[2] * y[3] * y[3] * z[1] -
- z[2] * x[1] * y[3] * y[3] + y[1] * x[1] * y[0] * z[4] +
- y[1] * z[1] * x[3] * y[0] - y[1] * x[1] * y[0] * z[3] +
- 2.0 * y[5] * x[5] * y[1] * z[4] - 2.0 * y[5] * x[5] * y[4] * z[1] +
- 2.0 * y[5] * z[5] * x[1] * y[4] - 2.0 * y[5] * z[5] * x[4] * y[1] -
- 2.0 * y[6] * x[6] * y[2] * z[7] + 2.0 * y[6] * x[6] * y[7] * z[2];
- s7 = s8 + 2.0 * y[6] * z[6] * x[7] * y[2] -
- 2.0 * y[6] * z[6] * x[2] * y[7] - y[1] * z[1] * x[4] * y[0] +
- y[1] * z[1] * x[0] * y[4] - y[1] * z[1] * x[0] * y[3] +
- 2.0 * y[6] * y[6] * x[7] * z[5] + 2.0 * y[5] * y[5] * x[6] * z[4] -
- 2.0 * y[5] * y[5] * x[4] * z[6] + x[6] * y[5] * y[5] * z[7] -
- y[3] * x[2] * y[1] * z[3] - y[3] * y[2] * x[3] * z[1] +
- y[3] * z[2] * x[3] * y[1] + y[3] * y[2] * x[1] * z[3] -
- y[2] * x[2] * y[0] * z[3] + y[2] * z[2] * x[3] * y[0];
- s8 = s7 + 2.0 * y[2] * x[2] * y[3] * z[1] -
- 2.0 * y[2] * x[2] * y[1] * z[3] + y[2] * y[1] * x[0] * z[2] -
- y[2] * y[1] * x[2] * z[0] + 2.0 * y[2] * z[2] * x[3] * y[1] -
- 2.0 * y[2] * z[2] * x[1] * y[3] - y[2] * z[2] * x[0] * y[3] +
- y[5] * z[6] * x[5] * y[7] - y[5] * x[6] * y[7] * z[5] -
- y[5] * y[6] * x[4] * z[7] - y[5] * y[6] * x[5] * z[7] -
- 2.0 * y[5] * x[5] * y[6] * z[4] + 2.0 * y[5] * x[5] * y[4] * z[6] -
- 2.0 * y[5] * z[5] * x[6] * y[4] + 2.0 * y[5] * z[5] * x[4] * y[6];
- s5 = s8 - y[1] * y[5] * x[0] * z[4] - z[6] * x[7] * y[5] * y[5] +
- y[6] * y[6] * x[7] * z[4] - y[6] * y[6] * x[4] * z[7] -
- 2.0 * y[6] * y[6] * x[5] * z[7] - x[5] * y[6] * y[6] * z[4] +
- z[5] * x[4] * y[6] * y[6] + z[6] * x[5] * y[7] * y[7] -
- x[6] * y[7] * y[7] * z[5] + y[1] * y[5] * x[4] * z[0] +
- y[7] * y[6] * x[7] * z[5] + y[6] * y[5] * x[7] * z[4] +
- y[5] * y[6] * x[7] * z[5] + y[6] * y[5] * x[6] * z[4] -
- y[6] * y[5] * x[4] * z[6] + 2.0 * y[6] * z[6] * x[5] * y[7];
- s8 = s5 - 2.0 * y[6] * x[6] * y[7] * z[5] +
- 2.0 * y[6] * x[6] * y[5] * z[7] - 2.0 * y[6] * z[6] * x[7] * y[5] -
- y[6] * x[5] * y[7] * z[4] - y[6] * x[6] * y[7] * z[4] +
- y[6] * x[6] * y[4] * z[7] - y[6] * z[6] * x[7] * y[4] +
- y[6] * z[5] * x[4] * y[7] + y[6] * z[6] * x[4] * y[7] +
- y[6] * x[5] * y[4] * z[6] - y[6] * z[5] * x[6] * y[4] +
- y[7] * x[6] * y[5] * z[7] - y[7] * z[6] * x[7] * y[5] -
- 2.0 * y[6] * x[6] * y[5] * z[2];
- s7 = s8 - y[7] * y[6] * x[5] * z[7] + 2.0 * y[4] * y[5] * x[4] * z[0] +
- 2.0 * x[3] * y[7] * y[7] * z[4] - 2.0 * x[4] * y[7] * y[7] * z[3] -
- z[0] * x[4] * y[7] * y[7] + x[0] * y[7] * y[7] * z[4] -
- y[0] * z[5] * x[4] * y[1] + y[0] * x[5] * y[1] * z[4] -
- y[0] * x[5] * y[4] * z[0] + y[0] * z[5] * x[0] * y[4] -
- y[5] * y[5] * x[0] * z[4] + y[5] * y[5] * x[4] * z[0] +
- 2.0 * y[1] * y[1] * x[2] * z[5] - 2.0 * y[1] * y[1] * x[5] * z[2] +
- z[1] * x[5] * y[2] * y[2];
- s8 = s7 - x[1] * y[2] * y[2] * z[5] - y[5] * z[5] * x[4] * y[0] +
- y[5] * z[5] * x[0] * y[4] - y[5] * x[5] * y[4] * z[0] -
- y[2] * x[1] * y[6] * z[5] - y[2] * y[1] * x[5] * z[6] +
- y[2] * z[1] * x[5] * y[6] + y[2] * y[1] * x[6] * z[5] -
- y[1] * z[1] * x[6] * y[5] - y[1] * x[1] * y[6] * z[5] +
- y[1] * x[1] * y[5] * z[6] + y[1] * z[1] * x[5] * y[6] +
- y[5] * x[5] * y[0] * z[4] + y[2] * y[1] * x[2] * z[5] -
- y[2] * z[1] * x[2] * y[5];
- s6 = s8 + y[2] * x[1] * y[5] * z[2] - y[2] * y[1] * x[5] * z[2] -
- y[1] * y[1] * x[5] * z[6] + y[1] * y[1] * x[6] * z[5] -
- z[1] * x[2] * y[5] * y[5] + x[1] * y[5] * y[5] * z[2] +
- 2.0 * y[1] * z[1] * x[5] * y[2] - 2.0 * y[1] * x[1] * y[2] * z[5] -
- 2.0 * y[1] * z[1] * x[2] * y[5] + 2.0 * y[1] * x[1] * y[5] * z[2] -
- y[1] * y[1] * x[6] * z[2] + y[1] * y[1] * x[2] * z[6] -
- 2.0 * y[5] * x[1] * y[6] * z[5] - 2.0 * y[5] * y[1] * x[5] * z[6] +
- 2.0 * y[5] * z[1] * x[5] * y[6] + 2.0 * y[5] * y[1] * x[6] * z[5];
- s8 = s6 - y[6] * z[1] * x[6] * y[5] - y[6] * y[1] * x[5] * z[6] +
- y[6] * x[1] * y[5] * z[6] + y[6] * y[1] * x[6] * z[5] -
- 2.0 * z[1] * x[6] * y[5] * y[5] + 2.0 * x[1] * y[5] * y[5] * z[6] -
- x[1] * y[6] * y[6] * z[5] + z[1] * x[5] * y[6] * y[6] +
- y[5] * z[1] * x[5] * y[2] - y[5] * x[1] * y[2] * z[5] +
- y[5] * y[1] * x[2] * z[5] - y[5] * y[1] * x[5] * z[2] -
- y[6] * z[1] * x[2] * y[5] + y[6] * x[1] * y[5] * z[2];
- s7 = s8 - y[1] * z[1] * x[2] * y[6] - y[1] * x[1] * y[2] * z[6] +
- y[1] * x[1] * y[6] * z[2] + y[1] * z[1] * x[6] * y[2] +
- y[5] * x[5] * y[6] * z[2] - y[5] * x[2] * y[6] * z[5] +
- y[5] * x[6] * y[2] * z[5] - y[5] * x[5] * y[2] * z[6] -
- x[6] * y[5] * y[5] * z[2] + x[2] * y[5] * y[5] * z[6] -
- y[5] * y[5] * x[4] * z[7] + y[5] * y[5] * x[7] * z[4] -
- y[1] * x[6] * y[5] * z[2] + y[1] * x[2] * y[5] * z[6] -
- y[2] * x[6] * y[5] * z[2] - 2.0 * y[2] * y[1] * x[6] * z[2];
- s8 = s7 - 2.0 * y[2] * z[1] * x[2] * y[6] +
- 2.0 * y[2] * x[1] * y[6] * z[2] + 2.0 * y[2] * y[1] * x[2] * z[6] -
- 2.0 * x[1] * y[2] * y[2] * z[6] + 2.0 * z[1] * x[6] * y[2] * y[2] +
- x[6] * y[2] * y[2] * z[5] - x[5] * y[2] * y[2] * z[6] +
- 2.0 * x[5] * y[6] * y[6] * z[2] - 2.0 * x[2] * y[6] * y[6] * z[5] -
- z[1] * x[2] * y[6] * y[6] - y[6] * y[1] * x[6] * z[2] -
- y[6] * x[1] * y[2] * z[6] + y[6] * z[1] * x[6] * y[2] +
- y[6] * y[1] * x[2] * z[6] + x[1] * y[6] * y[6] * z[2];
- s3 = s8 + y[2] * x[5] * y[6] * z[2] + y[2] * x[2] * y[5] * z[6] -
- y[2] * x[2] * y[6] * z[5] + y[5] * z[5] * x[4] * y[7] +
- y[5] * x[5] * y[4] * z[7] - y[5] * z[5] * x[7] * y[4] -
- y[5] * x[5] * y[7] * z[4] + 2.0 * y[4] * x[5] * y[0] * z[4] -
- y[3] * z[6] * x[3] * y[7] + y[3] * y[6] * x[3] * z[7] +
- y[3] * x[6] * y[7] * z[3] - y[3] * y[6] * x[7] * z[3] -
- y[2] * y[1] * x[3] * z[0] - y[2] * z[1] * x[0] * y[3] +
- y[2] * y[1] * x[0] * z[3] + y[2] * x[1] * y[3] * z[0];
- s8 = y[1] * x[0] * z[3] + x[1] * y[3] * z[0] - y[0] * x[3] * z[7] -
- x[1] * y[5] * z[0] - y[0] * x[3] * z[4] - x[1] * y[0] * z[2] +
- z[1] * x[2] * y[0] - y[1] * x[0] * z[5] - z[1] * x[0] * y[2] -
- y[1] * x[0] * z[4] + z[1] * x[5] * y[2] + z[0] * x[7] * y[4] +
- z[0] * x[3] * y[7] + z[1] * x[0] * y[4] - x[1] * y[2] * z[5] +
- x[2] * y[3] * z[0] + y[1] * x[2] * z[5] - x[2] * y[3] * z[7];
- s7 = s8 - z[1] * x[2] * y[5] - y[1] * x[3] * z[0] - x[0] * y[7] * z[3] -
- z[1] * x[0] * y[3] + y[5] * x[4] * z[0] - x[0] * y[4] * z[3] +
- y[5] * x[7] * z[4] - z[0] * x[4] * y[3] + x[1] * y[0] * z[4] -
- z[2] * x[3] * y[7] - y[6] * x[7] * z[2] + x[1] * y[5] * z[2] +
- y[6] * x[7] * z[5] + x[0] * y[7] * z[4] + x[1] * y[2] * z[0] -
- z[1] * x[4] * y[0] - z[0] * x[4] * y[7] - z[2] * x[0] * y[3];
- s8 = x[5] * y[0] * z[4] + z[1] * x[0] * y[5] - x[2] * y[0] * z[3] -
- z[1] * x[5] * y[0] + y[1] * x[5] * z[0] - x[1] * y[0] * z[3] -
- x[1] * y[4] * z[0] - y[1] * x[5] * z[2] + x[2] * y[7] * z[3] +
- y[0] * x[4] * z[3] - x[0] * y[4] * z[7] + x[1] * y[0] * z[5] -
- y[1] * x[6] * z[2] - y[2] * x[6] * z[3] + y[0] * x[7] * z[3] -
- y[2] * x[7] * z[3] + z[2] * x[7] * y[3] + y[2] * x[0] * z[3];
- s6 = s8 + y[2] * x[3] * z[7] - y[2] * x[3] * z[0] - x[6] * y[5] * z[2] -
- y[5] * x[0] * z[4] + z[2] * x[3] * y[0] + x[2] * y[3] * z[1] +
- x[0] * y[3] * z[7] - x[2] * y[1] * z[3] + y[1] * x[4] * z[0] +
- y[1] * x[0] * z[2] - z[1] * x[2] * y[6] + y[2] * x[3] * z[6] -
- y[1] * x[2] * z[0] + z[1] * x[3] * y[0] - x[1] * y[2] * z[6] -
- x[2] * y[3] * z[6] + x[0] * y[3] * z[4] + z[0] * x[3] * y[4] + s7;
- s8 = x[5] * y[4] * z[7] + s6 + y[5] * x[6] * z[4] - y[5] * x[4] * z[6] +
- z[6] * x[5] * y[7] - x[6] * y[2] * z[7] - x[6] * y[7] * z[5] +
- x[5] * y[6] * z[2] + x[6] * y[5] * z[7] + x[6] * y[7] * z[2] +
- y[6] * x[7] * z[4] - y[6] * x[4] * z[7] - y[6] * x[7] * z[3] +
- z[6] * x[7] * y[2] + x[2] * y[5] * z[6] - x[2] * y[6] * z[5] +
- y[6] * x[2] * z[7] + x[6] * y[2] * z[5];
- s7 = s8 - x[5] * y[2] * z[6] - z[6] * x[7] * y[5] - z[5] * x[7] * y[4] +
- z[5] * x[0] * y[4] - y[5] * x[4] * z[7] + y[0] * x[4] * z[7] -
- z[6] * x[2] * y[7] - x[5] * y[4] * z[0] - x[5] * y[7] * z[4] -
- y[0] * x[7] * z[4] + y[5] * x[4] * z[1] - x[6] * y[7] * z[4] +
- x[7] * y[4] * z[3] - x[4] * y[7] * z[3] + x[3] * y[7] * z[4] -
- x[7] * y[3] * z[4] - x[6] * y[3] * z[7] + x[6] * y[4] * z[7];
- s8 = -x[3] * y[4] * z[7] + x[4] * y[3] * z[7] - z[6] * x[7] * y[4] -
- z[1] * x[6] * y[5] + x[6] * y[7] * z[3] - x[1] * y[6] * z[5] -
- y[1] * x[5] * z[6] + z[5] * x[4] * y[7] - z[5] * x[4] * y[0] +
- x[1] * y[5] * z[6] - y[6] * x[5] * z[7] - y[2] * x[3] * z[1] +
- z[1] * x[5] * y[6] - y[5] * x[1] * z[4] + z[6] * x[4] * y[7] +
- x[5] * y[1] * z[4] - x[5] * y[6] * z[4] + y[6] * x[3] * z[7] -
- x[5] * y[4] * z[1];
- s5 = s8 + x[5] * y[4] * z[6] + z[5] * x[1] * y[4] + y[1] * x[6] * z[5] -
- z[6] * x[3] * y[7] + z[6] * x[7] * y[3] - z[5] * x[6] * y[4] -
- z[5] * x[4] * y[1] + z[5] * x[4] * y[6] + x[1] * y[6] * z[2] +
- x[2] * y[6] * z[3] + z[2] * x[6] * y[3] + z[1] * x[6] * y[2] +
- z[2] * x[3] * y[1] - z[2] * x[1] * y[3] - z[2] * x[3] * y[6] +
- y[2] * x[1] * z[3] + y[1] * x[2] * z[6] - z[0] * x[7] * y[3] + s7;
- s4 = 1 / s5;
- s2 = s3 * s4;
- const double unknown1 = s1 * s2;
- s1 = 1.0 / 6.0;
- s8 = -z[2] * x[1] * y[2] * z[5] + z[2] * y[1] * x[2] * z[5] -
- z[2] * z[1] * x[2] * y[5] + z[2] * z[1] * x[5] * y[2] +
- 2.0 * y[5] * x[7] * z[4] * z[4] - y[1] * x[2] * z[0] * z[0] +
- x[0] * y[3] * z[7] * z[7] - 2.0 * z[5] * z[5] * x[4] * y[1] +
- 2.0 * z[5] * z[5] * x[1] * y[4] + z[5] * z[5] * x[0] * y[4] -
- 2.0 * z[2] * z[2] * x[1] * y[3] + 2.0 * z[2] * z[2] * x[3] * y[1] -
- x[0] * y[4] * z[7] * z[7] - y[0] * x[3] * z[7] * z[7] +
- x[1] * y[0] * z[5] * z[5];
- s7 = s8 - y[1] * x[0] * z[5] * z[5] + z[1] * y[1] * x[2] * z[6] +
- y[1] * x[0] * z[2] * z[2] + z[2] * z[2] * x[3] * y[0] -
- z[2] * z[2] * x[0] * y[3] - x[1] * y[0] * z[2] * z[2] +
- 2.0 * z[5] * z[5] * x[4] * y[6] - 2.0 * z[5] * z[5] * x[6] * y[4] -
- z[5] * z[5] * x[7] * y[4] - x[6] * y[7] * z[5] * z[5] +
- 2.0 * z[2] * y[1] * x[2] * z[6] - 2.0 * z[2] * x[1] * y[2] * z[6] +
- 2.0 * z[2] * z[1] * x[6] * y[2] - y[6] * x[5] * z[7] * z[7] +
- 2.0 * x[6] * y[4] * z[7] * z[7];
- s8 = -2.0 * y[6] * x[4] * z[7] * z[7] + x[6] * y[5] * z[7] * z[7] -
- 2.0 * z[2] * z[1] * x[2] * y[6] + z[4] * y[6] * x[7] * z[5] +
- x[5] * y[4] * z[6] * z[6] + z[6] * z[6] * x[4] * y[7] -
- z[6] * z[6] * x[7] * y[4] - 2.0 * z[6] * z[6] * x[7] * y[5] +
- 2.0 * z[6] * z[6] * x[5] * y[7] - y[5] * x[4] * z[6] * z[6] +
- 2.0 * z[0] * z[0] * x[3] * y[4] - x[6] * y[5] * z[2] * z[2] +
- z[1] * z[1] * x[5] * y[6] - z[1] * z[1] * x[6] * y[5] -
- z[5] * z[5] * x[4] * y[0];
- s6 = s8 + 2.0 * x[1] * y[3] * z[0] * z[0] +
- 2.0 * x[1] * y[6] * z[2] * z[2] - 2.0 * y[1] * x[6] * z[2] * z[2] -
- y[1] * x[5] * z[2] * z[2] - z[1] * z[1] * x[2] * y[6] -
- 2.0 * z[1] * z[1] * x[2] * y[5] + 2.0 * z[1] * z[1] * x[5] * y[2] +
- z[1] * y[1] * x[6] * z[5] + y[1] * x[2] * z[5] * z[5] +
- z[2] * z[1] * x[2] * y[0] + z[1] * x[1] * y[5] * z[6] -
- z[1] * x[1] * y[6] * z[5] - z[1] * y[1] * x[5] * z[6] -
- z[1] * x[2] * y[6] * z[5] + z[1] * x[6] * y[2] * z[5] + s7;
- s8 = -x[1] * y[2] * z[5] * z[5] + z[1] * x[5] * y[6] * z[2] -
- 2.0 * z[2] * z[2] * x[3] * y[6] + 2.0 * z[2] * z[2] * x[6] * y[3] +
- z[2] * z[2] * x[7] * y[3] - z[2] * z[2] * x[3] * y[7] -
- z[1] * x[6] * y[5] * z[2] + 2.0 * z[1] * x[1] * y[5] * z[2] -
- 2.0 * x[3] * y[4] * z[7] * z[7] + 2.0 * x[4] * y[3] * z[7] * z[7] +
- x[5] * y[6] * z[2] * z[2] + y[1] * x[2] * z[6] * z[6] +
- y[0] * x[4] * z[7] * z[7] + z[2] * x[2] * y[3] * z[0] -
- x[1] * y[2] * z[6] * z[6];
- s7 = s8 - z[7] * z[2] * x[3] * y[7] + x[2] * y[6] * z[3] * z[3] -
- y[2] * x[6] * z[3] * z[3] - z[6] * x[2] * y[3] * z[7] -
- z[2] * z[1] * x[0] * y[2] + z[6] * z[2] * x[6] * y[3] -
- z[6] * z[2] * x[3] * y[6] + z[6] * x[2] * y[6] * z[3] +
- z[2] * x[1] * y[2] * z[0] + z[6] * y[2] * x[3] * z[7] -
- z[4] * z[5] * x[6] * y[4] + z[4] * z[5] * x[4] * y[6] -
- z[4] * y[6] * x[5] * z[7] + z[4] * z[6] * x[4] * y[7] +
- z[4] * x[5] * y[4] * z[6];
- s8 = -z[6] * y[2] * x[6] * z[3] - z[4] * y[5] * x[4] * z[6] -
- z[2] * y[1] * x[5] * z[6] + z[2] * x[1] * y[5] * z[6] +
- z[4] * x[6] * y[4] * z[7] + 2.0 * z[4] * z[5] * x[4] * y[7] -
- z[4] * z[6] * x[7] * y[4] + x[6] * y[7] * z[3] * z[3] -
- 2.0 * z[4] * z[5] * x[7] * y[4] - 2.0 * z[4] * y[5] * x[4] * z[7] -
- z[4] * y[6] * x[4] * z[7] + z[4] * x[6] * y[5] * z[7] -
- z[4] * x[6] * y[7] * z[5] + 2.0 * z[4] * x[5] * y[4] * z[7] +
- z[2] * x[2] * y[5] * z[6] - z[2] * x[2] * y[6] * z[5];
- s5 = s8 + z[2] * x[6] * y[2] * z[5] - z[2] * x[5] * y[2] * z[6] -
- z[2] * x[2] * y[3] * z[7] - x[2] * y[3] * z[7] * z[7] +
- 2.0 * z[2] * x[2] * y[3] * z[1] - z[2] * y[2] * x[3] * z[0] +
- z[2] * y[2] * x[0] * z[3] - z[2] * x[2] * y[0] * z[3] -
- z[7] * y[2] * x[7] * z[3] + z[7] * z[2] * x[7] * y[3] +
- z[7] * x[2] * y[7] * z[3] + z[6] * y[1] * x[2] * z[5] -
- z[6] * x[1] * y[2] * z[5] + z[5] * x[1] * y[5] * z[2] + s6 + s7;
- s8 = z[5] * z[1] * x[5] * y[2] - z[5] * z[1] * x[2] * y[5] -
- y[6] * x[7] * z[2] * z[2] + 2.0 * z[2] * x[2] * y[6] * z[3] -
- 2.0 * z[2] * x[2] * y[3] * z[6] + 2.0 * z[2] * y[2] * x[3] * z[6] +
- y[2] * x[3] * z[6] * z[6] + y[6] * x[7] * z[5] * z[5] +
- z[2] * y[2] * x[3] * z[7] - z[2] * y[2] * x[7] * z[3] -
- 2.0 * z[2] * y[2] * x[6] * z[3] + z[2] * x[2] * y[7] * z[3] +
- x[6] * y[2] * z[5] * z[5] - 2.0 * z[2] * x[2] * y[1] * z[3] -
- x[2] * y[6] * z[5] * z[5];
- s7 = s8 - y[1] * x[5] * z[6] * z[6] + z[6] * x[1] * y[6] * z[2] -
- z[3] * z[2] * x[3] * y[6] + z[6] * z[1] * x[6] * y[2] -
- z[6] * z[1] * x[2] * y[6] - z[6] * y[1] * x[6] * z[2] -
- 2.0 * x[5] * y[2] * z[6] * z[6] + z[4] * z[1] * x[0] * y[4] -
- z[3] * x[2] * y[3] * z[6] - z[5] * y[1] * x[5] * z[2] +
- z[3] * y[2] * x[3] * z[6] + 2.0 * x[2] * y[5] * z[6] * z[6] -
- z[5] * x[1] * y[5] * z[0] + y[2] * x[3] * z[7] * z[7] -
- x[2] * y[3] * z[6] * z[6];
- s8 = z[5] * y[5] * x[4] * z[0] + z[3] * z[2] * x[6] * y[3] +
- x[1] * y[5] * z[6] * z[6] + z[5] * y[5] * x[7] * z[4] -
- z[1] * x[1] * y[2] * z[6] + z[1] * x[1] * y[6] * z[2] +
- 2.0 * z[6] * y[6] * x[7] * z[5] - z[7] * y[6] * x[7] * z[2] -
- z[3] * y[6] * x[7] * z[2] + x[6] * y[7] * z[2] * z[2] -
- 2.0 * z[6] * y[6] * x[7] * z[2] - 2.0 * x[6] * y[3] * z[7] * z[7] -
- x[6] * y[2] * z[7] * z[7] - z[5] * x[6] * y[5] * z[2] +
- y[6] * x[2] * z[7] * z[7];
- s6 = s8 + 2.0 * y[6] * x[3] * z[7] * z[7] + z[6] * z[6] * x[7] * y[3] -
- y[6] * x[7] * z[3] * z[3] + z[5] * x[5] * y[0] * z[4] +
- 2.0 * z[6] * z[6] * x[7] * y[2] - 2.0 * z[6] * z[6] * x[2] * y[7] -
- z[6] * z[6] * x[3] * y[7] + z[7] * y[6] * x[7] * z[5] +
- z[7] * y[5] * x[7] * z[4] - 2.0 * z[7] * x[7] * y[3] * z[4] +
- 2.0 * z[7] * x[3] * y[7] * z[4] - 2.0 * z[7] * x[4] * y[7] * z[3] +
- 2.0 * z[7] * x[7] * y[4] * z[3] - z[7] * y[0] * x[7] * z[4] -
- 2.0 * z[7] * z[6] * x[3] * y[7] + s7;
- s8 = s6 + 2.0 * z[7] * z[6] * x[7] * y[3] +
- 2.0 * z[7] * x[6] * y[7] * z[3] + z[7] * x[6] * y[7] * z[2] -
- 2.0 * z[7] * y[6] * x[7] * z[3] + z[7] * z[6] * x[7] * y[2] -
- z[7] * z[6] * x[2] * y[7] + z[5] * y[1] * x[5] * z[0] -
- z[5] * z[1] * x[5] * y[0] + 2.0 * y[1] * x[6] * z[5] * z[5] -
- 2.0 * x[1] * y[6] * z[5] * z[5] + z[5] * z[1] * x[0] * y[5] +
- z[6] * y[6] * x[3] * z[7] + 2.0 * z[6] * x[6] * y[7] * z[2] -
- z[6] * y[6] * x[7] * z[3];
- s7 = s8 + 2.0 * z[6] * y[6] * x[2] * z[7] - z[6] * x[6] * y[3] * z[7] +
- z[6] * x[6] * y[7] * z[3] - 2.0 * z[6] * x[6] * y[2] * z[7] -
- 2.0 * z[1] * y[1] * x[5] * z[2] - z[1] * y[1] * x[6] * z[2] -
- z[7] * z[0] * x[7] * y[3] - 2.0 * z[6] * x[6] * y[5] * z[2] -
- z[2] * z[6] * x[3] * y[7] + z[2] * x[6] * y[7] * z[3] -
- z[2] * z[6] * x[2] * y[7] + y[5] * x[6] * z[4] * z[4] +
- z[2] * y[6] * x[2] * z[7] + y[6] * x[7] * z[4] * z[4] +
- z[2] * z[6] * x[7] * y[2] - 2.0 * x[5] * y[7] * z[4] * z[4];
- s8 = -x[6] * y[7] * z[4] * z[4] - z[5] * y[5] * x[0] * z[4] -
- z[2] * x[6] * y[2] * z[7] - x[5] * y[6] * z[4] * z[4] -
- 2.0 * z[5] * y[1] * x[5] * z[6] + 2.0 * z[5] * z[1] * x[5] * y[6] +
- 2.0 * z[5] * x[1] * y[5] * z[6] - 2.0 * z[5] * z[1] * x[6] * y[5] -
- z[5] * x[5] * y[2] * z[6] + z[5] * x[5] * y[6] * z[2] +
- z[5] * x[2] * y[5] * z[6] + z[5] * z[5] * x[4] * y[7] -
- y[5] * x[4] * z[7] * z[7] + x[5] * y[4] * z[7] * z[7] +
- z[6] * z[1] * x[5] * y[6] + z[6] * y[1] * x[6] * z[5];
- s4 = s8 - z[6] * z[1] * x[6] * y[5] - z[6] * x[1] * y[6] * z[5] +
- z[2] * z[6] * x[7] * y[3] + 2.0 * z[6] * x[6] * y[2] * z[5] +
- 2.0 * z[6] * x[5] * y[6] * z[2] - 2.0 * z[6] * x[2] * y[6] * z[5] +
- z[7] * z[0] * x[3] * y[7] + z[7] * z[0] * x[7] * y[4] +
- z[3] * z[6] * x[7] * y[3] - z[3] * z[6] * x[3] * y[7] -
- z[3] * x[6] * y[3] * z[7] + z[3] * y[6] * x[2] * z[7] -
- z[3] * x[6] * y[2] * z[7] + z[5] * x[5] * y[4] * z[7] + s5 + s7;
- s8 = s4 + z[3] * y[6] * x[3] * z[7] - z[7] * x[0] * y[7] * z[3] +
- z[6] * x[5] * y[4] * z[7] + z[7] * y[0] * x[7] * z[3] +
- z[5] * z[6] * x[4] * y[7] - 2.0 * z[5] * x[5] * y[6] * z[4] +
- 2.0 * z[5] * x[5] * y[4] * z[6] - z[5] * x[5] * y[7] * z[4] -
- z[5] * y[6] * x[5] * z[7] - z[5] * z[6] * x[7] * y[4] -
- z[7] * z[0] * x[4] * y[7] - z[5] * z[6] * x[7] * y[5] -
- z[5] * y[5] * x[4] * z[7] + z[7] * x[0] * y[7] * z[4];
- s7 = s8 - 2.0 * z[5] * y[5] * x[4] * z[6] + z[5] * z[6] * x[5] * y[7] +
- z[5] * x[6] * y[5] * z[7] + 2.0 * z[5] * y[5] * x[6] * z[4] +
- z[6] * z[5] * x[4] * y[6] - z[6] * x[5] * y[6] * z[4] -
- z[6] * z[5] * x[6] * y[4] - z[6] * x[6] * y[7] * z[4] -
- 2.0 * z[6] * y[6] * x[5] * z[7] + z[6] * x[6] * y[4] * z[7] -
- z[6] * y[5] * x[4] * z[7] - z[6] * y[6] * x[4] * z[7] +
- z[6] * y[6] * x[7] * z[4] + z[6] * y[5] * x[6] * z[4] +
- 2.0 * z[6] * x[6] * y[5] * z[7];
- s8 = -2.0 * z[6] * x[6] * y[7] * z[5] - z[2] * y[1] * x[2] * z[0] +
- 2.0 * z[7] * z[6] * x[4] * y[7] - 2.0 * z[7] * x[6] * y[7] * z[4] -
- 2.0 * z[7] * z[6] * x[7] * y[4] + z[7] * z[5] * x[4] * y[7] -
- z[7] * z[5] * x[7] * y[4] - z[7] * x[5] * y[7] * z[4] +
- 2.0 * z[7] * y[6] * x[7] * z[4] - z[7] * z[6] * x[7] * y[5] +
- z[7] * z[6] * x[5] * y[7] - z[7] * x[6] * y[7] * z[5] +
- z[1] * z[1] * x[6] * y[2] + s7 + x[1] * y[5] * z[2] * z[2];
- s6 = s8 + 2.0 * z[2] * y[2] * x[1] * z[3] -
- 2.0 * z[2] * y[2] * x[3] * z[1] - 2.0 * x[1] * y[4] * z[0] * z[0] +
- 2.0 * y[1] * x[4] * z[0] * z[0] + 2.0 * x[2] * y[7] * z[3] * z[3] -
- 2.0 * y[2] * x[7] * z[3] * z[3] - x[1] * y[5] * z[0] * z[0] +
- z[0] * z[0] * x[7] * y[4] + z[0] * z[0] * x[3] * y[7] +
- x[2] * y[3] * z[0] * z[0] - 2.0 * y[1] * x[3] * z[0] * z[0] +
- y[5] * x[4] * z[0] * z[0] - 2.0 * z[0] * z[0] * x[4] * y[3] +
- x[1] * y[2] * z[0] * z[0] - z[0] * z[0] * x[4] * y[7] +
- y[1] * x[5] * z[0] * z[0];
- s8 = s6 - y[2] * x[3] * z[0] * z[0] + y[1] * x[0] * z[3] * z[3] -
- 2.0 * x[0] * y[7] * z[3] * z[3] - x[0] * y[4] * z[3] * z[3] -
- 2.0 * x[2] * y[0] * z[3] * z[3] - x[1] * y[0] * z[3] * z[3] +
- y[0] * x[4] * z[3] * z[3] - 2.0 * z[0] * y[1] * x[0] * z[4] +
- 2.0 * z[0] * z[1] * x[0] * y[4] + 2.0 * z[0] * x[1] * y[0] * z[4] -
- 2.0 * z[0] * z[1] * x[4] * y[0] - 2.0 * z[3] * x[2] * y[3] * z[7] -
- 2.0 * z[3] * z[2] * x[3] * y[7] + 2.0 * z[3] * z[2] * x[7] * y[3];
- s7 = s8 + 2.0 * z[3] * y[2] * x[3] * z[7] +
- 2.0 * z[5] * y[5] * x[4] * z[1] + 2.0 * z[0] * y[1] * x[0] * z[3] -
- z[0] * y[0] * x[3] * z[7] - 2.0 * z[0] * y[0] * x[3] * z[4] -
- z[0] * x[1] * y[0] * z[2] + z[0] * z[1] * x[2] * y[0] -
- z[0] * y[1] * x[0] * z[5] - z[0] * z[1] * x[0] * y[2] -
- z[0] * x[0] * y[7] * z[3] - 2.0 * z[0] * z[1] * x[0] * y[3] -
- z[5] * x[5] * y[4] * z[0] - 2.0 * z[0] * x[0] * y[4] * z[3] +
- z[0] * x[0] * y[7] * z[4] - z[0] * z[2] * x[0] * y[3];
- s8 = s7 + z[0] * x[5] * y[0] * z[4] + z[0] * z[1] * x[0] * y[5] -
- z[0] * x[2] * y[0] * z[3] - z[0] * z[1] * x[5] * y[0] -
- 2.0 * z[0] * x[1] * y[0] * z[3] + 2.0 * z[0] * y[0] * x[4] * z[3] -
- z[0] * x[0] * y[4] * z[7] + z[0] * x[1] * y[0] * z[5] +
- z[0] * y[0] * x[7] * z[3] + z[0] * y[2] * x[0] * z[3] -
- z[0] * y[5] * x[0] * z[4] + z[0] * z[2] * x[3] * y[0] +
- z[0] * x[2] * y[3] * z[1] + z[0] * x[0] * y[3] * z[7] -
- z[0] * x[2] * y[1] * z[3];
- s5 = s8 + z[0] * y[1] * x[0] * z[2] + z[3] * x[1] * y[3] * z[0] -
- 2.0 * z[3] * y[0] * x[3] * z[7] - z[3] * y[0] * x[3] * z[4] -
- z[3] * x[1] * y[0] * z[2] + z[3] * z[0] * x[7] * y[4] +
- 2.0 * z[3] * z[0] * x[3] * y[7] + 2.0 * z[3] * x[2] * y[3] * z[0] -
- z[3] * y[1] * x[3] * z[0] - z[3] * z[1] * x[0] * y[3] -
- z[3] * z[0] * x[4] * y[3] + z[3] * x[1] * y[2] * z[0] -
- z[3] * z[0] * x[4] * y[7] - 2.0 * z[3] * z[2] * x[0] * y[3] -
- z[3] * x[0] * y[4] * z[7] - 2.0 * z[3] * y[2] * x[3] * z[0];
- s8 = s5 + 2.0 * z[3] * z[2] * x[3] * y[0] + z[3] * x[2] * y[3] * z[1] +
- 2.0 * z[3] * x[0] * y[3] * z[7] + z[3] * y[1] * x[0] * z[2] -
- z[4] * y[0] * x[3] * z[7] - z[4] * x[1] * y[5] * z[0] -
- z[4] * y[1] * x[0] * z[5] + 2.0 * z[4] * z[0] * x[7] * y[4] +
- z[4] * z[0] * x[3] * y[7] + 2.0 * z[4] * y[5] * x[4] * z[0] +
- 2.0 * y[0] * x[7] * z[3] * z[3] + 2.0 * y[2] * x[0] * z[3] * z[3] -
- x[2] * y[1] * z[3] * z[3] - y[0] * x[3] * z[4] * z[4];
- s7 = s8 - y[1] * x[0] * z[4] * z[4] + x[1] * y[0] * z[4] * z[4] +
- 2.0 * x[0] * y[7] * z[4] * z[4] + 2.0 * x[5] * y[0] * z[4] * z[4] -
- 2.0 * y[5] * x[0] * z[4] * z[4] + 2.0 * z[1] * z[1] * x[2] * y[0] -
- 2.0 * z[1] * z[1] * x[0] * y[2] + z[1] * z[1] * x[0] * y[4] -
- z[1] * z[1] * x[0] * y[3] - z[1] * z[1] * x[4] * y[0] +
- 2.0 * z[1] * z[1] * x[0] * y[5] - 2.0 * z[1] * z[1] * x[5] * y[0] +
- x[2] * y[3] * z[1] * z[1] - x[5] * y[4] * z[0] * z[0] -
- z[0] * z[0] * x[7] * y[3];
- s8 = s7 + x[7] * y[4] * z[3] * z[3] - x[4] * y[7] * z[3] * z[3] +
- y[2] * x[1] * z[3] * z[3] + x[0] * y[3] * z[4] * z[4] -
- 2.0 * y[0] * x[7] * z[4] * z[4] + x[3] * y[7] * z[4] * z[4] -
- x[7] * y[3] * z[4] * z[4] - y[5] * x[1] * z[4] * z[4] +
- x[5] * y[1] * z[4] * z[4] + z[1] * z[1] * x[3] * y[0] +
- y[5] * x[4] * z[1] * z[1] - y[2] * x[3] * z[1] * z[1] -
- x[5] * y[4] * z[1] * z[1] - z[4] * x[0] * y[4] * z[3] -
- z[4] * z[0] * x[4] * y[3];
- s6 = s8 - z[4] * z[1] * x[4] * y[0] - 2.0 * z[4] * z[0] * x[4] * y[7] +
- z[4] * y[1] * x[5] * z[0] - 2.0 * z[5] * x[5] * y[4] * z[1] -
- z[4] * x[1] * y[4] * z[0] + z[4] * y[0] * x[4] * z[3] -
- 2.0 * z[4] * x[0] * y[4] * z[7] + z[4] * x[1] * y[0] * z[5] -
- 2.0 * z[1] * x[1] * y[2] * z[5] + z[4] * x[0] * y[3] * z[7] +
- 2.0 * z[5] * x[5] * y[1] * z[4] + z[4] * y[1] * x[4] * z[0] +
- z[1] * y[1] * x[0] * z[3] + z[1] * x[1] * y[3] * z[0] -
- 2.0 * z[1] * x[1] * y[5] * z[0] - 2.0 * z[1] * x[1] * y[0] * z[2];
- s8 = s6 - 2.0 * z[1] * y[1] * x[0] * z[5] - z[1] * y[1] * x[0] * z[4] +
- 2.0 * z[1] * y[1] * x[2] * z[5] - z[1] * y[1] * x[3] * z[0] -
- 2.0 * z[5] * y[5] * x[1] * z[4] + z[1] * y[5] * x[4] * z[0] +
- z[1] * x[1] * y[0] * z[4] + 2.0 * z[1] * x[1] * y[2] * z[0] -
- z[1] * z[2] * x[0] * y[3] + 2.0 * z[1] * y[1] * x[5] * z[0] -
- z[1] * x[1] * y[0] * z[3] - z[1] * x[1] * y[4] * z[0] +
- 2.0 * z[1] * x[1] * y[0] * z[5] - z[1] * y[2] * x[3] * z[0];
- s7 = s8 + z[1] * z[2] * x[3] * y[0] - z[1] * x[2] * y[1] * z[3] +
- z[1] * y[1] * x[4] * z[0] + 2.0 * z[1] * y[1] * x[0] * z[2] +
- 2.0 * z[0] * z[1] * x[3] * y[0] + 2.0 * z[0] * x[0] * y[3] * z[4] +
- z[0] * z[5] * x[0] * y[4] + z[0] * y[0] * x[4] * z[7] -
- z[0] * y[0] * x[7] * z[4] - z[0] * x[7] * y[3] * z[4] -
- z[0] * z[5] * x[4] * y[0] - z[0] * x[5] * y[4] * z[1] +
- z[3] * z[1] * x[3] * y[0] + z[3] * x[0] * y[3] * z[4] +
- z[3] * z[0] * x[3] * y[4] + z[3] * y[0] * x[4] * z[7];
- s8 = s7 + z[3] * x[3] * y[7] * z[4] - z[3] * x[7] * y[3] * z[4] -
- z[3] * x[3] * y[4] * z[7] + z[3] * x[4] * y[3] * z[7] -
- z[3] * y[2] * x[3] * z[1] + z[3] * z[2] * x[3] * y[1] -
- z[3] * z[2] * x[1] * y[3] - 2.0 * z[3] * z[0] * x[7] * y[3] +
- z[4] * z[0] * x[3] * y[4] + 2.0 * z[4] * z[5] * x[0] * y[4] +
- 2.0 * z[4] * y[0] * x[4] * z[7] - 2.0 * z[4] * x[5] * y[4] * z[0] +
- z[4] * y[5] * x[4] * z[1] + z[4] * x[7] * y[4] * z[3] -
- z[4] * x[4] * y[7] * z[3];
- s3 = s8 - z[4] * x[3] * y[4] * z[7] + z[4] * x[4] * y[3] * z[7] -
- 2.0 * z[4] * z[5] * x[4] * y[0] - z[4] * x[5] * y[4] * z[1] +
- z[4] * z[5] * x[1] * y[4] - z[4] * z[5] * x[4] * y[1] -
- 2.0 * z[1] * y[1] * x[2] * z[0] + z[1] * z[5] * x[0] * y[4] -
- z[1] * z[5] * x[4] * y[0] - z[1] * y[5] * x[1] * z[4] +
- z[1] * x[5] * y[1] * z[4] + z[1] * z[5] * x[1] * y[4] -
- z[1] * z[5] * x[4] * y[1] + z[1] * z[2] * x[3] * y[1] -
- z[1] * z[2] * x[1] * y[3] + z[1] * y[2] * x[1] * z[3];
- s8 = y[1] * x[0] * z[3] + x[1] * y[3] * z[0] - y[0] * x[3] * z[7] -
- x[1] * y[5] * z[0] - y[0] * x[3] * z[4] - x[1] * y[0] * z[2] +
- z[1] * x[2] * y[0] - y[1] * x[0] * z[5] - z[1] * x[0] * y[2] -
- y[1] * x[0] * z[4] + z[1] * x[5] * y[2] + z[0] * x[7] * y[4] +
- z[0] * x[3] * y[7] + z[1] * x[0] * y[4] - x[1] * y[2] * z[5] +
- x[2] * y[3] * z[0] + y[1] * x[2] * z[5] - x[2] * y[3] * z[7];
- s7 = s8 - z[1] * x[2] * y[5] - y[1] * x[3] * z[0] - x[0] * y[7] * z[3] -
- z[1] * x[0] * y[3] + y[5] * x[4] * z[0] - x[0] * y[4] * z[3] +
- y[5] * x[7] * z[4] - z[0] * x[4] * y[3] + x[1] * y[0] * z[4] -
- z[2] * x[3] * y[7] - y[6] * x[7] * z[2] + x[1] * y[5] * z[2] +
- y[6] * x[7] * z[5] + x[0] * y[7] * z[4] + x[1] * y[2] * z[0] -
- z[1] * x[4] * y[0] - z[0] * x[4] * y[7] - z[2] * x[0] * y[3];
- s8 = x[5] * y[0] * z[4] + z[1] * x[0] * y[5] - x[2] * y[0] * z[3] -
- z[1] * x[5] * y[0] + y[1] * x[5] * z[0] - x[1] * y[0] * z[3] -
- x[1] * y[4] * z[0] - y[1] * x[5] * z[2] + x[2] * y[7] * z[3] +
- y[0] * x[4] * z[3] - x[0] * y[4] * z[7] + x[1] * y[0] * z[5] -
- y[1] * x[6] * z[2] - y[2] * x[6] * z[3] + y[0] * x[7] * z[3] -
- y[2] * x[7] * z[3] + z[2] * x[7] * y[3] + y[2] * x[0] * z[3];
- s6 = s8 + y[2] * x[3] * z[7] - y[2] * x[3] * z[0] - x[6] * y[5] * z[2] -
- y[5] * x[0] * z[4] + z[2] * x[3] * y[0] + x[2] * y[3] * z[1] +
- x[0] * y[3] * z[7] - x[2] * y[1] * z[3] + y[1] * x[4] * z[0] +
- y[1] * x[0] * z[2] - z[1] * x[2] * y[6] + y[2] * x[3] * z[6] -
- y[1] * x[2] * z[0] + z[1] * x[3] * y[0] - x[1] * y[2] * z[6] -
- x[2] * y[3] * z[6] + x[0] * y[3] * z[4] + z[0] * x[3] * y[4] + s7;
- s8 = x[5] * y[4] * z[7] + s6 + y[5] * x[6] * z[4] - y[5] * x[4] * z[6] +
- z[6] * x[5] * y[7] - x[6] * y[2] * z[7] - x[6] * y[7] * z[5] +
- x[5] * y[6] * z[2] + x[6] * y[5] * z[7] + x[6] * y[7] * z[2] +
- y[6] * x[7] * z[4] - y[6] * x[4] * z[7] - y[6] * x[7] * z[3] +
- z[6] * x[7] * y[2] + x[2] * y[5] * z[6] - x[2] * y[6] * z[5] +
- y[6] * x[2] * z[7] + x[6] * y[2] * z[5];
- s7 = s8 - x[5] * y[2] * z[6] - z[6] * x[7] * y[5] - z[5] * x[7] * y[4] +
- z[5] * x[0] * y[4] - y[5] * x[4] * z[7] + y[0] * x[4] * z[7] -
- z[6] * x[2] * y[7] - x[5] * y[4] * z[0] - x[5] * y[7] * z[4] -
- y[0] * x[7] * z[4] + y[5] * x[4] * z[1] - x[6] * y[7] * z[4] +
- x[7] * y[4] * z[3] - x[4] * y[7] * z[3] + x[3] * y[7] * z[4] -
- x[7] * y[3] * z[4] - x[6] * y[3] * z[7] + x[6] * y[4] * z[7];
- s8 = -x[3] * y[4] * z[7] + x[4] * y[3] * z[7] - z[6] * x[7] * y[4] -
- z[1] * x[6] * y[5] + x[6] * y[7] * z[3] - x[1] * y[6] * z[5] -
- y[1] * x[5] * z[6] + z[5] * x[4] * y[7] - z[5] * x[4] * y[0] +
- x[1] * y[5] * z[6] - y[6] * x[5] * z[7] - y[2] * x[3] * z[1] +
- z[1] * x[5] * y[6] - y[5] * x[1] * z[4] + z[6] * x[4] * y[7] +
- x[5] * y[1] * z[4] - x[5] * y[6] * z[4] + y[6] * x[3] * z[7] -
- x[5] * y[4] * z[1];
- s5 = s8 + x[5] * y[4] * z[6] + z[5] * x[1] * y[4] + y[1] * x[6] * z[5] -
- z[6] * x[3] * y[7] + z[6] * x[7] * y[3] - z[5] * x[6] * y[4] -
- z[5] * x[4] * y[1] + z[5] * x[4] * y[6] + x[1] * y[6] * z[2] +
- x[2] * y[6] * z[3] + z[2] * x[6] * y[3] + z[1] * x[6] * y[2] +
- z[2] * x[3] * y[1] - z[2] * x[1] * y[3] - z[2] * x[3] * y[6] +
- y[2] * x[1] * z[3] + y[1] * x[2] * z[6] - z[0] * x[7] * y[3] + s7;
- s4 = 1 / s5;
- s2 = s3 * s4;
- const double unknown2 = s1 * s2;
-
- return {unknown0, unknown1, unknown2};
+ if (accessor.reference_cell() == ReferenceCells::Tetrahedron)
+ {
+ // We define the center in the same way as a simplex barycenter
+ return accessor.center();
+ }
+ else if (accessor.reference_cell() == ReferenceCells::Hexahedron)
+ {
+ /*
+ Get the computation of the barycenter by this little Maple script. We
+ use the trilinear mapping of the unit hex to the real hex.
+
+ Remember that the area of the hex is given by
+ |K| = \int_K 1 dx dy dz = \int_{\hat K} |det J| d(xi) d(eta) d(zeta)
+ and that the barycenter is given by
+ \vec x_s = 1/|K| \int_K \vec x dx dy dz
+ = 1/|K| \int_{\hat K} \vec x(xi,eta,zeta) |det J| d(xi) d(eta) d(zeta)
+
+ Note, that in the ordering of the shape functions tphi[0]-tphi[7]
+ below, eta and zeta have been exchanged (zeta belongs to the y, and
+ eta to the z direction). However, the resulting Jacobian determinant
+ detJ should be the same, as a matrix and the matrix created from it
+ by exchanging two consecutive lines and two neighboring columns have
+ the same determinant.
+
+ # x, y and z are arrays holding the x-, y- and z-values of the four
+ vertices # of this cell in real space. x := array(0..7): y :=
+ array(0..7): z := array(0..7): tphi[0] := (1-xi)*(1-eta)*(1-zeta):
+ tphi[1] := xi*(1-eta)*(1-zeta):
+ tphi[2] := xi*eta*(1-zeta):
+ tphi[3] := (1-xi)*eta*(1-zeta):
+ tphi[4] := (1-xi)*(1-eta)*zeta:
+ tphi[5] := xi*(1-eta)*zeta:
+ tphi[6] := xi*eta*zeta:
+ tphi[7] := (1-xi)*eta*zeta:
+ x_real := sum(x[s]*tphi[s], s=0..7):
+ y_real := sum(y[s]*tphi[s], s=0..7):
+ z_real := sum(z[s]*tphi[s], s=0..7):
+ with (linalg):
+ J := matrix(3,3, [[diff(x_real, xi), diff(x_real, eta), diff(x_real,
+ zeta)], [diff(y_real, xi), diff(y_real, eta), diff(y_real, zeta)],
+ [diff(z_real, xi), diff(z_real, eta), diff(z_real, zeta)]]):
+ detJ := det (J):
+
+ measure := simplify ( int ( int ( int (detJ, xi=0..1), eta=0..1),
+ zeta=0..1)):
+
+ xs := simplify (1/measure * int ( int ( int (x_real * detJ, xi=0..1),
+ eta=0..1), zeta=0..1)): ys := simplify (1/measure * int ( int ( int
+ (y_real * detJ, xi=0..1), eta=0..1), zeta=0..1)): zs := simplify
+ (1/measure * int ( int ( int (z_real * detJ, xi=0..1), eta=0..1),
+ zeta=0..1)):
+
+ readlib(C):
+
+ C(array(1..3, [xs, ys, zs]));
+
+
+ This script takes more than several hours when using an old version
+ of maple on an old and slow computer. Therefore, when changing to
+ the new deal.II numbering scheme (lexicographic numbering) the code
+ lines below have not been reproduced with maple but only the
+ ordering of points in the definitions of x[], y[] and z[] have been
+ changed.
+
+ For the case, someone is willing to rerun the maple script, he/she
+ should use following ordering of shape functions:
+
+ tphi[0] := (1-xi)*(1-eta)*(1-zeta):
+ tphi[1] := xi*(1-eta)*(1-zeta):
+ tphi[2] := (1-xi)* eta*(1-zeta):
+ tphi[3] := xi* eta*(1-zeta):
+ tphi[4] := (1-xi)*(1-eta)*zeta:
+ tphi[5] := xi*(1-eta)*zeta:
+ tphi[6] := (1-xi)* eta*zeta:
+ tphi[7] := xi* eta*zeta:
+
+ and change the ordering of points in the definitions of x[], y[] and
+ z[] back to the standard ordering.
+ */
+
+ const double x[8] = {accessor.vertex(0)(0),
+ accessor.vertex(1)(0),
+ accessor.vertex(5)(0),
+ accessor.vertex(4)(0),
+ accessor.vertex(2)(0),
+ accessor.vertex(3)(0),
+ accessor.vertex(7)(0),
+ accessor.vertex(6)(0)};
+ const double y[8] = {accessor.vertex(0)(1),
+ accessor.vertex(1)(1),
+ accessor.vertex(5)(1),
+ accessor.vertex(4)(1),
+ accessor.vertex(2)(1),
+ accessor.vertex(3)(1),
+ accessor.vertex(7)(1),
+ accessor.vertex(6)(1)};
+ const double z[8] = {accessor.vertex(0)(2),
+ accessor.vertex(1)(2),
+ accessor.vertex(5)(2),
+ accessor.vertex(4)(2),
+ accessor.vertex(2)(2),
+ accessor.vertex(3)(2),
+ accessor.vertex(7)(2),
+ accessor.vertex(6)(2)};
+
+ double s1, s2, s3, s4, s5, s6, s7, s8;
+
+ s1 = 1.0 / 6.0;
+ s8 = -x[2] * x[2] * y[0] * z[3] - 2.0 * z[6] * x[7] * x[7] * y[4] -
+ z[5] * x[7] * x[7] * y[4] - z[6] * x[7] * x[7] * y[5] +
+ 2.0 * y[6] * x[7] * x[7] * z[4] - z[5] * x[6] * x[6] * y[4] +
+ x[6] * x[6] * y[4] * z[7] - z[1] * x[0] * x[0] * y[2] -
+ x[6] * x[6] * y[7] * z[4] + 2.0 * x[6] * x[6] * y[5] * z[7] -
+ 2.0 * x[6] * x[6] * y[7] * z[5] + y[5] * x[6] * x[6] * z[4] +
+ 2.0 * x[5] * x[5] * y[4] * z[6] + x[0] * x[0] * y[7] * z[4] -
+ 2.0 * x[5] * x[5] * y[6] * z[4];
+ s7 = s8 - y[6] * x[5] * x[5] * z[7] + z[6] * x[5] * x[5] * y[7] -
+ y[1] * x[0] * x[0] * z[5] + x[7] * z[5] * x[4] * y[7] -
+ x[7] * y[6] * x[5] * z[7] - 2.0 * x[7] * x[6] * y[7] * z[4] +
+ 2.0 * x[7] * x[6] * y[4] * z[7] - x[7] * x[5] * y[7] * z[4] -
+ 2.0 * x[7] * y[6] * x[4] * z[7] - x[7] * y[5] * x[4] * z[7] +
+ x[2] * x[2] * y[3] * z[0] - x[7] * x[6] * y[7] * z[5] +
+ x[7] * x[6] * y[5] * z[7] + 2.0 * x[1] * x[1] * y[0] * z[5] +
+ x[7] * z[6] * x[5] * y[7];
+ s8 = -2.0 * x[1] * x[1] * y[5] * z[0] + z[1] * x[0] * x[0] * y[5] +
+ 2.0 * x[2] * x[2] * y[3] * z[1] - z[5] * x[4] * x[4] * y[1] +
+ y[5] * x[4] * x[4] * z[1] - 2.0 * x[5] * x[5] * y[4] * z[1] +
+ 2.0 * x[5] * x[5] * y[1] * z[4] - 2.0 * x[2] * x[2] * y[1] * z[3] -
+ y[1] * x[2] * x[2] * z[0] + x[7] * y[2] * x[3] * z[7] +
+ x[7] * z[2] * x[6] * y[3] + 2.0 * x[7] * z[6] * x[4] * y[7] +
+ z[5] * x[1] * x[1] * y[4] + z[1] * x[2] * x[2] * y[0] -
+ 2.0 * y[0] * x[3] * x[3] * z[7];
+ s6 = s8 + 2.0 * z[0] * x[3] * x[3] * y[7] - x[7] * x[2] * y[3] * z[7] -
+ x[7] * z[2] * x[3] * y[7] + x[7] * x[2] * y[7] * z[3] -
+ x[7] * y[2] * x[6] * z[3] + x[4] * x[5] * y[1] * z[4] -
+ x[4] * x[5] * y[4] * z[1] + x[4] * z[5] * x[1] * y[4] -
+ x[4] * y[5] * x[1] * z[4] - 2.0 * x[5] * z[5] * x[4] * y[1] -
+ 2.0 * x[5] * y[5] * x[1] * z[4] + 2.0 * x[5] * z[5] * x[1] * y[4] +
+ 2.0 * x[5] * y[5] * x[4] * z[1] - x[6] * z[5] * x[7] * y[4] -
+ z[2] * x[3] * x[3] * y[6] + s7;
+ s8 = -2.0 * x[6] * z[6] * x[7] * y[5] - x[6] * y[6] * x[4] * z[7] +
+ y[2] * x[3] * x[3] * z[6] + x[6] * y[6] * x[7] * z[4] +
+ 2.0 * y[2] * x[3] * x[3] * z[7] + x[0] * x[1] * y[0] * z[5] +
+ x[0] * y[1] * x[5] * z[0] - x[0] * z[1] * x[5] * y[0] -
+ 2.0 * z[2] * x[3] * x[3] * y[7] + 2.0 * x[6] * z[6] * x[5] * y[7] -
+ x[0] * x[1] * y[5] * z[0] - x[6] * y[5] * x[4] * z[6] -
+ 2.0 * x[3] * z[0] * x[7] * y[3] - x[6] * z[6] * x[7] * y[4] -
+ 2.0 * x[1] * z[1] * x[5] * y[0];
+ s7 = s8 + 2.0 * x[1] * y[1] * x[5] * z[0] +
+ 2.0 * x[1] * z[1] * x[0] * y[5] + 2.0 * x[3] * y[0] * x[7] * z[3] +
+ 2.0 * x[3] * x[0] * y[3] * z[7] - 2.0 * x[3] * x[0] * y[7] * z[3] -
+ 2.0 * x[1] * y[1] * x[0] * z[5] - 2.0 * x[6] * y[6] * x[5] * z[7] +
+ s6 - y[5] * x[1] * x[1] * z[4] + x[6] * z[6] * x[4] * y[7] -
+ 2.0 * x[2] * y[2] * x[3] * z[1] + x[6] * z[5] * x[4] * y[6] +
+ x[6] * x[5] * y[4] * z[6] - y[6] * x[7] * x[7] * z[2] -
+ x[6] * x[5] * y[6] * z[4];
+ s8 = x[3] * x[3] * y[7] * z[4] - 2.0 * y[6] * x[7] * x[7] * z[3] +
+ z[6] * x[7] * x[7] * y[2] + 2.0 * z[6] * x[7] * x[7] * y[3] +
+ 2.0 * y[1] * x[0] * x[0] * z[3] + 2.0 * x[0] * x[1] * y[3] * z[0] -
+ 2.0 * x[0] * y[0] * x[3] * z[4] - 2.0 * x[0] * z[1] * x[4] * y[0] -
+ 2.0 * x[0] * y[1] * x[3] * z[0] + 2.0 * x[0] * y[0] * x[4] * z[3] -
+ 2.0 * x[0] * z[0] * x[4] * y[3] + 2.0 * x[0] * x[1] * y[0] * z[4] +
+ 2.0 * x[0] * z[1] * x[3] * y[0] - 2.0 * x[0] * x[1] * y[0] * z[3] -
+ 2.0 * x[0] * x[1] * y[4] * z[0] + 2.0 * x[0] * y[1] * x[4] * z[0];
+ s5 = s8 + 2.0 * x[0] * z[0] * x[3] * y[4] + x[1] * y[1] * x[0] * z[3] -
+ x[1] * z[1] * x[4] * y[0] - x[1] * y[1] * x[0] * z[4] +
+ x[1] * z[1] * x[0] * y[4] - x[1] * y[1] * x[3] * z[0] -
+ x[1] * z[1] * x[0] * y[3] - x[0] * z[5] * x[4] * y[1] +
+ x[0] * y[5] * x[4] * z[1] - 2.0 * x[4] * x[0] * y[4] * z[7] -
+ 2.0 * x[4] * y[5] * x[0] * z[4] + 2.0 * x[4] * z[5] * x[0] * y[4] -
+ 2.0 * x[4] * x[5] * y[4] * z[0] - 2.0 * x[4] * y[0] * x[7] * z[4] -
+ x[5] * y[5] * x[0] * z[4] + s7;
+ s8 = x[5] * z[5] * x[0] * y[4] - x[5] * z[5] * x[4] * y[0] +
+ x[1] * z[5] * x[0] * y[4] + x[5] * y[5] * x[4] * z[0] -
+ x[0] * y[0] * x[7] * z[4] - x[0] * z[5] * x[4] * y[0] -
+ x[1] * y[5] * x[0] * z[4] + x[0] * z[0] * x[7] * y[4] +
+ x[0] * y[5] * x[4] * z[0] - x[0] * z[0] * x[4] * y[7] +
+ x[0] * x[5] * y[0] * z[4] + x[0] * y[0] * x[4] * z[7] -
+ x[0] * x[5] * y[4] * z[0] - x[3] * x[3] * y[4] * z[7] +
+ 2.0 * x[2] * z[2] * x[3] * y[1];
+ s7 = s8 - x[5] * x[5] * y[4] * z[0] + 2.0 * y[5] * x[4] * x[4] * z[0] -
+ 2.0 * z[0] * x[4] * x[4] * y[7] + 2.0 * y[0] * x[4] * x[4] * z[7] -
+ 2.0 * z[5] * x[4] * x[4] * y[0] + x[5] * x[5] * y[4] * z[7] -
+ x[5] * x[5] * y[7] * z[4] - 2.0 * y[5] * x[4] * x[4] * z[7] +
+ 2.0 * z[5] * x[4] * x[4] * y[7] - x[0] * x[0] * y[7] * z[3] +
+ y[2] * x[0] * x[0] * z[3] + x[0] * x[0] * y[3] * z[7] -
+ x[5] * x[1] * y[4] * z[0] + x[5] * y[1] * x[4] * z[0] -
+ x[4] * y[0] * x[3] * z[4];
+ s8 = -x[4] * y[1] * x[0] * z[4] + x[4] * z[1] * x[0] * y[4] +
+ x[4] * x[0] * y[3] * z[4] - x[4] * x[0] * y[4] * z[3] +
+ x[4] * x[1] * y[0] * z[4] - x[4] * x[1] * y[4] * z[0] +
+ x[4] * z[0] * x[3] * y[4] + x[5] * x[1] * y[0] * z[4] +
+ x[1] * z[1] * x[3] * y[0] + x[1] * y[1] * x[4] * z[0] -
+ x[5] * z[1] * x[4] * y[0] - 2.0 * y[1] * x[0] * x[0] * z[4] +
+ 2.0 * z[1] * x[0] * x[0] * y[4] + 2.0 * x[0] * x[0] * y[3] * z[4] -
+ 2.0 * z[1] * x[0] * x[0] * y[3];
+ s6 = s8 - 2.0 * x[0] * x[0] * y[4] * z[3] + x[1] * x[1] * y[3] * z[0] +
+ x[1] * x[1] * y[0] * z[4] - x[1] * x[1] * y[0] * z[3] -
+ x[1] * x[1] * y[4] * z[0] - z[1] * x[4] * x[4] * y[0] +
+ y[0] * x[4] * x[4] * z[3] - z[0] * x[4] * x[4] * y[3] +
+ y[1] * x[4] * x[4] * z[0] - x[0] * x[0] * y[4] * z[7] -
+ y[5] * x[0] * x[0] * z[4] + z[5] * x[0] * x[0] * y[4] +
+ x[5] * x[5] * y[0] * z[4] - x[0] * y[0] * x[3] * z[7] +
+ x[0] * z[0] * x[3] * y[7] + s7;
+ s8 = s6 + x[0] * x[2] * y[3] * z[0] - x[0] * x[2] * y[0] * z[3] +
+ x[0] * y[0] * x[7] * z[3] - x[0] * y[2] * x[3] * z[0] +
+ x[0] * z[2] * x[3] * y[0] - x[0] * z[0] * x[7] * y[3] +
+ x[1] * x[2] * y[3] * z[0] - z[2] * x[0] * x[0] * y[3] +
+ x[3] * z[2] * x[6] * y[3] - x[3] * x[2] * y[3] * z[6] +
+ x[3] * x[2] * y[6] * z[3] - x[3] * y[2] * x[6] * z[3] -
+ 2.0 * x[3] * y[2] * x[7] * z[3] + 2.0 * x[3] * z[2] * x[7] * y[3];
+ s7 = s8 + 2.0 * x[4] * y[5] * x[7] * z[4] +
+ 2.0 * x[4] * x[5] * y[4] * z[7] - 2.0 * x[4] * z[5] * x[7] * y[4] -
+ 2.0 * x[4] * x[5] * y[7] * z[4] + x[5] * y[5] * x[7] * z[4] -
+ x[5] * z[5] * x[7] * y[4] - x[5] * y[5] * x[4] * z[7] +
+ x[5] * z[5] * x[4] * y[7] + 2.0 * x[3] * x[2] * y[7] * z[3] -
+ 2.0 * x[2] * z[2] * x[1] * y[3] + 2.0 * x[4] * z[0] * x[7] * y[4] +
+ 2.0 * x[4] * x[0] * y[7] * z[4] + 2.0 * x[4] * x[5] * y[0] * z[4] -
+ x[7] * x[6] * y[2] * z[7] - 2.0 * x[3] * x[2] * y[3] * z[7] -
+ x[0] * x[4] * y[7] * z[3];
+ s8 = x[0] * x[3] * y[7] * z[4] - x[0] * x[3] * y[4] * z[7] +
+ x[0] * x[4] * y[3] * z[7] - 2.0 * x[7] * z[6] * x[3] * y[7] +
+ x[3] * x[7] * y[4] * z[3] - x[3] * x[4] * y[7] * z[3] -
+ x[3] * x[7] * y[3] * z[4] + x[3] * x[4] * y[3] * z[7] +
+ 2.0 * x[2] * y[2] * x[1] * z[3] + y[6] * x[3] * x[3] * z[7] -
+ z[6] * x[3] * x[3] * y[7] - x[1] * z[5] * x[4] * y[1] -
+ x[1] * x[5] * y[4] * z[1] - x[1] * z[2] * x[0] * y[3] -
+ x[1] * x[2] * y[0] * z[3] + x[1] * y[2] * x[0] * z[3];
+ s4 = s8 + x[1] * x[5] * y[1] * z[4] + x[1] * y[5] * x[4] * z[1] +
+ x[4] * y[0] * x[7] * z[3] - x[4] * z[0] * x[7] * y[3] -
+ x[4] * x[4] * y[7] * z[3] + x[4] * x[4] * y[3] * z[7] +
+ x[3] * z[6] * x[7] * y[3] - x[3] * x[6] * y[3] * z[7] +
+ x[3] * x[6] * y[7] * z[3] - x[3] * z[6] * x[2] * y[7] -
+ x[3] * y[6] * x[7] * z[3] + x[3] * z[6] * x[7] * y[2] +
+ x[3] * y[6] * x[2] * z[7] + 2.0 * x[5] * z[5] * x[4] * y[6] + s5 +
+ s7;
+ s8 = s4 - 2.0 * x[5] * z[5] * x[6] * y[4] - x[5] * z[6] * x[7] * y[5] +
+ x[5] * x[6] * y[5] * z[7] - x[5] * x[6] * y[7] * z[5] -
+ 2.0 * x[5] * y[5] * x[4] * z[6] + 2.0 * x[5] * y[5] * x[6] * z[4] -
+ x[3] * y[6] * x[7] * z[2] + x[4] * x[7] * y[4] * z[3] +
+ x[4] * x[3] * y[7] * z[4] - x[4] * x[7] * y[3] * z[4] -
+ x[4] * x[3] * y[4] * z[7] - z[1] * x[5] * x[5] * y[0] +
+ y[1] * x[5] * x[5] * z[0] + x[4] * y[6] * x[7] * z[4];
+ s7 = s8 - x[4] * x[6] * y[7] * z[4] + x[4] * x[6] * y[4] * z[7] -
+ x[4] * z[6] * x[7] * y[4] - x[5] * y[6] * x[4] * z[7] -
+ x[5] * x[6] * y[7] * z[4] + x[5] * x[6] * y[4] * z[7] +
+ x[5] * z[6] * x[4] * y[7] - y[6] * x[4] * x[4] * z[7] +
+ z[6] * x[4] * x[4] * y[7] + x[7] * x[5] * y[4] * z[7] -
+ y[2] * x[7] * x[7] * z[3] + z[2] * x[7] * x[7] * y[3] -
+ y[0] * x[3] * x[3] * z[4] - y[1] * x[3] * x[3] * z[0] +
+ z[1] * x[3] * x[3] * y[0];
+ s8 = z[0] * x[3] * x[3] * y[4] - x[2] * y[1] * x[3] * z[0] +
+ x[2] * z[1] * x[3] * y[0] + x[3] * y[1] * x[0] * z[3] +
+ x[3] * x[1] * y[3] * z[0] + x[3] * x[0] * y[3] * z[4] -
+ x[3] * z[1] * x[0] * y[3] - x[3] * x[0] * y[4] * z[3] +
+ x[3] * y[0] * x[4] * z[3] - x[3] * z[0] * x[4] * y[3] -
+ x[3] * x[1] * y[0] * z[3] + x[3] * z[0] * x[7] * y[4] -
+ x[3] * y[0] * x[7] * z[4] + z[0] * x[7] * x[7] * y[4] -
+ y[0] * x[7] * x[7] * z[4];
+ s6 = s8 + y[1] * x[0] * x[0] * z[2] - 2.0 * y[2] * x[3] * x[3] * z[0] +
+ 2.0 * z[2] * x[3] * x[3] * y[0] - 2.0 * x[1] * x[1] * y[0] * z[2] +
+ 2.0 * x[1] * x[1] * y[2] * z[0] - y[2] * x[3] * x[3] * z[1] +
+ z[2] * x[3] * x[3] * y[1] - y[5] * x[4] * x[4] * z[6] +
+ z[5] * x[4] * x[4] * y[6] + x[7] * x[0] * y[7] * z[4] -
+ x[7] * z[0] * x[4] * y[7] - x[7] * x[0] * y[4] * z[7] +
+ x[7] * y[0] * x[4] * z[7] - x[0] * x[1] * y[0] * z[2] +
+ x[0] * z[1] * x[2] * y[0] + s7;
+ s8 = s6 + x[0] * x[1] * y[2] * z[0] - x[0] * y[1] * x[2] * z[0] -
+ x[3] * z[1] * x[0] * y[2] + 2.0 * x[3] * x[2] * y[3] * z[0] +
+ y[0] * x[7] * x[7] * z[3] - z[0] * x[7] * x[7] * y[3] -
+ 2.0 * x[3] * z[2] * x[0] * y[3] - 2.0 * x[3] * x[2] * y[0] * z[3] +
+ 2.0 * x[3] * y[2] * x[0] * z[3] + x[3] * x[2] * y[3] * z[1] -
+ x[3] * x[2] * y[1] * z[3] - x[5] * y[1] * x[0] * z[5] +
+ x[3] * y[1] * x[0] * z[2] + x[4] * y[6] * x[7] * z[5];
+ s7 = s8 - x[5] * x[1] * y[5] * z[0] + 2.0 * x[1] * z[1] * x[2] * y[0] -
+ 2.0 * x[1] * z[1] * x[0] * y[2] + x[1] * x[2] * y[3] * z[1] -
+ x[1] * x[2] * y[1] * z[3] + 2.0 * x[1] * y[1] * x[0] * z[2] -
+ 2.0 * x[1] * y[1] * x[2] * z[0] - z[2] * x[1] * x[1] * y[3] +
+ y[2] * x[1] * x[1] * z[3] + y[5] * x[7] * x[7] * z[4] +
+ y[6] * x[7] * x[7] * z[5] + x[7] * x[6] * y[7] * z[2] +
+ x[7] * y[6] * x[2] * z[7] - x[7] * z[6] * x[2] * y[7] -
+ 2.0 * x[7] * x[6] * y[3] * z[7];
+ s8 = s7 + 2.0 * x[7] * x[6] * y[7] * z[3] +
+ 2.0 * x[7] * y[6] * x[3] * z[7] - x[3] * z[2] * x[1] * y[3] +
+ x[3] * y[2] * x[1] * z[3] + x[5] * x[1] * y[0] * z[5] +
+ x[4] * y[5] * x[6] * z[4] + x[5] * z[1] * x[0] * y[5] -
+ x[4] * z[6] * x[7] * y[5] - x[4] * x[5] * y[6] * z[4] +
+ x[4] * x[5] * y[4] * z[6] - x[4] * z[5] * x[6] * y[4] -
+ x[1] * y[2] * x[3] * z[1] + x[1] * z[2] * x[3] * y[1] -
+ x[2] * x[1] * y[0] * z[2] - x[2] * z[1] * x[0] * y[2];
+ s5 = s8 + x[2] * x[1] * y[2] * z[0] - x[2] * z[2] * x[0] * y[3] +
+ x[2] * y[2] * x[0] * z[3] - x[2] * y[2] * x[3] * z[0] +
+ x[2] * z[2] * x[3] * y[0] + x[2] * y[1] * x[0] * z[2] +
+ x[5] * y[6] * x[7] * z[5] + x[6] * y[5] * x[7] * z[4] +
+ 2.0 * x[6] * y[6] * x[7] * z[5] - x[7] * y[0] * x[3] * z[7] +
+ x[7] * z[0] * x[3] * y[7] - x[7] * x[0] * y[7] * z[3] +
+ x[7] * x[0] * y[3] * z[7] + 2.0 * x[7] * x[7] * y[4] * z[3] -
+ 2.0 * x[7] * x[7] * y[3] * z[4] - 2.0 * x[1] * x[1] * y[2] * z[5];
+ s8 = s5 - 2.0 * x[7] * x[4] * y[7] * z[3] +
+ 2.0 * x[7] * x[3] * y[7] * z[4] - 2.0 * x[7] * x[3] * y[4] * z[7] +
+ 2.0 * x[7] * x[4] * y[3] * z[7] + 2.0 * x[1] * x[1] * y[5] * z[2] -
+ x[1] * x[1] * y[2] * z[6] + x[1] * x[1] * y[6] * z[2] +
+ z[1] * x[5] * x[5] * y[2] - y[1] * x[5] * x[5] * z[2] -
+ x[1] * x[1] * y[6] * z[5] + x[1] * x[1] * y[5] * z[6] +
+ x[5] * x[5] * y[6] * z[2] - x[5] * x[5] * y[2] * z[6] -
+ 2.0 * y[1] * x[5] * x[5] * z[6];
+ s7 = s8 + 2.0 * z[1] * x[5] * x[5] * y[6] +
+ 2.0 * x[1] * z[1] * x[5] * y[2] + 2.0 * x[1] * y[1] * x[2] * z[5] -
+ 2.0 * x[1] * z[1] * x[2] * y[5] - 2.0 * x[1] * y[1] * x[5] * z[2] -
+ x[1] * y[1] * x[6] * z[2] - x[1] * z[1] * x[2] * y[6] +
+ x[1] * z[1] * x[6] * y[2] + x[1] * y[1] * x[2] * z[6] -
+ x[5] * x[1] * y[2] * z[5] + x[5] * y[1] * x[2] * z[5] -
+ x[5] * z[1] * x[2] * y[5] + x[5] * x[1] * y[5] * z[2] -
+ x[5] * y[1] * x[6] * z[2] - x[5] * x[1] * y[2] * z[6];
+ s8 = s7 + x[5] * x[1] * y[6] * z[2] + x[5] * z[1] * x[6] * y[2] +
+ x[1] * x[2] * y[5] * z[6] - x[1] * x[2] * y[6] * z[5] -
+ x[1] * z[1] * x[6] * y[5] - x[1] * y[1] * x[5] * z[6] +
+ x[1] * z[1] * x[5] * y[6] + x[1] * y[1] * x[6] * z[5] -
+ x[5] * x[6] * y[5] * z[2] + x[5] * x[2] * y[5] * z[6] -
+ x[5] * x[2] * y[6] * z[5] + x[5] * x[6] * y[2] * z[5] -
+ 2.0 * x[5] * z[1] * x[6] * y[5] - 2.0 * x[5] * x[1] * y[6] * z[5] +
+ 2.0 * x[5] * x[1] * y[5] * z[6];
+ s6 = s8 + 2.0 * x[5] * y[1] * x[6] * z[5] +
+ 2.0 * x[2] * x[1] * y[6] * z[2] + 2.0 * x[2] * z[1] * x[6] * y[2] -
+ 2.0 * x[2] * x[1] * y[2] * z[6] + x[2] * x[5] * y[6] * z[2] +
+ x[2] * x[6] * y[2] * z[5] - x[2] * x[5] * y[2] * z[6] +
+ y[1] * x[2] * x[2] * z[5] - z[1] * x[2] * x[2] * y[5] -
+ 2.0 * x[2] * y[1] * x[6] * z[2] - x[2] * x[6] * y[5] * z[2] -
+ 2.0 * z[1] * x[2] * x[2] * y[6] + x[2] * x[2] * y[5] * z[6] -
+ x[2] * x[2] * y[6] * z[5] + 2.0 * y[1] * x[2] * x[2] * z[6] +
+ x[2] * z[1] * x[5] * y[2];
+ s8 = s6 - x[2] * x[1] * y[2] * z[5] + x[2] * x[1] * y[5] * z[2] -
+ x[2] * y[1] * x[5] * z[2] + x[6] * y[1] * x[2] * z[5] -
+ x[6] * z[1] * x[2] * y[5] - z[1] * x[6] * x[6] * y[5] +
+ y[1] * x[6] * x[6] * z[5] - y[1] * x[6] * x[6] * z[2] -
+ 2.0 * x[6] * x[6] * y[5] * z[2] + 2.0 * x[6] * x[6] * y[2] * z[5] +
+ z[1] * x[6] * x[6] * y[2] - x[6] * x[1] * y[6] * z[5] -
+ x[6] * y[1] * x[5] * z[6] + x[6] * x[1] * y[5] * z[6];
+ s7 = s8 + x[6] * z[1] * x[5] * y[6] - x[6] * z[1] * x[2] * y[6] -
+ x[6] * x[1] * y[2] * z[6] + 2.0 * x[6] * x[5] * y[6] * z[2] +
+ 2.0 * x[6] * x[2] * y[5] * z[6] - 2.0 * x[6] * x[2] * y[6] * z[5] -
+ 2.0 * x[6] * x[5] * y[2] * z[6] + x[6] * x[1] * y[6] * z[2] +
+ x[6] * y[1] * x[2] * z[6] - x[2] * x[2] * y[3] * z[7] +
+ x[2] * x[2] * y[7] * z[3] - x[2] * z[2] * x[3] * y[7] -
+ x[2] * y[2] * x[7] * z[3] + x[2] * z[2] * x[7] * y[3] +
+ x[2] * y[2] * x[3] * z[7] - x[6] * x[6] * y[3] * z[7];
+ s8 = s7 + x[6] * x[6] * y[7] * z[3] - x[6] * x[2] * y[3] * z[7] +
+ x[6] * x[2] * y[7] * z[3] - x[6] * y[6] * x[7] * z[3] +
+ x[6] * y[6] * x[3] * z[7] - x[6] * z[6] * x[3] * y[7] +
+ x[6] * z[6] * x[7] * y[3] + y[6] * x[2] * x[2] * z[7] -
+ z[6] * x[2] * x[2] * y[7] + 2.0 * x[2] * x[2] * y[6] * z[3] -
+ x[2] * y[6] * x[7] * z[2] - 2.0 * x[2] * y[2] * x[6] * z[3] -
+ 2.0 * x[2] * x[2] * y[3] * z[6] + 2.0 * x[2] * y[2] * x[3] * z[6] -
+ x[2] * x[6] * y[2] * z[7];
+ s3 = s8 + x[2] * x[6] * y[7] * z[2] + x[2] * z[6] * x[7] * y[2] +
+ 2.0 * x[2] * z[2] * x[6] * y[3] - 2.0 * x[2] * z[2] * x[3] * y[6] -
+ y[2] * x[6] * x[6] * z[3] - 2.0 * x[6] * x[6] * y[2] * z[7] +
+ 2.0 * x[6] * x[6] * y[7] * z[2] + z[2] * x[6] * x[6] * y[3] -
+ 2.0 * x[6] * y[6] * x[7] * z[2] + x[6] * y[2] * x[3] * z[6] -
+ x[6] * x[2] * y[3] * z[6] + 2.0 * x[6] * z[6] * x[7] * y[2] +
+ 2.0 * x[6] * y[6] * x[2] * z[7] - 2.0 * x[6] * z[6] * x[2] * y[7] +
+ x[6] * x[2] * y[6] * z[3] - x[6] * z[2] * x[3] * y[6];
+ s8 = y[1] * x[0] * z[3] + x[1] * y[3] * z[0] - y[0] * x[3] * z[7] -
+ x[1] * y[5] * z[0] - y[0] * x[3] * z[4] - x[1] * y[0] * z[2] +
+ z[1] * x[2] * y[0] - y[1] * x[0] * z[5] - z[1] * x[0] * y[2] -
+ y[1] * x[0] * z[4] + z[1] * x[5] * y[2] + z[0] * x[7] * y[4] +
+ z[0] * x[3] * y[7] + z[1] * x[0] * y[4] - x[1] * y[2] * z[5] +
+ x[2] * y[3] * z[0] + y[1] * x[2] * z[5] - x[2] * y[3] * z[7];
+ s7 = s8 - z[1] * x[2] * y[5] - y[1] * x[3] * z[0] - x[0] * y[7] * z[3] -
+ z[1] * x[0] * y[3] + y[5] * x[4] * z[0] - x[0] * y[4] * z[3] +
+ y[5] * x[7] * z[4] - z[0] * x[4] * y[3] + x[1] * y[0] * z[4] -
+ z[2] * x[3] * y[7] - y[6] * x[7] * z[2] + x[1] * y[5] * z[2] +
+ y[6] * x[7] * z[5] + x[0] * y[7] * z[4] + x[1] * y[2] * z[0] -
+ z[1] * x[4] * y[0] - z[0] * x[4] * y[7] - z[2] * x[0] * y[3];
+ s8 = x[5] * y[0] * z[4] + z[1] * x[0] * y[5] - x[2] * y[0] * z[3] -
+ z[1] * x[5] * y[0] + y[1] * x[5] * z[0] - x[1] * y[0] * z[3] -
+ x[1] * y[4] * z[0] - y[1] * x[5] * z[2] + x[2] * y[7] * z[3] +
+ y[0] * x[4] * z[3] - x[0] * y[4] * z[7] + x[1] * y[0] * z[5] -
+ y[1] * x[6] * z[2] - y[2] * x[6] * z[3] + y[0] * x[7] * z[3] -
+ y[2] * x[7] * z[3] + z[2] * x[7] * y[3] + y[2] * x[0] * z[3];
+ s6 = s8 + y[2] * x[3] * z[7] - y[2] * x[3] * z[0] - x[6] * y[5] * z[2] -
+ y[5] * x[0] * z[4] + z[2] * x[3] * y[0] + x[2] * y[3] * z[1] +
+ x[0] * y[3] * z[7] - x[2] * y[1] * z[3] + y[1] * x[4] * z[0] +
+ y[1] * x[0] * z[2] - z[1] * x[2] * y[6] + y[2] * x[3] * z[6] -
+ y[1] * x[2] * z[0] + z[1] * x[3] * y[0] - x[1] * y[2] * z[6] -
+ x[2] * y[3] * z[6] + x[0] * y[3] * z[4] + z[0] * x[3] * y[4] + s7;
+ s8 = x[5] * y[4] * z[7] + s6 + y[5] * x[6] * z[4] - y[5] * x[4] * z[6] +
+ z[6] * x[5] * y[7] - x[6] * y[2] * z[7] - x[6] * y[7] * z[5] +
+ x[5] * y[6] * z[2] + x[6] * y[5] * z[7] + x[6] * y[7] * z[2] +
+ y[6] * x[7] * z[4] - y[6] * x[4] * z[7] - y[6] * x[7] * z[3] +
+ z[6] * x[7] * y[2] + x[2] * y[5] * z[6] - x[2] * y[6] * z[5] +
+ y[6] * x[2] * z[7] + x[6] * y[2] * z[5];
+ s7 = s8 - x[5] * y[2] * z[6] - z[6] * x[7] * y[5] - z[5] * x[7] * y[4] +
+ z[5] * x[0] * y[4] - y[5] * x[4] * z[7] + y[0] * x[4] * z[7] -
+ z[6] * x[2] * y[7] - x[5] * y[4] * z[0] - x[5] * y[7] * z[4] -
+ y[0] * x[7] * z[4] + y[5] * x[4] * z[1] - x[6] * y[7] * z[4] +
+ x[7] * y[4] * z[3] - x[4] * y[7] * z[3] + x[3] * y[7] * z[4] -
+ x[7] * y[3] * z[4] - x[6] * y[3] * z[7] + x[6] * y[4] * z[7];
+ s8 = -x[3] * y[4] * z[7] + x[4] * y[3] * z[7] - z[6] * x[7] * y[4] -
+ z[1] * x[6] * y[5] + x[6] * y[7] * z[3] - x[1] * y[6] * z[5] -
+ y[1] * x[5] * z[6] + z[5] * x[4] * y[7] - z[5] * x[4] * y[0] +
+ x[1] * y[5] * z[6] - y[6] * x[5] * z[7] - y[2] * x[3] * z[1] +
+ z[1] * x[5] * y[6] - y[5] * x[1] * z[4] + z[6] * x[4] * y[7] +
+ x[5] * y[1] * z[4] - x[5] * y[6] * z[4] + y[6] * x[3] * z[7] -
+ x[5] * y[4] * z[1];
+ s5 = s8 + x[5] * y[4] * z[6] + z[5] * x[1] * y[4] + y[1] * x[6] * z[5] -
+ z[6] * x[3] * y[7] + z[6] * x[7] * y[3] - z[5] * x[6] * y[4] -
+ z[5] * x[4] * y[1] + z[5] * x[4] * y[6] + x[1] * y[6] * z[2] +
+ x[2] * y[6] * z[3] + z[2] * x[6] * y[3] + z[1] * x[6] * y[2] +
+ z[2] * x[3] * y[1] - z[2] * x[1] * y[3] - z[2] * x[3] * y[6] +
+ y[2] * x[1] * z[3] + y[1] * x[2] * z[6] - z[0] * x[7] * y[3] + s7;
+ s4 = 1 / s5;
+ s2 = s3 * s4;
+ const double unknown0 = s1 * s2;
+ s1 = 1.0 / 6.0;
+ s8 = 2.0 * x[1] * y[0] * y[0] * z[4] + x[5] * y[0] * y[0] * z[4] -
+ x[1] * y[4] * y[4] * z[0] + z[1] * x[0] * y[4] * y[4] +
+ x[1] * y[0] * y[0] * z[5] - z[1] * x[5] * y[0] * y[0] -
+ 2.0 * z[1] * x[4] * y[0] * y[0] + 2.0 * z[1] * x[3] * y[0] * y[0] +
+ z[2] * x[3] * y[0] * y[0] + y[0] * y[0] * x[7] * z[3] +
+ 2.0 * y[0] * y[0] * x[4] * z[3] - 2.0 * x[1] * y[0] * y[0] * z[3] -
+ 2.0 * x[5] * y[4] * y[4] * z[0] + 2.0 * z[5] * x[0] * y[4] * y[4] +
+ 2.0 * y[4] * y[5] * x[7] * z[4];
+ s7 = s8 - x[3] * y[4] * y[4] * z[7] + x[7] * y[4] * y[4] * z[3] +
+ z[0] * x[3] * y[4] * y[4] - 2.0 * x[0] * y[4] * y[4] * z[7] -
+ y[1] * x[1] * y[4] * z[0] - x[0] * y[4] * y[4] * z[3] +
+ 2.0 * z[0] * x[7] * y[4] * y[4] + y[4] * z[6] * x[4] * y[7] -
+ y[0] * y[0] * x[7] * z[4] + y[0] * y[0] * x[4] * z[7] +
+ 2.0 * y[4] * z[5] * x[4] * y[7] - 2.0 * y[4] * x[5] * y[7] * z[4] -
+ y[4] * x[6] * y[7] * z[4] - y[4] * y[6] * x[4] * z[7] -
+ 2.0 * y[4] * y[5] * x[4] * z[7];
+ s8 = y[4] * y[6] * x[7] * z[4] - y[7] * y[2] * x[7] * z[3] +
+ y[7] * z[2] * x[7] * y[3] + y[7] * y[2] * x[3] * z[7] +
+ 2.0 * x[5] * y[4] * y[4] * z[7] - y[7] * x[2] * y[3] * z[7] -
+ y[0] * z[0] * x[4] * y[7] + z[6] * x[7] * y[3] * y[3] -
+ y[0] * x[0] * y[4] * z[7] + y[0] * x[0] * y[7] * z[4] -
+ 2.0 * x[2] * y[3] * y[3] * z[7] - z[5] * x[4] * y[0] * y[0] +
+ y[0] * z[0] * x[7] * y[4] - 2.0 * z[6] * x[3] * y[7] * y[7] +
+ z[1] * x[2] * y[0] * y[0];
+ s6 = s8 + y[4] * y[0] * x[4] * z[3] - 2.0 * y[4] * z[0] * x[4] * y[7] +
+ 2.0 * y[4] * x[0] * y[7] * z[4] - y[4] * z[0] * x[4] * y[3] -
+ y[4] * x[0] * y[7] * z[3] + y[4] * z[0] * x[3] * y[7] -
+ y[4] * y[0] * x[3] * z[4] + y[0] * x[4] * y[3] * z[7] -
+ y[0] * x[7] * y[3] * z[4] - y[0] * x[3] * y[4] * z[7] +
+ y[0] * x[7] * y[4] * z[3] + x[2] * y[7] * y[7] * z[3] -
+ z[2] * x[3] * y[7] * y[7] - 2.0 * z[2] * x[0] * y[3] * y[3] +
+ 2.0 * y[0] * z[1] * x[0] * y[4] + s7;
+ s8 = -2.0 * y[0] * y[1] * x[0] * z[4] - y[0] * y[1] * x[0] * z[5] -
+ y[0] * y[0] * x[3] * z[7] - z[1] * x[0] * y[3] * y[3] -
+ y[0] * x[1] * y[5] * z[0] - 2.0 * z[0] * x[7] * y[3] * y[3] +
+ x[0] * y[3] * y[3] * z[4] + 2.0 * x[0] * y[3] * y[3] * z[7] -
+ z[0] * x[4] * y[3] * y[3] + 2.0 * x[2] * y[3] * y[3] * z[0] +
+ x[1] * y[3] * y[3] * z[0] + 2.0 * y[7] * z[6] * x[7] * y[3] +
+ 2.0 * y[7] * y[6] * x[3] * z[7] - 2.0 * y[7] * y[6] * x[7] * z[3] -
+ 2.0 * y[7] * x[6] * y[3] * z[7];
+ s7 = s8 + y[4] * x[4] * y[3] * z[7] - y[4] * x[4] * y[7] * z[3] +
+ y[4] * x[3] * y[7] * z[4] - y[4] * x[7] * y[3] * z[4] +
+ 2.0 * y[4] * y[0] * x[4] * z[7] - 2.0 * y[4] * y[0] * x[7] * z[4] +
+ 2.0 * x[6] * y[7] * y[7] * z[3] + y[4] * x[0] * y[3] * z[4] +
+ y[0] * y[1] * x[5] * z[0] + y[0] * z[1] * x[0] * y[5] -
+ x[2] * y[0] * y[0] * z[3] + x[4] * y[3] * y[3] * z[7] -
+ x[7] * y[3] * y[3] * z[4] - x[5] * y[4] * y[4] * z[1] +
+ y[3] * z[0] * x[3] * y[4];
+ s8 = y[3] * y[0] * x[4] * z[3] + 2.0 * y[3] * y[0] * x[7] * z[3] +
+ 2.0 * y[3] * y[2] * x[0] * z[3] - 2.0 * y[3] * y[2] * x[3] * z[0] +
+ 2.0 * y[3] * z[2] * x[3] * y[0] + y[3] * z[1] * x[3] * y[0] -
+ 2.0 * y[3] * x[2] * y[0] * z[3] - y[3] * x[1] * y[0] * z[3] -
+ y[3] * y[1] * x[3] * z[0] - 2.0 * y[3] * x[0] * y[7] * z[3] -
+ y[3] * x[0] * y[4] * z[3] - 2.0 * y[3] * y[0] * x[3] * z[7] -
+ y[3] * y[0] * x[3] * z[4] + 2.0 * y[3] * z[0] * x[3] * y[7] +
+ y[3] * y[1] * x[0] * z[3] + z[5] * x[1] * y[4] * y[4];
+ s5 = s8 - 2.0 * y[0] * y[0] * x[3] * z[4] -
+ 2.0 * y[0] * x[1] * y[4] * z[0] + y[3] * x[7] * y[4] * z[3] -
+ y[3] * x[4] * y[7] * z[3] + y[3] * x[3] * y[7] * z[4] -
+ y[3] * x[3] * y[4] * z[7] + y[3] * x[0] * y[7] * z[4] -
+ y[3] * z[0] * x[4] * y[7] - 2.0 * y[4] * y[5] * x[0] * z[4] + s6 +
+ y[7] * x[0] * y[3] * z[7] - y[7] * z[0] * x[7] * y[3] +
+ y[7] * y[0] * x[7] * z[3] - y[7] * y[0] * x[3] * z[7] +
+ 2.0 * y[0] * y[1] * x[4] * z[0] + s7;
+ s8 = -2.0 * y[7] * x[7] * y[3] * z[4] -
+ 2.0 * y[7] * x[3] * y[4] * z[7] + 2.0 * y[7] * x[4] * y[3] * z[7] +
+ y[7] * y[0] * x[4] * z[7] - y[7] * y[0] * x[7] * z[4] +
+ 2.0 * y[7] * x[7] * y[4] * z[3] - y[7] * x[0] * y[4] * z[7] +
+ y[7] * z[0] * x[7] * y[4] + z[5] * x[4] * y[7] * y[7] +
+ 2.0 * z[6] * x[4] * y[7] * y[7] - x[5] * y[7] * y[7] * z[4] -
+ 2.0 * x[6] * y[7] * y[7] * z[4] + 2.0 * y[7] * x[6] * y[4] * z[7] -
+ 2.0 * y[7] * z[6] * x[7] * y[4] + 2.0 * y[7] * y[6] * x[7] * z[4];
+ s7 = s8 - 2.0 * y[7] * y[6] * x[4] * z[7] - y[7] * z[5] * x[7] * y[4] -
+ y[7] * y[5] * x[4] * z[7] - x[0] * y[7] * y[7] * z[3] +
+ z[0] * x[3] * y[7] * y[7] + y[7] * x[5] * y[4] * z[7] +
+ y[7] * y[5] * x[7] * z[4] - y[4] * x[1] * y[5] * z[0] -
+ x[1] * y[0] * y[0] * z[2] - y[4] * y[5] * x[1] * z[4] -
+ 2.0 * y[4] * z[5] * x[4] * y[0] - y[4] * y[1] * x[0] * z[4] +
+ y[4] * y[5] * x[4] * z[1] + y[0] * z[0] * x[3] * y[7] -
+ y[0] * z[1] * x[0] * y[2];
+ s8 = 2.0 * y[0] * x[1] * y[3] * z[0] + y[4] * y[1] * x[4] * z[0] +
+ 2.0 * y[0] * y[1] * x[0] * z[3] + y[4] * x[1] * y[0] * z[5] -
+ y[4] * z[1] * x[5] * y[0] + y[4] * z[1] * x[0] * y[5] -
+ y[4] * z[1] * x[4] * y[0] + y[4] * x[1] * y[0] * z[4] -
+ y[4] * z[5] * x[4] * y[1] + x[5] * y[4] * y[4] * z[6] -
+ z[5] * x[6] * y[4] * y[4] + y[4] * x[5] * y[1] * z[4] -
+ y[0] * z[2] * x[0] * y[3] + y[0] * y[5] * x[4] * z[0] +
+ y[0] * x[1] * y[2] * z[0];
+ s6 = s8 - 2.0 * y[0] * z[0] * x[4] * y[3] -
+ 2.0 * y[0] * x[0] * y[4] * z[3] - 2.0 * y[0] * z[1] * x[0] * y[3] -
+ y[0] * x[0] * y[7] * z[3] - 2.0 * y[0] * y[1] * x[3] * z[0] +
+ y[0] * x[2] * y[3] * z[0] - y[0] * y[1] * x[2] * z[0] +
+ y[0] * y[1] * x[0] * z[2] - y[0] * x[2] * y[1] * z[3] +
+ y[0] * x[0] * y[3] * z[7] + y[0] * x[2] * y[3] * z[1] -
+ y[0] * y[2] * x[3] * z[0] + y[0] * y[2] * x[0] * z[3] -
+ y[0] * y[5] * x[0] * z[4] - y[4] * y[5] * x[4] * z[6] + s7;
+ s8 = s6 + y[4] * z[6] * x[5] * y[7] - y[4] * x[6] * y[7] * z[5] +
+ y[4] * x[6] * y[5] * z[7] - y[4] * z[6] * x[7] * y[5] -
+ y[4] * x[5] * y[6] * z[4] + y[4] * z[5] * x[4] * y[6] +
+ y[4] * y[5] * x[6] * z[4] - 2.0 * y[1] * y[1] * x[0] * z[5] +
+ 2.0 * y[1] * y[1] * x[5] * z[0] - 2.0 * y[2] * y[2] * x[6] * z[3] +
+ x[5] * y[1] * y[1] * z[4] - z[5] * x[4] * y[1] * y[1] -
+ x[6] * y[2] * y[2] * z[7] + z[6] * x[7] * y[2] * y[2];
+ s7 = s8 - x[1] * y[5] * y[5] * z[0] + z[1] * x[0] * y[5] * y[5] +
+ y[1] * y[5] * x[4] * z[1] - y[1] * y[5] * x[1] * z[4] -
+ 2.0 * y[2] * z[2] * x[3] * y[6] + 2.0 * y[1] * z[1] * x[0] * y[5] -
+ 2.0 * y[1] * z[1] * x[5] * y[0] + 2.0 * y[1] * x[1] * y[0] * z[5] -
+ y[2] * x[2] * y[3] * z[7] - y[2] * z[2] * x[3] * y[7] +
+ y[2] * x[2] * y[7] * z[3] + y[2] * z[2] * x[7] * y[3] -
+ 2.0 * y[2] * x[2] * y[3] * z[6] + 2.0 * y[2] * x[2] * y[6] * z[3] +
+ 2.0 * y[2] * z[2] * x[6] * y[3] - y[3] * y[2] * x[6] * z[3];
+ s8 = y[3] * y[2] * x[3] * z[6] + y[3] * x[2] * y[6] * z[3] -
+ y[3] * z[2] * x[3] * y[6] - y[2] * y[2] * x[7] * z[3] +
+ 2.0 * y[2] * y[2] * x[3] * z[6] + y[2] * y[2] * x[3] * z[7] -
+ 2.0 * y[1] * x[1] * y[5] * z[0] - x[2] * y[3] * y[3] * z[6] +
+ z[2] * x[6] * y[3] * y[3] + 2.0 * y[6] * x[2] * y[5] * z[6] +
+ 2.0 * y[6] * x[6] * y[2] * z[5] - 2.0 * y[6] * x[5] * y[2] * z[6] +
+ 2.0 * y[3] * x[2] * y[7] * z[3] - 2.0 * y[3] * z[2] * x[3] * y[7] -
+ y[0] * z[0] * x[7] * y[3] - y[0] * z[2] * x[1] * y[3];
+ s4 = s8 - y[2] * y[6] * x[7] * z[2] + y[0] * z[2] * x[3] * y[1] +
+ y[1] * z[5] * x[1] * y[4] - y[1] * x[5] * y[4] * z[1] +
+ 2.0 * y[0] * z[0] * x[3] * y[4] + 2.0 * y[0] * x[0] * y[3] * z[4] +
+ 2.0 * z[2] * x[7] * y[3] * y[3] - 2.0 * z[5] * x[7] * y[4] * y[4] +
+ x[6] * y[4] * y[4] * z[7] - z[6] * x[7] * y[4] * y[4] +
+ y[1] * y[1] * x[0] * z[3] + y[3] * x[6] * y[7] * z[2] -
+ y[3] * z[6] * x[2] * y[7] + 2.0 * y[3] * y[2] * x[3] * z[7] + s5 +
+ s7;
+ s8 = s4 + y[2] * x[6] * y[7] * z[2] - y[2] * y[6] * x[7] * z[3] +
+ y[2] * y[6] * x[2] * z[7] - y[2] * z[6] * x[2] * y[7] -
+ y[2] * x[6] * y[3] * z[7] + y[2] * y[6] * x[3] * z[7] +
+ y[2] * z[6] * x[7] * y[3] - 2.0 * y[3] * y[2] * x[7] * z[3] -
+ x[6] * y[3] * y[3] * z[7] + y[1] * y[1] * x[4] * z[0] -
+ y[1] * y[1] * x[3] * z[0] + x[2] * y[6] * y[6] * z[3] -
+ z[2] * x[3] * y[6] * y[6] - y[1] * y[1] * x[0] * z[4];
+ s7 = s8 + y[5] * x[1] * y[0] * z[5] + y[6] * x[2] * y[7] * z[3] -
+ y[6] * y[2] * x[6] * z[3] + y[6] * y[2] * x[3] * z[6] -
+ y[6] * x[2] * y[3] * z[6] + y[6] * z[2] * x[6] * y[3] -
+ y[5] * y[1] * x[0] * z[5] - y[5] * z[1] * x[5] * y[0] +
+ y[5] * y[1] * x[5] * z[0] - y[6] * z[2] * x[3] * y[7] -
+ y[7] * y[6] * x[7] * z[2] + 2.0 * y[6] * y[6] * x[2] * z[7] +
+ y[6] * y[6] * x[3] * z[7] + x[6] * y[7] * y[7] * z[2] -
+ z[6] * x[2] * y[7] * y[7];
+ s8 = -x[2] * y[1] * y[1] * z[3] + 2.0 * y[1] * y[1] * x[0] * z[2] -
+ 2.0 * y[1] * y[1] * x[2] * z[0] + z[2] * x[3] * y[1] * y[1] -
+ z[1] * x[0] * y[2] * y[2] + x[1] * y[2] * y[2] * z[0] +
+ y[2] * y[2] * x[0] * z[3] - y[2] * y[2] * x[3] * z[0] -
+ 2.0 * y[2] * y[2] * x[3] * z[1] + y[1] * x[1] * y[3] * z[0] -
+ 2.0 * y[6] * y[6] * x[7] * z[2] + 2.0 * y[5] * y[5] * x[4] * z[1] -
+ 2.0 * y[5] * y[5] * x[1] * z[4] - y[6] * y[6] * x[7] * z[3] -
+ 2.0 * y[1] * x[1] * y[0] * z[2];
+ s6 = s8 + 2.0 * y[1] * z[1] * x[2] * y[0] -
+ 2.0 * y[1] * z[1] * x[0] * y[2] + 2.0 * y[1] * x[1] * y[2] * z[0] +
+ y[1] * x[2] * y[3] * z[1] - y[1] * y[2] * x[3] * z[1] -
+ y[1] * z[2] * x[1] * y[3] + y[1] * y[2] * x[1] * z[3] -
+ y[2] * x[1] * y[0] * z[2] + y[2] * z[1] * x[2] * y[0] +
+ y[2] * x[2] * y[3] * z[0] - y[7] * x[6] * y[2] * z[7] +
+ y[7] * z[6] * x[7] * y[2] + y[7] * y[6] * x[2] * z[7] -
+ y[6] * x[6] * y[3] * z[7] + y[6] * x[6] * y[7] * z[3] + s7;
+ s8 = s6 - y[6] * z[6] * x[3] * y[7] + y[6] * z[6] * x[7] * y[3] +
+ 2.0 * y[2] * y[2] * x[1] * z[3] + x[2] * y[3] * y[3] * z[1] -
+ z[2] * x[1] * y[3] * y[3] + y[1] * x[1] * y[0] * z[4] +
+ y[1] * z[1] * x[3] * y[0] - y[1] * x[1] * y[0] * z[3] +
+ 2.0 * y[5] * x[5] * y[1] * z[4] - 2.0 * y[5] * x[5] * y[4] * z[1] +
+ 2.0 * y[5] * z[5] * x[1] * y[4] - 2.0 * y[5] * z[5] * x[4] * y[1] -
+ 2.0 * y[6] * x[6] * y[2] * z[7] + 2.0 * y[6] * x[6] * y[7] * z[2];
+ s7 = s8 + 2.0 * y[6] * z[6] * x[7] * y[2] -
+ 2.0 * y[6] * z[6] * x[2] * y[7] - y[1] * z[1] * x[4] * y[0] +
+ y[1] * z[1] * x[0] * y[4] - y[1] * z[1] * x[0] * y[3] +
+ 2.0 * y[6] * y[6] * x[7] * z[5] + 2.0 * y[5] * y[5] * x[6] * z[4] -
+ 2.0 * y[5] * y[5] * x[4] * z[6] + x[6] * y[5] * y[5] * z[7] -
+ y[3] * x[2] * y[1] * z[3] - y[3] * y[2] * x[3] * z[1] +
+ y[3] * z[2] * x[3] * y[1] + y[3] * y[2] * x[1] * z[3] -
+ y[2] * x[2] * y[0] * z[3] + y[2] * z[2] * x[3] * y[0];
+ s8 = s7 + 2.0 * y[2] * x[2] * y[3] * z[1] -
+ 2.0 * y[2] * x[2] * y[1] * z[3] + y[2] * y[1] * x[0] * z[2] -
+ y[2] * y[1] * x[2] * z[0] + 2.0 * y[2] * z[2] * x[3] * y[1] -
+ 2.0 * y[2] * z[2] * x[1] * y[3] - y[2] * z[2] * x[0] * y[3] +
+ y[5] * z[6] * x[5] * y[7] - y[5] * x[6] * y[7] * z[5] -
+ y[5] * y[6] * x[4] * z[7] - y[5] * y[6] * x[5] * z[7] -
+ 2.0 * y[5] * x[5] * y[6] * z[4] + 2.0 * y[5] * x[5] * y[4] * z[6] -
+ 2.0 * y[5] * z[5] * x[6] * y[4] + 2.0 * y[5] * z[5] * x[4] * y[6];
+ s5 = s8 - y[1] * y[5] * x[0] * z[4] - z[6] * x[7] * y[5] * y[5] +
+ y[6] * y[6] * x[7] * z[4] - y[6] * y[6] * x[4] * z[7] -
+ 2.0 * y[6] * y[6] * x[5] * z[7] - x[5] * y[6] * y[6] * z[4] +
+ z[5] * x[4] * y[6] * y[6] + z[6] * x[5] * y[7] * y[7] -
+ x[6] * y[7] * y[7] * z[5] + y[1] * y[5] * x[4] * z[0] +
+ y[7] * y[6] * x[7] * z[5] + y[6] * y[5] * x[7] * z[4] +
+ y[5] * y[6] * x[7] * z[5] + y[6] * y[5] * x[6] * z[4] -
+ y[6] * y[5] * x[4] * z[6] + 2.0 * y[6] * z[6] * x[5] * y[7];
+ s8 = s5 - 2.0 * y[6] * x[6] * y[7] * z[5] +
+ 2.0 * y[6] * x[6] * y[5] * z[7] - 2.0 * y[6] * z[6] * x[7] * y[5] -
+ y[6] * x[5] * y[7] * z[4] - y[6] * x[6] * y[7] * z[4] +
+ y[6] * x[6] * y[4] * z[7] - y[6] * z[6] * x[7] * y[4] +
+ y[6] * z[5] * x[4] * y[7] + y[6] * z[6] * x[4] * y[7] +
+ y[6] * x[5] * y[4] * z[6] - y[6] * z[5] * x[6] * y[4] +
+ y[7] * x[6] * y[5] * z[7] - y[7] * z[6] * x[7] * y[5] -
+ 2.0 * y[6] * x[6] * y[5] * z[2];
+ s7 = s8 - y[7] * y[6] * x[5] * z[7] + 2.0 * y[4] * y[5] * x[4] * z[0] +
+ 2.0 * x[3] * y[7] * y[7] * z[4] - 2.0 * x[4] * y[7] * y[7] * z[3] -
+ z[0] * x[4] * y[7] * y[7] + x[0] * y[7] * y[7] * z[4] -
+ y[0] * z[5] * x[4] * y[1] + y[0] * x[5] * y[1] * z[4] -
+ y[0] * x[5] * y[4] * z[0] + y[0] * z[5] * x[0] * y[4] -
+ y[5] * y[5] * x[0] * z[4] + y[5] * y[5] * x[4] * z[0] +
+ 2.0 * y[1] * y[1] * x[2] * z[5] - 2.0 * y[1] * y[1] * x[5] * z[2] +
+ z[1] * x[5] * y[2] * y[2];
+ s8 = s7 - x[1] * y[2] * y[2] * z[5] - y[5] * z[5] * x[4] * y[0] +
+ y[5] * z[5] * x[0] * y[4] - y[5] * x[5] * y[4] * z[0] -
+ y[2] * x[1] * y[6] * z[5] - y[2] * y[1] * x[5] * z[6] +
+ y[2] * z[1] * x[5] * y[6] + y[2] * y[1] * x[6] * z[5] -
+ y[1] * z[1] * x[6] * y[5] - y[1] * x[1] * y[6] * z[5] +
+ y[1] * x[1] * y[5] * z[6] + y[1] * z[1] * x[5] * y[6] +
+ y[5] * x[5] * y[0] * z[4] + y[2] * y[1] * x[2] * z[5] -
+ y[2] * z[1] * x[2] * y[5];
+ s6 = s8 + y[2] * x[1] * y[5] * z[2] - y[2] * y[1] * x[5] * z[2] -
+ y[1] * y[1] * x[5] * z[6] + y[1] * y[1] * x[6] * z[5] -
+ z[1] * x[2] * y[5] * y[5] + x[1] * y[5] * y[5] * z[2] +
+ 2.0 * y[1] * z[1] * x[5] * y[2] - 2.0 * y[1] * x[1] * y[2] * z[5] -
+ 2.0 * y[1] * z[1] * x[2] * y[5] + 2.0 * y[1] * x[1] * y[5] * z[2] -
+ y[1] * y[1] * x[6] * z[2] + y[1] * y[1] * x[2] * z[6] -
+ 2.0 * y[5] * x[1] * y[6] * z[5] - 2.0 * y[5] * y[1] * x[5] * z[6] +
+ 2.0 * y[5] * z[1] * x[5] * y[6] + 2.0 * y[5] * y[1] * x[6] * z[5];
+ s8 = s6 - y[6] * z[1] * x[6] * y[5] - y[6] * y[1] * x[5] * z[6] +
+ y[6] * x[1] * y[5] * z[6] + y[6] * y[1] * x[6] * z[5] -
+ 2.0 * z[1] * x[6] * y[5] * y[5] + 2.0 * x[1] * y[5] * y[5] * z[6] -
+ x[1] * y[6] * y[6] * z[5] + z[1] * x[5] * y[6] * y[6] +
+ y[5] * z[1] * x[5] * y[2] - y[5] * x[1] * y[2] * z[5] +
+ y[5] * y[1] * x[2] * z[5] - y[5] * y[1] * x[5] * z[2] -
+ y[6] * z[1] * x[2] * y[5] + y[6] * x[1] * y[5] * z[2];
+ s7 = s8 - y[1] * z[1] * x[2] * y[6] - y[1] * x[1] * y[2] * z[6] +
+ y[1] * x[1] * y[6] * z[2] + y[1] * z[1] * x[6] * y[2] +
+ y[5] * x[5] * y[6] * z[2] - y[5] * x[2] * y[6] * z[5] +
+ y[5] * x[6] * y[2] * z[5] - y[5] * x[5] * y[2] * z[6] -
+ x[6] * y[5] * y[5] * z[2] + x[2] * y[5] * y[5] * z[6] -
+ y[5] * y[5] * x[4] * z[7] + y[5] * y[5] * x[7] * z[4] -
+ y[1] * x[6] * y[5] * z[2] + y[1] * x[2] * y[5] * z[6] -
+ y[2] * x[6] * y[5] * z[2] - 2.0 * y[2] * y[1] * x[6] * z[2];
+ s8 = s7 - 2.0 * y[2] * z[1] * x[2] * y[6] +
+ 2.0 * y[2] * x[1] * y[6] * z[2] + 2.0 * y[2] * y[1] * x[2] * z[6] -
+ 2.0 * x[1] * y[2] * y[2] * z[6] + 2.0 * z[1] * x[6] * y[2] * y[2] +
+ x[6] * y[2] * y[2] * z[5] - x[5] * y[2] * y[2] * z[6] +
+ 2.0 * x[5] * y[6] * y[6] * z[2] - 2.0 * x[2] * y[6] * y[6] * z[5] -
+ z[1] * x[2] * y[6] * y[6] - y[6] * y[1] * x[6] * z[2] -
+ y[6] * x[1] * y[2] * z[6] + y[6] * z[1] * x[6] * y[2] +
+ y[6] * y[1] * x[2] * z[6] + x[1] * y[6] * y[6] * z[2];
+ s3 = s8 + y[2] * x[5] * y[6] * z[2] + y[2] * x[2] * y[5] * z[6] -
+ y[2] * x[2] * y[6] * z[5] + y[5] * z[5] * x[4] * y[7] +
+ y[5] * x[5] * y[4] * z[7] - y[5] * z[5] * x[7] * y[4] -
+ y[5] * x[5] * y[7] * z[4] + 2.0 * y[4] * x[5] * y[0] * z[4] -
+ y[3] * z[6] * x[3] * y[7] + y[3] * y[6] * x[3] * z[7] +
+ y[3] * x[6] * y[7] * z[3] - y[3] * y[6] * x[7] * z[3] -
+ y[2] * y[1] * x[3] * z[0] - y[2] * z[1] * x[0] * y[3] +
+ y[2] * y[1] * x[0] * z[3] + y[2] * x[1] * y[3] * z[0];
+ s8 = y[1] * x[0] * z[3] + x[1] * y[3] * z[0] - y[0] * x[3] * z[7] -
+ x[1] * y[5] * z[0] - y[0] * x[3] * z[4] - x[1] * y[0] * z[2] +
+ z[1] * x[2] * y[0] - y[1] * x[0] * z[5] - z[1] * x[0] * y[2] -
+ y[1] * x[0] * z[4] + z[1] * x[5] * y[2] + z[0] * x[7] * y[4] +
+ z[0] * x[3] * y[7] + z[1] * x[0] * y[4] - x[1] * y[2] * z[5] +
+ x[2] * y[3] * z[0] + y[1] * x[2] * z[5] - x[2] * y[3] * z[7];
+ s7 = s8 - z[1] * x[2] * y[5] - y[1] * x[3] * z[0] - x[0] * y[7] * z[3] -
+ z[1] * x[0] * y[3] + y[5] * x[4] * z[0] - x[0] * y[4] * z[3] +
+ y[5] * x[7] * z[4] - z[0] * x[4] * y[3] + x[1] * y[0] * z[4] -
+ z[2] * x[3] * y[7] - y[6] * x[7] * z[2] + x[1] * y[5] * z[2] +
+ y[6] * x[7] * z[5] + x[0] * y[7] * z[4] + x[1] * y[2] * z[0] -
+ z[1] * x[4] * y[0] - z[0] * x[4] * y[7] - z[2] * x[0] * y[3];
+ s8 = x[5] * y[0] * z[4] + z[1] * x[0] * y[5] - x[2] * y[0] * z[3] -
+ z[1] * x[5] * y[0] + y[1] * x[5] * z[0] - x[1] * y[0] * z[3] -
+ x[1] * y[4] * z[0] - y[1] * x[5] * z[2] + x[2] * y[7] * z[3] +
+ y[0] * x[4] * z[3] - x[0] * y[4] * z[7] + x[1] * y[0] * z[5] -
+ y[1] * x[6] * z[2] - y[2] * x[6] * z[3] + y[0] * x[7] * z[3] -
+ y[2] * x[7] * z[3] + z[2] * x[7] * y[3] + y[2] * x[0] * z[3];
+ s6 = s8 + y[2] * x[3] * z[7] - y[2] * x[3] * z[0] - x[6] * y[5] * z[2] -
+ y[5] * x[0] * z[4] + z[2] * x[3] * y[0] + x[2] * y[3] * z[1] +
+ x[0] * y[3] * z[7] - x[2] * y[1] * z[3] + y[1] * x[4] * z[0] +
+ y[1] * x[0] * z[2] - z[1] * x[2] * y[6] + y[2] * x[3] * z[6] -
+ y[1] * x[2] * z[0] + z[1] * x[3] * y[0] - x[1] * y[2] * z[6] -
+ x[2] * y[3] * z[6] + x[0] * y[3] * z[4] + z[0] * x[3] * y[4] + s7;
+ s8 = x[5] * y[4] * z[7] + s6 + y[5] * x[6] * z[4] - y[5] * x[4] * z[6] +
+ z[6] * x[5] * y[7] - x[6] * y[2] * z[7] - x[6] * y[7] * z[5] +
+ x[5] * y[6] * z[2] + x[6] * y[5] * z[7] + x[6] * y[7] * z[2] +
+ y[6] * x[7] * z[4] - y[6] * x[4] * z[7] - y[6] * x[7] * z[3] +
+ z[6] * x[7] * y[2] + x[2] * y[5] * z[6] - x[2] * y[6] * z[5] +
+ y[6] * x[2] * z[7] + x[6] * y[2] * z[5];
+ s7 = s8 - x[5] * y[2] * z[6] - z[6] * x[7] * y[5] - z[5] * x[7] * y[4] +
+ z[5] * x[0] * y[4] - y[5] * x[4] * z[7] + y[0] * x[4] * z[7] -
+ z[6] * x[2] * y[7] - x[5] * y[4] * z[0] - x[5] * y[7] * z[4] -
+ y[0] * x[7] * z[4] + y[5] * x[4] * z[1] - x[6] * y[7] * z[4] +
+ x[7] * y[4] * z[3] - x[4] * y[7] * z[3] + x[3] * y[7] * z[4] -
+ x[7] * y[3] * z[4] - x[6] * y[3] * z[7] + x[6] * y[4] * z[7];
+ s8 = -x[3] * y[4] * z[7] + x[4] * y[3] * z[7] - z[6] * x[7] * y[4] -
+ z[1] * x[6] * y[5] + x[6] * y[7] * z[3] - x[1] * y[6] * z[5] -
+ y[1] * x[5] * z[6] + z[5] * x[4] * y[7] - z[5] * x[4] * y[0] +
+ x[1] * y[5] * z[6] - y[6] * x[5] * z[7] - y[2] * x[3] * z[1] +
+ z[1] * x[5] * y[6] - y[5] * x[1] * z[4] + z[6] * x[4] * y[7] +
+ x[5] * y[1] * z[4] - x[5] * y[6] * z[4] + y[6] * x[3] * z[7] -
+ x[5] * y[4] * z[1];
+ s5 = s8 + x[5] * y[4] * z[6] + z[5] * x[1] * y[4] + y[1] * x[6] * z[5] -
+ z[6] * x[3] * y[7] + z[6] * x[7] * y[3] - z[5] * x[6] * y[4] -
+ z[5] * x[4] * y[1] + z[5] * x[4] * y[6] + x[1] * y[6] * z[2] +
+ x[2] * y[6] * z[3] + z[2] * x[6] * y[3] + z[1] * x[6] * y[2] +
+ z[2] * x[3] * y[1] - z[2] * x[1] * y[3] - z[2] * x[3] * y[6] +
+ y[2] * x[1] * z[3] + y[1] * x[2] * z[6] - z[0] * x[7] * y[3] + s7;
+ s4 = 1 / s5;
+ s2 = s3 * s4;
+ const double unknown1 = s1 * s2;
+ s1 = 1.0 / 6.0;
+ s8 = -z[2] * x[1] * y[2] * z[5] + z[2] * y[1] * x[2] * z[5] -
+ z[2] * z[1] * x[2] * y[5] + z[2] * z[1] * x[5] * y[2] +
+ 2.0 * y[5] * x[7] * z[4] * z[4] - y[1] * x[2] * z[0] * z[0] +
+ x[0] * y[3] * z[7] * z[7] - 2.0 * z[5] * z[5] * x[4] * y[1] +
+ 2.0 * z[5] * z[5] * x[1] * y[4] + z[5] * z[5] * x[0] * y[4] -
+ 2.0 * z[2] * z[2] * x[1] * y[3] + 2.0 * z[2] * z[2] * x[3] * y[1] -
+ x[0] * y[4] * z[7] * z[7] - y[0] * x[3] * z[7] * z[7] +
+ x[1] * y[0] * z[5] * z[5];
+ s7 = s8 - y[1] * x[0] * z[5] * z[5] + z[1] * y[1] * x[2] * z[6] +
+ y[1] * x[0] * z[2] * z[2] + z[2] * z[2] * x[3] * y[0] -
+ z[2] * z[2] * x[0] * y[3] - x[1] * y[0] * z[2] * z[2] +
+ 2.0 * z[5] * z[5] * x[4] * y[6] - 2.0 * z[5] * z[5] * x[6] * y[4] -
+ z[5] * z[5] * x[7] * y[4] - x[6] * y[7] * z[5] * z[5] +
+ 2.0 * z[2] * y[1] * x[2] * z[6] - 2.0 * z[2] * x[1] * y[2] * z[6] +
+ 2.0 * z[2] * z[1] * x[6] * y[2] - y[6] * x[5] * z[7] * z[7] +
+ 2.0 * x[6] * y[4] * z[7] * z[7];
+ s8 = -2.0 * y[6] * x[4] * z[7] * z[7] + x[6] * y[5] * z[7] * z[7] -
+ 2.0 * z[2] * z[1] * x[2] * y[6] + z[4] * y[6] * x[7] * z[5] +
+ x[5] * y[4] * z[6] * z[6] + z[6] * z[6] * x[4] * y[7] -
+ z[6] * z[6] * x[7] * y[4] - 2.0 * z[6] * z[6] * x[7] * y[5] +
+ 2.0 * z[6] * z[6] * x[5] * y[7] - y[5] * x[4] * z[6] * z[6] +
+ 2.0 * z[0] * z[0] * x[3] * y[4] - x[6] * y[5] * z[2] * z[2] +
+ z[1] * z[1] * x[5] * y[6] - z[1] * z[1] * x[6] * y[5] -
+ z[5] * z[5] * x[4] * y[0];
+ s6 = s8 + 2.0 * x[1] * y[3] * z[0] * z[0] +
+ 2.0 * x[1] * y[6] * z[2] * z[2] - 2.0 * y[1] * x[6] * z[2] * z[2] -
+ y[1] * x[5] * z[2] * z[2] - z[1] * z[1] * x[2] * y[6] -
+ 2.0 * z[1] * z[1] * x[2] * y[5] + 2.0 * z[1] * z[1] * x[5] * y[2] +
+ z[1] * y[1] * x[6] * z[5] + y[1] * x[2] * z[5] * z[5] +
+ z[2] * z[1] * x[2] * y[0] + z[1] * x[1] * y[5] * z[6] -
+ z[1] * x[1] * y[6] * z[5] - z[1] * y[1] * x[5] * z[6] -
+ z[1] * x[2] * y[6] * z[5] + z[1] * x[6] * y[2] * z[5] + s7;
+ s8 = -x[1] * y[2] * z[5] * z[5] + z[1] * x[5] * y[6] * z[2] -
+ 2.0 * z[2] * z[2] * x[3] * y[6] + 2.0 * z[2] * z[2] * x[6] * y[3] +
+ z[2] * z[2] * x[7] * y[3] - z[2] * z[2] * x[3] * y[7] -
+ z[1] * x[6] * y[5] * z[2] + 2.0 * z[1] * x[1] * y[5] * z[2] -
+ 2.0 * x[3] * y[4] * z[7] * z[7] + 2.0 * x[4] * y[3] * z[7] * z[7] +
+ x[5] * y[6] * z[2] * z[2] + y[1] * x[2] * z[6] * z[6] +
+ y[0] * x[4] * z[7] * z[7] + z[2] * x[2] * y[3] * z[0] -
+ x[1] * y[2] * z[6] * z[6];
+ s7 = s8 - z[7] * z[2] * x[3] * y[7] + x[2] * y[6] * z[3] * z[3] -
+ y[2] * x[6] * z[3] * z[3] - z[6] * x[2] * y[3] * z[7] -
+ z[2] * z[1] * x[0] * y[2] + z[6] * z[2] * x[6] * y[3] -
+ z[6] * z[2] * x[3] * y[6] + z[6] * x[2] * y[6] * z[3] +
+ z[2] * x[1] * y[2] * z[0] + z[6] * y[2] * x[3] * z[7] -
+ z[4] * z[5] * x[6] * y[4] + z[4] * z[5] * x[4] * y[6] -
+ z[4] * y[6] * x[5] * z[7] + z[4] * z[6] * x[4] * y[7] +
+ z[4] * x[5] * y[4] * z[6];
+ s8 = -z[6] * y[2] * x[6] * z[3] - z[4] * y[5] * x[4] * z[6] -
+ z[2] * y[1] * x[5] * z[6] + z[2] * x[1] * y[5] * z[6] +
+ z[4] * x[6] * y[4] * z[7] + 2.0 * z[4] * z[5] * x[4] * y[7] -
+ z[4] * z[6] * x[7] * y[4] + x[6] * y[7] * z[3] * z[3] -
+ 2.0 * z[4] * z[5] * x[7] * y[4] - 2.0 * z[4] * y[5] * x[4] * z[7] -
+ z[4] * y[6] * x[4] * z[7] + z[4] * x[6] * y[5] * z[7] -
+ z[4] * x[6] * y[7] * z[5] + 2.0 * z[4] * x[5] * y[4] * z[7] +
+ z[2] * x[2] * y[5] * z[6] - z[2] * x[2] * y[6] * z[5];
+ s5 = s8 + z[2] * x[6] * y[2] * z[5] - z[2] * x[5] * y[2] * z[6] -
+ z[2] * x[2] * y[3] * z[7] - x[2] * y[3] * z[7] * z[7] +
+ 2.0 * z[2] * x[2] * y[3] * z[1] - z[2] * y[2] * x[3] * z[0] +
+ z[2] * y[2] * x[0] * z[3] - z[2] * x[2] * y[0] * z[3] -
+ z[7] * y[2] * x[7] * z[3] + z[7] * z[2] * x[7] * y[3] +
+ z[7] * x[2] * y[7] * z[3] + z[6] * y[1] * x[2] * z[5] -
+ z[6] * x[1] * y[2] * z[5] + z[5] * x[1] * y[5] * z[2] + s6 + s7;
+ s8 = z[5] * z[1] * x[5] * y[2] - z[5] * z[1] * x[2] * y[5] -
+ y[6] * x[7] * z[2] * z[2] + 2.0 * z[2] * x[2] * y[6] * z[3] -
+ 2.0 * z[2] * x[2] * y[3] * z[6] + 2.0 * z[2] * y[2] * x[3] * z[6] +
+ y[2] * x[3] * z[6] * z[6] + y[6] * x[7] * z[5] * z[5] +
+ z[2] * y[2] * x[3] * z[7] - z[2] * y[2] * x[7] * z[3] -
+ 2.0 * z[2] * y[2] * x[6] * z[3] + z[2] * x[2] * y[7] * z[3] +
+ x[6] * y[2] * z[5] * z[5] - 2.0 * z[2] * x[2] * y[1] * z[3] -
+ x[2] * y[6] * z[5] * z[5];
+ s7 = s8 - y[1] * x[5] * z[6] * z[6] + z[6] * x[1] * y[6] * z[2] -
+ z[3] * z[2] * x[3] * y[6] + z[6] * z[1] * x[6] * y[2] -
+ z[6] * z[1] * x[2] * y[6] - z[6] * y[1] * x[6] * z[2] -
+ 2.0 * x[5] * y[2] * z[6] * z[6] + z[4] * z[1] * x[0] * y[4] -
+ z[3] * x[2] * y[3] * z[6] - z[5] * y[1] * x[5] * z[2] +
+ z[3] * y[2] * x[3] * z[6] + 2.0 * x[2] * y[5] * z[6] * z[6] -
+ z[5] * x[1] * y[5] * z[0] + y[2] * x[3] * z[7] * z[7] -
+ x[2] * y[3] * z[6] * z[6];
+ s8 = z[5] * y[5] * x[4] * z[0] + z[3] * z[2] * x[6] * y[3] +
+ x[1] * y[5] * z[6] * z[6] + z[5] * y[5] * x[7] * z[4] -
+ z[1] * x[1] * y[2] * z[6] + z[1] * x[1] * y[6] * z[2] +
+ 2.0 * z[6] * y[6] * x[7] * z[5] - z[7] * y[6] * x[7] * z[2] -
+ z[3] * y[6] * x[7] * z[2] + x[6] * y[7] * z[2] * z[2] -
+ 2.0 * z[6] * y[6] * x[7] * z[2] - 2.0 * x[6] * y[3] * z[7] * z[7] -
+ x[6] * y[2] * z[7] * z[7] - z[5] * x[6] * y[5] * z[2] +
+ y[6] * x[2] * z[7] * z[7];
+ s6 = s8 + 2.0 * y[6] * x[3] * z[7] * z[7] + z[6] * z[6] * x[7] * y[3] -
+ y[6] * x[7] * z[3] * z[3] + z[5] * x[5] * y[0] * z[4] +
+ 2.0 * z[6] * z[6] * x[7] * y[2] - 2.0 * z[6] * z[6] * x[2] * y[7] -
+ z[6] * z[6] * x[3] * y[7] + z[7] * y[6] * x[7] * z[5] +
+ z[7] * y[5] * x[7] * z[4] - 2.0 * z[7] * x[7] * y[3] * z[4] +
+ 2.0 * z[7] * x[3] * y[7] * z[4] - 2.0 * z[7] * x[4] * y[7] * z[3] +
+ 2.0 * z[7] * x[7] * y[4] * z[3] - z[7] * y[0] * x[7] * z[4] -
+ 2.0 * z[7] * z[6] * x[3] * y[7] + s7;
+ s8 = s6 + 2.0 * z[7] * z[6] * x[7] * y[3] +
+ 2.0 * z[7] * x[6] * y[7] * z[3] + z[7] * x[6] * y[7] * z[2] -
+ 2.0 * z[7] * y[6] * x[7] * z[3] + z[7] * z[6] * x[7] * y[2] -
+ z[7] * z[6] * x[2] * y[7] + z[5] * y[1] * x[5] * z[0] -
+ z[5] * z[1] * x[5] * y[0] + 2.0 * y[1] * x[6] * z[5] * z[5] -
+ 2.0 * x[1] * y[6] * z[5] * z[5] + z[5] * z[1] * x[0] * y[5] +
+ z[6] * y[6] * x[3] * z[7] + 2.0 * z[6] * x[6] * y[7] * z[2] -
+ z[6] * y[6] * x[7] * z[3];
+ s7 = s8 + 2.0 * z[6] * y[6] * x[2] * z[7] - z[6] * x[6] * y[3] * z[7] +
+ z[6] * x[6] * y[7] * z[3] - 2.0 * z[6] * x[6] * y[2] * z[7] -
+ 2.0 * z[1] * y[1] * x[5] * z[2] - z[1] * y[1] * x[6] * z[2] -
+ z[7] * z[0] * x[7] * y[3] - 2.0 * z[6] * x[6] * y[5] * z[2] -
+ z[2] * z[6] * x[3] * y[7] + z[2] * x[6] * y[7] * z[3] -
+ z[2] * z[6] * x[2] * y[7] + y[5] * x[6] * z[4] * z[4] +
+ z[2] * y[6] * x[2] * z[7] + y[6] * x[7] * z[4] * z[4] +
+ z[2] * z[6] * x[7] * y[2] - 2.0 * x[5] * y[7] * z[4] * z[4];
+ s8 = -x[6] * y[7] * z[4] * z[4] - z[5] * y[5] * x[0] * z[4] -
+ z[2] * x[6] * y[2] * z[7] - x[5] * y[6] * z[4] * z[4] -
+ 2.0 * z[5] * y[1] * x[5] * z[6] + 2.0 * z[5] * z[1] * x[5] * y[6] +
+ 2.0 * z[5] * x[1] * y[5] * z[6] - 2.0 * z[5] * z[1] * x[6] * y[5] -
+ z[5] * x[5] * y[2] * z[6] + z[5] * x[5] * y[6] * z[2] +
+ z[5] * x[2] * y[5] * z[6] + z[5] * z[5] * x[4] * y[7] -
+ y[5] * x[4] * z[7] * z[7] + x[5] * y[4] * z[7] * z[7] +
+ z[6] * z[1] * x[5] * y[6] + z[6] * y[1] * x[6] * z[5];
+ s4 = s8 - z[6] * z[1] * x[6] * y[5] - z[6] * x[1] * y[6] * z[5] +
+ z[2] * z[6] * x[7] * y[3] + 2.0 * z[6] * x[6] * y[2] * z[5] +
+ 2.0 * z[6] * x[5] * y[6] * z[2] - 2.0 * z[6] * x[2] * y[6] * z[5] +
+ z[7] * z[0] * x[3] * y[7] + z[7] * z[0] * x[7] * y[4] +
+ z[3] * z[6] * x[7] * y[3] - z[3] * z[6] * x[3] * y[7] -
+ z[3] * x[6] * y[3] * z[7] + z[3] * y[6] * x[2] * z[7] -
+ z[3] * x[6] * y[2] * z[7] + z[5] * x[5] * y[4] * z[7] + s5 + s7;
+ s8 = s4 + z[3] * y[6] * x[3] * z[7] - z[7] * x[0] * y[7] * z[3] +
+ z[6] * x[5] * y[4] * z[7] + z[7] * y[0] * x[7] * z[3] +
+ z[5] * z[6] * x[4] * y[7] - 2.0 * z[5] * x[5] * y[6] * z[4] +
+ 2.0 * z[5] * x[5] * y[4] * z[6] - z[5] * x[5] * y[7] * z[4] -
+ z[5] * y[6] * x[5] * z[7] - z[5] * z[6] * x[7] * y[4] -
+ z[7] * z[0] * x[4] * y[7] - z[5] * z[6] * x[7] * y[5] -
+ z[5] * y[5] * x[4] * z[7] + z[7] * x[0] * y[7] * z[4];
+ s7 = s8 - 2.0 * z[5] * y[5] * x[4] * z[6] + z[5] * z[6] * x[5] * y[7] +
+ z[5] * x[6] * y[5] * z[7] + 2.0 * z[5] * y[5] * x[6] * z[4] +
+ z[6] * z[5] * x[4] * y[6] - z[6] * x[5] * y[6] * z[4] -
+ z[6] * z[5] * x[6] * y[4] - z[6] * x[6] * y[7] * z[4] -
+ 2.0 * z[6] * y[6] * x[5] * z[7] + z[6] * x[6] * y[4] * z[7] -
+ z[6] * y[5] * x[4] * z[7] - z[6] * y[6] * x[4] * z[7] +
+ z[6] * y[6] * x[7] * z[4] + z[6] * y[5] * x[6] * z[4] +
+ 2.0 * z[6] * x[6] * y[5] * z[7];
+ s8 = -2.0 * z[6] * x[6] * y[7] * z[5] - z[2] * y[1] * x[2] * z[0] +
+ 2.0 * z[7] * z[6] * x[4] * y[7] - 2.0 * z[7] * x[6] * y[7] * z[4] -
+ 2.0 * z[7] * z[6] * x[7] * y[4] + z[7] * z[5] * x[4] * y[7] -
+ z[7] * z[5] * x[7] * y[4] - z[7] * x[5] * y[7] * z[4] +
+ 2.0 * z[7] * y[6] * x[7] * z[4] - z[7] * z[6] * x[7] * y[5] +
+ z[7] * z[6] * x[5] * y[7] - z[7] * x[6] * y[7] * z[5] +
+ z[1] * z[1] * x[6] * y[2] + s7 + x[1] * y[5] * z[2] * z[2];
+ s6 = s8 + 2.0 * z[2] * y[2] * x[1] * z[3] -
+ 2.0 * z[2] * y[2] * x[3] * z[1] - 2.0 * x[1] * y[4] * z[0] * z[0] +
+ 2.0 * y[1] * x[4] * z[0] * z[0] + 2.0 * x[2] * y[7] * z[3] * z[3] -
+ 2.0 * y[2] * x[7] * z[3] * z[3] - x[1] * y[5] * z[0] * z[0] +
+ z[0] * z[0] * x[7] * y[4] + z[0] * z[0] * x[3] * y[7] +
+ x[2] * y[3] * z[0] * z[0] - 2.0 * y[1] * x[3] * z[0] * z[0] +
+ y[5] * x[4] * z[0] * z[0] - 2.0 * z[0] * z[0] * x[4] * y[3] +
+ x[1] * y[2] * z[0] * z[0] - z[0] * z[0] * x[4] * y[7] +
+ y[1] * x[5] * z[0] * z[0];
+ s8 = s6 - y[2] * x[3] * z[0] * z[0] + y[1] * x[0] * z[3] * z[3] -
+ 2.0 * x[0] * y[7] * z[3] * z[3] - x[0] * y[4] * z[3] * z[3] -
+ 2.0 * x[2] * y[0] * z[3] * z[3] - x[1] * y[0] * z[3] * z[3] +
+ y[0] * x[4] * z[3] * z[3] - 2.0 * z[0] * y[1] * x[0] * z[4] +
+ 2.0 * z[0] * z[1] * x[0] * y[4] + 2.0 * z[0] * x[1] * y[0] * z[4] -
+ 2.0 * z[0] * z[1] * x[4] * y[0] - 2.0 * z[3] * x[2] * y[3] * z[7] -
+ 2.0 * z[3] * z[2] * x[3] * y[7] + 2.0 * z[3] * z[2] * x[7] * y[3];
+ s7 = s8 + 2.0 * z[3] * y[2] * x[3] * z[7] +
+ 2.0 * z[5] * y[5] * x[4] * z[1] + 2.0 * z[0] * y[1] * x[0] * z[3] -
+ z[0] * y[0] * x[3] * z[7] - 2.0 * z[0] * y[0] * x[3] * z[4] -
+ z[0] * x[1] * y[0] * z[2] + z[0] * z[1] * x[2] * y[0] -
+ z[0] * y[1] * x[0] * z[5] - z[0] * z[1] * x[0] * y[2] -
+ z[0] * x[0] * y[7] * z[3] - 2.0 * z[0] * z[1] * x[0] * y[3] -
+ z[5] * x[5] * y[4] * z[0] - 2.0 * z[0] * x[0] * y[4] * z[3] +
+ z[0] * x[0] * y[7] * z[4] - z[0] * z[2] * x[0] * y[3];
+ s8 = s7 + z[0] * x[5] * y[0] * z[4] + z[0] * z[1] * x[0] * y[5] -
+ z[0] * x[2] * y[0] * z[3] - z[0] * z[1] * x[5] * y[0] -
+ 2.0 * z[0] * x[1] * y[0] * z[3] + 2.0 * z[0] * y[0] * x[4] * z[3] -
+ z[0] * x[0] * y[4] * z[7] + z[0] * x[1] * y[0] * z[5] +
+ z[0] * y[0] * x[7] * z[3] + z[0] * y[2] * x[0] * z[3] -
+ z[0] * y[5] * x[0] * z[4] + z[0] * z[2] * x[3] * y[0] +
+ z[0] * x[2] * y[3] * z[1] + z[0] * x[0] * y[3] * z[7] -
+ z[0] * x[2] * y[1] * z[3];
+ s5 = s8 + z[0] * y[1] * x[0] * z[2] + z[3] * x[1] * y[3] * z[0] -
+ 2.0 * z[3] * y[0] * x[3] * z[7] - z[3] * y[0] * x[3] * z[4] -
+ z[3] * x[1] * y[0] * z[2] + z[3] * z[0] * x[7] * y[4] +
+ 2.0 * z[3] * z[0] * x[3] * y[7] + 2.0 * z[3] * x[2] * y[3] * z[0] -
+ z[3] * y[1] * x[3] * z[0] - z[3] * z[1] * x[0] * y[3] -
+ z[3] * z[0] * x[4] * y[3] + z[3] * x[1] * y[2] * z[0] -
+ z[3] * z[0] * x[4] * y[7] - 2.0 * z[3] * z[2] * x[0] * y[3] -
+ z[3] * x[0] * y[4] * z[7] - 2.0 * z[3] * y[2] * x[3] * z[0];
+ s8 = s5 + 2.0 * z[3] * z[2] * x[3] * y[0] + z[3] * x[2] * y[3] * z[1] +
+ 2.0 * z[3] * x[0] * y[3] * z[7] + z[3] * y[1] * x[0] * z[2] -
+ z[4] * y[0] * x[3] * z[7] - z[4] * x[1] * y[5] * z[0] -
+ z[4] * y[1] * x[0] * z[5] + 2.0 * z[4] * z[0] * x[7] * y[4] +
+ z[4] * z[0] * x[3] * y[7] + 2.0 * z[4] * y[5] * x[4] * z[0] +
+ 2.0 * y[0] * x[7] * z[3] * z[3] + 2.0 * y[2] * x[0] * z[3] * z[3] -
+ x[2] * y[1] * z[3] * z[3] - y[0] * x[3] * z[4] * z[4];
+ s7 = s8 - y[1] * x[0] * z[4] * z[4] + x[1] * y[0] * z[4] * z[4] +
+ 2.0 * x[0] * y[7] * z[4] * z[4] + 2.0 * x[5] * y[0] * z[4] * z[4] -
+ 2.0 * y[5] * x[0] * z[4] * z[4] + 2.0 * z[1] * z[1] * x[2] * y[0] -
+ 2.0 * z[1] * z[1] * x[0] * y[2] + z[1] * z[1] * x[0] * y[4] -
+ z[1] * z[1] * x[0] * y[3] - z[1] * z[1] * x[4] * y[0] +
+ 2.0 * z[1] * z[1] * x[0] * y[5] - 2.0 * z[1] * z[1] * x[5] * y[0] +
+ x[2] * y[3] * z[1] * z[1] - x[5] * y[4] * z[0] * z[0] -
+ z[0] * z[0] * x[7] * y[3];
+ s8 = s7 + x[7] * y[4] * z[3] * z[3] - x[4] * y[7] * z[3] * z[3] +
+ y[2] * x[1] * z[3] * z[3] + x[0] * y[3] * z[4] * z[4] -
+ 2.0 * y[0] * x[7] * z[4] * z[4] + x[3] * y[7] * z[4] * z[4] -
+ x[7] * y[3] * z[4] * z[4] - y[5] * x[1] * z[4] * z[4] +
+ x[5] * y[1] * z[4] * z[4] + z[1] * z[1] * x[3] * y[0] +
+ y[5] * x[4] * z[1] * z[1] - y[2] * x[3] * z[1] * z[1] -
+ x[5] * y[4] * z[1] * z[1] - z[4] * x[0] * y[4] * z[3] -
+ z[4] * z[0] * x[4] * y[3];
+ s6 = s8 - z[4] * z[1] * x[4] * y[0] - 2.0 * z[4] * z[0] * x[4] * y[7] +
+ z[4] * y[1] * x[5] * z[0] - 2.0 * z[5] * x[5] * y[4] * z[1] -
+ z[4] * x[1] * y[4] * z[0] + z[4] * y[0] * x[4] * z[3] -
+ 2.0 * z[4] * x[0] * y[4] * z[7] + z[4] * x[1] * y[0] * z[5] -
+ 2.0 * z[1] * x[1] * y[2] * z[5] + z[4] * x[0] * y[3] * z[7] +
+ 2.0 * z[5] * x[5] * y[1] * z[4] + z[4] * y[1] * x[4] * z[0] +
+ z[1] * y[1] * x[0] * z[3] + z[1] * x[1] * y[3] * z[0] -
+ 2.0 * z[1] * x[1] * y[5] * z[0] - 2.0 * z[1] * x[1] * y[0] * z[2];
+ s8 = s6 - 2.0 * z[1] * y[1] * x[0] * z[5] - z[1] * y[1] * x[0] * z[4] +
+ 2.0 * z[1] * y[1] * x[2] * z[5] - z[1] * y[1] * x[3] * z[0] -
+ 2.0 * z[5] * y[5] * x[1] * z[4] + z[1] * y[5] * x[4] * z[0] +
+ z[1] * x[1] * y[0] * z[4] + 2.0 * z[1] * x[1] * y[2] * z[0] -
+ z[1] * z[2] * x[0] * y[3] + 2.0 * z[1] * y[1] * x[5] * z[0] -
+ z[1] * x[1] * y[0] * z[3] - z[1] * x[1] * y[4] * z[0] +
+ 2.0 * z[1] * x[1] * y[0] * z[5] - z[1] * y[2] * x[3] * z[0];
+ s7 = s8 + z[1] * z[2] * x[3] * y[0] - z[1] * x[2] * y[1] * z[3] +
+ z[1] * y[1] * x[4] * z[0] + 2.0 * z[1] * y[1] * x[0] * z[2] +
+ 2.0 * z[0] * z[1] * x[3] * y[0] + 2.0 * z[0] * x[0] * y[3] * z[4] +
+ z[0] * z[5] * x[0] * y[4] + z[0] * y[0] * x[4] * z[7] -
+ z[0] * y[0] * x[7] * z[4] - z[0] * x[7] * y[3] * z[4] -
+ z[0] * z[5] * x[4] * y[0] - z[0] * x[5] * y[4] * z[1] +
+ z[3] * z[1] * x[3] * y[0] + z[3] * x[0] * y[3] * z[4] +
+ z[3] * z[0] * x[3] * y[4] + z[3] * y[0] * x[4] * z[7];
+ s8 = s7 + z[3] * x[3] * y[7] * z[4] - z[3] * x[7] * y[3] * z[4] -
+ z[3] * x[3] * y[4] * z[7] + z[3] * x[4] * y[3] * z[7] -
+ z[3] * y[2] * x[3] * z[1] + z[3] * z[2] * x[3] * y[1] -
+ z[3] * z[2] * x[1] * y[3] - 2.0 * z[3] * z[0] * x[7] * y[3] +
+ z[4] * z[0] * x[3] * y[4] + 2.0 * z[4] * z[5] * x[0] * y[4] +
+ 2.0 * z[4] * y[0] * x[4] * z[7] - 2.0 * z[4] * x[5] * y[4] * z[0] +
+ z[4] * y[5] * x[4] * z[1] + z[4] * x[7] * y[4] * z[3] -
+ z[4] * x[4] * y[7] * z[3];
+ s3 = s8 - z[4] * x[3] * y[4] * z[7] + z[4] * x[4] * y[3] * z[7] -
+ 2.0 * z[4] * z[5] * x[4] * y[0] - z[4] * x[5] * y[4] * z[1] +
+ z[4] * z[5] * x[1] * y[4] - z[4] * z[5] * x[4] * y[1] -
+ 2.0 * z[1] * y[1] * x[2] * z[0] + z[1] * z[5] * x[0] * y[4] -
+ z[1] * z[5] * x[4] * y[0] - z[1] * y[5] * x[1] * z[4] +
+ z[1] * x[5] * y[1] * z[4] + z[1] * z[5] * x[1] * y[4] -
+ z[1] * z[5] * x[4] * y[1] + z[1] * z[2] * x[3] * y[1] -
+ z[1] * z[2] * x[1] * y[3] + z[1] * y[2] * x[1] * z[3];
+ s8 = y[1] * x[0] * z[3] + x[1] * y[3] * z[0] - y[0] * x[3] * z[7] -
+ x[1] * y[5] * z[0] - y[0] * x[3] * z[4] - x[1] * y[0] * z[2] +
+ z[1] * x[2] * y[0] - y[1] * x[0] * z[5] - z[1] * x[0] * y[2] -
+ y[1] * x[0] * z[4] + z[1] * x[5] * y[2] + z[0] * x[7] * y[4] +
+ z[0] * x[3] * y[7] + z[1] * x[0] * y[4] - x[1] * y[2] * z[5] +
+ x[2] * y[3] * z[0] + y[1] * x[2] * z[5] - x[2] * y[3] * z[7];
+ s7 = s8 - z[1] * x[2] * y[5] - y[1] * x[3] * z[0] - x[0] * y[7] * z[3] -
+ z[1] * x[0] * y[3] + y[5] * x[4] * z[0] - x[0] * y[4] * z[3] +
+ y[5] * x[7] * z[4] - z[0] * x[4] * y[3] + x[1] * y[0] * z[4] -
+ z[2] * x[3] * y[7] - y[6] * x[7] * z[2] + x[1] * y[5] * z[2] +
+ y[6] * x[7] * z[5] + x[0] * y[7] * z[4] + x[1] * y[2] * z[0] -
+ z[1] * x[4] * y[0] - z[0] * x[4] * y[7] - z[2] * x[0] * y[3];
+ s8 = x[5] * y[0] * z[4] + z[1] * x[0] * y[5] - x[2] * y[0] * z[3] -
+ z[1] * x[5] * y[0] + y[1] * x[5] * z[0] - x[1] * y[0] * z[3] -
+ x[1] * y[4] * z[0] - y[1] * x[5] * z[2] + x[2] * y[7] * z[3] +
+ y[0] * x[4] * z[3] - x[0] * y[4] * z[7] + x[1] * y[0] * z[5] -
+ y[1] * x[6] * z[2] - y[2] * x[6] * z[3] + y[0] * x[7] * z[3] -
+ y[2] * x[7] * z[3] + z[2] * x[7] * y[3] + y[2] * x[0] * z[3];
+ s6 = s8 + y[2] * x[3] * z[7] - y[2] * x[3] * z[0] - x[6] * y[5] * z[2] -
+ y[5] * x[0] * z[4] + z[2] * x[3] * y[0] + x[2] * y[3] * z[1] +
+ x[0] * y[3] * z[7] - x[2] * y[1] * z[3] + y[1] * x[4] * z[0] +
+ y[1] * x[0] * z[2] - z[1] * x[2] * y[6] + y[2] * x[3] * z[6] -
+ y[1] * x[2] * z[0] + z[1] * x[3] * y[0] - x[1] * y[2] * z[6] -
+ x[2] * y[3] * z[6] + x[0] * y[3] * z[4] + z[0] * x[3] * y[4] + s7;
+ s8 = x[5] * y[4] * z[7] + s6 + y[5] * x[6] * z[4] - y[5] * x[4] * z[6] +
+ z[6] * x[5] * y[7] - x[6] * y[2] * z[7] - x[6] * y[7] * z[5] +
+ x[5] * y[6] * z[2] + x[6] * y[5] * z[7] + x[6] * y[7] * z[2] +
+ y[6] * x[7] * z[4] - y[6] * x[4] * z[7] - y[6] * x[7] * z[3] +
+ z[6] * x[7] * y[2] + x[2] * y[5] * z[6] - x[2] * y[6] * z[5] +
+ y[6] * x[2] * z[7] + x[6] * y[2] * z[5];
+ s7 = s8 - x[5] * y[2] * z[6] - z[6] * x[7] * y[5] - z[5] * x[7] * y[4] +
+ z[5] * x[0] * y[4] - y[5] * x[4] * z[7] + y[0] * x[4] * z[7] -
+ z[6] * x[2] * y[7] - x[5] * y[4] * z[0] - x[5] * y[7] * z[4] -
+ y[0] * x[7] * z[4] + y[5] * x[4] * z[1] - x[6] * y[7] * z[4] +
+ x[7] * y[4] * z[3] - x[4] * y[7] * z[3] + x[3] * y[7] * z[4] -
+ x[7] * y[3] * z[4] - x[6] * y[3] * z[7] + x[6] * y[4] * z[7];
+ s8 = -x[3] * y[4] * z[7] + x[4] * y[3] * z[7] - z[6] * x[7] * y[4] -
+ z[1] * x[6] * y[5] + x[6] * y[7] * z[3] - x[1] * y[6] * z[5] -
+ y[1] * x[5] * z[6] + z[5] * x[4] * y[7] - z[5] * x[4] * y[0] +
+ x[1] * y[5] * z[6] - y[6] * x[5] * z[7] - y[2] * x[3] * z[1] +
+ z[1] * x[5] * y[6] - y[5] * x[1] * z[4] + z[6] * x[4] * y[7] +
+ x[5] * y[1] * z[4] - x[5] * y[6] * z[4] + y[6] * x[3] * z[7] -
+ x[5] * y[4] * z[1];
+ s5 = s8 + x[5] * y[4] * z[6] + z[5] * x[1] * y[4] + y[1] * x[6] * z[5] -
+ z[6] * x[3] * y[7] + z[6] * x[7] * y[3] - z[5] * x[6] * y[4] -
+ z[5] * x[4] * y[1] + z[5] * x[4] * y[6] + x[1] * y[6] * z[2] +
+ x[2] * y[6] * z[3] + z[2] * x[6] * y[3] + z[1] * x[6] * y[2] +
+ z[2] * x[3] * y[1] - z[2] * x[1] * y[3] - z[2] * x[3] * y[6] +
+ y[2] * x[1] * z[3] + y[1] * x[2] * z[6] - z[0] * x[7] * y[3] + s7;
+ s4 = 1 / s5;
+ s2 = s3 * s4;
+ const double unknown2 = s1 * s2;
+
+ return {unknown0, unknown1, unknown2};
+ }
+ else
+ {
+ // Be somewhat particular in which exception we throw
+ Assert(accessor.reference_cell() != ReferenceCells::Pyramid &&
+ accessor.reference_cell() != ReferenceCells::Wedge,
+ ExcNotImplemented());
+ Assert(false, ExcInternalError());
+
+ return {};
+ }
}
projects / dealii.git / commitdiff