polyfem/auto__mooney__rivlin__gradient__hessian_8cpp_source.html

#include "auto_mooney_rivlin_gradient_hessian.hpp"


namespace polyfem

{

    namespace autogen

    {


        template <>


        void generate_gradient_templated(const double c1, const double c2, const double c3, const double d1, const Eigen::Matrix<double, 2, 2> &def_grad, Eigen::Matrix<double, 2, 2> &gradient)

        {


            const double helper_0 = def_grad(0) * def_grad(3) - def_grad(1) * def_grad(2);

            const double helper_1 = 1.0 / helper_0;

            const double helper_2 = 2 * def_grad(3);

            const double helper_3 = d1 * log(helper_0);

            const double helper_4 = 2 * def_grad(0);

            const double helper_5 = def_grad(0) * def_grad(0) + def_grad(1) * def_grad(1);

            const double helper_6 = def_grad(2) * def_grad(2) + def_grad(3) * def_grad(3);

            const double helper_7 = helper_5 + helper_6;

            const double helper_8 = helper_1 * helper_7;

            const double helper_9 = helper_4 - helper_8 * def_grad(3);

            const double helper_10 = pow(helper_0, -2);

            const double helper_11 = def_grad(0) * def_grad(2) + def_grad(1) * def_grad(3);

            const double helper_12 = 2 * helper_11 * helper_11 + helper_5 * helper_5 + helper_6 * helper_6 - helper_7 * helper_7;

            const double helper_13 = (1.0 / 2.0) * c3;

            const double helper_14 = helper_13 * (helper_10 * helper_12 + 4);

            const double helper_15 = 2 * def_grad(2);

            const double helper_16 = helper_1 * helper_12;

            const double helper_17 = helper_11 * helper_15 - helper_16 * def_grad(3) + helper_4 * helper_5 - helper_4 * helper_7;

            const double helper_18 = c2 * helper_1;

            const double helper_19 = 2 - helper_8;

            const double helper_20 = c3 * helper_1 * helper_19;

            const double helper_21 = 2 * def_grad(1);

            const double helper_22 = helper_21 + helper_8 * def_grad(2);

            const double helper_23 = helper_13 * (helper_10 * helper_12 + 4);

            const double helper_24 = helper_11 * helper_2 + helper_16 * def_grad(2) + helper_21 * helper_5 - helper_21 * helper_7;

            const double helper_25 = helper_15 + helper_8 * def_grad(1);

            const double helper_26 = helper_11 * helper_4 + helper_15 * helper_6 - helper_15 * helper_7 + helper_16 * def_grad(1);

            const double helper_27 = helper_2 - helper_8 * def_grad(0);

            const double helper_28 = helper_11 * helper_21 - helper_16 * def_grad(0) + helper_2 * helper_6 - helper_2 * helper_7;

            gradient(0, 0) = helper_1 * (c1 * helper_9 - helper_14 * helper_9 - helper_17 * helper_18 + helper_17 * helper_20 + helper_2 * helper_3);

            gradient(0, 1) = helper_1 * (c1 * helper_22 + c3 * helper_1 * helper_19 * helper_24 - helper_15 * helper_3 - helper_18 * helper_24 - helper_22 * helper_23);

            gradient(1, 0) = helper_1 * (c1 * helper_25 + c3 * helper_1 * helper_19 * helper_26 - helper_18 * helper_26 - helper_21 * helper_3 - helper_23 * helper_25);

            gradient(1, 1) = helper_1 * (c1 * helper_27 - helper_14 * helper_27 - helper_18 * helper_28 + helper_20 * helper_28 + helper_3 * helper_4);

        }


        template <>


        void generate_hessian_templated(const double c1, const double c2, const double c3, const double d1, const Eigen::Matrix<double, 2, 2> &def_grad, Eigen::Matrix<double, 4, 4> &hessian)

        {


            const double helper_0 = def_grad(0) * def_grad(3);

            const double helper_1 = def_grad(1) * def_grad(2);

            const double helper_2 = helper_0 - helper_1;

            const double helper_3 = 1.0 / helper_2;

            const double helper_4 = def_grad(3) * def_grad(3);

            const double helper_5 = log(helper_2);

            const double helper_6 = 2 * d1;

            const double helper_7 = helper_5 * helper_6;

            const double helper_8 = helper_3 * helper_7;

            const double helper_9 = pow(helper_2, -2);

            const double helper_10 = def_grad(0) * def_grad(0);

            const double helper_11 = def_grad(1) * def_grad(1);

            const double helper_12 = helper_10 + helper_11;

            const double helper_13 = def_grad(2) * def_grad(2);

            const double helper_14 = helper_13 + helper_4;

            const double helper_15 = helper_12 + helper_14;

            const double helper_16 = helper_15 * helper_9;

            const double helper_17 = 2 * helper_0;

            const double helper_18 = -helper_17 * helper_3 + 1;

            const double helper_19 = helper_16 * helper_4 + helper_18;

            const double helper_20 = def_grad(0) * def_grad(2);

            const double helper_21 = def_grad(1) * def_grad(3);

            const double helper_22 = helper_20 + helper_21;

            const double helper_23 = helper_12 * helper_12 + helper_14 * helper_14 - helper_15 * helper_15 + 2 * helper_22 * helper_22;

            const double helper_24 = helper_23 * helper_9;

            const double helper_25 = helper_24 + 4;

            const double helper_26 = c3 * helper_25;

            const double helper_27 = 2 * def_grad(3);

            const double helper_28 = helper_12 * def_grad(0);

            const double helper_29 = helper_22 * def_grad(2);

            const double helper_30 = helper_15 * def_grad(0);

            const double helper_31 = helper_28 + helper_29 - helper_30;

            const double helper_32 = 8 * helper_3;

            const double helper_33 = 3 * helper_24;

            const double helper_34 = helper_27 + helper_31 * helper_32 - helper_33 * def_grad(3);

            const double helper_35 = helper_23 * helper_3;

            const double helper_36 = 2 * helper_28 + 2 * helper_29 - 2 * helper_30 - helper_35 * def_grad(3);

            const double helper_37 = 2 * def_grad(0);

            const double helper_38 = helper_15 * helper_3;

            const double helper_39 = helper_37 - helper_38 * def_grad(3);

            const double helper_40 = c3 * helper_9;

            const double helper_41 = helper_39 * helper_40;

            const double helper_42 = 2 - helper_38;

            const double helper_43 = c3 * helper_3 * helper_42;

            const double helper_44 = helper_27 * def_grad(2);

            const double helper_45 = def_grad(2) * def_grad(3);

            const double helper_46 = -helper_20 + helper_21 + helper_38 * helper_45;

            const double helper_47 = 2 * c1;

            const double helper_48 = helper_12 * def_grad(1);

            const double helper_49 = helper_15 * def_grad(1);

            const double helper_50 = helper_22 * helper_27 + helper_35 * def_grad(2) + 2 * helper_48 - 2 * helper_49;

            const double helper_51 = c3 * helper_3;

            const double helper_52 = helper_39 * helper_51;

            const double helper_53 = 2 * def_grad(1);

            const double helper_54 = helper_38 * def_grad(2) + helper_53;

            const double helper_55 = helper_36 * helper_51;

            const double helper_56 = 4 * helper_3;

            const double helper_57 = helper_31 * helper_56;

            const double helper_58 = helper_22 * def_grad(3) + helper_48 - helper_49;

            const double helper_59 = helper_56 * def_grad(3);

            const double helper_60 = -helper_33 * helper_45 + helper_44 + helper_57 * def_grad(2) - helper_58 * helper_59;

            const double helper_61 = helper_9 * (-c2 * helper_60 + c3 * helper_25 * helper_46 + c3 * helper_42 * helper_60 - d1 * helper_44 + 2 * d1 * helper_5 * def_grad(2) * def_grad(3) - helper_46 * helper_47 - helper_50 * helper_52 - helper_54 * helper_55);

            const double helper_62 = 2 * helper_21;

            const double helper_63 = def_grad(0) * def_grad(1);

            const double helper_64 = helper_21 * helper_38 + helper_45 - helper_63;

            const double helper_65 = helper_14 * def_grad(2);

            const double helper_66 = helper_15 * def_grad(2);

            const double helper_67 = helper_22 * helper_37 + helper_35 * def_grad(1) + 2 * helper_65 - 2 * helper_66;

            const double helper_68 = 2 * def_grad(2);

            const double helper_69 = helper_38 * def_grad(1) + helper_68;

            const double helper_70 = helper_22 * def_grad(0) + helper_65 - helper_66;

            const double helper_71 = -helper_21 * helper_33 + helper_57 * def_grad(1) - helper_59 * helper_70 + helper_62;

            const double helper_72 = helper_9 * (-c2 * helper_71 + c3 * helper_25 * helper_64 + c3 * helper_42 * helper_71 + 2 * d1 * helper_5 * def_grad(1) * def_grad(3) - d1 * helper_62 - helper_47 * helper_64 - helper_52 * helper_67 - helper_55 * helper_69);

            const double helper_73 = 3 * helper_10 + helper_11 + helper_13 - helper_17 * helper_38 + 3 * helper_4;

            const double helper_74 = helper_14 * helper_27 - helper_15 * helper_27 + helper_22 * helper_53 - helper_35 * def_grad(0);

            const double helper_75 = helper_3 * helper_30;

            const double helper_76 = helper_27 - helper_75;

            const double helper_77 = helper_40 * helper_76;

            const double helper_78 = helper_14 * def_grad(3) - helper_15 * def_grad(3) + helper_22 * def_grad(1);

            const double helper_79 = -4 * helper_0 + 3 * helper_23 * helper_9 * def_grad(0) * def_grad(3) - helper_35 - helper_57 * def_grad(0) - helper_59 * helper_78 + 2 * def_grad(1) * def_grad(2);

            const double helper_80 = c2 * helper_3;

            const double helper_81 = helper_3 * (-c1 * helper_3 * helper_73 + (1.0 / 2.0) * c3 * helper_25 * helper_3 * helper_73 + c3 * helper_3 * helper_42 * helper_79 + 2 * d1 * helper_3 * def_grad(0) * def_grad(3) - helper_0 * helper_8 - helper_36 * helper_77 - helper_41 * helper_74 + helper_7 - helper_79 * helper_80);

            const double helper_82 = 2 * helper_1;

            const double helper_83 = helper_3 * helper_82 + 1;

            const double helper_84 = helper_13 * helper_16 + helper_83;

            const double helper_85 = helper_32 * helper_58 + helper_33 * def_grad(2) - helper_68;

            const double helper_86 = helper_40 * helper_54;

            const double helper_87 = helper_10 + 3 * helper_11 + 3 * helper_13 + helper_38 * helper_82 + helper_4;

            const double helper_88 = helper_40 * helper_69;

            const double helper_89 = helper_56 * def_grad(2);

            const double helper_90 = helper_56 * helper_58;

            const double helper_91 = helper_1 * helper_33 - 4 * helper_1 + helper_17 + helper_35 + helper_70 * helper_89 + helper_90 * def_grad(1);

            const double helper_92 = helper_3 * (c1 * helper_3 * helper_87 + c3 * helper_3 * helper_42 * helper_91 + 2 * d1 * helper_3 * def_grad(1) * def_grad(2) - helper_1 * helper_8 - 1.0 / 2.0 * helper_26 * helper_3 * helper_87 - helper_50 * helper_88 - helper_67 * helper_86 - helper_7 - helper_80 * helper_91);

            const double helper_93 = helper_20 * helper_38 - helper_45 + helper_63;

            const double helper_94 = helper_51 * helper_74;

            const double helper_95 = helper_51 * helper_76;

            const double helper_96 = -helper_20 * helper_33 + 2 * helper_20 + helper_78 * helper_89 - helper_90 * def_grad(0);

            const double helper_97 = helper_9 * (-c2 * helper_96 + c3 * helper_25 * helper_93 + c3 * helper_42 * helper_96 + 2 * d1 * helper_5 * def_grad(0) * def_grad(2) - helper_20 * helper_6 - helper_47 * helper_93 - helper_50 * helper_95 - helper_54 * helper_94);

            const double helper_98 = helper_11 * helper_16 + helper_83;

            const double helper_99 = helper_32 * helper_70 + helper_33 * def_grad(1) - helper_53;

            const double helper_100 = helper_37 * def_grad(1);

            const double helper_101 = helper_20 - helper_21 + helper_75 * def_grad(1);

            const double helper_102 = helper_100 - helper_33 * helper_63 - helper_56 * helper_70 * def_grad(0) + helper_56 * helper_78 * def_grad(1);

            const double helper_103 = helper_9 * (-c2 * helper_102 + c3 * helper_101 * helper_25 + c3 * helper_102 * helper_42 - d1 * helper_100 + 2 * d1 * helper_5 * def_grad(0) * def_grad(1) - helper_101 * helper_47 - helper_67 * helper_95 - helper_69 * helper_94);

            const double helper_104 = helper_10 * helper_16 + helper_18;

            const double helper_105 = helper_32 * helper_78 - helper_33 * def_grad(0) + helper_37;

            hessian(0, 0) = helper_3 * (2 * c1 * helper_19 + c2 * helper_3 * helper_34 * def_grad(3) + 2 * d1 * helper_3 * helper_4 - helper_19 * helper_26 - helper_34 * helper_43 * def_grad(3) - 2 * helper_36 * helper_41 - helper_4 * helper_8);

            hessian(0, 1) = helper_61;

            hessian(0, 2) = helper_72;

            hessian(0, 3) = helper_81;

            hessian(1, 0) = helper_61;

            hessian(1, 1) = helper_3 * (2 * c1 * helper_84 + c3 * helper_3 * helper_42 * helper_85 * def_grad(2) + 2 * d1 * helper_13 * helper_3 - helper_13 * helper_8 - helper_26 * helper_84 - 2 * helper_50 * helper_86 - helper_80 * helper_85 * def_grad(2));

            hessian(1, 2) = helper_92;

            hessian(1, 3) = helper_97;

            hessian(2, 0) = helper_72;

            hessian(2, 1) = helper_92;

            hessian(2, 2) = helper_3 * (2 * c1 * helper_98 + c3 * helper_3 * helper_42 * helper_99 * def_grad(1) + 2 * d1 * helper_11 * helper_3 - helper_11 * helper_8 - helper_26 * helper_98 - 2 * helper_67 * helper_88 - helper_80 * helper_99 * def_grad(1));

            hessian(2, 3) = helper_103;

            hessian(3, 0) = helper_81;

            hessian(3, 1) = helper_97;

            hessian(3, 2) = helper_103;

            hessian(3, 3) = helper_3 * (2 * c1 * helper_104 + c2 * helper_105 * helper_3 * def_grad(0) + 2 * d1 * helper_10 * helper_3 - helper_10 * helper_8 - helper_104 * helper_26 - helper_105 * helper_43 * def_grad(0) - 2 * helper_74 * helper_77);

        }


        template <>


        void generate_gradient_templated(const double c1, const double c2, const double c3, const double d1, const Eigen::Matrix<double, 3, 3> &def_grad, Eigen::Matrix<double, 3, 3> &gradient)

        {


            const double helper_0 = def_grad(4) * def_grad(8);

            const double helper_1 = def_grad(5) * def_grad(6);

            const double helper_2 = def_grad(3) * def_grad(7);

            const double helper_3 = def_grad(5) * def_grad(7);

            const double helper_4 = def_grad(3) * def_grad(8);

            const double helper_5 = def_grad(4) * def_grad(6);

            const double helper_6 = helper_0 * def_grad(0) + helper_1 * def_grad(1) + helper_2 * def_grad(2) - helper_3 * def_grad(0) - helper_4 * def_grad(1) - helper_5 * def_grad(2);

            const double helper_7 = 1.0 / helper_6;

            const double helper_8 = helper_0 - helper_3;

            const double helper_9 = helper_7 * helper_8;

            const double helper_10 = d1 * log(helper_6);

            const double helper_11 = pow(helper_6, -2.0 / 3.0);

            const double helper_12 = 3 * def_grad(0);

            const double helper_13 = def_grad(0) * def_grad(0) + def_grad(1) * def_grad(1) + def_grad(2) * def_grad(2);

            const double helper_14 = def_grad(3) * def_grad(3) + def_grad(4) * def_grad(4) + def_grad(5) * def_grad(5);

            const double helper_15 = def_grad(6) * def_grad(6) + def_grad(7) * def_grad(7) + def_grad(8) * def_grad(8);

            const double helper_16 = helper_13 + helper_14 + helper_15;

            const double helper_17 = helper_11 * (-helper_12 + helper_16 * helper_9);

            const double helper_18 = (1.0 / 3.0) * c1;

            const double helper_19 = pow(helper_6, -4.0 / 3.0);

            const double helper_20 = def_grad(0) * def_grad(3) + def_grad(1) * def_grad(4) + def_grad(2) * def_grad(5);

            const double helper_21 = def_grad(0) * def_grad(6) + def_grad(1) * def_grad(7) + def_grad(2) * def_grad(8);

            const double helper_22 = def_grad(3) * def_grad(6) + def_grad(4) * def_grad(7) + def_grad(5) * def_grad(8);

            const double helper_23 = helper_13 * helper_13 + helper_14 * helper_14 + helper_15 * helper_15 - helper_16 * helper_16 + 2 * helper_20 * helper_20 + 2 * helper_21 * helper_21 + 2 * helper_22 * helper_22;

            const double helper_24 = (1.0 / 6.0) * c3;

            const double helper_25 = helper_24 * (helper_19 * helper_23 + 6);

            const double helper_26 = 3 * def_grad(3);

            const double helper_27 = 3 * def_grad(6);

            const double helper_28 = -helper_12 * helper_13 + 3 * helper_16 * def_grad(0) - helper_20 * helper_26 - helper_21 * helper_27 + helper_23 * helper_7 * helper_8;

            const double helper_29 = (1.0 / 3.0) * helper_19;

            const double helper_30 = c2 * helper_29;

            const double helper_31 = -helper_11 * helper_16 + 3;

            const double helper_32 = c3 * helper_29 * helper_31;

            const double helper_33 = helper_7 * (-helper_1 + helper_4);

            const double helper_34 = 3 * def_grad(1);

            const double helper_35 = helper_16 * helper_33 + helper_34;

            const double helper_36 = helper_11 * helper_24 * (helper_19 * helper_23 + 6);

            const double helper_37 = 3 * def_grad(4);

            const double helper_38 = 3 * def_grad(7);

            const double helper_39 = helper_13 * helper_34 - helper_16 * helper_34 + helper_20 * helper_37 + helper_21 * helper_38 + helper_23 * helper_33;

            const double helper_40 = helper_2 - helper_5;

            const double helper_41 = helper_40 * helper_7;

            const double helper_42 = 3 * def_grad(2);

            const double helper_43 = helper_16 * helper_41 - helper_42;

            const double helper_44 = helper_11 * helper_18;

            const double helper_45 = helper_11 * helper_25;

            const double helper_46 = 3 * def_grad(5);

            const double helper_47 = 3 * def_grad(8);

            const double helper_48 = -helper_13 * helper_42 + 3 * helper_16 * def_grad(2) - helper_20 * helper_46 - helper_21 * helper_47 + helper_23 * helper_40 * helper_7;

            const double helper_49 = helper_7 * (def_grad(1) * def_grad(8) - def_grad(2) * def_grad(7));

            const double helper_50 = helper_16 * helper_49 + helper_26;

            const double helper_51 = helper_12 * helper_20 + helper_14 * helper_26 - helper_16 * helper_26 + helper_22 * helper_27 + helper_23 * helper_49;

            const double helper_52 = def_grad(0) * def_grad(8) - def_grad(2) * def_grad(6);

            const double helper_53 = helper_52 * helper_7;

            const double helper_54 = helper_16 * helper_53 - helper_37;

            const double helper_55 = -helper_14 * helper_37 + 3 * helper_16 * def_grad(4) - helper_20 * helper_34 - helper_22 * helper_38 + helper_23 * helper_52 * helper_7;

            const double helper_56 = helper_7 * (def_grad(0) * def_grad(7) - def_grad(1) * def_grad(6));

            const double helper_57 = helper_16 * helper_56 + helper_46;

            const double helper_58 = helper_14 * helper_46 - helper_16 * helper_46 + helper_20 * helper_42 + helper_22 * helper_47 + helper_23 * helper_56;

            const double helper_59 = def_grad(1) * def_grad(5) - def_grad(2) * def_grad(4);

            const double helper_60 = helper_59 * helper_7;

            const double helper_61 = helper_16 * helper_60 - helper_27;

            const double helper_62 = -helper_12 * helper_21 - helper_15 * helper_27 + 3 * helper_16 * def_grad(6) - helper_22 * helper_26 + helper_23 * helper_59 * helper_7;

            const double helper_63 = helper_7 * (def_grad(0) * def_grad(5) - def_grad(2) * def_grad(3));

            const double helper_64 = helper_16 * helper_63 + helper_38;

            const double helper_65 = helper_15 * helper_38 - helper_16 * helper_38 + helper_21 * helper_34 + helper_22 * helper_37 + helper_23 * helper_63;

            const double helper_66 = def_grad(0) * def_grad(4) - def_grad(1) * def_grad(3);

            const double helper_67 = helper_66 * helper_7;

            const double helper_68 = helper_16 * helper_67 - helper_47;

            const double helper_69 = -helper_15 * helper_47 + 3 * helper_16 * def_grad(8) - helper_21 * helper_42 - helper_22 * helper_46 + helper_23 * helper_66 * helper_7;

            gradient(0, 0) = 2 * helper_10 * helper_9 - 2 * helper_17 * helper_18 + 2 * helper_17 * helper_25 + 2 * helper_28 * helper_30 - 2 * helper_28 * helper_32;

            gradient(0, 1) = (2.0 / 3.0) * c1 * helper_11 * helper_35 + (2.0 / 3.0) * c3 * helper_19 * helper_31 * helper_39 - 2 * helper_10 * helper_33 - 2 * helper_30 * helper_39 - 2 * helper_35 * helper_36;

            gradient(0, 2) = 2 * helper_10 * helper_41 + 2 * helper_30 * helper_48 - 2 * helper_32 * helper_48 - 2 * helper_43 * helper_44 + 2 * helper_43 * helper_45;

            gradient(1, 0) = (2.0 / 3.0) * c1 * helper_11 * helper_50 + (2.0 / 3.0) * c3 * helper_19 * helper_31 * helper_51 - 2 * helper_10 * helper_49 - 2 * helper_30 * helper_51 - 2 * helper_36 * helper_50;

            gradient(1, 1) = 2 * helper_10 * helper_53 + 2 * helper_30 * helper_55 - 2 * helper_32 * helper_55 - 2 * helper_44 * helper_54 + 2 * helper_45 * helper_54;

            gradient(1, 2) = (2.0 / 3.0) * c1 * helper_11 * helper_57 + (2.0 / 3.0) * c3 * helper_19 * helper_31 * helper_58 - 2 * helper_10 * helper_56 - 2 * helper_30 * helper_58 - 2 * helper_36 * helper_57;

            gradient(2, 0) = 2 * helper_10 * helper_60 + 2 * helper_30 * helper_62 - 2 * helper_32 * helper_62 - 2 * helper_44 * helper_61 + 2 * helper_45 * helper_61;

            gradient(2, 1) = (2.0 / 3.0) * c1 * helper_11 * helper_64 + (2.0 / 3.0) * c3 * helper_19 * helper_31 * helper_65 - 2 * helper_10 * helper_63 - 2 * helper_30 * helper_65 - 2 * helper_36 * helper_64;

            gradient(2, 2) = 2 * helper_10 * helper_67 + 2 * helper_30 * helper_69 - 2 * helper_32 * helper_69 - 2 * helper_44 * helper_68 + 2 * helper_45 * helper_68;

        }


        template <>


        void generate_hessian_templated(const double c1, const double c2, const double c3, const double d1, const Eigen::Matrix<double, 3, 3> &def_grad, Eigen::Matrix<double, 9, 9> &hessian)

        {


            const double helper_0 = def_grad(4) * def_grad(8);

            const double helper_1 = def_grad(5) * def_grad(7);

            const double helper_2 = helper_0 - helper_1;

            const double helper_3 = helper_2 * helper_2;

            const double helper_4 = def_grad(5) * def_grad(6);

            const double helper_5 = def_grad(3) * def_grad(7);

            const double helper_6 = def_grad(3) * def_grad(8);

            const double helper_7 = def_grad(4) * def_grad(6);

            const double helper_8 = helper_0 * def_grad(0) - helper_1 * def_grad(0) + helper_4 * def_grad(1) + helper_5 * def_grad(2) - helper_6 * def_grad(1) - helper_7 * def_grad(2);

            const double helper_9 = pow(helper_8, -2);

            const double helper_10 = log(helper_8);

            const double helper_11 = d1 * helper_9;

            const double helper_12 = pow(helper_8, -2.0 / 3.0);

            const double helper_13 = 1.0 / helper_8;

            const double helper_14 = helper_13 * helper_2;

            const double helper_15 = 12 * helper_14;

            const double helper_16 = helper_3 * helper_9;

            const double helper_17 = def_grad(0) * def_grad(0);

            const double helper_18 = def_grad(1) * def_grad(1);

            const double helper_19 = def_grad(2) * def_grad(2);

            const double helper_20 = helper_17 + helper_18 + helper_19;

            const double helper_21 = def_grad(3) * def_grad(3);

            const double helper_22 = def_grad(4) * def_grad(4);

            const double helper_23 = def_grad(5) * def_grad(5);

            const double helper_24 = helper_21 + helper_22 + helper_23;

            const double helper_25 = def_grad(6) * def_grad(6);

            const double helper_26 = def_grad(7) * def_grad(7);

            const double helper_27 = def_grad(8) * def_grad(8);

            const double helper_28 = helper_25 + helper_26 + helper_27;

            const double helper_29 = helper_20 + helper_24 + helper_28;

            const double helper_30 = 5 * helper_29;

            const double helper_31 = -helper_15 * def_grad(0) + helper_16 * helper_30 + 9;

            const double helper_32 = pow(helper_8, -4.0 / 3.0);

            const double helper_33 = def_grad(0) * def_grad(3);

            const double helper_34 = def_grad(1) * def_grad(4);

            const double helper_35 = def_grad(2) * def_grad(5);

            const double helper_36 = helper_33 + helper_34 + helper_35;

            const double helper_37 = def_grad(0) * def_grad(6);

            const double helper_38 = def_grad(1) * def_grad(7);

            const double helper_39 = def_grad(2) * def_grad(8);

            const double helper_40 = helper_37 + helper_38 + helper_39;

            const double helper_41 = def_grad(3) * def_grad(6);

            const double helper_42 = def_grad(4) * def_grad(7);

            const double helper_43 = def_grad(5) * def_grad(8);

            const double helper_44 = helper_41 + helper_42 + helper_43;

            const double helper_45 = helper_20 * helper_20 + helper_24 * helper_24 + helper_28 * helper_28 - helper_29 * helper_29 + 2 * helper_36 * helper_36 + 2 * helper_40 * helper_40 + 2 * helper_44 * helper_44;

            const double helper_46 = helper_32 * helper_45 + 6;

            const double helper_47 = (1.0 / 18.0) * c3 * helper_46;

            const double helper_48 = 7 * helper_45;

            const double helper_49 = helper_20 * def_grad(0);

            const double helper_50 = helper_36 * def_grad(3);

            const double helper_51 = helper_40 * def_grad(6);

            const double helper_52 = helper_29 * def_grad(0);

            const double helper_53 = helper_49 + helper_50 + helper_51 - helper_52;

            const double helper_54 = 9 * helper_23;

            const double helper_55 = 9 * helper_27;

            const double helper_56 = helper_54 + helper_55;

            const double helper_57 = 9 * helper_22;

            const double helper_58 = 9 * helper_26;

            const double helper_59 = helper_57 + helper_58;

            const double helper_60 = 24 * helper_14 * helper_53 - helper_16 * helper_48 + helper_56 + helper_59;

            const double helper_61 = helper_13 * helper_2 * helper_45 + 3 * helper_29 * def_grad(0) - 3 * helper_49 - 3 * helper_50 - 3 * helper_51;

            const double helper_62 = 3 * def_grad(0);

            const double helper_63 = helper_14 * helper_29;

            const double helper_64 = c3 * helper_9;

            const double helper_65 = helper_64 * (-helper_62 + helper_63);

            const double helper_66 = -helper_12 * helper_29 + 3;

            const double helper_67 = (1.0 / 9.0) * helper_32;

            const double helper_68 = c3 * helper_66 * helper_67;

            const double helper_69 = -helper_4 + helper_6;

            const double helper_70 = helper_11 * helper_2;

            const double helper_71 = helper_69 * helper_70;

            const double helper_72 = 6 * def_grad(0);

            const double helper_73 = 6 * helper_2;

            const double helper_74 = 5 * helper_63;

            const double helper_75 = -helper_69 * helper_72 + helper_69 * helper_74 + helper_73 * def_grad(1);

            const double helper_76 = pow(helper_8, -5.0 / 3.0);

            const double helper_77 = (1.0 / 9.0) * c1 * helper_76;

            const double helper_78 = helper_47 * helper_76;

            const double helper_79 = 3 * def_grad(1);

            const double helper_80 = helper_13 * helper_69;

            const double helper_81 = helper_29 * helper_80;

            const double helper_82 = helper_64 * (helper_79 + helper_81);

            const double helper_83 = (2.0 / 9.0) * helper_61;

            const double helper_84 = helper_20 * def_grad(1);

            const double helper_85 = helper_36 * def_grad(4);

            const double helper_86 = helper_40 * def_grad(7);

            const double helper_87 = helper_29 * def_grad(1);

            const double helper_88 = 3 * helper_87;

            const double helper_89 = -helper_88;

            const double helper_90 = helper_45 * helper_80 + 3 * helper_84 + 3 * helper_85 + 3 * helper_86 + helper_89;

            const double helper_91 = (2.0 / 9.0) * helper_65;

            const double helper_92 = 9 * def_grad(3);

            const double helper_93 = helper_92 * def_grad(4);

            const double helper_94 = 9 * def_grad(6);

            const double helper_95 = helper_94 * def_grad(7);

            const double helper_96 = 12 * helper_53;

            const double helper_97 = helper_84 + helper_85 + helper_86 - helper_87;

            const double helper_98 = helper_48 * helper_9;

            const double helper_99 = helper_2 * helper_98;

            const double helper_100 = -helper_15 * helper_97 - helper_69 * helper_99 + helper_80 * helper_96 + helper_93 + helper_95;

            const double helper_101 = c2 * helper_67;

            const double helper_102 = 2 * helper_10 * helper_71 - 2 * helper_100 * helper_101 + 2 * helper_100 * helper_68 - 2 * helper_71 - 2 * helper_75 * helper_77 + 2 * helper_75 * helper_78 + 2 * helper_82 * helper_83 + 2 * helper_90 * helper_91;

            const double helper_103 = helper_5 - helper_7;

            const double helper_104 = helper_103 * helper_72 - helper_103 * helper_74 + helper_73 * def_grad(2);

            const double helper_105 = 3 * def_grad(2);

            const double helper_106 = helper_103 * helper_13;

            const double helper_107 = helper_106 * helper_29;

            const double helper_108 = -helper_105 + helper_107;

            const double helper_109 = helper_64 * helper_83;

            const double helper_110 = helper_20 * def_grad(2);

            const double helper_111 = helper_36 * def_grad(5);

            const double helper_112 = helper_40 * def_grad(8);

            const double helper_113 = helper_29 * def_grad(2);

            const double helper_114 = 3 * helper_113;

            const double helper_115 = -helper_114;

            const double helper_116 = helper_103 * helper_13 * helper_45 - 3 * helper_110 - 3 * helper_111 - 3 * helper_112 - helper_115;

            const double helper_117 = helper_92 * def_grad(5);

            const double helper_118 = helper_94 * def_grad(8);

            const double helper_119 = helper_110 + helper_111 + helper_112 - helper_113;

            const double helper_120 = helper_103 * helper_99 - helper_106 * helper_96 + helper_117 + helper_118 - helper_119 * helper_15;

            const double helper_121 = (1.0 / 9.0) * c3 * helper_104 * helper_46 * helper_76 + (2.0 / 9.0) * c3 * helper_120 * helper_32 * helper_66 + 2 * d1 * helper_103 * helper_2 * helper_9 - 2 * helper_10 * helper_103 * helper_70 - 2 * helper_101 * helper_120 - 2 * helper_104 * helper_77 - 2 * helper_108 * helper_109 - 2 * helper_116 * helper_91;

            const double helper_122 = def_grad(1) * def_grad(8);

            const double helper_123 = def_grad(2) * def_grad(7);

            const double helper_124 = helper_122 - helper_123;

            const double helper_125 = helper_124 * helper_70;

            const double helper_126 = -helper_124 * helper_72 + helper_124 * helper_74 + helper_73 * def_grad(3);

            const double helper_127 = 3 * def_grad(3);

            const double helper_128 = helper_124 * helper_13;

            const double helper_129 = helper_128 * helper_29;

            const double helper_130 = helper_127 + helper_129;

            const double helper_131 = helper_24 * def_grad(3);

            const double helper_132 = helper_44 * def_grad(6);

            const double helper_133 = helper_29 * def_grad(3);

            const double helper_134 = 3 * helper_133;

            const double helper_135 = -helper_134;

            const double helper_136 = helper_128 * helper_45 + 3 * helper_131 + 3 * helper_132 + helper_135 + helper_36 * helper_62;

            const double helper_137 = 9 * helper_34;

            const double helper_138 = 9 * helper_35;

            const double helper_139 = helper_131 + helper_132 - helper_133 + helper_36 * def_grad(0);

            const double helper_140 = -helper_124 * helper_99 + helper_128 * helper_96 + helper_137 + helper_138 - helper_139 * helper_15;

            const double helper_141 = 2 * helper_10 * helper_125 - 2 * helper_101 * helper_140 + 2 * helper_109 * helper_130 - 2 * helper_125 - 2 * helper_126 * helper_77 + 2 * helper_126 * helper_78 + 2 * helper_136 * helper_91 + 2 * helper_140 * helper_68;

            const double helper_142 = def_grad(0) * def_grad(8);

            const double helper_143 = def_grad(2) * def_grad(6);

            const double helper_144 = helper_142 - helper_143;

            const double helper_145 = d1 * helper_10 * helper_13;

            const double helper_146 = helper_145 * def_grad(8);

            const double helper_147 = helper_29 * def_grad(8);

            const double helper_148 = 3 * helper_147;

            const double helper_149 = helper_144 * helper_72 - helper_144 * helper_74 + helper_148 + helper_73 * def_grad(4);

            const double helper_150 = 3 * def_grad(4);

            const double helper_151 = helper_13 * helper_144;

            const double helper_152 = helper_151 * helper_29;

            const double helper_153 = -helper_150 + helper_152;

            const double helper_154 = helper_24 * def_grad(4);

            const double helper_155 = helper_44 * def_grad(7);

            const double helper_156 = helper_29 * def_grad(4);

            const double helper_157 = 3 * helper_156;

            const double helper_158 = helper_13 * helper_144 * helper_45 - 3 * helper_154 - 3 * helper_155 + helper_157 - helper_36 * helper_79;

            const double helper_159 = def_grad(0) * def_grad(4);

            const double helper_160 = def_grad(1) * def_grad(3);

            const double helper_161 = helper_154 + helper_155 - helper_156 + helper_36 * def_grad(1);

            const double helper_162 = 3 * def_grad(8);

            const double helper_163 = helper_13 * helper_45;

            const double helper_164 = helper_162 * helper_163;

            const double helper_165 = -helper_144 * helper_99 + helper_15 * helper_161 + helper_151 * helper_96 + 18 * helper_159 - 9 * helper_160 + helper_164;

            const double helper_166 = (2.0 / 9.0) * c2 * helper_165 * helper_32 + (1.0 / 9.0) * c3 * helper_149 * helper_46 * helper_76 + 2 * d1 * helper_144 * helper_2 * helper_9 - 2 * helper_10 * helper_144 * helper_70 - 2 * helper_109 * helper_153 + 2 * helper_146 - 2 * helper_149 * helper_77 - 2 * helper_158 * helper_91 - 2 * helper_165 * helper_68;

            const double helper_167 = def_grad(0) * def_grad(7);

            const double helper_168 = def_grad(1) * def_grad(6);

            const double helper_169 = helper_167 - helper_168;

            const double helper_170 = helper_29 * def_grad(7);

            const double helper_171 = 3 * helper_170;

            const double helper_172 = -helper_171;

            const double helper_173 = -helper_169 * helper_72 + helper_169 * helper_74 + helper_172 + helper_73 * def_grad(5);

            const double helper_174 = def_grad(0) * def_grad(5);

            const double helper_175 = def_grad(2) * def_grad(3);

            const double helper_176 = helper_13 * helper_169;

            const double helper_177 = helper_24 * def_grad(5);

            const double helper_178 = helper_44 * def_grad(8);

            const double helper_179 = helper_29 * def_grad(5);

            const double helper_180 = helper_177 + helper_178 - helper_179 + helper_36 * def_grad(2);

            const double helper_181 = 3 * def_grad(7);

            const double helper_182 = helper_163 * helper_181;

            const double helper_183 = helper_15 * helper_180 + helper_169 * helper_99 + 18 * helper_174 - 9 * helper_175 - helper_176 * helper_96 - helper_182;

            const double helper_184 = helper_145 * def_grad(7);

            const double helper_185 = helper_169 * helper_70;

            const double helper_186 = 3 * helper_179;

            const double helper_187 = -helper_186;

            const double helper_188 = helper_105 * helper_36 + helper_176 * helper_45 + 3 * helper_177 + 3 * helper_178 + helper_187;

            const double helper_189 = 3 * def_grad(5);

            const double helper_190 = helper_176 * helper_29;

            const double helper_191 = helper_189 + helper_190;

            const double helper_192 = helper_10 * helper_185 + helper_101 * helper_183 + helper_109 * helper_191 - helper_183 * helper_68 - helper_184 - helper_185 + helper_188 * helper_91;

            const double helper_193 = 9 * helper_38;

            const double helper_194 = 9 * helper_39;

            const double helper_195 = def_grad(1) * def_grad(5);

            const double helper_196 = def_grad(2) * def_grad(4);

            const double helper_197 = helper_195 - helper_196;

            const double helper_198 = helper_13 * helper_197;

            const double helper_199 = helper_28 * def_grad(6);

            const double helper_200 = helper_29 * def_grad(6);

            const double helper_201 = helper_199 - helper_200 + helper_40 * def_grad(0) + helper_44 * def_grad(3);

            const double helper_202 = -helper_15 * helper_201 + helper_193 + helper_194 + helper_197 * helper_99 - helper_198 * helper_96;

            const double helper_203 = helper_197 * helper_72 - helper_197 * helper_74 + helper_73 * def_grad(6);

            const double helper_204 = 3 * helper_200;

            const double helper_205 = -helper_204;

            const double helper_206 = -helper_127 * helper_44 + helper_13 * helper_197 * helper_45 - 3 * helper_199 - helper_205 - helper_40 * helper_62;

            const double helper_207 = 3 * def_grad(6);

            const double helper_208 = helper_198 * helper_29;

            const double helper_209 = -helper_207 + helper_208;

            const double helper_210 = -1.0 / 18.0 * c3 * helper_203 * helper_46 * helper_76 - d1 * helper_197 * helper_2 * helper_9 + helper_10 * helper_197 * helper_70 + helper_109 * helper_209 + helper_203 * helper_77 + helper_206 * helper_91;

            const double helper_211 = helper_174 - helper_175;

            const double helper_212 = helper_187 - helper_211 * helper_72 + helper_211 * helper_74 + helper_73 * def_grad(7);

            const double helper_213 = helper_13 * helper_211;

            const double helper_214 = helper_28 * def_grad(7);

            const double helper_215 = -helper_170 + helper_214 + helper_40 * def_grad(1) + helper_44 * def_grad(4);

            const double helper_216 = helper_163 * helper_189;

            const double helper_217 = helper_15 * helper_215 + 18 * helper_167 - 9 * helper_168 + helper_211 * helper_99 - helper_213 * helper_96 - helper_216;

            const double helper_218 = helper_145 * def_grad(5);

            const double helper_219 = helper_211 * helper_70;

            const double helper_220 = helper_150 * helper_44 + helper_172 + helper_213 * helper_45 + 3 * helper_214 + helper_40 * helper_79;

            const double helper_221 = helper_213 * helper_29;

            const double helper_222 = helper_181 + helper_221;

            const double helper_223 = helper_10 * helper_219 + helper_101 * helper_217 + helper_109 * helper_222 - helper_217 * helper_68 - helper_218 - helper_219 + helper_220 * helper_91;

            const double helper_224 = helper_159 - helper_160;

            const double helper_225 = helper_145 * def_grad(4);

            const double helper_226 = helper_157 + helper_224 * helper_72 - helper_224 * helper_74 + helper_73 * def_grad(8);

            const double helper_227 = helper_13 * helper_224;

            const double helper_228 = -helper_162 + helper_227 * helper_29;

            const double helper_229 = helper_28 * def_grad(8);

            const double helper_230 = -helper_105 * helper_40 + helper_13 * helper_224 * helper_45 - helper_189 * helper_44 - 3 * helper_229 + 3 * helper_29 * def_grad(8);

            const double helper_231 = -helper_147 + helper_229 + helper_40 * def_grad(2) + helper_44 * def_grad(5);

            const double helper_232 = helper_150 * helper_163;

            const double helper_233 = 18 * helper_142 - 9 * helper_143 + helper_15 * helper_231 - helper_224 * helper_99 + helper_227 * helper_96 + helper_232;

            const double helper_234 = (2.0 / 9.0) * c2 * helper_233 * helper_32 + (1.0 / 9.0) * c3 * helper_226 * helper_46 * helper_76 + 2 * d1 * helper_2 * helper_224 * helper_9 - 2 * helper_10 * helper_224 * helper_70 - 2 * helper_109 * helper_228 + 2 * helper_225 - 2 * helper_226 * helper_77 - 2 * helper_230 * helper_91 - 2 * helper_233 * helper_68;

            const double helper_235 = helper_69 * helper_69;

            const double helper_236 = 12 * helper_80;

            const double helper_237 = helper_235 * helper_30 * helper_9 + helper_236 * def_grad(1) + 9;

            const double helper_238 = helper_12 * helper_47;

            const double helper_239 = 9 * helper_21;

            const double helper_240 = 9 * helper_25;

            const double helper_241 = helper_239 + helper_240;

            const double helper_242 = 24 * helper_13 * helper_69 * helper_97 + 7 * helper_235 * helper_45 * helper_9 - helper_241 - helper_56;

            const double helper_243 = helper_11 * helper_69;

            const double helper_244 = helper_103 * helper_243;

            const double helper_245 = 6 * def_grad(1);

            const double helper_246 = 6 * helper_69;

            const double helper_247 = 5 * helper_81;

            const double helper_248 = helper_103 * helper_245 + helper_103 * helper_247 - helper_246 * def_grad(2);

            const double helper_249 = helper_108 * helper_64;

            const double helper_250 = (2.0 / 9.0) * helper_90;

            const double helper_251 = (2.0 / 9.0) * helper_82;

            const double helper_252 = 9 * def_grad(4) * def_grad(5);

            const double helper_253 = 9 * def_grad(7) * def_grad(8);

            const double helper_254 = 12 * helper_103 * helper_13 * helper_97 + 7 * helper_103 * helper_45 * helper_69 * helper_9 - helper_119 * helper_236 - helper_252 - helper_253;

            const double helper_255 = 2 * helper_10 * helper_244 + 2 * helper_101 * helper_254 + 2 * helper_116 * helper_251 - 2 * helper_244 - 2 * helper_248 * helper_77 + 2 * helper_248 * helper_78 + 2 * helper_249 * helper_250 - 2 * helper_254 * helper_68;

            const double helper_256 = helper_124 * helper_245 + helper_124 * helper_247 + helper_148 + helper_246 * def_grad(3);

            const double helper_257 = helper_250 * helper_64;

            const double helper_258 = 12 * helper_97;

            const double helper_259 = helper_69 * helper_98;

            const double helper_260 = helper_124 * helper_259 + helper_128 * helper_258 + helper_139 * helper_236 + 9 * helper_159 - 18 * helper_160 + helper_164;

            const double helper_261 = (2.0 / 9.0) * c1 * helper_256 * helper_76 + (2.0 / 9.0) * c3 * helper_260 * helper_32 * helper_66 + 2 * d1 * helper_124 * helper_69 * helper_9 - 2 * helper_10 * helper_124 * helper_243 - 2 * helper_101 * helper_260 - 2 * helper_130 * helper_257 - 2 * helper_136 * helper_251 - 2 * helper_146 - 2 * helper_256 * helper_78;

            const double helper_262 = helper_144 * helper_243;

            const double helper_263 = helper_144 * helper_245 + helper_144 * helper_247 - helper_246 * def_grad(4);

            const double helper_264 = 9 * helper_33;

            const double helper_265 = helper_138 - helper_144 * helper_259 - helper_151 * helper_258 + helper_161 * helper_236 + helper_264;

            const double helper_266 = 2 * helper_10 * helper_262 - 2 * helper_101 * helper_265 + 2 * helper_153 * helper_257 + 2 * helper_158 * helper_251 - 2 * helper_262 - 2 * helper_263 * helper_77 + 2 * helper_263 * helper_78 + 2 * helper_265 * helper_68;

            const double helper_267 = helper_145 * def_grad(6);

            const double helper_268 = helper_169 * helper_245 + helper_169 * helper_247 + helper_205 + helper_246 * def_grad(5);

            const double helper_269 = helper_163 * helper_207;

            const double helper_270 = helper_169 * helper_259 + helper_176 * helper_258 + helper_180 * helper_236 - 18 * helper_195 + 9 * helper_196 - helper_269;

            const double helper_271 = (2.0 / 9.0) * c1 * helper_268 * helper_76 + (2.0 / 9.0) * c3 * helper_270 * helper_32 * helper_66 + 2 * d1 * helper_169 * helper_69 * helper_9 - 2 * helper_10 * helper_169 * helper_243 - 2 * helper_101 * helper_270 - 2 * helper_188 * helper_251 - 2 * helper_191 * helper_257 + 2 * helper_267 - 2 * helper_268 * helper_78;

            const double helper_272 = helper_197 * helper_243;

            const double helper_273 = helper_186 + helper_197 * helper_245 + helper_197 * helper_247 - helper_246 * def_grad(6);

            const double helper_274 = -9 * helper_167 + 18 * helper_168 + helper_197 * helper_259 + helper_198 * helper_258 - helper_201 * helper_236 + helper_216;

            const double helper_275 = 2 * helper_10 * helper_272 + 2 * helper_101 * helper_274 + 2 * helper_206 * helper_251 + 2 * helper_209 * helper_257 + 2 * helper_218 - 2 * helper_272 - 2 * helper_273 * helper_77 + 2 * helper_273 * helper_78 - 2 * helper_274 * helper_68;

            const double helper_276 = helper_211 * helper_245 + helper_211 * helper_247 + helper_246 * def_grad(7);

            const double helper_277 = 9 * helper_37;

            const double helper_278 = helper_194 + helper_211 * helper_259 + helper_213 * helper_258 + helper_215 * helper_236 + helper_277;

            const double helper_279 = (2.0 / 9.0) * c1 * helper_276 * helper_76 + (2.0 / 9.0) * c3 * helper_278 * helper_32 * helper_66 + 2 * d1 * helper_211 * helper_69 * helper_9 - 2 * helper_10 * helper_211 * helper_243 - 2 * helper_101 * helper_278 - 2 * helper_220 * helper_251 - 2 * helper_222 * helper_257 - 2 * helper_276 * helper_78;

            const double helper_280 = helper_224 * helper_243;

            const double helper_281 = helper_145 * def_grad(3);

            const double helper_282 = helper_135 + helper_224 * helper_245 + helper_224 * helper_247 - helper_246 * def_grad(8);

            const double helper_283 = helper_127 * helper_163;

            const double helper_284 = 18 * helper_122 - 9 * helper_123 + helper_224 * helper_259 + helper_227 * helper_258 - helper_231 * helper_236 - helper_283;

            const double helper_285 = 2 * helper_10 * helper_280 + 2 * helper_101 * helper_284 + 2 * helper_228 * helper_257 + 2 * helper_230 * helper_251 - 2 * helper_280 - 2 * helper_281 - 2 * helper_282 * helper_77 + 2 * helper_282 * helper_78 - 2 * helper_284 * helper_68;

            const double helper_286 = helper_103 * helper_103;

            const double helper_287 = 12 * helper_106;

            const double helper_288 = helper_286 * helper_9;

            const double helper_289 = -helper_287 * def_grad(2) + helper_288 * helper_30 + 9;

            const double helper_290 = 24 * helper_106 * helper_119 + helper_241 - helper_288 * helper_48 + helper_59;

            const double helper_291 = helper_103 * helper_11;

            const double helper_292 = helper_124 * helper_291;

            const double helper_293 = 6 * def_grad(2);

            const double helper_294 = 6 * helper_103;

            const double helper_295 = 5 * helper_107;

            const double helper_296 = -helper_124 * helper_293 + helper_124 * helper_295 + helper_171 + helper_294 * def_grad(3);

            const double helper_297 = helper_130 * helper_64;

            const double helper_298 = (2.0 / 9.0) * helper_116;

            const double helper_299 = (2.0 / 9.0) * helper_249;

            const double helper_300 = 12 * helper_119;

            const double helper_301 = helper_103 * helper_98;

            const double helper_302 = helper_124 * helper_301 - helper_128 * helper_300 + helper_139 * helper_287 - 9 * helper_174 + 18 * helper_175 + helper_182;

            const double helper_303 = 2 * helper_10 * helper_292 + 2 * helper_101 * helper_302 + 2 * helper_136 * helper_299 + 2 * helper_184 - 2 * helper_292 - 2 * helper_296 * helper_77 + 2 * helper_296 * helper_78 + 2 * helper_297 * helper_298 - 2 * helper_302 * helper_68;

            const double helper_304 = -helper_144 * helper_293 + helper_144 * helper_295 + helper_204 - helper_294 * def_grad(4);

            const double helper_305 = helper_144 * helper_301 - helper_151 * helper_300 - helper_161 * helper_287 + 9 * helper_195 - 18 * helper_196 + helper_269;

            const double helper_306 = helper_298 * helper_64;

            const double helper_307 = -1.0 / 9.0 * c3 * helper_305 * helper_32 * helper_66 - d1 * helper_103 * helper_144 * helper_9 + helper_10 * helper_144 * helper_291 + helper_101 * helper_305 + helper_153 * helper_306 + helper_158 * helper_299 + helper_267;

            const double helper_308 = helper_169 * helper_291;

            const double helper_309 = -helper_169 * helper_293 + helper_169 * helper_295 + helper_294 * def_grad(5);

            const double helper_310 = helper_137 - helper_169 * helper_301 + helper_176 * helper_300 - helper_180 * helper_287 + helper_264;

            const double helper_311 = 2 * helper_10 * helper_308 - 2 * helper_101 * helper_310 + 2 * helper_188 * helper_299 + 2 * helper_191 * helper_306 - 2 * helper_308 - 2 * helper_309 * helper_77 + 2 * helper_309 * helper_78 + 2 * helper_310 * helper_68;

            const double helper_312 = helper_157 - helper_197 * helper_293 + helper_197 * helper_295 - helper_294 * def_grad(6);

            const double helper_313 = 9 * helper_142 - 18 * helper_143 + helper_197 * helper_301 - helper_198 * helper_300 - helper_201 * helper_287 + helper_232;

            const double helper_314 = -1.0 / 9.0 * c3 * helper_313 * helper_32 * helper_66 - d1 * helper_103 * helper_197 * helper_9 + helper_10 * helper_197 * helper_291 + helper_101 * helper_313 + helper_206 * helper_299 + helper_209 * helper_306 + helper_225;

            const double helper_315 = helper_211 * helper_291;

            const double helper_316 = helper_134 - helper_211 * helper_293 + helper_211 * helper_295 + helper_294 * def_grad(7);

            const double helper_317 = -9 * helper_122 + 18 * helper_123 + helper_211 * helper_301 - helper_213 * helper_300 + helper_215 * helper_287 + helper_283;

            const double helper_318 = 2 * helper_10 * helper_315 + 2 * helper_101 * helper_317 + 2 * helper_220 * helper_299 + 2 * helper_222 * helper_306 + 2 * helper_281 - 2 * helper_315 - 2 * helper_316 * helper_77 + 2 * helper_316 * helper_78 - 2 * helper_317 * helper_68;

            const double helper_319 = helper_193 + helper_224 * helper_301 - helper_227 * helper_300 - helper_231 * helper_287 + helper_277;

            const double helper_320 = helper_224 * helper_293 - helper_224 * helper_295 + helper_294 * def_grad(8);

            const double helper_321 = -1.0 / 18.0 * c3 * helper_320 * helper_46 * helper_76 - d1 * helper_103 * helper_224 * helper_9 + helper_10 * helper_224 * helper_291 + helper_228 * helper_306 + helper_230 * helper_299 + helper_320 * helper_77;

            const double helper_322 = helper_124 * helper_124;

            const double helper_323 = 12 * helper_128;

            const double helper_324 = helper_30 * helper_322 * helper_9 + helper_323 * def_grad(3) + 9;

            const double helper_325 = 9 * helper_19;

            const double helper_326 = helper_325 + helper_55;

            const double helper_327 = 9 * helper_18;

            const double helper_328 = helper_327 + helper_58;

            const double helper_329 = 24 * helper_124 * helper_13 * helper_139 + 7 * helper_322 * helper_45 * helper_9 - helper_326 - helper_328;

            const double helper_330 = helper_11 * helper_124;

            const double helper_331 = helper_144 * helper_330;

            const double helper_332 = 6 * def_grad(3);

            const double helper_333 = 6 * helper_124;

            const double helper_334 = 5 * helper_129;

            const double helper_335 = helper_144 * helper_332 + helper_144 * helper_334 - helper_333 * def_grad(4);

            const double helper_336 = helper_153 * helper_64;

            const double helper_337 = (2.0 / 9.0) * helper_136;

            const double helper_338 = (2.0 / 9.0) * helper_297;

            const double helper_339 = 9 * def_grad(0);

            const double helper_340 = helper_339 * def_grad(1);

            const double helper_341 = 12 * helper_139;

            const double helper_342 = helper_124 * helper_98;

            const double helper_343 = -helper_144 * helper_342 - helper_151 * helper_341 + helper_161 * helper_323 + helper_340 + helper_95;

            const double helper_344 = 2 * helper_10 * helper_331 - 2 * helper_101 * helper_343 + 2 * helper_158 * helper_338 - 2 * helper_331 - 2 * helper_335 * helper_77 + 2 * helper_335 * helper_78 + 2 * helper_336 * helper_337 + 2 * helper_343 * helper_68;

            const double helper_345 = helper_169 * helper_332 + helper_169 * helper_334 + helper_333 * def_grad(5);

            const double helper_346 = helper_337 * helper_64;

            const double helper_347 = helper_339 * def_grad(2);

            const double helper_348 = helper_118 + helper_169 * helper_342 + helper_176 * helper_341 + helper_180 * helper_323 + helper_347;

            const double helper_349 = (2.0 / 9.0) * c1 * helper_345 * helper_76 + (2.0 / 9.0) * c3 * helper_32 * helper_348 * helper_66 + 2 * d1 * helper_124 * helper_169 * helper_9 - 2 * helper_10 * helper_169 * helper_330 - 2 * helper_101 * helper_348 - 2 * helper_188 * helper_338 - 2 * helper_191 * helper_346 - 2 * helper_345 * helper_78;

            const double helper_350 = helper_197 * helper_330;

            const double helper_351 = helper_197 * helper_332 + helper_197 * helper_334 - helper_333 * def_grad(6);

            const double helper_352 = 9 * helper_42;

            const double helper_353 = 9 * helper_43;

            const double helper_354 = 7 * helper_124 * helper_197 * helper_45 * helper_9 + 12 * helper_13 * helper_139 * helper_197 - helper_201 * helper_323 - helper_352 - helper_353;

            const double helper_355 = 2 * helper_10 * helper_350 + 2 * helper_101 * helper_354 + 2 * helper_206 * helper_338 + 2 * helper_209 * helper_346 - 2 * helper_350 - 2 * helper_351 * helper_77 + 2 * helper_351 * helper_78 - 2 * helper_354 * helper_68;

            const double helper_356 = helper_145 * def_grad(2);

            const double helper_357 = helper_115 + helper_211 * helper_332 + helper_211 * helper_334 + helper_333 * def_grad(7);

            const double helper_358 = helper_105 * helper_163;

            const double helper_359 = helper_211 * helper_342 + helper_213 * helper_341 + helper_215 * helper_323 - helper_358 - 18 * helper_5 + 9 * helper_7;

            const double helper_360 = (2.0 / 9.0) * c1 * helper_357 * helper_76 + (2.0 / 9.0) * c3 * helper_32 * helper_359 * helper_66 + 2 * d1 * helper_124 * helper_211 * helper_9 - 2 * helper_10 * helper_211 * helper_330 - 2 * helper_101 * helper_359 - 2 * helper_220 * helper_338 - 2 * helper_222 * helper_346 + 2 * helper_356 - 2 * helper_357 * helper_78;

            const double helper_361 = helper_224 * helper_330;

            const double helper_362 = helper_145 * def_grad(1);

            const double helper_363 = helper_224 * helper_332 + helper_224 * helper_334 - helper_333 * def_grad(8) + helper_89;

            const double helper_364 = helper_163 * helper_79;

            const double helper_365 = helper_224 * helper_342 + helper_227 * helper_341 - helper_231 * helper_323 - helper_364 - 9 * helper_4 + 18 * helper_6;

            const double helper_366 = 2 * helper_10 * helper_361 + 2 * helper_101 * helper_365 + 2 * helper_228 * helper_346 + 2 * helper_230 * helper_338 - 2 * helper_361 - 2 * helper_362 - 2 * helper_363 * helper_77 + 2 * helper_363 * helper_78 - 2 * helper_365 * helper_68;

            const double helper_367 = -helper_304;

            const double helper_368 = helper_144 * helper_144;

            const double helper_369 = 12 * helper_151;

            const double helper_370 = helper_368 * helper_9;

            const double helper_371 = helper_30 * helper_370 - helper_369 * def_grad(4) + 9;

            const double helper_372 = 9 * helper_17;

            const double helper_373 = helper_240 + helper_372;

            const double helper_374 = 24 * helper_151 * helper_161 + helper_326 - helper_370 * helper_48 + helper_373;

            const double helper_375 = 9 * def_grad(1) * def_grad(2);

            const double helper_376 = 12 * helper_161;

            const double helper_377 = -12 * helper_13 * helper_144 * helper_180 - 7 * helper_144 * helper_169 * helper_45 * helper_9 + helper_176 * helper_376 + helper_253 + helper_375;

            const double helper_378 = -helper_377;

            const double helper_379 = 6 * def_grad(4);

            const double helper_380 = 6 * helper_144;

            const double helper_381 = 5 * helper_152;

            const double helper_382 = -helper_169 * helper_379 + helper_169 * helper_381 + helper_380 * def_grad(5);

            const double helper_383 = helper_11 * helper_144;

            const double helper_384 = helper_169 * helper_383;

            const double helper_385 = (2.0 / 9.0) * helper_336;

            const double helper_386 = helper_191 * helper_64;

            const double helper_387 = (2.0 / 9.0) * helper_158;

            const double helper_388 = helper_10 * helper_384 + helper_188 * helper_385 - helper_382 * helper_77 + helper_382 * helper_78 - helper_384 + helper_386 * helper_387;

            const double helper_389 = helper_114 - 6 * helper_144 * def_grad(6) + helper_197 * helper_381 - 6 * helper_197 * def_grad(4);

            const double helper_390 = -helper_389;

            const double helper_391 = helper_144 * helper_98;

            const double helper_392 = helper_197 * helper_391 - helper_198 * helper_376 - helper_201 * helper_369 + helper_358 + 9 * helper_5 - 18 * helper_7;

            const double helper_393 = helper_387 * helper_64;

            const double helper_394 = -1.0 / 9.0 * c3 * helper_32 * helper_392 * helper_66 - d1 * helper_144 * helper_197 * helper_9 + helper_10 * helper_197 * helper_383 + helper_101 * helper_392 + helper_206 * helper_385 + helper_209 * helper_393 + helper_356;

            const double helper_395 = 9 * helper_41;

            const double helper_396 = -12 * helper_13 * helper_144 * helper_215 - 7 * helper_144 * helper_211 * helper_45 * helper_9 + helper_213 * helper_376 + helper_353 + helper_395;

            const double helper_397 = -helper_396;

            const double helper_398 = -helper_211 * helper_379 + helper_211 * helper_381 + helper_380 * def_grad(7);

            const double helper_399 = helper_211 * helper_383;

            const double helper_400 = helper_10 * helper_399 + helper_220 * helper_385 + helper_222 * helper_393 - helper_398 * helper_77 + helper_398 * helper_78 - helper_399;

            const double helper_401 = helper_145 * def_grad(0);

            const double helper_402 = 3 * helper_52;

            const double helper_403 = helper_224 * helper_379 - helper_224 * helper_381 + helper_380 * def_grad(8) + helper_402;

            const double helper_404 = helper_163 * helper_62;

            const double helper_405 = 18 * helper_0 - 9 * helper_1 - helper_224 * helper_391 + helper_227 * helper_376 + helper_231 * helper_369 + helper_404;

            const double helper_406 = (2.0 / 9.0) * c2 * helper_32 * helper_405 + (1.0 / 9.0) * c3 * helper_403 * helper_46 * helper_76 + 2 * d1 * helper_144 * helper_224 * helper_9 - 2 * helper_10 * helper_224 * helper_383 - 2 * helper_228 * helper_393 - 2 * helper_230 * helper_385 + 2 * helper_401 - 2 * helper_403 * helper_77 - 2 * helper_405 * helper_68;

            const double helper_407 = -helper_173;

            const double helper_408 = helper_169 * helper_169;

            const double helper_409 = 12 * helper_176;

            const double helper_410 = helper_30 * helper_408 * helper_9 + helper_409 * def_grad(5) + 9;

            const double helper_411 = 24 * helper_13 * helper_169 * helper_180 - helper_328 - helper_373 + 7 * helper_408 * helper_45 * helper_9;

            const double helper_412 = helper_11 * helper_169;

            const double helper_413 = helper_197 * helper_412;

            const double helper_414 = 6 * helper_169;

            const double helper_415 = 6 * def_grad(5);

            const double helper_416 = 5 * helper_190;

            const double helper_417 = helper_197 * helper_415 + helper_197 * helper_416 - helper_414 * def_grad(6) + helper_88;

            const double helper_418 = (2.0 / 9.0) * helper_386;

            const double helper_419 = helper_209 * helper_64;

            const double helper_420 = (2.0 / 9.0) * helper_188;

            const double helper_421 = 12 * helper_180;

            const double helper_422 = helper_169 * helper_98;

            const double helper_423 = helper_197 * helper_422 + helper_198 * helper_421 - helper_201 * helper_409 + helper_364 + 18 * helper_4 - 9 * helper_6;

            const double helper_424 = 2 * helper_10 * helper_413 + 2 * helper_101 * helper_423 + 2 * helper_206 * helper_418 + 2 * helper_362 - 2 * helper_413 - 2 * helper_417 * helper_77 + 2 * helper_417 * helper_78 + 2 * helper_419 * helper_420 - 2 * helper_423 * helper_68;

            const double helper_425 = helper_211 * helper_415 + helper_211 * helper_416 + helper_402 + helper_414 * def_grad(7);

            const double helper_426 = helper_420 * helper_64;

            const double helper_427 = 9 * helper_0 - 18 * helper_1 + helper_211 * helper_422 + helper_213 * helper_421 + helper_215 * helper_409 + helper_404;

            const double helper_428 = (2.0 / 9.0) * c1 * helper_425 * helper_76 + (2.0 / 9.0) * c3 * helper_32 * helper_427 * helper_66 + 2 * d1 * helper_169 * helper_211 * helper_9 - 2 * helper_10 * helper_211 * helper_412 - 2 * helper_101 * helper_427 - 2 * helper_220 * helper_418 - 2 * helper_222 * helper_426 - 2 * helper_401 - 2 * helper_425 * helper_78;

            const double helper_429 = helper_224 * helper_412;

            const double helper_430 = helper_224 * helper_415 + helper_224 * helper_416 - helper_414 * def_grad(8);

            const double helper_431 = 12 * helper_13 * helper_180 * helper_224 + 7 * helper_169 * helper_224 * helper_45 * helper_9 - helper_231 * helper_409 - helper_352 - helper_395;

            const double helper_432 = 2 * helper_10 * helper_429 + 2 * helper_101 * helper_431 + 2 * helper_228 * helper_426 + 2 * helper_230 * helper_418 - 2 * helper_429 - 2 * helper_430 * helper_77 + 2 * helper_430 * helper_78 - 2 * helper_431 * helper_68;

            const double helper_433 = -helper_202;

            const double helper_434 = -helper_312;

            const double helper_435 = helper_197 * helper_197;

            const double helper_436 = 12 * helper_198;

            const double helper_437 = helper_435 * helper_9;

            const double helper_438 = helper_30 * helper_437 - helper_436 * def_grad(6) + 9;

            const double helper_439 = helper_325 + helper_54;

            const double helper_440 = helper_327 + helper_57;

            const double helper_441 = 24 * helper_198 * helper_201 - helper_437 * helper_48 + helper_439 + helper_440;

            const double helper_442 = helper_11 * helper_197;

            const double helper_443 = helper_211 * helper_442;

            const double helper_444 = 6 * def_grad(6);

            const double helper_445 = 6 * helper_197;

            const double helper_446 = 5 * helper_208;

            const double helper_447 = -helper_211 * helper_444 + helper_211 * helper_446 + helper_445 * def_grad(7);

            const double helper_448 = helper_222 * helper_64;

            const double helper_449 = (2.0 / 9.0) * helper_206;

            const double helper_450 = (2.0 / 9.0) * helper_419;

            const double helper_451 = 12 * helper_201;

            const double helper_452 = helper_197 * helper_98;

            const double helper_453 = -helper_211 * helper_452 + helper_213 * helper_451 - helper_215 * helper_436 + helper_340 + helper_93;

            const double helper_454 = 2 * helper_10 * helper_443 - 2 * helper_101 * helper_453 + 2 * helper_220 * helper_450 - 2 * helper_443 - 2 * helper_447 * helper_77 + 2 * helper_447 * helper_78 + 2 * helper_448 * helper_449 + 2 * helper_453 * helper_68;

            const double helper_455 = helper_224 * helper_444 - helper_224 * helper_446 + helper_445 * def_grad(8);

            const double helper_456 = helper_228 * helper_64;

            const double helper_457 = helper_117 + helper_224 * helper_452 - helper_227 * helper_451 - helper_231 * helper_436 + helper_347;

            const double helper_458 = (2.0 / 9.0) * c3 * helper_32 * helper_457 * helper_66 + (1.0 / 9.0) * c3 * helper_455 * helper_46 * helper_76 + 2 * d1 * helper_197 * helper_224 * helper_9 - 2 * helper_10 * helper_224 * helper_442 - 2 * helper_101 * helper_457 - 2 * helper_230 * helper_450 - 2 * helper_449 * helper_456 - 2 * helper_455 * helper_77;

            const double helper_459 = -helper_212;

            const double helper_460 = helper_211 * helper_211;

            const double helper_461 = 12 * helper_213;

            const double helper_462 = helper_30 * helper_460 * helper_9 + helper_461 * def_grad(7) + 9;

            const double helper_463 = helper_239 + helper_372;

            const double helper_464 = 24 * helper_13 * helper_211 * helper_215 - helper_439 + 7 * helper_45 * helper_460 * helper_9 - helper_463;

            const double helper_465 = helper_11 * helper_211 * helper_224;

            const double helper_466 = -6 * helper_211 * def_grad(8) + 5 * helper_221 * helper_224 + 6 * helper_224 * def_grad(7);

            const double helper_467 = 12 * helper_13 * helper_215 * helper_224 + 7 * helper_211 * helper_224 * helper_45 * helper_9 - helper_231 * helper_461 - helper_252 - helper_375;

            const double helper_468 = 2 * helper_10 * helper_465 + 2 * helper_101 * helper_467 + (4.0 / 9.0) * helper_220 * helper_456 + (4.0 / 9.0) * helper_230 * helper_448 - 2 * helper_465 - 2 * helper_466 * helper_77 + 2 * helper_466 * helper_78 - 2 * helper_467 * helper_68;

            const double helper_469 = -helper_319;

            const double helper_470 = helper_224 * helper_224;

            const double helper_471 = helper_470 * helper_9;

            const double helper_472 = -12 * helper_227 * def_grad(8) + helper_30 * helper_471 + 9;

            const double helper_473 = 24 * helper_227 * helper_231 + helper_440 + helper_463 - helper_471 * helper_48;

            hessian(0, 0) = (2.0 / 9.0) * c1 * helper_12 * helper_31 + (2.0 / 9.0) * c2 * helper_32 * helper_60 + 2 * d1 * helper_3 * helper_9 - 2 * helper_10 * helper_11 * helper_3 - 2 * helper_12 * helper_31 * helper_47 - 2 * helper_60 * helper_68 - 8.0 / 9.0 * helper_61 * helper_65;

            hessian(0, 1) = helper_102;

            hessian(0, 2) = helper_121;

            hessian(0, 3) = helper_141;

            hessian(0, 4) = helper_166;

            hessian(0, 5) = -2 * helper_173 * helper_77 + 2 * helper_173 * helper_78 + 2 * helper_192;

            hessian(0, 6) = (2.0 / 9.0) * c3 * helper_202 * helper_32 * helper_66 - 2 * helper_101 * helper_202 - 2 * helper_210;

            hessian(0, 7) = -2 * helper_212 * helper_77 + 2 * helper_212 * helper_78 + 2 * helper_223;

            hessian(0, 8) = helper_234;

            hessian(1, 0) = helper_102;

            hessian(1, 1) = (2.0 / 9.0) * c1 * helper_12 * helper_237 + (2.0 / 9.0) * c3 * helper_242 * helper_32 * helper_66 + 2 * d1 * helper_235 * helper_9 - 2 * helper_10 * helper_11 * helper_235 - 2 * helper_101 * helper_242 - 2 * helper_237 * helper_238 - 8.0 / 9.0 * helper_82 * helper_90;

            hessian(1, 2) = helper_255;

            hessian(1, 3) = helper_261;

            hessian(1, 4) = helper_266;

            hessian(1, 5) = helper_271;

            hessian(1, 6) = helper_275;

            hessian(1, 7) = helper_279;

            hessian(1, 8) = helper_285;

            hessian(2, 0) = helper_121;

            hessian(2, 1) = helper_255;

            hessian(2, 2) = (2.0 / 9.0) * c1 * helper_12 * helper_289 + (2.0 / 9.0) * c2 * helper_290 * helper_32 + 2 * d1 * helper_286 * helper_9 - 2 * helper_10 * helper_11 * helper_286 - 8.0 / 9.0 * helper_116 * helper_249 - 2 * helper_238 * helper_289 - 2 * helper_290 * helper_68;

            hessian(2, 3) = helper_303;

            hessian(2, 4) = (2.0 / 9.0) * c1 * helper_304 * helper_76 - 2 * helper_304 * helper_78 - 2 * helper_307;

            hessian(2, 5) = helper_311;

            hessian(2, 6) = (2.0 / 9.0) * c1 * helper_312 * helper_76 - 2 * helper_312 * helper_78 - 2 * helper_314;

            hessian(2, 7) = helper_318;

            hessian(2, 8) = (2.0 / 9.0) * c3 * helper_319 * helper_32 * helper_66 - 2 * helper_101 * helper_319 - 2 * helper_321;

            hessian(3, 0) = helper_141;

            hessian(3, 1) = helper_261;

            hessian(3, 2) = helper_303;

            hessian(3, 3) = (2.0 / 9.0) * c1 * helper_12 * helper_324 + (2.0 / 9.0) * c3 * helper_32 * helper_329 * helper_66 + 2 * d1 * helper_322 * helper_9 - 2 * helper_10 * helper_11 * helper_322 - 2 * helper_101 * helper_329 - 8.0 / 9.0 * helper_136 * helper_297 - 2 * helper_238 * helper_324;

            hessian(3, 4) = helper_344;

            hessian(3, 5) = helper_349;

            hessian(3, 6) = helper_355;

            hessian(3, 7) = helper_360;

            hessian(3, 8) = helper_366;

            hessian(4, 0) = helper_166;

            hessian(4, 1) = helper_266;

            hessian(4, 2) = (1.0 / 9.0) * c3 * helper_367 * helper_46 * helper_76 - 2 * helper_307 - 2 * helper_367 * helper_77;

            hessian(4, 3) = helper_344;

            hessian(4, 4) = (2.0 / 9.0) * c1 * helper_12 * helper_371 + (2.0 / 9.0) * c2 * helper_32 * helper_374 + 2 * d1 * helper_368 * helper_9 - 2 * helper_10 * helper_11 * helper_368 - 8.0 / 9.0 * helper_158 * helper_336 - 2 * helper_238 * helper_371 - 2 * helper_374 * helper_68;

            hessian(4, 5) = 2 * helper_101 * helper_378 - 2 * helper_378 * helper_68 + 2 * helper_388;

            hessian(4, 6) = (1.0 / 9.0) * c3 * helper_390 * helper_46 * helper_76 - 2 * helper_390 * helper_77 - 2 * helper_394;

            hessian(4, 7) = 2 * helper_101 * helper_397 - 2 * helper_397 * helper_68 + 2 * helper_400;

            hessian(4, 8) = helper_406;

            hessian(5, 0) = 2 * helper_192 + 2 * helper_407 * helper_77 - 2 * helper_407 * helper_78;

            hessian(5, 1) = helper_271;

            hessian(5, 2) = helper_311;

            hessian(5, 3) = helper_349;

            hessian(5, 4) = -2 * helper_101 * helper_377 + 2 * helper_377 * helper_68 + 2 * helper_388;

            hessian(5, 5) = (2.0 / 9.0) * c1 * helper_12 * helper_410 + (2.0 / 9.0) * c3 * helper_32 * helper_411 * helper_66 + 2 * d1 * helper_408 * helper_9 - 2 * helper_10 * helper_11 * helper_408 - 2 * helper_101 * helper_411 - 8.0 / 9.0 * helper_188 * helper_386 - 2 * helper_238 * helper_410;

            hessian(5, 6) = helper_424;

            hessian(5, 7) = helper_428;

            hessian(5, 8) = helper_432;

            hessian(6, 0) = (2.0 / 9.0) * c2 * helper_32 * helper_433 - 2 * helper_210 - 2 * helper_433 * helper_68;

            hessian(6, 1) = helper_275;

            hessian(6, 2) = (1.0 / 9.0) * c3 * helper_434 * helper_46 * helper_76 - 2 * helper_314 - 2 * helper_434 * helper_77;

            hessian(6, 3) = helper_355;

            hessian(6, 4) = (2.0 / 9.0) * c1 * helper_389 * helper_76 - 2 * helper_389 * helper_78 - 2 * helper_394;

            hessian(6, 5) = helper_424;

            hessian(6, 6) = (2.0 / 9.0) * c1 * helper_12 * helper_438 + (2.0 / 9.0) * c2 * helper_32 * helper_441 + 2 * d1 * helper_435 * helper_9 - 2 * helper_10 * helper_11 * helper_435 - 8.0 / 9.0 * helper_206 * helper_419 - 2 * helper_238 * helper_438 - 2 * helper_441 * helper_68;

            hessian(6, 7) = helper_454;

            hessian(6, 8) = helper_458;

            hessian(7, 0) = 2 * helper_223 + 2 * helper_459 * helper_77 - 2 * helper_459 * helper_78;

            hessian(7, 1) = helper_279;

            hessian(7, 2) = helper_318;

            hessian(7, 3) = helper_360;

            hessian(7, 4) = -2 * helper_101 * helper_396 + 2 * helper_396 * helper_68 + 2 * helper_400;

            hessian(7, 5) = helper_428;

            hessian(7, 6) = helper_454;

            hessian(7, 7) = (2.0 / 9.0) * c1 * helper_12 * helper_462 + (2.0 / 9.0) * c3 * helper_32 * helper_464 * helper_66 + 2 * d1 * helper_460 * helper_9 - 2 * helper_10 * helper_11 * helper_460 - 2 * helper_101 * helper_464 - 8.0 / 9.0 * helper_220 * helper_448 - 2 * helper_238 * helper_462;

            hessian(7, 8) = helper_468;

            hessian(8, 0) = helper_234;

            hessian(8, 1) = helper_285;

            hessian(8, 2) = (2.0 / 9.0) * c2 * helper_32 * helper_469 - 2 * helper_321 - 2 * helper_469 * helper_68;

            hessian(8, 3) = helper_366;

            hessian(8, 4) = helper_406;

            hessian(8, 5) = helper_432;

            hessian(8, 6) = helper_458;

            hessian(8, 7) = helper_468;

            hessian(8, 8) = (2.0 / 9.0) * c1 * helper_12 * helper_472 + (2.0 / 9.0) * c2 * helper_32 * helper_473 + 2 * d1 * helper_470 * helper_9 - 2 * helper_10 * helper_11 * helper_470 - 8.0 / 9.0 * helper_230 * helper_456 - 2 * helper_238 * helper_472 - 2 * helper_473 * helper_68;

        }


        void generate_gradient(const double c1, const double c2, const double c3, const double d1, const Eigen::MatrixXd &def_grad, Eigen::MatrixXd &gradient)

        {

            int dim = def_grad.rows();


            if (dim == 2)

            {

                Eigen::Matrix<double, 2, 2> temp;

                generate_gradient_templated<2>(c1, c2, c3, d1, def_grad, temp);

                gradient = temp;

            }

            if (dim == 3)

            {

                Eigen::Matrix<double, 3, 3> temp;

                generate_gradient_templated<3>(c1, c2, c3, d1, def_grad, temp);

                gradient = temp;

            }

        }


        void generate_hessian(const double c1, const double c2, const double c3, const double d1, const Eigen::MatrixXd &def_grad, Eigen::MatrixXd &hessian)

        {

            int dim = def_grad.rows();


            if (dim == 2)

            {

                Eigen::Matrix<double, 4, 4> temp;

                generate_hessian_templated<2>(c1, c2, c3, d1, def_grad, temp);

                hessian = temp;

            }

            if (dim == 3)

            {

                Eigen::Matrix<double, 9, 9> temp;

                generate_hessian_templated<3>(c1, c2, c3, d1, def_grad, temp);

                hessian = temp;

            }

        }


    } // namespace autogen

} // namespace polyfem

auto_mooney_rivlin_gradient_hessian.hpp

polyfem::autogen::generate_hessian
void generate_hessian(const double c1, const double c2, const double c3, const double d1, const Eigen::MatrixXd &def_grad, Eigen::MatrixXd &hessian)
Definition auto_mooney_rivlin_gradient_hessian.cpp:840

polyfem::autogen::generate_gradient_templated
void generate_gradient_templated(const double c1, const double c2, const double c3, const double d1, const Eigen::Matrix< double, 2, 2 > &def_grad, Eigen::Matrix< double, 2, 2 > &gradient)
Definition auto_mooney_rivlin_gradient_hessian.cpp:10

polyfem::autogen::generate_gradient
void generate_gradient(const double c1, const double c2, const double c3, const double d1, const Eigen::MatrixXd &def_grad, Eigen::MatrixXd &gradient)
Definition auto_mooney_rivlin_gradient_hessian.cpp:822

polyfem::autogen::generate_hessian_templated
void generate_hessian_templated(const double c1, const double c2, const double c3, const double d1, const Eigen::Matrix< double, 2, 2 > &def_grad, Eigen::Matrix< double, 4, 4 > &hessian)
Definition auto_mooney_rivlin_gradient_hessian.cpp:49

polyfem
Definition AMIPSEnergy.cpp:6