/********************************************************************/
/*  Schroder's methods for root calculation, implemented in C.      */
/*  This is the 'generic' version for any function with derivatives */
/*  ----------------------------------------------------------------*/
/*  Reference: "On Infinitely Many Algorithms For Solving Equations"*/
/*             by Ernst Schroder, Translated by G. W. Stewart.      */
/*  ----------------------------------------------------------------*/
/*  Copyright (C) 1996 by Dann Corbit                               */
/* =================================================================*/
/*  Inspired by the following reference:                            */
/*  Local convergence rates can be made arbitrarily large.          */
/*  Ernst Schroder showed, over 100 years ago, how a family         */
/*  of explicit single-point formulas could be designed to          */
/*  have arbitrarily high orders of (local) convergence.            */
/*  You can obtain a translation of Schroder's paper at:            */
/*                                                                  */
/*     ftp://ftp.cs.umd.edu/pub/papers/papers/2990/2990.ps.Z        */
/*                                                                  */
/* =================================================================*/
/*  A posthumous thanks to Mr. Schroder, & thanks to Pete Stewart.  */
/********************************************************************/
#include "sch_ld.h"
/*
** Notation:
**
**  'number' is a typedef for whatever numeric type is being used.
**
**  'ftype' is a typedef for a function taking a number and returning
**   a number.
**
**   f(x) is the original function.
**   f1(x) is the first derivative of the function.
**   f2(x) is the second derivative of the function.
**   f3(x) is the third derivative of the function.
**   f4(x) is the fourth derivative of the function.
**   f5(x) is the fifth derivative of the function.
**   f6(x) is the sixth derivative of the function.
**   f7(x) is the seventh derivative of the function.
**   f8(x) is the eighth derivative of the function.
**   f9(x) is the ninth derivative of the function.
**   f10(x) is the tenth derivative of the function.
**
**  For internal function naming, the first letter is
**  the series used, the second letter is always an l
**  (which indicates non-zero lamda can be used)
**  and the ending is the order of the method used.
**
** For instance: 
**   number al1(ftype f, ftype f1, number l, number x)
** Indicates that the function is
**  Schroder's Method, Series A, Lamda variable, Omega = 1
**  and the function returns a number, takes two functions
**  and two numbers and returns a number.
*/

number
al1 (ftype f, ftype f1, number l, number x)
{
  number t1 = f (x);
  return x - x * t1 / (f1 (x) * x - l * t1);
}

number
bl1 (ftype f, ftype f1, ftype f2, number l, number x)
{
  number t1 = f1 (x);
  number t3 = f (x);
  number t4 = t1 * t1;
  return x + x * t1 * t3 / (-t4 * x + t3 * f2 (x) * x + l * t3 * t1);
}

number
al2 (ftype f, ftype f1, ftype f2, number l, number x)
{
  number t1 = f (x);
  number t3 = f1 (x);
  number t4 = t3 * x;
  number t5 = l * t1;
  number t7 = t3 * t3;
  number t8 = x * x;
  number t14 = l * l;
  number t15 = t1 * t1;
  return x + 2.0 * t1 * x * (t4 - t5) / (-2.0 * t7 * t8 + t1 * f2 (x) * t8 + 2.0 * t5 * t4 - t14 * t15 + l * t15);
}

number
bl2 (ftype f, ftype f1, ftype f2, ftype f3, number l, number x)
{
  number t1 = f (x);
  number t3 = f1 (x);
  number t4 = t3 * t3;
  number t5 = t4 * x;
  number t6 = f2 (x);
  number t7 = t1 * t6;
  number t9 = l * t1;
  number t13 = x * x;
  number t17 = t1 * t1;
  number t22 = l * t17;
  number t25 = l * l;
  return x - 2.0 * t1 * x * (-t5 + t7 * x + t9 * t3) / (-2.0 * t4 * t3 * t13 + 3.0 * t7 * t3 * t13 - t17 * f3 (x)
    * t13 + 2.0 * t9 * t5 - 2.0 * t22 * t6 * x - t25 * t17 * t3 + t22 * t3);
}

number
al3 (ftype f, ftype f1, ftype f2, ftype f3, number l, number x)
{
  number t1 = f (x);
  number t3 = f1 (x);
  number t4 = t3 * t3;
  number t5 = x * x;
  number t6 = t4 * t5;
  number t7 = f2 (x);
  number t8 = t1 * t7;
  number t10 = l * t1;
  number t11 = t3 * x;
  number t13 = l * l;
  number t14 = t1 * t1;
  number t15 = t13 * t14;
  number t16 = l * t14;
  number t19 = t5 * x;
  number t32 = t14 * t1;
  return x + 3.0 * t1 * x * (-2.0 * t6 + t8 * t5 + 2.0 * t10 * t11 - t15 + t16) /
    (6.0 * t4 * t3 * t19 - 6.0 * t8 * t3 * t19 + t14 * f3 (x) * t19 - 6.0 * t10 * t6 + 3.0 * t16 * t7
     * t5 + 3.0 * t15 * t11 - 3.0 * t16 * t11 - t13 * l * t32 + 3.0 * t13 * t32 - 2.0 * l * t32);
}

number
bl3 (ftype f, ftype f1, ftype f2, ftype f3, ftype f4, number l, number x)
{
  number t1 = f (x);
  number t3 = f1 (x);
  number t4 = t3 * t3;
  number t6 = x * x;
  number t7 = t4 * t3 * t6;
  number t8 = f2 (x);
  number t9 = t1 * t8;
  number t12 = t1 * t1;
  number t13 = f3 (x);
  number t14 = t12 * t13;
  number t16 = l * t1;
  number t17 = t4 * x;
  number t19 = l * t12;
  number t20 = t8 * x;
  number t22 = l * l;
  number t23 = t22 * t12;
  number t27 = t4 * t4;
  number t28 = t6 * x;
  number t34 = t8 * t8;
  number t37 = t12 * t1;
  number t45 = l * t37;
  number t49 = t22 * t37;
  number t58 = -6.0 * t27 * t28 + 12.0 * t9 * t4 * t28 - 4.0 * t14 * t3 * t28 - 3.0 * t12 * t34 * t28 + t37 * f4 (x)
  * t28 + 6.0 * t16 * t7 - 9.0 * t19 * t8 * t3 * t6 + 3.0 * t45 * t13 * t6 - 3.0 * t23 * t17 + 3.0 * t49 * t20
  + 3.0 * t19 * t17 - 3.0 * t45 * t20 + t22 * l * t37 * t3 - 3.0 * t49 * t3 + 2.0 * t45 * t3;
  return x + 3.0 * t1 * x * (2.0 * t7 - 3.0 * t9 * t3 * t6 + t14 * t6 - 2.0 * t16 * t17 + 2.0 * t19 * t20 + t23 * t3 - t19 * t3) / t58;
}

number
al4 (ftype f, ftype f1, ftype f2, ftype f3, ftype f4, number l, number x)
{
  number t1 = f (x);
  number t3 = f1 (x);
  number t4 = t3 * t3;
  number t6 = x * x;
  number t7 = t6 * x;
  number t8 = t4 * t3 * t7;
  number t9 = f2 (x);
  number t10 = t1 * t9;
  number t13 = t1 * t1;
  number t14 = f3 (x);
  number t15 = t13 * t14;
  number t17 = l * t1;
  number t18 = t4 * t6;
  number t20 = l * t13;
  number t21 = t9 * t6;
  number t23 = l * l;
  number t24 = t23 * t13;
  number t25 = t3 * x;
  number t28 = t23 * l;
  number t29 = t13 * t1;
  number t30 = t28 * t29;
  number t31 = t23 * t29;
  number t32 = l * t29;
  number t34 = t4 * t4;
  number t35 = t6 * t6;
  number t41 = t9 * t9;
  number t60 = t23 * t23;
  number t61 = t13 * t13;
  number t66 = 24.0 * t34 * t35 - 36.0 * t10 * t4 * t35 + 8.0 * t15 * t3 * t35 + 6.0 * t13 * t41 * t35 - t29
  * f4 (x) * t35 - 24.0 * t17 * t8 + 24.0 * t20 * t9 * t3 * t7 - 4.0 * t32
  * t14 * t7 + 12.0 * t24 * t18 - 6.0 * t31 * t21 - 12.0 * t20 * t18 + 6.0 * t32 * t21 - 4.0 * t30 * t25 + 12.0 * t31
  * t25 - 8.0 * t32 * t25 + t60 * t61 - 6.0 * t28 * t61 + 11.0 * t23 * t61 - 6.0 * l * t61;
  return x + 4.0 * t1 * x * (-6.0 * t8 + 6.0 * t10 * t3 * t7 - t15 * t7 + 6.0 * t17 * t18 - 3.0 * t20 * t21
   - 3.0 * t24 * t25 + 3.0 * t20 * t25 + t30 - 3.0 * t31 + 2.0 * t32) / t66;
}

number
bl4 (ftype f, ftype f1, ftype f2, ftype f3, ftype f4, ftype f5, number l, number x)
{
  number t1 = f (x);
  number t3 = f1 (x);
  number t4 = t3 * t3;
  number t5 = t4 * t4;
  number t6 = x * x;
  number t7 = t6 * x;
  number t8 = t5 * t7;
  number t9 = f2 (x);
  number t10 = t1 * t9;
  number t13 = t1 * t1;
  number t14 = f3 (x);
  number t15 = t13 * t14;
  number t18 = t9 * t9;
  number t21 = t13 * t1;
  number t22 = f4 (x);
  number t23 = t21 * t22;
  number t25 = l * t1;
  number t26 = t4 * t3;
  number t27 = t26 * t6;
  number t29 = l * t13;
  number t31 = t9 * t3 * t6;
  number t33 = l * t21;
  number t34 = t14 * t6;
  number t36 = l * l;
  number t37 = t36 * t13;
  number t38 = t4 * x;
  number t40 = t36 * t21;
  number t41 = t9 * x;
  number t45 = t36 * l;
  number t46 = t45 * t21;
  number t50 = 6.0 * t8 - 12.0 * t10 * t4 * t7 + 4.0 * t15 * t3 * t7 + 3.0 * t13 * t18 * t7 - t23 * t7 - 6.0 * t25
  * t27 + 9.0 * t29 * t31 - 3.0 * t33 * t34 + 3.0 * t37 * t38 - 3.0 * t40 * t41 - 3.0 * t29 * t38 + 3.0 * t33 * t41 - t46
  * t3 + 3.0 * t40 * t3 - 2.0 * t33 * t3;
  number t51 = t36 * t36;
  number t52 = t13 * t13;
  number t55 = l * t52;
  number t59 = t6 * t6;
  number t66 = t36 * t52;
  number t81 = t51 * t52 * t3 - 6.0 * t55 * t3 - 12.0 * t29 * t27 + 30.0 * t3 * t13 * t18 * t59
  + t52 * f5 (x) * t59 - 8.0 * t33 * t38 + 6.0 * t66 * t34 - 16.0 * t33
  * t14 * t3 * t7 - 12.0 * t33 * t18 * t7 + 8.0 * t55 * t41 - 24.0 * t25 * t8 + 20.0 * t15 * t4 * t59 - 60.0 * t10 * t26
  * t59 - 5.0 * t23 * t3 * t59;
  number t82 = t45 * t52;
  number t103 = -6.0 * t82 * t3 - 10.0 * t21 * t9 * t14 * t59 - 18.0 * t40 * t31 + 24.0 * t5 * t3 * t59 + 12.0
  * t37 * t27 - 6.0 * t55 * t34 - 4.0 * t46 * t38 + 12.0 * t40 * t38 + 4.0 * t55 * t22 * t7 + 48.0 * t29 * t9 * t4 * t7
  - 12.0 * t66 * t41 + 4.0 * t82 * t41 + 18.0 * t33 * t31 + 11.0 * t66 * t3;
  return x - 4.0 * t1 * x * t50 / (t81 + t103);
}

number
al5 (ftype f, ftype f1, ftype f2, ftype f3, ftype f4, ftype f5, number l, number x)
{
  number t1 = f (x);
  number t3 = f1 (x);
  number t4 = t3 * t3;
  number t5 = t4 * t4;
  number t6 = x * x;
  number t7 = t6 * t6;
  number t8 = t5 * t7;
  number t9 = f2 (x);
  number t10 = t1 * t9;
  number t13 = t1 * t1;
  number t14 = f3 (x);
  number t15 = t13 * t14;
  number t18 = t9 * t9;
  number t21 = t13 * t1;
  number t22 = f4 (x);
  number t23 = t21 * t22;
  number t25 = l * t1;
  number t26 = t4 * t3;
  number t27 = t6 * x;
  number t28 = t26 * t27;
  number t30 = l * t13;
  number t32 = t9 * t3 * t27;
  number t34 = l * t21;
  number t35 = t14 * t27;
  number t37 = l * l;
  number t38 = t37 * t13;
  number t39 = t4 * t6;
  number t41 = t37 * t21;
  number t42 = t9 * t6;
  number t46 = t37 * l;
  number t47 = t46 * t21;
  number t48 = t3 * x;
  number t52 = t37 * t37;
  number t53 = t13 * t13;
  number t54 = t52 * t53;
  number t55 = t46 * t53;
  number t56 = t37 * t53;
  number t57 = l * t53;
  number t58 = 24.0 * t8 - 36.0 * t10 * t4 * t7 + 8.0 * t15 * t3 * t7 + 6.0 * t13 * t18 * t7 - t23 * t7 - 24.0 * t25
  * t28 + 24.0 * t30 * t32 - 4.0 * t34 * t35 + 12.0 * t38 * t39 - 6.0 * t41 * t42 - 12.0 * t30 * t39 + 6.0 * t34 * t42
  - 4.0 * t47 * t48 + 12.0 * t41 * t48 - 8.0 * t34 * t48 + t54 - 6.0 * t55 + 11.0 * t56 - 6.0 * t57;
  number t59 = t53 * t1;
  number t63 = t7 * x;
  number t88 = -10.0 * t52 * t59 - t53 * f5 (x) * t63
  - 50.0 * t37 * t59 + 24.0 * l * t59 - 120.0 * t5 * t3 * t63 + t52 * l * t59 + 60.0 * t41 * t32 - 60.0 * t34 * t32
  - 180.0 * t30 * t9 * t4 * t7 + 30.0 * t55 * t48 - 5.0 * t57 * t22 * t7 - 60.0 * t38 * t28 + 30.0 * t34 * t18 * t7
  + 120.0 * t25 * t8 + 40.0 * t34 * t14 * t3 * t7 + 240.0 * t10 * t26 * t63;
  number t112 = -60.0 * t15 * t4 * t63 - 90.0 * t3 * t13 * t18 * t63 - 10.0 * t55 * t42 + 10.0 * t23 * t3 * t63
  + 10.0 * t57 * t35 + 60.0 * t30 * t28 + 30.0 * t56 * t42 + 20.0 * t47 * t39 + 20.0 * t21 * t9 * t14 * t63 + 35.0
  * t46 * t59 - 10.0 * t56 * t35 - 60.0 * t41 * t39 + 40.0 * t34 * t39 + 30.0 * t57 * t48 - 20.0 * t57 * t42 - 5.0
  * t54 * t48 - 55.0 * t56 * t48;
  return x + 5.0 * t1 * x * t58 / (t88 + t112);
}

number
bl5 (ftype f, ftype f1, ftype f2, ftype f3, ftype f4, ftype f5, ftype f6, number l, number x)
{
  number t1 = f (x);
  number t3 = t1 * t1;
  number t4 = t3 * t3;
  number t5 = l * t4;
  number t6 = f1 (x);
  number t8 = l * l;
  number t9 = t8 * t4;
  number t11 = t8 * t8;
  number t12 = t11 * t4;
  number t14 = f5 (x);
  number t15 = t4 * t14;
  number t16 = x * x;
  number t17 = t16 * t16;
  number t19 = t8 * l;
  number t20 = t19 * t4;
  number t22 = t3 * t1;
  number t23 = f2 (x);
  number t25 = f3 (x);
  number t28 = t8 * t22;
  number t30 = t23 * t6 * t16;
  number t32 = t6 * t6;
  number t33 = t32 * x;
  number t35 = t32 * t32;
  number t37 = t35 * t6 * t17;
  number t38 = t19 * t22;
  number t40 = t25 * t16;
  number t42 = t8 * t3;
  number t43 = t32 * t6;
  number t44 = t43 * t16;
  number t46 = f4 (x);
  number t47 = t16 * x;
  number t48 = t46 * t47;
  number t50 = l * t3;
  number t52 = t23 * t32 * t47;
  number t54 = -6.0 * t5 * t6 + 11.0 * t9 * t6 + t12 * t6 + t15 * t17 - 6.0 * t20 * t6 - 10.0 * t22 * t23 * t25
  * t17 - 18.0 * t28 * t30 + 12.0 * t28 * t33 + 24.0 * t37 - 4.0 * t38 * t33 - 6.0 * t5 * t40 + 12.0 * t42 * t44 + 4.0
  * t5 * t48 + 48.0 * t50 * t52;
  number t55 = t23 * x;
  number t58 = l * t22;
  number t61 = t23 * t23;
  number t68 = t25 * t6 * t47;
  number t70 = t61 * t47;
  number t73 = l * t1;
  number t74 = t35 * t47;
  number t76 = t3 * t25;
  number t79 = t1 * t23;
  number t82 = t22 * t46;
  number t85 = -12.0 * t9 * t55 + 4.0 * t20 * t55 + 18.0 * t58 * t30 + 30.0 * t6 * t3 * t61 * t17 - 12.0 * t50
  * t44 - 8.0 * t58 * t33 + 6.0 * t9 * t40 - 16.0 * t58 * t68 - 12.0 * t58 * t70 + 8.0 * t5 * t55 - 24.0 * t73 * t74
  + 20.0 * t76 * t32 * t17 - 60.0 * t79 * t43 * t17 - 5.0 * t82 * t6 * t17;
  number t87 = t4 * t1;
  number t88 = t19 * t87;
  number t90 = t8 * t87;
  number t92 = t25 * t25;
  number t94 = t17 * x;
  number t99 = t11 * t87;
  number t104 = l * t87;
  number t109 = t23 * t25;
  number t119 = -35.0 * t88 * t6 + 50.0 * t90 * t6 + 10.0 * t4 * t92 * t94
  - t87 * f6 (x) * t94 + 10.0 * t99 * t6 - 30.0 * t22 * t61 * t23 * t94 - 24.0 * t104
  * t6 - t11 * l * t87 * t6 + 50.0 * t5 * t109 * t17 + 25.0 * t5 * t46 * t6 * t17 - 20.0 * t38 * t44 - 150.0 * t58 * t6
  * t61 * t17;
  number t135 = 5.0 * t12 * t33 - 55.0 * t90 * t55 + 120.0 * t35 * t32 * t94 + 120.0 * t58 * t52 + 55.0 * t9
  * t33 + 60.0 * t28 * t44 - 90.0 * t9 * t30 - 30.0 * t20 * t33 + 40.0 * t9 * t68 - 5.0 * t99 * t55 - 360.0 * t79 * t35
  * t94 + 30.0 * t20 * t30 - 120.0 * t73 * t37;
  number t150 = 10.0 * t104 * t48 + 30.0 * t90 * t40 + 60.0 * t42 * t74 - 40.0 * t5 * t68 - 30.0 * t5 * t70
  - 120.0 * t28 * t52 - 60.0 * t50 * t74 - 10.0 * t90 * t48 + 30.0 * t9 * t70 - 5.0 * t104 * t14 * t17 - 10.0 * t88
  * t40 + 30.0 * t104 * t55;
  number t177 = -30.0 * t5 * t33 - 100.0 * t58 * t25 * t32 * t17 + 30.0 * t88 * t55 + 6.0 * t15 * t6 * t94
  - 30.0 * t82 * t32 * t94 + 270.0 * t32 * t3 * t61 * t94 + 120.0 * t76 * t43 * t94 - 120.0 * t6 * t22 * t109 * t94
  + 15.0 * t4 * t23 * t46 * t94 + 300.0 * t50 * t23 * t43 * t17 + 60.0 * t5 * t30 - 20.0 * t104 * t40 - 40.0 * t58 * t44;
  return x - 5.0 * t1 * x * (t54 + t85) / (t119 + t135 + t150 + t177);
}

number
al6 (ftype f, ftype f1, ftype f2, ftype f3, ftype f4, ftype f5, ftype f6, number l, number x)
{
  number t1 = f (x);
  number t3 = t1 * t1;
  number t4 = t3 * t1;
  number t5 = l * t4;
  number t6 = f1 (x);
  number t7 = t6 * t6;
  number t8 = x * x;
  number t9 = t7 * t8;
  number t11 = l * l;
  number t12 = t3 * t3;
  number t13 = t11 * t12;
  number t14 = t6 * x;
  number t16 = t11 * t11;
  number t17 = t16 * t12;
  number t19 = f5 (x);
  number t20 = t12 * t19;
  number t21 = t8 * t8;
  number t22 = t21 * x;
  number t24 = t11 * t4;
  number t25 = f2 (x);
  number t27 = t8 * x;
  number t28 = t25 * t6 * t27;
  number t31 = l * t12;
  number t33 = f3 (x);
  number t34 = t33 * t27;
  number t37 = t25 * t8;
  number t39 = t11 * l;
  number t40 = t12 * t1;
  number t41 = t39 * t40;
  number t42 = t11 * t40;
  number t43 = t7 * t7;
  number t45 = t43 * t6 * t22;
  number t46 = l * t40;
  number t47 = t16 * l;
  number t48 = t47 * t40;
  number t49 = t39 * t4;
  number t51 = -40.0 * t5 * t9 + 55.0 * t13 * t14 + 5.0 * t17 * t14 + t20 * t22 - 60.0 * t24 * t28 + 60.0 * t5
  * t28 - 30.0 * t31 * t14 + 10.0 * t13 * t34 + 60.0 * t24 * t9 + 20.0 * t31 * t37 - 35.0 * t41 + 50.0 * t42 + 120.0
  * t45 - 24.0 * t46 - t48 - 20.0 * t49 * t9;
  number t55 = t16 * t40;
  number t58 = l * t3;
  number t59 = t7 * t6;
  number t60 = t59 * t27;
  number t62 = f4 (x);
  number t63 = t4 * t62;
  number t66 = t39 * t12;
  number t69 = t25 * t25;
  number t72 = t1 * t25;
  number t75 = t3 * t33;
  number t79 = t33 * t6 * t21;
  number t81 = l * t1;
  number t82 = t43 * t21;
  number t84 = t69 * t21;
  number t86 = t11 * t3;
  number t88 = t62 * t21;
  number t91 = t25 * t7 * t21;
  number t94 = -20.0 * t4 * t25 * t33 * t22 + 10.0 * t55 - 30.0 * t13 * t37 - 10.0 * t31 * t34 - 60.0 * t58
  * t60 - 10.0 * t63 * t6 * t22 + 10.0 * t66 * t37 + 90.0 * t6 * t3 * t69 * t22 - 240.0 * t72 * t59 * t22 + 60.0 * t75
  * t7 * t22 - 40.0 * t5 * t79 - 120.0 * t81 * t82 - 30.0 * t5 * t84 + 60.0 * t86 * t60 + 5.0 * t31 * t88 + 180.0 * t58
  * t91 - 30.0 * t66 * t14;
  number t96 = t12 * t3;
  number t101 = t21 * t8;
  number t110 = t25 * t33;
  number t119 = -15.0 * t47 * t96 - 120.0 * l * t96 + 274.0 * t11 * t96 + 720.0 * t43 * t7 * t101 + 12.0 * t20
  * t6 * t101 - t40 * f6 (x) * t101 - 20.0 * t41
  * t34 - 360.0 * t6 * t4 * t110 * t101 + 120.0 * t66 * t28 - 120.0 * t49 * t60 + 300.0 * t42 * t14 - 210.0 * t41
  * t14 - 6.0 * t48 * t14 + 60.0 * t55 * t14;
  number t142 = -180.0 * t66 * t9 - 15.0 * t55 * t37 + 30.0 * t17 * t9 - 40.0 * t46 * t34 + 240.0 * t31 * t28
  - 240.0 * t5 * t60 - 6.0 * t46 * t19 * t22 + 120.0 * t31 * t110 * t22 + 60.0 * t31 * t62 * t6 * t22 - 540.0 * t5
  * t6 * t69 * t22 - 360.0 * t5 * t33 * t7 * t22 + 360.0 * t86 * t82 - 144.0 * t46 * t14 - 225.0 * t39 * t96;
  number t155 = t33 * t33;
  number t166 = 85.0 * t16 * t96 + t16 * t11 * t96 + 1440.0 * t58 * t25 * t59 * t22 - 720.0 * t81 * t45 + 15.0
  * t46 * t88 - 120.0 * t31 * t79 + 90.0 * t46 * t37 + 60.0 * t42 * t34 + 20.0 * t12 * t155 * t101 - 90.0 * t4 * t69
  * t25 * t101 - 180.0 * t31 * t9 - 165.0 * t42 * t37 - 90.0 * t63 * t7 * t101 + 330.0 * t13 * t9;
  number t187 = 1080.0 * t7 * t3 * t69 * t101 + 480.0 * t75 * t59 * t101 + 30.0 * t12 * t25 * t62 * t101
  - 1800.0 * t72 * t43 * t101 + 90.0 * t41 * t37 - 90.0 * t31 * t84 + 540.0 * t5 * t91 - 360.0 * t58 * t82 - 15.0
  * t42 * t88 + 90.0 * t13 * t84 + 120.0 * t13 * t79 - 540.0 * t24 * t91 - 360.0 * t13 * t28 + 360.0 * t24 * t60;
  return x - 6.0 * t1 * x * (t51 + t94) / (t119 + t142 + t166 + t187);
}

number
bl6 (ftype f, ftype f1, ftype f2, ftype f3, ftype f4, ftype f5, ftype f6, ftype f7, number l, number x)
{
  number t1 = f (x);
  number t3 = t1 * t1;
  number t4 = t3 * t3;
  number t5 = t4 * t1;
  number t6 = l * t5;
  number t7 = f1 (x);
  number t9 = l * l;
  number t10 = t9 * t9;
  number t11 = t10 * l;
  number t12 = t11 * t5;
  number t14 = t9 * l;
  number t15 = t14 * t5;
  number t17 = t9 * t5;
  number t19 = f3 (x);
  number t20 = t19 * t19;
  number t22 = x * x;
  number t23 = t22 * t22;
  number t24 = t23 * x;
  number t26 = f6 (x);
  number t27 = t5 * t26;
  number t29 = t10 * t5;
  number t31 = t3 * t1;
  number t32 = f2 (x);
  number t33 = t32 * t32;
  number t34 = t33 * t32;
  number t37 = t10 * t4;
  number t38 = t7 * t7;
  number t39 = t38 * x;
  number t41 = t38 * t38;
  number t43 = t41 * t38 * t24;
  number t44 = l * t31;
  number t46 = t22 * x;
  number t47 = t32 * t38 * t46;
  number t49 = t32 * x;
  number t51 = -24.0 * t6 * t7 - t12 * t7 - 35.0 * t15 * t7 + 50.0 * t17 * t7 + 10.0 * t4 * t20 * t24 - t27 * t24
  + 10.0 * t29 * t7 - 30.0 * t31 * t34 * t24 + 5.0 * t37 * t39 + 120.0 * t43 + 120.0 * t44 * t47 - 55.0 * t17 * t49;
  number t52 = t9 * t4;
  number t54 = t32 * t7 * t22;
  number t57 = t9 * t31;
  number t58 = t38 * t7;
  number t59 = t58 * t22;
  number t61 = t1 * t32;
  number t66 = t19 * t7 * t46;
  number t68 = t14 * t4;
  number t70 = l * t1;
  number t71 = t41 * t7;
  number t72 = t71 * t23;
  number t75 = t19 * t22;
  number t77 = f4 (x);
  number t78 = t77 * t46;
  number t80 = t9 * t3;
  number t81 = t41 * t46;
  number t84 = -90.0 * t52 * t54 + 55.0 * t52 * t39 + 60.0 * t57 * t59 - 360.0 * t61 * t41 * t24 - 5.0 * t29
  * t49 + 40.0 * t52 * t66 + 30.0 * t68 * t54 - 120.0 * t70 * t72 - 30.0 * t68 * t39 + 30.0 * t17 * t75 + 10.0 * t6
  * t78 + 60.0 * t80 * t81 - 120.0 * t57 * t47;
  number t86 = l * t4;
  number t88 = t33 * t46;
  number t90 = l * t3;
  number t94 = f5 (x);
  number t95 = t94 * t23;
  number t101 = t19 * t38 * t23;
  number t107 = -40.0 * t86 * t66 - 30.0 * t86 * t88 - 60.0 * t90 * t81 + 30.0 * t52 * t88 - 10.0 * t17 * t78
  - 5.0 * t6 * t95 - 10.0 * t15 * t75 + 30.0 * t6 * t49 - 30.0 * t86 * t39 - 100.0 * t44 * t101 + 30.0 * t15 * t49
  + 270.0 * t38 * t3 * t33 * t24;
  number t108 = t31 * t77;
  number t111 = t3 * t19;
  number t118 = t32 * t58 * t23;
  number t120 = t7 * t31;
  number t121 = t32 * t19;
  number t122 = t121 * t24;
  number t124 = t4 * t94;
  number t130 = t121 * t23;
  number t133 = t77 * t7 * t23;
  number t135 = t14 * t31;
  number t138 = t7 * t33 * t23;
  number t140 = -30.0 * t108 * t38 * t24 + 120.0 * t111 * t58 * t24 + 15.0 * t4 * t32 * t77 * t24 + 300.0
  * t90 * t118 - 120.0 * t120 * t122 + 6.0 * t124 * t7 * t24 - 20.0 * t6 * t75 - 40.0 * t44 * t59 + 60.0 * t86 * t54
  + 50.0 * t86 * t130 + 25.0 * t86 * t133 - 20.0 * t135 * t59 - 150.0 * t44 * t138;
  number t143 = t4 * t3;
  number t144 = t11 * t143;
  number t149 = t10 * t143;
  number t151 = t14 * t143;
  number t153 = t9 * t143;
  number t157 = t23 * t22;
  number t159 = l * t143;
  number t167 = t7 * t4;
  number t168 = t32 * t77;
  number t182 = 15.0 * t144 * t7 - t10 * t9 * t143 * t7 - 85.0 * t149 * t7 + 225.0 * t151 * t7 - 274.0 * t153
  * t7 - t143 * f7 (x) * t157 + 120.0
  * t159 * t7 - 720.0 * t41 * t58 * t157 - 20.0 * t151 * t78 + 1260.0 * t38 * t31 * t121 * t157 - 210.0 * t167
  * t168 * t157 - 210.0 * t4 * t33 * t19 * t157 + 720.0 * t70 * t43 - 240.0 * t68 * t47 - 150.0 * t6 * t130 + 15.0
  * t159 * t95 - 75.0 * t6 * t133 + 120.0 * t135 * t81 + 80.0 * t15 * t66 - 480.0 * t86 * t47;
  number t214 = 360.0 * t90 * t72 - 720.0 * t86 * t7 * t122 - 180.0 * t86 * t77 * t38 * t24 + 1620.0 * t44
  * t38 * t33 * t24 + 300.0 * t153 * t49 - 210.0 * t151 * t49 - 300.0 * t17 * t39 + 45.0 * t29 * t54 - 15.0 * t149
  * t75 - 30.0 * t37 * t59 - 6.0 * t159 * t26 * t24;
  number t246 = -144.0 * t159 * t49 - 40.0 * t159 * t78 + 900.0 * t57 * t118 + 160.0 * t6 * t66 + 240.0
  * t44 * t81 + 90.0 * t6 * t168 * t24 - 15.0 * t153 * t95 + 120.0 * t6 * t88 + 90.0 * t159 * t75 - 180.0 * t86 * t34
  * t24 - 270.0 * t6 * t54;
  number t282 = -360.0 * t80 * t72 - 2520.0 * t58 * t3 * t33 * t157 + 210.0 * t108 * t58 * t157 - 840.0
  * t111 * t41 * t157 + 2520.0 * t61 * t71 * t157 + 21.0 * t5 * t32 * t94 * t157 + 35.0 * t5 * t19 * t77 * t157 + 7.0
  * t27 * t7 * t157 + 630.0 * t120 * t34 * t157 - 42.0 * t124 * t38 * t157 + 720.0 * t52 * t47;
  return x + 6.0 * t1 * x * (t51 + t84 + t107 + t140) /
    (-2160.0 * t90 * t32 * t41 * t24 + 60.0 * t6 * t20 * t24 + 720.0 * t44 * t19 * t58 * t24
     - 140.0 * t167 * t20 * t157 + 36.0 * t6 * t94 * t7 * t24 + t182 + 144.0
     * t6 * t39 + 450.0 * t86 * t138 + 210.0 * t15 * t39 + 300.0 * t86 * t101 + t214 - 450.0 * t52 * t138 - 900.0
     * t44 * t118 + 150.0 * t17 * t130 + 75.0 * t17 * t133 - 240.0 * t17 * t66 + 60.0 * t153 * t78 + 60.0 * t15 * t88
     + 495.0 * t17 * t54 - 180.0 * t17 * t88 - 165.0 * t153 * t75 - 360.0 * t57 * t81 + t246 + 180.0 * t86 * t59
     + 90.0 * t151 * t75 - 330.0 * t52 * t59 - 270.0 * t15 * t54 + 180.0 * t68 * t59 + 60.0 * t149 * t49 + 6.0 * t12
   * t39 - 300.0 * t52 * t101 - 6.0 * t144 * t49 - 60.0 * t29 * t39 + t282);
}

number
al7 (ftype f, ftype f1, ftype f2, ftype f3, ftype f4, ftype f5, ftype f6, ftype f7, number l, number x)
{
  number t1 = f (x);
  number t3 = t1 * t1;
  number t4 = t3 * t3;
  number t5 = f3 (x);
  number t6 = t5 * t5;
  number t8 = x * x;
  number t9 = t8 * t8;
  number t10 = t9 * t8;
  number t12 = t3 * t1;
  number t13 = f2 (x);
  number t14 = t13 * t13;
  number t15 = t14 * t13;
  number t18 = t4 * t1;
  number t19 = f6 (x);
  number t20 = t18 * t19;
  number t22 = l * t4;
  number t23 = f4 (x);
  number t24 = f1 (x);
  number t26 = t9 * x;
  number t27 = t23 * t24 * t26;
  number t29 = l * t12;
  number t31 = t24 * t14 * t26;
  number t33 = t24 * t24;
  number t35 = t5 * t33 * t26;
  number t37 = l * l;
  number t38 = t4 * t3;
  number t39 = t37 * t38;
  number t40 = t37 * t3;
  number t41 = t33 * t33;
  number t42 = t41 * t9;
  number t44 = t37 * l;
  number t45 = t44 * t38;
  number t46 = l * t18;
  number t47 = t24 * x;
  number t49 = l * t38;
  number t50 = t37 * t37;
  number t51 = t50 * l;
  number t52 = t51 * t38;
  number t53 = t8 * x;
  number t54 = t5 * t53;
  number t57 = t13 * t24 * t53;
  number t59 = 20.0 * t4 * t6 * t10 - 90.0 * t12 * t15 * t10 - t20 * t10 + 60.0 * t22 * t27 - 540.0 * t29 * t31
  - 360.0 * t29 * t35 + 274.0 * t39 + 360.0 * t40 * t42 - 225.0 * t45 - 144.0 * t46 * t47 - 120.0 * t49 - 15.0
  * t52 - 40.0 * t46 * t54 + 240.0 * t22 * t57;
  number t60 = t33 * t24;
  number t61 = t60 * t53;
  number t64 = t41 * t33 * t10;
  number t65 = f5 (x);
  number t66 = t65 * t26;
  number t68 = t13 * t5;
  number t69 = t68 * t26;
  number t71 = t44 * t18;
  number t73 = t50 * t18;
  number t75 = t51 * t18;
  number t77 = t44 * t4;
  number t78 = t33 * t8;
  number t80 = t13 * t8;
  number t82 = t50 * t4;
  number t84 = t37 * t12;
  number t86 = t4 * t65;
  number t89 = t24 * t12;
  number t90 = t68 * t10;
  number t93 = -240.0 * t29 * t61 + 720.0 * t64 - 6.0 * t46 * t66 + 120.0 * t22 * t69 - 210.0 * t71 * t47
  + 60.0 * t73 * t47 - 6.0 * t75 * t47 - 180.0 * t77 * t78 - 15.0 * t73 * t80 + 30.0 * t82 * t78 + 360.0 * t84 * t61
  + 12.0 * t86 * t24 * t10 - 360.0 * t89 * t90 - 20.0 * t71 * t54;
  number t96 = t37 * t18;
  number t98 = t44 * t12;
  number t100 = t23 * t9;
  number t102 = t37 * t4;
  number t103 = t14 * t9;
  number t106 = t5 * t24 * t9;
  number t109 = t13 * t33 * t9;
  number t115 = l * t3;
  number t117 = t3 * t5;
  number t123 = 120.0 * t77 * t57 + 300.0 * t96 * t47 - 120.0 * t98 * t61 - 15.0 * t96 * t100 + 90.0 * t102
  * t103 + 120.0 * t102 * t106 - 540.0 * t84 * t109 - 360.0 * t102 * t57 + 90.0 * t71 * t80 + 540.0 * t29 * t109
  - 90.0 * t22 * t103 - 360.0 * t115 * t42 + 480.0 * t117 * t60 * t10 + 1080.0 * t33 * t3 * t14 * t10;
  number t124 = t1 * t13;
  number t134 = t12 * t23;
  number t137 = t50 * t38;
  number t139 = t13 * t60 * t26;
  number t141 = l * t1;
  number t142 = t41 * t24;
  number t143 = t142 * t26;
  number t145 = t50 * t37;
  number t146 = t145 * t38;
  number t150 = -1800.0 * t124 * t41 * t10 + 30.0 * t4 * t13 * t23 * t10 + 90.0 * t46 * t80 + 60.0 * t96 * t54
  - 180.0 * t22 * t78 + 330.0 * t102 * t78 - 90.0 * t134 * t33 * t10 + 85.0 * t137 + 1440.0 * t115 * t139
  - 720.0 * t141 * t143 + t146 + 15.0 * t46 * t100 - 165.0 * t96 * t80 - 120.0 * t22 * t106;
  number t153 = t9 * t53;
  number t156 = t24 * t4;
  number t157 = t13 * t23;
  number t163 = t4 * t12;
  number t173 = -4200.0 * t117 * t41 * t153 - 630.0 * t156 * t157 * t153 + 280.0 * t71 * t106 + 5040.0
  * t141 * t64 - 5040.0 * t29 * t139 - 1764.0 * t37 * t163 + 1680.0 * t29 * t42 + 840.0 * t98 * t42 + 840.0 * t49
  * t47 - 126.0 * t86 * t33 * t153
  - t38 * f7 (x) * t153;
  number t187 = -735.0 * t50 * t163 - 5040.0 * t41 * t60 * t153 + 720.0 * l * t163 + 1624.0 * t44 * t163
  + t50 * t44 * t163 + 560.0 * t46 * t106 - 595.0 * t137 * t47 + 105.0 * t52 * t47 + 175.0 * t51 * t163 - 2310.0
  * t102 * t61 + 3780.0 * t102 * t109;
  number t200 = 1470.0 * t71 * t78 + 210.0 * t137 * t80 + 42.0 * t75 * t78 + 420.0 * t46 * t103 + 1050.0
  * t39 * t80 - 210.0 * t82 * t61 + 210.0 * t45 * t54 - 1918.0 * t39 * t47 - 735.0 * t45 * t80 - 21.0 * t52 * t80
  + 105.0 * t39 * t100;
  number t214 = 1260.0 * t22 * t61 - 385.0 * t39 * t54 + 210.0 * t73 * t57 + 1575.0 * t45 * t47 - 7.0 * t146
  * t47 - 420.0 * t46 * t69 + 2310.0 * t96 * t57 + 1008.0 * t46 * t78 + 140.0 * t46 * t6 * t10 - 504.0 * t49 * t80
  + 210.0 * t71 * t103 - 2100.0 * t96 * t78;
  number t237 = 7560.0 * t29 * t33 * t14 * t10 + 84.0 * t46 * t65 * t24 * t10 - 7.0 * t49 * t19 * t10 - 2520.0
  * t22 * t24 * t90 - 630.0 * t22 * t23 * t33 * t10 - 1260.0 * t71 * t57 - 210.0 * t46 * t27 - 1260.0 * t46 * t57
  + 210.0 * t46 * t157 * t10 - 2520.0 * t84 * t42 - 1890.0 * t102 * t31;
  number t256 = -35.0 * t137 * t54 - 2520.0 * t40 * t143 - 630.0 * t22 * t15 * t10 + 3360.0 * t29 * t5 * t60
  * t10 - 1260.0 * t77 * t109 + 1260.0 * t77 * t61 + 210.0 * t96 * t27 - 1260.0 * t102 * t35 + 420.0 * t96 * t69
  - 12600.0 * t60 * t3 * t14 * t153 + 70.0 * t18 * t5 * t23 * t153;
  number t274 = -35.0 * t45 * t100 - 630.0 * t96 * t103 + 5040.0 * t84 * t139 + 210.0 * t49 * t54 + 21.0
  * t49 * t66 + 15120.0 * t124 * t142 * t153 - 630.0 * t4 * t14 * t5 * t153 + 42.0 * t18 * t13 * t65 * t153 - 420.0
  * t73 * t78 - 840.0 * t96 * t106 - 21.0 * t39 * t66;
  number t295 = -420.0 * t156 * t6 * t153 + 1890.0 * t22 * t31 - 12600.0 * t115 * t13 * t41 * t10 - 21.0
  * t145 * t163 + 2520.0 * t115 * t143 - 70.0 * t49 * t100 + 840.0 * t134 * t60 * t153 + 14.0 * t20 * t24 * t153
  + 5040.0 * t33 * t12 * t68 * t153 + 1260.0 * t22 * t35 - 2520.0 * t22 * t109 + 2520.0 * t89 * t15 * t153;
  return x + 7.0 * t1 * x * (t59 + t93 + t123 + t150) / (t173 + t187 + t200 + t214 + t237 + t256 + t274
                                                         + t295);
}

number
bl7 (ftype f, ftype f1, ftype f2, ftype f3, ftype f4, ftype f5, ftype f6, ftype f7, ftype f8, number l, number x)
{
  number t1 = f (x);
  number t3 = l * l;
  number t4 = t3 * t3;
  number t5 = t4 * t3;
  number t6 = t1 * t1;
  number t7 = t6 * t6;
  number t8 = t7 * t6;
  number t9 = t5 * t8;
  number t10 = f1 (x);
  number t12 = t4 * l;
  number t13 = t12 * t8;
  number t15 = t4 * t8;
  number t17 = t3 * l;
  number t18 = t17 * t8;
  number t20 = t3 * t8;
  number t22 = f7 (x);
  number t23 = t8 * t22;
  number t24 = x * x;
  number t25 = t24 * t24;
  number t26 = t25 * t24;
  number t28 = l * t8;
  number t30 = f2 (x);
  number t31 = t30 * x;
  number t33 = t7 * t1;
  number t34 = t3 * t33;
  number t35 = t10 * t10;
  number t36 = t35 * x;
  number t38 = f3 (x);
  number t39 = t38 * t24;
  number t42 = t4 * t33;
  number t44 = t30 * t10 * t24;
  number t46 = t4 * t7;
  number t47 = t35 * t10;
  number t48 = t47 * t24;
  number t50 = l * t33;
  number t51 = f5 (x);
  number t53 = t25 * x;
  number t54 = t51 * t10 * t53;
  number t56 = t6 * t1;
  number t57 = l * t56;
  number t59 = t38 * t47 * t53;
  number t61 = f6 (x);
  number t62 = t61 * t53;
  number t65 = t10 * t7;
  number t66 = t38 * t38;
  number t69 = t30 * t30;
  number t70 = t24 * x;
  number t71 = t69 * t70;
  number t73 = t3 * t56;
  number t74 = t35 * t35;
  number t75 = t74 * t70;
  number t77 = t9 * t10 - 15.0 * t13 * t10 + 85.0 * t15 * t10 - 225.0 * t18 * t10 + 274.0 * t20 * t10 + t23
  * t26 - 120.0 * t28 * t10 - 300.0 * t20 * t31 + 300.0 * t34 * t36 + 15.0 * t15 * t39 + 210.0 * t18 * t31 - 45.0
  * t42 * t44 + 30.0 * t46 * t48 - 36.0 * t50 * t54 - 720.0 * t57 * t59 + 6.0 * t28 * t62 + 165.0 * t20 * t39 + 140.0
  * t65 * t66 * t26 + 180.0 * t34 * t71 + 360.0 * t73 * t75;
  number t78 = f4 (x);
  number t79 = t78 * t70;
  number t82 = t74 * t47 * t26;
  number t83 = l * t7;
  number t85 = t3 * t7;
  number t87 = t17 * t33;
  number t89 = t17 * t7;
  number t94 = t12 * t33;
  number t97 = t6 * t38;
  number t103 = t56 * t78;
  number t107 = t38 * t35 * t25;
  number t109 = t3 * t6;
  number t110 = t74 * t10;
  number t111 = t110 * t25;
  number t113 = t1 * t30;
  number t116 = t33 * t61;
  number t123 = t69 * t30;
  number t126 = t33 * t30;
  number t130 = t30 * t35 * t70;
  number t132 = 840.0 * t97 * t74 * t26 + 2520.0 * t47 * t6 * t69 * t26 - 210.0 * t103 * t47 * t26 + 300.0
  * t85 * t107 + 360.0 * t109 * t111 - 2520.0 * t113 * t110 * t26 - 7.0 * t116 * t10 * t26 - 35.0 * t33 * t38 * t78
  * t26 - 630.0 * t10 * t56 * t123 * t26 - 21.0 * t126 * t51 * t26 - 720.0 * t85 * t130;
  number t135 = t7 * t51;
  number t138 = t35 * t56;
  number t139 = t30 * t38;
  number t140 = t139 * t26;
  number t142 = t30 * t78;
  number t143 = t142 * t26;
  number t148 = l * t1;
  number t149 = t74 * t35;
  number t150 = t149 * t53;
  number t153 = t139 * t25;
  number t155 = t51 * t25;
  number t158 = t38 * t10 * t70;
  number t161 = t78 * t10 * t25;
  number t164 = t17 * t56;
  number t167 = l * t6;
  number t169 = t30 * t74 * t53;
  number t172 = t10 * t69 * t25;
  number t175 = t66 * t53;
  number t180 = t30 * t47 * t25;
  number t184 = -120.0 * t164 * t75 - 144.0 * t50 * t36 + 2160.0 * t167 * t169 - 450.0 * t83 * t172
  + 480.0 * t83 * t130 - 60.0 * t50 * t175 - 210.0 * t87 * t36 - 150.0 * t34 * t153 + 900.0 * t57 * t180 - 300.0
  * t83 * t107 - 75.0 * t34 * t161;
  number t188 = t139 * t53;
  number t192 = t78 * t35 * t53;
  number t195 = t35 * t69 * t53;
  number t209 = t142 * t53;
  number t211 = t123 * t53;
  number t216 = 40.0 * t28 * t79 - 900.0 * t73 * t180 + 15.0 * t20 * t155 - 240.0 * t57 * t75 - 160.0 * t50
  * t158 - 120.0 * t50 * t71 - 90.0 * t50 * t209 + 180.0 * t83 * t211 - 90.0 * t28 * t39 + 270.0 * t50 * t44 - 90.0
  * t18 * t39;
  number t220 = t7 * t56;
  number t221 = t4 * t220;
  number t223 = t17 * t220;
  number t225 = l * t220;
  number t229 = t25 * t70;
  number t231 = t78 * t78;
  number t234 = t12 * t220;
  number t236 = t5 * t220;
  number t241 = t69 * t69;
  number t244 = t3 * t220;
  number t246 = t74 * t74;
  number t255 = 735.0 * t221 * t10 - 1624.0 * t223 * t10 - 720.0 * t225 * t10
  - t220 * f8 (x) * t229 + 35.0 * t8 * t231 * t229
  - 175.0 * t234 * t10 + 21.0 * t236 * t10 - t4 * t17 * t220 * t10 + 630.0 * t7 * t241 * t229 + 1764.0 * t244
  * t10 + 5040.0 * t246 * t229 - 630.0 * t15 * t44 + 28.0 * t8 * t30 * t61 * t229 - 420.0 * t42 * t130 + 595.0
  * t15 * t36 + 7560.0 * t57 * t169;
  number t269 = t35 * t7;
  number t272 = t10 * t33;
  number t273 = t38 * t78;
  number t282 = t66 * t229;
  number t285 = 1575.0 * t223 * t31 - 1680.0 * t103 * t74 * t229 + 8.0 * t23 * t10 * t229 + 105.0 * t234
  * t31 + 25200.0 * t74 * t6 * t69 * t229 + 1050.0 * t244 * t39 - 126.0 * t28 * t54 - 525.0 * t20 * t161 - 35.0
  * t221 * t79 + 2520.0 * t269 * t142 * t229 - 560.0 * t272 * t273 * t229 - 105.0 * t13 * t36 + 7.0 * t9 * t36
  - 20160.0 * t113 * t149 * t229 - 56.0 * t116 * t35 * t229 + 1680.0 * t269 * t282 - 210.0 * t28 * t175;
  number t301 = t30 * t51;
  number t306 = t69 * t38;
  number t317 = 2100.0 * t34 * t48 - 2520.0 * t83 * t59 + 49.0 * t28 * t61 * t10 * t26 + 21.0 * t225 * t62
  + 2520.0 * t85 * t59 - 630.0 * t34 * t192 + 840.0 * t225 * t31 + 56.0 * t8 * t38 * t51 * t229 + 6720.0 * t97
  * t110 * t229 - 336.0 * t272 * t301 * t229 + 336.0 * t135 * t47 * t229 + 5040.0 * t65 * t306 * t229 - 10080.0
  * t138 * t123 * t229 + 4200.0 * t83 * t180 - 560.0 * t126 * t282 - 420.0 * t33 * t69 * t78 * t229 - 840.0
  * t18 * t158;
  number t340 = -2100.0 * t50 * t172 - 13440.0 * t47 * t56 * t139 * t229 + 630.0 * t50 * t211 - 2520.0
  * t167 * t150 + 2205.0 * t18 * t44 - 1575.0 * t18 * t36 - 595.0 * t221 * t31 + 210.0 * t221 * t39 + 1918.0
  * t20 * t36 - 7.0 * t236 * t31 + 2520.0 * t109 * t150 - 840.0 * t28 * t36 - 1918.0 * t244 * t31 + 630.0 * t50
  * t192 - 5670.0 * t83 * t195 + 8820.0 * t83 * t35 * t140 + 17640.0 * t167 * t30 * t110 * t26;
  number t362 = t50 * t10;
  number t366 = 1155.0 * t20 * t71 + 210.0 * t20 * t175 + 315.0 * t20 * t209 - 7.0 * t225 * t22 * t26
  - 630.0 * t34 * t211 + 126.0 * t20 * t54 - 5040.0 * t148 * t82 - 1008.0 * t50 * t48 - 2520.0 * t34 * t10
  * t188 + 140.0 * t15 * t158 - 17640.0 * t57 * t47 * t69 * t26 - 980.0 * t50 * t10 * t66 * t26 - 700.0 * t87
  * t107 + 2520.0 * t362 * t188 + 2100.0 * t89 * t180 - 1050.0 * t87 * t172;
  number t388 = 1470.0 * t83 * t78 * t47 * t26 - 70.0 * t225 * t155 - 1400.0 * t50 * t107 + 210.0 * t46
  * t75 + 2520.0 * t87 * t130 + 700.0 * t28 * t153 + 1540.0 * t20 * t158 - 4620.0 * t34 * t130 - 1470.0 * t87
  * t48 - 294.0 * t50 * t51 * t35 * t26 - 3150.0 * t20 * t44 - 840.0 * t164 * t111 - 21.0 * t244 * t62 + 175.0
  * t18 * t161 - 1680.0 * t57 * t111 + 210.0 * t225 * t79 - 1050.0 * t20 * t153;
  number t409 = 210.0 * t223 * t79 - 735.0 * t223 * t39 + 63.0 * t13 * t44 - 6300.0 * t85 * t180 + 1512.0
  * t28 * t44 - 504.0 * t225 * t39 + 420.0 * t42 * t48 + 350.0 * t18 * t153 - 630.0 * t18 * t71 - 21.0 * t234 * t39
  - 1260.0 * t83 * t75 + 3150.0 * t34 * t172 + 2100.0 * t34 * t107 - 35.0 * t223 * t155 - 385.0 * t244 * t79
  + 105.0 * t244 * t155 + 4410.0 * t83 * t10 * t123 * t26;
  number t432 = 147.0 * t28 * t301 * t26 - 1470.0 * t50 * t306 * t26 - 315.0 * t28 * t209 + 105.0 * t15
  * t71 - 840.0 * t28 * t158 - 630.0 * t28 * t71 - 42.0 * t94 * t48 + 350.0 * t28 * t161 + 2520.0 * t50 * t130
  - 1470.0 * t362 * t143 + 245.0 * t28 * t273 * t26 - 5880.0 * t57 * t38 * t74 * t26 - 7560.0 * t73 * t169
  + 5670.0 * t85 * t195 + 2520.0 * t73 * t111 - 1260.0 * t89 * t75 + 2310.0 * t85 * t75;
  return x - 7.0 * t1 * x
    * (42.0 * t135 * t35 * t26 - 60.0 * t15 * t31 + 330.0 * t85 * t48 - 180.0 * t89
       * t48 + 60.0 * t42 * t36 + 6.0 * t13 * t31 - 6.0 * t94 * t36 + 20.0 * t18 * t79 + 720.0 * t83 * t10 * t188 + 210.0
       * t7 * t69 * t38 * t26 - 1260.0 * t138 * t140 + 210.0 * t65 * t143 - 720.0 * t148 * t150 + 240.0 * t89 * t130
       + 150.0 * t50 * t153 - 15.0 * t28 * t155 - 80.0 * t87 * t158 + t77 + 720.0 * t82 + 270.0 * t87 * t44 - 180.0
       * t83 * t48 + t132 + 75.0 * t50 * t161 + t184 + 450.0 * t85 * t172 - 360.0 * t167 * t111 + t216 + 180.0 * t83
       * t192 - 1620.0 * t57 * t195 - 495.0 * t34 * t44 - 60.0 * t87 * t71 - 60.0 * t20 * t79 + 144.0 * t28 * t31
       + 240.0 * t34 * t158) / (t255 + t285 + t317 + t340 + t366 + t388 + t409 + t432);
}

number
al8 (ftype f, ftype f1, ftype f2, ftype f3, ftype f4, ftype f5, ftype f6, ftype f7, ftype f8, number l, number x)
{
  number t1 = f (x);
  number t3 = t1 * t1;
  number t4 = t3 * t3;
  number t5 = t4 * t3;
  number t6 = f7 (x);
  number t7 = t5 * t6;
  number t8 = x * x;
  number t9 = t8 * x;
  number t10 = t8 * t8;
  number t11 = t10 * t9;
  number t13 = l * l;
  number t14 = t13 * t13;
  number t15 = t14 * l;
  number t16 = t3 * t1;
  number t17 = t4 * t16;
  number t18 = t15 * t17;
  number t19 = t14 * t5;
  number t20 = f1 (x);
  number t21 = t20 * x;
  number t23 = t15 * t5;
  number t25 = t20 * t20;
  number t26 = t25 * t20;
  number t27 = t25 * t25;
  number t29 = t27 * t26 * t11;
  number t30 = t14 * t17;
  number t31 = t13 * l;
  number t32 = t31 * t17;
  number t33 = l * t17;
  number t34 = t14 * t31;
  number t35 = t34 * t17;
  number t36 = l * t4;
  number t37 = t26 * t9;
  number t39 = t13 * t5;
  number t40 = f4 (x);
  number t41 = t40 * t10;
  number t43 = -t7 * t11 + 175.0 * t18 - 595.0 * t19 * t21 + 105.0 * t23 * t21 - 5040.0 * t29 - 735.0 * t30
  + 1624.0 * t32 + 720.0 * t33 + t35 + 1260.0 * t36 * t37 + 105.0 * t39 * t41;
  number t44 = f3 (x);
  number t45 = t44 * t9;
  number t47 = t4 * t1;
  number t48 = t14 * t47;
  number t49 = f2 (x);
  number t51 = t49 * t20 * t9;
  number t53 = t49 * t8;
  number t55 = t31 * t5;
  number t57 = t14 * t4;
  number t62 = t31 * t47;
  number t63 = t25 * t8;
  number t66 = t15 * t47;
  number t68 = -385.0 * t39 * t45 + 210.0 * t48 * t51 - 21.0 * t23 * t53 + 1575.0 * t55 * t21 - 210.0 * t57
  * t37 + 210.0 * t55 * t45 - 735.0 * t55 * t53 - 1918.0 * t39 * t21 + 1470.0 * t62 * t63 + 210.0 * t19 * t53
  + 42.0 * t66 * t63;
  number t70 = l * t47;
  number t71 = t49 * t49;
  number t72 = t71 * t10;
  number t75 = t13 * t4;
  number t78 = t49 * t25 * t10;
  number t81 = t44 * t20 * t10;
  number t83 = t31 * t4;
  number t86 = l * t16;
  number t88 = t10 * t8;
  number t89 = t44 * t26 * t88;
  number t92 = t13 * t3;
  number t93 = t27 * t20;
  number t94 = t10 * x;
  number t95 = t93 * t94;
  number t97 = t49 * t40;
  number t98 = t97 * t88;
  number t100 = 420.0 * t70 * t72 + 1050.0 * t39 * t53 - 2310.0 * t75 * t37 + 3780.0 * t75 * t78 + 560.0
  * t70 * t81 + 1260.0 * t83 * t37 - 1260.0 * t83 * t78 + 3360.0 * t86 * t89 - 35.0 * t19 * t45 - 2520.0 * t92
  * t95 + 210.0 * t70 * t98;
  number t101 = t71 * t49;
  number t102 = t101 * t88;
  number t104 = t13 * t16;
  number t105 = t27 * t10;
  number t108 = t20 * t71 * t94;
  number t113 = t40 * t20 * t94;
  number t116 = t49 * t44;
  number t117 = t116 * t88;
  number t120 = t40 * t25 * t88;
  number t123 = t25 * t71 * t88;
  number t125 = f5 (x);
  number t127 = t125 * t20 * t88;
  number t129 = t44 * t44;
  number t130 = t129 * t88;
  number t132 = l * t5;
  number t134 = -630.0 * t36 * t102 - 2520.0 * t104 * t105 - 1890.0 * t75 * t108 - 1260.0 * t70 * t51
  - 1260.0 * t62 * t51 - 210.0 * t70 * t113 - 2520.0 * t36 * t20 * t117 - 630.0 * t36 * t120 + 7560.0 * t86
  * t123 + 84.0 * t70 * t127 + 140.0 * t70 * t130 - 504.0 * t132 * t53;
  number t137 = f6 (x);
  number t138 = t137 * t88;
  number t140 = t13 * t47;
  number t143 = t14 * t13;
  number t144 = t143 * t5;
  number t146 = t116 * t94;
  number t150 = t20 * t4;
  number t151 = t97 * t11;
  number t154 = t3 * t44;
  number t157 = l * t1;
  number t158 = t27 * t25;
  number t159 = t158 * t88;
  number t161 = -7.0 * t132 * t138 - 2100.0 * t140 * t63 + 210.0 * t62 * t72 - 7.0 * t144 * t21 - 420.0
  * t70 * t146 + 1008.0 * t70 * t63 + 2310.0 * t140 * t51 - 630.0 * t150 * t151 + 280.0 * t62 * t81 - 4200.0
  * t154 * t27 * t11 + 5040.0 * t157 * t159;
  number t163 = t49 * t26 * t94;
  number t169 = t13 * t17;
  number t170 = t25 * t16;
  number t171 = t116 * t11;
  number t174 = t44 * t25 * t94;
  number t176 = t47 * t137;
  number t179 = t16 * t40;
  number t183 = l * t3;
  number t186 = t49 * t27 * t88;
  number t188 = -5040.0 * t86 * t163 - 2520.0 * t36 * t78 + 2520.0 * t20 * t16 * t101 * t11 - 1764.0
  * t169 + 5040.0 * t170 * t171 + 1260.0 * t36 * t174 + 14.0 * t176 * t20 * t11 + 840.0 * t179 * t26 * t11 - 70.0
  * t132 * t41 + 2520.0 * t183 * t95 - 12600.0 * t183 * t186;
  number t190 = t143 * t17;
  number t194 = t125 * t94;
  number t198 = t47 * t49;
  number t204 = t1 * t49;
  number t209 = -21.0 * t190 - 420.0 * t150 * t129 * t11 + 1890.0 * t36 * t108 - 21.0 * t39 * t194 - 840.0
  * t140 * t81 - 420.0 * t48 * t63 + 42.0 * t198 * t125 * t11 - 630.0 * t4 * t71 * t44 * t11 + 15120.0 * t204
  * t93 * t11 + 21.0 * t132 * t194 + 210.0 * t132 * t45;
  number t222 = t31 * t16;
  number t225 = t4 * t125;
  number t229 = 5040.0 * t104 * t163 - 12600.0 * t26 * t3 * t71 * t11 - 630.0 * t140 * t72 - 1260.0 * t75
  * t174 + 420.0 * t140 * t146 + 70.0 * t47 * t44 * t40 * t11 + 210.0 * t140 * t113 + 1680.0 * t86 * t105 + 840.0
  * t222 * t105 + 840.0 * t132 * t21 - 126.0 * t225 * t25 * t11 - 35.0 * t55 * t41;
  number t233 = t71 * t71;
  number t235 = t10 * t10;
  number t237 = t40 * t40;
  number t243 = t4 * t4;
  number t248 = t14 * t14;
  number t251 = t20 * t47;
  number t252 = t44 * t40;
  number t257 = t71 * t44;
  number t265 = 2520.0 * t4 * t233 * t235 + 70.0 * t5 * t237 * t235
  - t17 * f8 (x) * t235 - 5040.0 * l * t243 + 6769.0 * t14 * t243
  + 13068.0 * t13 * t243 + 322.0 * t143 * t243 + t248 * t243 - 27720.0 * t140 * t78 - 1680.0 * t251 * t252
  * t235 - 141120.0 * t204 * t158 * t235 + 20160.0 * t150 * t257 * t235 - 10080.0 * t36 * t105 + 560.0 * t30
  * t45 - 70.0 * t30 * t41 + 1680.0 * t57 * t105 - 10080.0 * t70 * t108;
  number t267 = t25 * t4;
  number t268 = t129 * t235;
  number t272 = t27 * t27;
  number t283 = t49 * t125;
  number t290 = 26880.0 * t36 * t163 + 6720.0 * t267 * t268 + 1120.0 * t55 * t146 + 11760.0 * t55 * t51
  + 40320.0 * t272 * t235 - 13132.0 * t31 * t243 - 1960.0 * t15 * t243 - 28.0 * t34 * t243 + 28.0 * t33 * t138
  - 13440.0 * t86 * t95 + 15120.0 * t62 * t78 + 420.0 * t32 * t41 - 3360.0 * t55 * t81 + 6160.0 * t39 * t81
  - 1008.0 * t251 * t283 * t235 - 50400.0 * t104 * t186 - 168.0 * t176 * t25 * t235 - 770.0 * t169 * t41;
  number t310 = t70 * t20;
  number t320 = 112.0 * t5 * t44 * t125 * t235 + 40320.0 * t154 * t93 * t235 + 2520.0 * t70 * t102 + 16.0
  * t7 * t20 * t235 - 8400.0 * t179 * t27 * t235 - 50400.0 * t170 * t101 * t235 + 1344.0 * t225 * t26 * t235
  + 13440.0 * t83 * t163 + 20160.0 * t104 * t95 - 56.0 * t32 * t194 + 16800.0 * t140 * t37 + 10080.0 * t310
  * t117 - 560.0 * t132 * t130 - 3360.0 * t70 * t20 * t129 * t11 - 336.0 * t132 * t127 + 560.0 * t19 * t81
  + 8064.0 * t132 * t51 - 40320.0 * t75 * t163;
  number t352 = 151200.0 * t27 * t3 * t71 * t235 - 67200.0 * t26 * t16 * t116 * t235 - 10080.0 * t83
  * t105 - 1008.0 * t70 * t125 * t25 * t11 + 2800.0 * t169 * t45 - 6720.0 * t222 * t95 - 40320.0 * t157 * t29
  - 5040.0 * t310 * t151 + 2520.0 * t70 * t120 + 112.0 * t132 * t137 * t20 * t11 + 420.0 * t19 * t72 - 33600.0
  * t86 * t44 * t27 * t11 - 5040.0 * t62 * t108 - 100800.0 * t86 * t26 * t71 * t11 + 560.0 * t132 * t252 * t11
  - 1960.0 * t32 * t45 - 3360.0 * t62 * t174 - 16800.0 * t39 * t51;
  number t380 = 560.0 * t55 * t113 - 840.0 * t132 * t98 + 336.0 * t132 * t283 * t11 + 4760.0 * t19 * t63
  - 8064.0 * t70 * t37 - 1344.0 * t33 * t45 + 10080.0 * t140 * t174 - 11760.0 * t62 * t37 - 10080.0 * t140
  * t20 * t117 - 28.0 * t169 * t138 + 13440.0 * t75 * t89 - 8.0 * t33 * t6 * t11 - 5040.0 * t70 * t257 * t11
  + 20160.0 * t36 * t20 * t101 * t11 + 120960.0 * t183 * t49 * t93 * t11 - 2520.0 * t48 * t78 - 1400.0 * t18
  * t21;
  number t399 = 4620.0 * t39 * t72 + 3360.0 * t33 * t53 - 840.0 * t23 * t63 - 2520.0 * t140 * t102
  - 13440.0 * t36 * t89 + 560.0 * t39 * t130 + 50400.0 * t86 * t186 - 1680.0 * t39 * t113 - 30240.0 * t36
  * t123 + 14112.0 * t169 * t21 + 20160.0 * t92 * t159 + 15344.0 * t39 * t63 - 2520.0 * t55 * t72 + 6300.0
  * t32 * t53 + 336.0 * t23 * t51 - 12600.0 * t55 * t63 - 7672.0 * t169 * t53 - 12992.0 * t32 * t21;
  number t420 = -336.0 * t66 * t37 - 8.0 * t35 * t21 + 5880.0 * t30 * t21 + 168.0 * t190 * t21 - 2380.0
  * t30 * t53 - 5760.0 * t33 * t21 - 28.0 * t190 * t53 + 840.0 * t39 * t98 - 6720.0 * t132 * t63 - 2520.0 * t140
  * t120 + 336.0 * t39 * t127 + 40320.0 * t36 * t25 * t171 + 30240.0 * t75 * t123 + 15120.0 * t140 * t108
  - 20160.0 * t183 * t159 + 2240.0 * t132 * t146 + 168.0 * t169 * t194 - 112.0 * t33 * t194;
  number t446 = -3360.0 * t19 * t51 - 1260.0 * t47 * t71 * t40 * t235 - 1680.0 * t198 * t268 + 56.0 * t5
  * t49 * t137 * t235 + 10080.0 * t267 * t97 * t235 + 420.0 * t18 * t53 + 56.0 * t144 * t63 + 6720.0 * t36 * t40
  * t26 * t11 + 15120.0 * t70 * t78 + 3360.0 * t48 * t37 - 56.0 * t18 * t45 - 3360.0 * t132 * t81 - 3360.0 * t39
  * t146 + 18480.0 * t75 * t105 + 1120.0 * t132 * t113 - 6720.0 * t70 * t174 + 420.0 * t33 * t41 - 2520.0
  * t132 * t72;
  return x + 8.0 * t1 * x * (t43 + t68 + t100 + t134 + t161 + t188 + t209 + t229) /
    (t265 + t290 + t320 + t352 + t380 + t399 + t420 + t446);
}

number
bl8 (ftype f, ftype f1, ftype f2, ftype f3, ftype f4, ftype f5, ftype f6, ftype f7, ftype f8, ftype f9, number l, number x)
{
  number t1 = f (x);
  number t3 = t1 * t1;
  number t4 = t3 * t1;
  number t5 = t3 * t3;
  number t6 = t5 * t4;
  number t7 = f8 (x);
  number t8 = t6 * t7;
  number t9 = x * x;
  number t10 = t9 * x;
  number t11 = t9 * t9;
  number t12 = t11 * t10;
  number t14 = t5 * t3;
  number t15 = f4 (x);
  number t16 = t15 * t15;
  number t19 = l * t6;
  number t20 = f1 (x);
  number t22 = l * l;
  number t23 = t22 * l;
  number t24 = t22 * t22;
  number t25 = t24 * t23;
  number t26 = t25 * t6;
  number t28 = t23 * t6;
  number t30 = t24 * t6;
  number t32 = t24 * l;
  number t33 = t32 * t6;
  number t35 = t24 * t22;
  number t36 = t35 * t6;
  number t38 = f2 (x);
  number t39 = t38 * t38;
  number t40 = t39 * t39;
  number t43 = t22 * t6;
  number t45 = t5 * t1;
  number t46 = t20 * t45;
  number t47 = f3 (x);
  number t48 = t47 * t15;
  number t49 = t48 * t12;
  number t51 = t20 * t20;
  number t52 = t51 * t5;
  number t53 = t38 * t15;
  number t54 = t53 * t12;
  number t56 = l * t5;
  number t57 = t51 * t20;
  number t59 = t11 * t9;
  number t60 = t15 * t57 * t59;
  number t62 = t35 * t14;
  number t63 = t51 * x;
  number t65 = t32 * t14;
  number t67 = t1 * t38;
  number t68 = t51 * t51;
  number t69 = t68 * t51;
  number t72 = -t8 * t12 + 35.0 * t14 * t16 * t12 - 720.0 * t19 * t20 - t26 * t20 - 1624.0 * t28 * t20 + 735.0
  * t30 * t20 - 175.0 * t33 * t20 + 21.0 * t36 * t20 + 630.0 * t5 * t40 * t12 + 1764.0 * t43 * t20 - 560.0 * t46
  * t49 + 2520.0 * t52 * t54 + 1470.0 * t56 * t60 + 7.0 * t62 * t63 - 105.0 * t65 * t63 - 20160.0 * t67 * t69 * t12;
  number t73 = t47 * t47;
  number t74 = t73 * t12;
  number t76 = f6 (x);
  number t77 = t45 * t76;
  number t83 = t47 * t9;
  number t85 = t15 * t10;
  number t87 = t22 * t14;
  number t89 = t15 * t20 * t11;
  number t91 = t38 * x;
  number t93 = t24 * t14;
  number t95 = t23 * t14;
  number t97 = t68 * t68;
  number t98 = t97 * t12;
  number t99 = t24 * t45;
  number t101 = t38 * t51 * t10;
  number t105 = t14 * t38;
  number t109 = t47 * t20 * t10;
  number t114 = l * t45;
  number t115 = t39 * t38;
  number t116 = t11 * x;
  number t117 = t115 * t116;
  number t119 = 1680.0 * t52 * t74 - 56.0 * t77 * t51 * t12 + 25200.0 * t68 * t3 * t39 * t12 + 1050.0 * t43
  * t83 - 35.0 * t30 * t85 - 525.0 * t87 * t89 + 1575.0 * t28 * t91 + 595.0 * t93 * t63 - 1575.0 * t95 * t63
  + 5040.0 * t98 - 420.0 * t99 * t101 + 1918.0 * t87 * t63 - 7.0 * t36 * t91 + 28.0 * t105 * t76 * t12 - 840.0
  * t95 * t109 - 420.0 * t45 * t39 * t15 * t12 + 630.0 * t114 * t117;
  number t121 = l * t3;
  number t122 = t69 * t116;
  number t125 = t20 * t39 * t11;
  number t127 = f5 (x);
  number t129 = t127 * t20 * t116;
  number t131 = t22 * t45;
  number t134 = t38 * t47;
  number t135 = t134 * t116;
  number t138 = t20 * t73 * t59;
  number t140 = l * t4;
  number t142 = t57 * t39 * t59;
  number t145 = t57 * t9;
  number t147 = t114 * t20;
  number t149 = t24 * t5;
  number t150 = t68 * t10;
  number t152 = t127 * t11;
  number t155 = t47 * t51 * t11;
  number t158 = t23 * t45;
  number t161 = l * t14;
  number t162 = t73 * t116;
  number t164 = -2520.0 * t121 * t122 - 2100.0 * t114 * t125 + 126.0 * t87 * t129 - 630.0 * t131 * t117
  - 2520.0 * t131 * t20 * t135 - 980.0 * t114 * t138 - 17640.0 * t140 * t142 + 140.0 * t93 * t109 - 1008.0
  * t114 * t145 + 2520.0 * t147 * t135 + 210.0 * t149 * t150 - 70.0 * t19 * t152 - 1400.0 * t114 * t155
  + 1540.0 * t87 * t109 + 2520.0 * t158 * t101 - 4620.0 * t131 * t101 - 210.0 * t161 * t162;
  number t166 = t76 * t20 * t59;
  number t170 = t15 * t51 * t116;
  number t172 = t22 * t5;
  number t174 = t47 * t57 * t116;
  number t176 = t38 * t127;
  number t177 = t176 * t12;
  number t179 = t3 * t47;
  number t180 = t68 * t20;
  number t184 = t38 * t57 * t11;
  number t189 = t20 * t5;
  number t190 = t39 * t47;
  number t191 = t190 * t12;
  number t194 = t127 * t51 * t59;
  number t196 = t76 * t116;
  number t202 = t51 * t39 * t116;
  number t206 = 49.0 * t161 * t166 + 2100.0 * t131 * t145 - 630.0 * t131 * t170 + 2520.0 * t172 * t174
  - 336.0 * t46 * t177 + 6720.0 * t179 * t180 * t12 + 4200.0 * t56 * t184 - 10080.0 * t51 * t4 * t115 * t12
  + 5040.0 * t189 * t191 - 294.0 * t114 * t194 - 21.0 * t43 * t196 + 175.0 * t95 * t89 + 105.0 * t33 * t91
  - 1918.0 * t43 * t91 - 5670.0 * t56 * t202 + 630.0 * t114 * t170 + 210.0 * t87 * t162;
  number t209 = t39 * t10;
  number t214 = t20 * t115 * t59;
  number t219 = t38 * t20 * t9;
  number t221 = t53 * t116;
  number t225 = t23 * t5;
  number t228 = t180 * t11;
  number t232 = t134 * t11;
  number t234 = 1155.0 * t87 * t209 + 3150.0 * t131 * t125 - 1260.0 * t56 * t150 + 4410.0 * t56 * t214
  - 385.0 * t43 * t85 + 105.0 * t43 * t152 - 3150.0 * t87 * t219 - 315.0 * t161 * t221 + 105.0 * t93 * t209
  - 630.0 * t95 * t209 - 1260.0 * t225 * t150 + 210.0 * t19 * t85 - 1680.0 * t140 * t228 - 6300.0 * t172
  * t184 + 63.0 * t65 * t219 + 350.0 * t95 * t232;
  number t237 = t48 * t59;
  number t239 = t32 * t45;
  number t244 = t53 * t59;
  number t248 = t47 * t68 * t59;
  number t252 = t4 * t15;
  number t255 = f7 (x);
  number t256 = t14 * t255;
  number t260 = t38 * t68 * t116;
  number t264 = 420.0 * t99 * t145 + 1512.0 * t161 * t219 + 245.0 * t161 * t237 - 42.0 * t239 * t145
  - 840.0 * t161 * t109 + 350.0 * t161 * t89 + 2520.0 * t114 * t101 - 1470.0 * t147 * t244 + 5670.0 * t172
  * t202 - 5880.0 * t140 * t248 - 840.0 * t161 * t63 - 126.0 * t161 * t129 - 1680.0 * t252 * t68 * t12 + 8.0
  * t256 * t20 * t12 + 7560.0 * t140 * t260 - 630.0 * t93 * t219 + 210.0 * t30 * t83;
  number t268 = t57 * t4;
  number t269 = t134 * t12;
  number t273 = t5 * t127;
  number t287 = l * t1;
  number t288 = t68 * t57;
  number t289 = t288 * t59;
  number t292 = t255 * t59;
  number t294 = -595.0 * t30 * t91 + 2205.0 * t95 * t219 - 13440.0 * t268 * t269 - 560.0 * t45 * t38 * t74
  + 336.0 * t273 * t57 * t12 + 56.0 * t14 * t47 * t127 * t12 + 840.0 * t19 * t91 + 21.0 * t19 * t196 - 2520.0
  * t56 * t174 - 1470.0 * t158 * t145 + 700.0 * t161 * t232 - 1050.0 * t158 * t125 + 2100.0 * t225 * t184
  - 700.0 * t158 * t155 - 5040.0 * t287 * t289 + 315.0 * t87 * t221 - 7.0 * t19 * t292;
  number t296 = t38 * t180 * t59;
  number t299 = t134 * t59;
  number t301 = t22 * t3;
  number t303 = t23 * t4;
  number t305 = t190 * t59;
  number t307 = t176 * t59;
  number t316 = t22 * t4;
  number t321 = 17640.0 * t121 * t296 + 8820.0 * t56 * t51 * t299 + 2520.0 * t301 * t122 - 840.0 * t303
  * t228 - 1470.0 * t114 * t305 + 147.0 * t161 * t307 - 35.0 * t28 * t152 + 2100.0 * t131 * t155 - 21.0 * t33
  * t83 - 504.0 * t19 * t83 - 735.0 * t28 * t83 - 1050.0 * t87 * t232 + 210.0 * t28 * t85 + 2520.0 * t316 * t228
  + 2310.0 * t172 * t150 - 7560.0 * t316 * t260 - 630.0 * t161 * t209;
  number t325 = t5 * t5;
  number t326 = t24 * t325;
  number t328 = t24 * t24;
  number t333 = t11 * t11;
  number t335 = t25 * t325;
  number t340 = t22 * t325;
  number t342 = t35 * t325;
  number t344 = t32 * t325;
  number t346 = l * t325;
  number t348 = t23 * t325;
  number t353 = 6769.0 * t326 * t20 + t328 * t325 * t20
  + t325 * f9 (x) * t333 - 28.0 * t335 * t20 + 560.0 * t14 * t73
  * t47 * t333 + 13068.0 * t340 * t20 + 322.0 * t342 * t20 - 1960.0 * t344 * t20 - 5040.0 * t346 * t20
  - 13132.0 * t348 * t20 - 5376.0 * t19 * t109 - 4200.0 * t99 * t184 + 1680.0 * t95 * t117;
  number t367 = -1680.0 * t19 * t221 - 168.0 * t33 * t209 + 2100.0 * t28 * t89 - 30240.0 * t114 * t202
  - 46200.0 * t131 * t184 + 15400.0 * t87 * t155 + 16128.0 * t161 * t101 - 13440.0 * t114 * t174 - 168.0
  * t340 * t196 - 5880.0 * t28 * t209 + 45360.0 * t131 * t202 - 6720.0 * t158 * t174 + 56.0 * t348 * t196;
  number t378 = t161 * t20;
  number t385 = -6720.0 * t303 * t122 - 560.0 * t28 * t162 + 20160.0 * t225 * t260 + 6720.0 * t95 * t20
  * t135 - 15120.0 * t158 * t202 - 224.0 * t33 * t109 + 40320.0 * t97 * t20 * t333 + 13440.0 * t378 * t135
  - 5760.0 * t19 * t63 - 14112.0 * t340 * t91 - 12992.0 * t28 * t63 + 12992.0 * t348 * t91 + 5880.0 * t30
  * t63;
  number t400 = 14112.0 * t43 * t63 - 5880.0 * t326 * t91 - 672.0 * t19 * t129 + 3360.0 * t161 * t117
  - 5040.0 * t87 * t117 - 33600.0 * t87 * t101 - 7840.0 * t28 * t109 - 1400.0 * t33 * t63 - 2800.0 * t340
  * t85 + 588.0 * t19 * t307 - 6720.0 * t93 * t101 - 560.0 * t326 * t85 + 107520.0 * t56 * t57 * t269;
  number t416 = -12600.0 * t161 * t125 - 84.0 * t36 * t219 + 1260.0 * t33 * t219 - 6300.0 * t348 * t83
  - 4032.0 * t19 * t209 + 1344.0 * t346 * t85 + 4760.0 * t93 * t145 + 16800.0 * t131 * t150 + 15344.0 * t87
  * t145 - 336.0 * t239 * t150 + 23520.0 * t95 * t101 + 11200.0 * t43 * t109 - 7140.0 * t30 * t219;
  number t425 = t39 * t15;
  number t432 = 18900.0 * t28 * t219 - 8064.0 * t114 * t150 + 10080.0 * t19 * t219 - 40320.0 * t287
  * t98 - 23520.0 * t56 * t248 + 17640.0 * t114 * t214 + 5880.0 * t87 * t305 - 70560.0 * t56 * t142 + 3360.0
  * t161 * t425 * t12 - 3850.0 * t43 * t89 + 3360.0 * t161 * t170 + 18480.0 * t172 * t228 - 700.0 * t30 * t232;
  number t447 = 980.0 * t19 * t237 - 12600.0 * t95 * t145 + 2520.0 * t43 * t221 + 1008.0 * t43 * t129
  - 1120.0 * t19 * t162 + 112.0 * t346 * t196 - 13440.0 * t140 * t122 + 770.0 * t340 * t152 - 7700.0 * t43
  * t232 + 4200.0 * t19 * t232 - 840.0 * t65 * t145 - 420.0 * t344 * t83 + 8.0 * t335 * t91;
  number t463 = 56.0 * t62 * t145 + 28.0 * t342 * t83 + 7672.0 * t340 * t83 - 3360.0 * t346 * t83 - 6720.0
  * t161 * t145 - 23016.0 * t43 * t219 - 8.0 * t26 * t63 - 840.0 * t28 * t221 + 2100.0 * t19 * t89 - 10080.0
  * t56 * t228 + 25200.0 * t114 * t184 + 3024.0 * t273 * t68 * t333 + 60480.0 * t179 * t69 * t333;
  number t481 = t114 * t51;
  number t492 = 22680.0 * t189 * t40 * t333 + 20160.0 * t131 * t174 - 336.0 * t28 * t129 + 2380.0 * t326
  * t83 - 1176.0 * t161 * t194 - 15120.0 * t252 * t180 * t333 + 272160.0 * t180 * t3 * t39 * t333 + 2688.0
  * t378 * t177 - 280.0 * t19 * t16 * t12 + 35280.0 * t481 * t299 + 13440.0 * t56 * t15 * t68 * t12 - 53760.0
  * t140 * t47 * t180 * t12 - 201600.0 * t140 * t68 * t39 * t12;
  number t493 = t87 * t20;
  number t501 = t51 * t45;
  number t502 = t48 * t333;
  number t504 = t57 * t5;
  number t514 = t38 * t73;
  number t517 = t20 * t14;
  number t518 = t38 * t76;
  number t523 = -20160.0 * t493 * t135 - 350.0 * t30 * t89 - 10080.0 * t225 * t228 - 980.0 * t43 * t237
  - 84.0 * t6 * t47 * t76 * t333 - 7560.0 * t501 * t502 + 20160.0 * t504 * t73 * t333 - 151200.0 * t268 * t115
  * t333 - 151200.0 * t68 * t4 * t134 * t333 + 90720.0 * t52 * t190 * t333 - 15120.0 * t46 * t514 * t333
  + 504.0 * t517 * t518 * t333 - 4536.0 * t501 * t176 * t333;
  number t527 = t47 * t127;
  number t545 = -504.0 * t77 * t57 * t333 + 1008.0 * t517 * t527 * t333 + 30240.0 * t504 * t53 * t333
  - 36.0 * t6 * t38 * t255 * t333 + 70.0 * t326 * t152 + 196.0 * t19 * t166 - 588.0 * t43 * t307 - 35280.0
  * t131 * t51 * t299 + 5880.0 * t493 * t244 - 20160.0 * t121 * t289 - 20160.0 * t481 * t54 + 4480.0 * t378
  * t49 + 1176.0 * t87 * t194;
  number t552 = t127 * t333;
  number t571 = 20160.0 * t301 * t289 + 72.0 * t256 * t51 * t333 - 9.0 * t8 * t20 * t333 - 126.0 * t6 * t15
  * t552 - 11340.0 * t46 * t425 * t333 + 756.0 * t14 * t39 * t552 - 7560.0 * t45 * t115 * t47 * t333 + 80640.0
  * t56 * t51 * t115 * t12 + 1400.0 * t344 * t91 + 3360.0 * t99 * t150 - 11760.0 * t158 * t150 - 168.0 * t342
  * t91 - 13440.0 * t114 * t51 * t73 * t12;
  number t594 = 161280.0 * t121 * t38 * t69 * t12 + 630.0 * t517 * t16 * t333 + 2520.0 * t105 * t502
  + 23100.0 * t87 * t125 + 4200.0 * t28 * t232 - 5880.0 * t378 * t244 + 70560.0 * t140 * t296 + 5760.0 * t346
  * t91 - 5040.0 * t114 * t40 * t12 + 40320.0 * t56 * t260 - 64.0 * t19 * t255 * t20 * t12 - 12600.0 * t95
  * t125 - 448.0 * t19 * t527 * t12;
  number t609 = 28.0 * t340 * t292 - 420.0 * t346 * t152 + 4480.0 * t161 * t514 * t12 + 25200.0 * t158
  * t184 - 5880.0 * t131 * t60 + 70560.0 * t172 * t142 - 28.0 * t346 * t292 + 23520.0 * t172 * t248 - 196.0
  * t43 * t166 - 70560.0 * t316 * t296 + 1960.0 * t348 * t85 + 1680.0 * t95 * t170 + 168.0 * t36 * t63;
  number t630 = 5880.0 * t114 * t60 + 448.0 * t161 * t76 * t51 * t12 + 8.0 * t346 * t7 * t12 + 3920.0 * t87
  * t138 - 5880.0 * t161 * t305 - 3920.0 * t161 * t138 - 181440.0 * t67 * t288 * t333 + 1680.0 * t149 * t228
  - 2688.0 * t114 * t127 * t57 * t12 - 420.0 * t348 * t152 - 17640.0 * t131 * t214 + 2100.0 * t93 * t125
  - 8400.0 * t95 * t155;
  number t645 = 1400.0 * t93 * t155 - 8400.0 * t161 * t155 - 224.0 * t19 * t518 * t12 + 1680.0 * t43
  * t162 + 2240.0 * t30 * t109 + 672.0 * t65 * t101 - 5040.0 * t87 * t170 + 20160.0 * t316 * t122 + 8400.0
  * t43 * t209 - 60480.0 * t172 * t260 - 40320.0 * t147 * t191 + 1680.0 * t30 * t209 + 56.0 * t344 * t85;
  return x - 8.0 * t1 * x * (t72 + t119 + t164 + t206 + t234 + t264 + t294 + t321) /
    (t353 + t367 + t385 + t400 + t416 + t432 + t447 + t463 + t492 + t523 + t545 + t571 + t594 + t609 + t630 + t645);
}

number
al9 (ftype f, ftype f1, ftype f2, ftype f3, ftype f4, ftype f5, ftype f6, ftype f7, ftype f8, ftype f9, number l, number x)
{
  number t1 = f (x);
  number t3 = t1 * t1;
  number t4 = t3 * t1;
  number t5 = t3 * t3;
  number t6 = t5 * t4;
  number t7 = f8 (x);
  number t8 = t6 * t7;
  number t9 = x * x;
  number t10 = t9 * t9;
  number t11 = t10 * t10;
  number t13 = f2 (x);
  number t14 = t13 * t13;
  number t15 = t14 * t14;
  number t18 = t5 * t3;
  number t19 = f4 (x);
  number t20 = t19 * t19;
  number t23 = l * l;
  number t24 = t23 * t23;
  number t25 = t24 * l;
  number t26 = t5 * t5;
  number t27 = t25 * t26;
  number t28 = t23 * l;
  number t29 = t28 * t26;
  number t30 = t24 * t28;
  number t31 = t30 * t26;
  number t32 = l * t26;
  number t33 = t24 * t26;
  number t34 = t23 * t26;
  number t35 = t24 * t23;
  number t36 = t35 * t26;
  number t37 = t24 * t24;
  number t38 = t37 * t26;
  number t39 = t28 * t18;
  number t40 = f3 (x);
  number t41 = t13 * t40;
  number t42 = t10 * x;
  number t43 = t41 * t42;
  number t45 = f1 (x);
  number t47 = t9 * x;
  number t48 = t13 * t45 * t47;
  number t50 = t45 * t45;
  number t51 = t50 * t50;
  number t52 = t51 * t51;
  number t53 = t52 * t11;
  number t54 = t5 * t1;
  number t55 = l * t54;
  number t57 = t45 * t14 * t42;
  number t59 = l * t5;
  number t60 = t50 * t45;
  number t62 = t13 * t60 * t42;
  number t64 = t50 * t5;
  number t65 = t40 * t40;
  number t66 = t65 * t11;
  number t68 = -t8 * t11 + 2520.0 * t5 * t15 * t11 + 70.0 * t18 * t20 * t11 - 1960.0 * t27 - 13132.0 * t29
  - 28.0 * t31 - 5040.0 * t32 + 6769.0 * t33 + 13068.0 * t34 + 322.0 * t36 + t38 + 1120.0 * t39 * t43
  + 11760.0 * t39 * t48 + 40320.0 * t53 - 10080.0 * t55 * t57 + 26880.0 * t59 * t62 + 6720.0 * t64 * t66;
  number t69 = l * t18;
  number t70 = f5 (x);
  number t72 = t10 * t9;
  number t73 = t70 * t45 * t72;
  number t76 = t10 * t47;
  number t77 = t45 * t65 * t76;
  number t83 = t23 * t5;
  number t85 = t14 * t10;
  number t87 = t60 * t4;
  number t88 = t41 * t11;
  number t90 = t24 * t18;
  number t92 = t40 * t45 * t10;
  number t94 = t55 * t45;
  number t95 = t41 * t72;
  number t97 = t28 * t5;
  number t98 = t51 * t10;
  number t100 = t23 * t6;
  number t101 = t19 * t10;
  number t103 = f6 (x);
  number t104 = t54 * t103;
  number t111 = t14 * t13;
  number t114 = t4 * t19;
  number t117 = t5 * t70;
  number t120 = f7 (x);
  number t121 = t18 * t120;
  number t124 = t3 * t40;
  number t125 = t51 * t45;
  number t128 = -336.0 * t69 * t73 - 3360.0 * t55 * t77 + 8064.0 * t69 * t48 + 151200.0 * t51 * t3 * t14
  * t11 - 40320.0 * t83 * t62 - 2520.0 * t39 * t85 - 67200.0 * t87 * t88 + 560.0 * t90 * t92 + 10080.0 * t94
  * t95 - 10080.0 * t97 * t98 - 770.0 * t100 * t101 - 168.0 * t104 * t50 * t11 + 112.0 * t18 * t40 * t70 * t11
  - 50400.0 * t50 * t4 * t111 * t11 - 8400.0 * t114 * t51 * t11 + 1344.0 * t117 * t60 * t11 + 16.0 * t121 * t45
  * t11 + 40320.0 * t124 * t125 * t11;
  number t130 = t111 * t72;
  number t132 = t23 * t4;
  number t134 = t13 * t51 * t72;
  number t136 = t45 * t54;
  number t137 = t13 * t70;
  number t138 = t137 * t11;
  number t140 = l * t6;
  number t141 = t103 * t72;
  number t144 = t28 * t6;
  number t146 = l * t4;
  number t147 = t125 * t42;
  number t149 = t45 * t5;
  number t150 = t14 * t40;
  number t151 = t150 * t11;
  number t153 = t40 * t19;
  number t154 = t153 * t11;
  number t156 = t1 * t13;
  number t157 = t51 * t50;
  number t160 = t24 * t6;
  number t161 = t40 * t47;
  number t165 = t103 * t45 * t76;
  number t168 = t19 * t50 * t72;
  number t172 = t70 * t50 * t76;
  number t174 = t137 * t76;
  number t177 = 2520.0 * t55 * t130 - 50400.0 * t132 * t134 - 1008.0 * t136 * t138 + 28.0 * t140 * t141
  - 3360.0 * t39 * t92 + 420.0 * t144 * t101 - 13440.0 * t146 * t147 + 20160.0 * t149 * t151 - 1680.0 * t136
  * t154 - 141120.0 * t156 * t157 * t11 + 560.0 * t160 * t161 - 10080.0 * t59 * t98 + 112.0 * t69 * t165
  + 2520.0 * t55 * t168 + 2800.0 * t100 * t161 - 1008.0 * t55 * t172 + 336.0 * t69 * t174 + 420.0 * t90 * t85;
  number t180 = t70 * t42;
  number t182 = t65 * t72;
  number t184 = t23 * t54;
  number t185 = t60 * t47;
  number t188 = t153 * t76;
  number t190 = t28 * t54;
  number t192 = t23 * t18;
  number t195 = t19 * t45 * t42;
  number t197 = t13 * t19;
  number t198 = t197 * t72;
  number t201 = t25 * t6;
  number t202 = t45 * x;
  number t204 = l * t1;
  number t205 = t51 * t60;
  number t206 = t205 * t76;
  number t208 = t28 * t4;
  number t210 = t197 * t76;
  number t213 = t40 * t50 * t42;
  number t216 = t40 * t60 * t72;
  number t218 = -1960.0 * t144 * t161 + 20160.0 * t132 * t147 - 56.0 * t144 * t180 - 560.0 * t69 * t182
  + 16800.0 * t184 * t185 + 13440.0 * t97 * t62 + 560.0 * t69 * t188 - 5040.0 * t190 * t57 - 16800.0 * t192
  * t48 + 560.0 * t39 * t195 - 840.0 * t69 * t198 - 11760.0 * t190 * t185 - 1400.0 * t201 * t202 - 40320.0
  * t204 * t206 - 6720.0 * t208 * t147 - 5040.0 * t94 * t210 - 3360.0 * t190 * t213 + 13440.0 * t83 * t216;
  number t224 = t150 * t76;
  number t226 = t120 * t76;
  number t228 = t13 * t9;
  number t230 = t24 * t54;
  number t232 = t13 * t50 * t10;
  number t235 = t45 * t111 * t76;
  number t237 = l * t3;
  number t239 = t13 * t125 * t76;
  number t241 = t50 * t9;
  number t246 = t25 * t18;
  number t252 = -28.0 * t100 * t141 - 10080.0 * t184 * t45 * t95 - 5040.0 * t55 * t224 - 8.0 * t140 * t226
  + 6300.0 * t144 * t228 - 2520.0 * t230 * t232 + 20160.0 * t59 * t235 + 120960.0 * t237 * t239 + 4760.0
  * t90 * t241 + 10080.0 * t184 * t213 - 1344.0 * t140 * t161 - 8064.0 * t55 * t185 + 336.0 * t246 * t48
  - 2520.0 * t184 * t130 - 840.0 * t246 * t241 - 13440.0 * t59 * t216 + 50400.0 * t146 * t134;
  number t258 = t41 * t76;
  number t261 = t35 * t6;
  number t264 = t23 * t3;
  number t265 = t157 * t72;
  number t269 = t50 * t14 * t72;
  number t278 = 3360.0 * t140 * t228 + 4620.0 * t192 * t85 - 12600.0 * t39 * t241 - 7672.0 * t100 * t228
  + 40320.0 * t59 * t50 * t258 - 6720.0 * t69 * t241 - 28.0 * t261 * t228 - 5760.0 * t140 * t202 + 20160.0
  * t264 * t265 + 560.0 * t192 * t182 - 30240.0 * t59 * t269 + 15344.0 * t192 * t241 - 1680.0 * t192 * t195
  + 14112.0 * t100 * t202 + 15120.0 * t184 * t57 - 2520.0 * t69 * t85 + 420.0 * t140 * t101 - 6720.0 * t55
  * t213;
  number t284 = t18 * t13;
  number t290 = t197 * t11;
  number t297 = t25 * t54;
  number t300 = t30 * t6;
  number t306 = 2240.0 * t69 * t43 - 1260.0 * t54 * t14 * t19 * t11 + 56.0 * t284 * t103 * t11 - 112.0
  * t140 * t180 - 1680.0 * t54 * t13 * t66 + 10080.0 * t64 * t290 - 3360.0 * t90 * t48 + 168.0 * t100 * t180
  - 20160.0 * t237 * t265 + 5880.0 * t160 * t202 - 12992.0 * t144 * t202 - 336.0 * t297 * t185 - 2380.0
  * t160 * t228 - 8.0 * t300 * t202 + 168.0 * t261 * t202 + 840.0 * t192 * t198 - 2520.0 * t184 * t168 + 336.0
  * t192 * t73;
  number t309 = t60 * t14 * t76;
  number t312 = t40 * t51 * t76;
  number t322 = t19 * t60 * t76;
  number t324 = t35 * t18;
  number t327 = t24 * t5;
  number t333 = 30240.0 * t83 * t269 - 100800.0 * t146 * t309 - 33600.0 * t146 * t312 - 3360.0 * t192
  * t43 + 18480.0 * t83 * t98 + 1120.0 * t69 * t195 - 3360.0 * t69 * t92 - 56.0 * t201 * t161 + 3360.0 * t230
  * t185 + 15120.0 * t55 * t232 + 6720.0 * t59 * t322 + 56.0 * t324 * t241 + 420.0 * t201 * t228 + 1680.0
  * t327 * t98 - 70.0 * t160 * t101 - 27720.0 * t184 * t232 + 15120.0 * t190 * t232 + 6160.0 * t192 * t92;
  number t339 = t11 * x;
  number t344 = t26 * t1;
  number t351 = t70 * t339;
  number t358 = t26 * f9 (x) * t339
  + 1680.0 * t18 * t65 * t40 * t339 + 67284.0 * t24 * t344 - 118124.0 * t28 * t344
  + 36.0 * t37 * t344 - 22449.0 * t25 * t344 - 546.0 * t30 * t344 + 2268.0 * t18 * t14 * t351 + 4536.0 * t35
  * t344 - 24192.0 * t140 * t92 - 3024.0 * t297 * t98 + 11340.0 * t90 * t57 - 1680.0 * t144 * t182;
  number t372 = t13 * t65;
  number t378 = -40320.0 * l * t344 - t37 * l * t344 - 26460.0 * t144 * t85 + 37800.0 * t100 * t85
  + 108864.0 * t69 * t232 + 109584.0 * t23 * t344 - 118188.0 * t29 * t202 - 72.0 * t300 * t241 + 7560.0
  * t201 * t48 + 1512.0 * t140 * t174 + 604800.0 * t59 * t60 * t88 + 15120.0 * t69 * t372 * t11 - 1451520.0
  * t156 * t205 * t339 + 60921.0 * t33 * t202;
  number t394 = -45360.0 * t32 * t202 + 25920.0 * t32 * t228 - 116928.0 * t144 * t241 + 52920.0 * t160
  * t241 - 26460.0 * t33 * t228 - 51840.0 * t140 * t241 - 63504.0 * t34 * t228 + 58464.0 * t29 * t228
  + 2898.0 * t36 * t202 - 35280.0 * t144 * t92 + 158760.0 * t39 * t232 + 117612.0 * t34 * t202 + 15120.0
  * t117 * t51 * t339;
  number t414 = 1512.0 * t261 * t241 - 12600.0 * t201 * t241 + 127008.0 * t100 * t241 + 7560.0 * t100
  * t198 + 15120.0 * t192 * t77 + 504.0 * t140 * t165 - 90720.0 * t114 * t125 * t339 + 1905120.0 * t125 * t3
  * t14 * t339 + 423360.0 * t124 * t157 * t339 + 113400.0 * t149 * t15 * t339 + 84.0 * t36 * t161 + 6300.0
  * t27 * t228 - 17640.0 * t27 * t202 - 756.0 * t36 * t228;
  number t426 = t13 * t103;
  number t433 = 124740.0 * t192 * t57 + 15120.0 * t144 * t43 + 30240.0 * t230 * t98 - 252.0 * t31 * t202
  - 105840.0 * t190 * t98 - 453600.0 * t59 * t309 - 45360.0 * t39 * t213 - 60480.0 * t69 * t185 - 45360.0
  * t69 * t213 - 504.0 * t140 * t426 * t11 - 68040.0 * t69 * t57 + 362880.0 * t52 * t45 * t339 - 181440.0 * t94
  * t151;
  number t436 = t69 * t45;
  number t450 = t192 * t45;
  number t452 = 30240.0 * t39 * t45 * t95 - 22680.0 * t436 * t210 + 7560.0 * t90 * t213 - 90720.0 * t59
  * t147 - 2520.0 * t160 * t43 + 15120.0 * t327 * t147 + 22680.0 * t192 * t224 - 1512.0 * t100 * t174 + 9.0
  * t32 * t7 * t11 - 90720.0 * t190 * t269 - 4536.0 * t69 * t172 - 15120.0 * t69 * t77 - 90720.0 * t184 * t235
  + 22680.0 * t450 * t210;
  number t480 = -181440.0 * t237 * t206 - 22680.0 * t69 * t224 + 90720.0 * t55 * t235 - 12096.0 * t55
  * t70 * t60 * t11 - 22680.0 * t192 * t168 - 90720.0 * t97 * t147 + 7560.0 * t140 * t195 - 362880.0 * t146
  * t40 * t125 * t11 - 630.0 * t140 * t20 * t11 + 1270080.0 * t237 * t13 * t157 * t11 + 1512.0 * t69 * t103 * t50
  * t11 + 75600.0 * t59 * t19 * t51 * t11 - 60480.0 * t55 * t50 * t65 * t11;
  number t492 = t14 * t19;
  number t498 = t40 * t70;
  number t504 = -362880.0 * t204 * t53 + 151200.0 * t83 * t312 + 453600.0 * t59 * t50 * t111 * t11
  - 181440.0 * t184 * t50 * t258 + 30240.0 * t55 * t322 - 144.0 * t140 * t120 * t45 * t11 + 11340.0 * t69
  * t492 * t11 - 30240.0 * t230 * t62 + 15120.0 * t69 * t130 - 22680.0 * t192 * t130 - 1008.0 * t140 * t498
  * t11 + 36.0 * t34 * t226 - 756.0 * t32 * t180 + 5040.0 * t100 * t182;
  number t523 = 60480.0 * t436 * t95 + 15120.0 * t140 * t43 - 90720.0 * t450 * t95 - 1360800.0 * t146
  * t51 * t14 * t11 - 756.0 * t201 * t85 - 45360.0 * t90 * t232 - 1260.0 * t33 * t101 + 10080.0 * t160 * t92
  + 9.0 * t38 * t202 + 4536.0 * t246 * t232 - 2016.0 * t140 * t73 + 60480.0 * t140 * t48 - 113400.0 * t39
  * t185;
  number t535 = t60 * t5;
  number t538 = t50 * t54;
  number t539 = t153 * t339;
  number t544 = -10080.0 * t32 * t161 - 1008.0 * t144 * t73 - 2520.0 * t144 * t198 + 166320.0 * t83
  * t147 - 13860.0 * t100 * t195 - 332640.0 * t184 * t62 + 7560.0 * t144 * t195 - 181440.0 * t55 * t269
  + 168.0 * t32 * t141 + 7560.0 * t39 * t130 - 18144.0 * t140 * t85 + 151200.0 * t535 * t197 * t339 - 30240.0
  * t538 * t539 - 72.0 * t6 * t13 * t120 * t339;
  number t556 = t55 * t50;
  number t562 = -18144.0 * t538 * t137 * t339 - 226800.0 * t192 * t232 - 68040.0 * t39 * t57
  + 181440.0 * t190 * t62 + 126.0 * t27 * t101 - 22680.0 * t55 * t15 * t11 - 7560.0 * t246 * t185 - 1260.0
  * t27 * t161 + 181440.0 * t556 * t258 + 4410.0 * t29 * t101 - 6300.0 * t34 * t101 + 9072.0 * t436 * t138
  - 72576.0 * t55 * t98;
  number t578 = -1008.0 * t201 * t92 - 1260.0 * t160 * t195 + 4536.0 * t192 * t172 + 181440.0 * t264
  * t206 + 272160.0 * t184 * t269 - 36.0 * t32 * t226 + 453600.0 * t83 * t309 + 15120.0 * t436 * t154
  - 30240.0 * t184 * t322 - 544320.0 * t132 * t239 - 90720.0 * t556 * t290 + 181440.0 * t55 * t62 - 504.0
  * t100 * t165 + 100800.0 * t535 * t65 * t339;
  number t588 = t45 * t18;
  number t601 = -907200.0 * t87 * t111 * t339 - 2016.0 * t104 * t60 * t339 - 907200.0 * t51 * t4 * t41
  * t339 + 3024.0 * t588 * t498 * t339 - 504.0 * t261 * t48 + 36.0 * t31 * t228 + 504.0 * t324 * t185 + 50400.0
  * t100 * t92 + 151200.0 * t184 * t98 + 1512.0 * t588 * t426 * t339 + 42840.0 * t90 * t185 + 3024.0 * t32
  * t101 - 18900.0 * t29 * t161;
  number t616 = 84.0 * t29 * t141 - 60480.0 * t208 * t265 - 120960.0 * t146 * t265 + 1386.0 * t34 * t180
  - 27720.0 * t100 * t43 + 15120.0 * t69 * t168 - 40320.0 * t190 * t216 - 5040.0 * t140 * t198 - 3360.0
  * t140 * t182 + 83160.0 * t192 * t213 - 756.0 * t29 * t180 + 126.0 * t33 * t180 + 7560.0 * t39 * t168
  + 120960.0 * t184 * t216;
  number t632 = 3024.0 * t100 * t73 - 453600.0 * t83 * t134 - 151200.0 * t59 * t312 + 2520.0 * t140
  * t188 + 544320.0 * t146 * t239 - 2520.0 * t100 * t188 + 7140.0 * t33 * t161 - 138096.0 * t100 * t48
  + 23016.0 * t34 * t161 + 138096.0 * t192 * t185 - 42840.0 * t160 * t48 + 113400.0 * t144 * t48 - 252.0
  * t34 * t141 + 151200.0 * t97 * t134;
  number t658 = 7560.0 * t160 * t85 + 181440.0 * t132 * t265 - 80640.0 * t55 * t216 + 302400.0 * t59
  * t134 - 60480.0 * t136 * t372 * t339 + 453600.0 * t64 * t150 * t339 + 216.0 * t121 * t50 * t339 - 30240.0
  * t54 * t111 * t40 * t339 - 45360.0 * t136 * t492 * t339 + 1890.0 * t588 * t20 * t339 - 18.0 * t8 * t45 * t339
  - 252.0 * t6 * t19 * t351 + 7560.0 * t284 * t539 - 168.0 * t6 * t40 * t103 * t339;
  return x - 9.0 * t1 * x * (t68 + t128 + t177 + t218 + t252 + t278 + t306 + t333) /
    (t358 + t378 + t394 + t414 + t433 + t452 + t480 + t504 + t523 + t544 + t562 + t578 + t601 + t616 + t632 + t658);
}

number
bl9 (ftype f, ftype f1, ftype f2, ftype f3, ftype f4, ftype f5, ftype f6, ftype f7, ftype f8, ftype f9, ftype f10, number l, number x)
{
  number t1 = f (x);
  number t3 = l * l;
  number t4 = t3 * t3;
  number t5 = t4 * t4;
  number t6 = t1 * t1;
  number t7 = t6 * t6;
  number t8 = t7 * t7;
  number t9 = t5 * t8;
  number t10 = f1 (x);
  number t12 = t7 * t6;
  number t13 = f3 (x);
  number t14 = t13 * t13;
  number t15 = t14 * t13;
  number t17 = x * x;
  number t18 = t17 * t17;
  number t19 = t18 * t18;
  number t21 = t3 * t8;
  number t23 = t3 * l;
  number t24 = t4 * t23;
  number t25 = t24 * t8;
  number t27 = t4 * t3;
  number t28 = t27 * t8;
  number t30 = t4 * t8;
  number t32 = t4 * l;
  number t33 = t32 * t8;
  number t35 = t23 * t8;
  number t37 = l * t8;
  number t39 = f9 (x);
  number t40 = t8 * t39;
  number t42 = t10 * t10;
  number t43 = t42 * t42;
  number t44 = t43 * t43;
  number t46 = t44 * t10 * t19;
  number t47 = t32 * t12;
  number t48 = f2 (x);
  number t50 = t17 * x;
  number t51 = t48 * t42 * t50;
  number t53 = t6 * t1;
  number t54 = t7 * t53;
  number t55 = t4 * t54;
  number t57 = t13 * t10 * t50;
  number t59 = -t9 * t10 - 560.0 * t12 * t15 * t19 - 13068.0 * t21 * t10 + 28.0 * t25 * t10 - 322.0 * t28
  * t10 - 6769.0 * t30 * t10 + 1960.0 * t33 * t10 + 13132.0 * t35 * t10 + 5040.0 * t37 * t10 - t40 * t19
  - 40320.0 * t46 - 672.0 * t47 * t51 - 2240.0 * t55 * t57;
  number t60 = t32 * t54;
  number t62 = t23 * t7;
  number t64 = t18 * x;
  number t65 = t48 * t43 * t64;
  number t67 = t7 * t1;
  number t68 = t23 * t67;
  number t69 = t42 * t10;
  number t71 = t13 * t69 * t64;
  number t73 = t23 * t12;
  number t75 = t48 * t13;
  number t76 = t75 * t64;
  number t78 = t48 * t48;
  number t80 = t42 * t78 * t64;
  number t82 = t3 * t54;
  number t83 = t78 * t50;
  number t85 = t23 * t54;
  number t87 = l * t67;
  number t89 = f6 (x);
  number t90 = t89 * t64;
  number t92 = t3 * t53;
  number t93 = t43 * t42;
  number t94 = t93 * t64;
  number t96 = t14 * t64;
  number t98 = t3 * t12;
  number t99 = f4 (x);
  number t101 = t99 * t42 * t64;
  number t103 = t3 * t67;
  number t105 = 224.0 * t60 * t57 - 20160.0 * t62 * t65 + 6720.0 * t68 * t71 - 6720.0 * t73 * t10 * t76
  + 15120.0 * t68 * t80 - 8400.0 * t82 * t83 + 5880.0 * t85 * t83 + 13440.0 * t87 * t71 + 168.0 * t21 * t90
  - 20160.0 * t92 * t94 + 560.0 * t85 * t96 + 5040.0 * t98 * t101 - 45360.0 * t103 * t80;
  number t107 = t23 * t53;
  number t110 = t3 * t7;
  number t113 = l * t54;
  number t114 = t48 * t99;
  number t115 = t114 * t64;
  number t118 = t78 * t48;
  number t119 = t118 * t64;
  number t122 = t99 * t10 * t18;
  number t124 = l * t12;
  number t127 = t48 * t69 * t18;
  number t130 = t13 * t42 * t18;
  number t133 = t78 * t13;
  number t134 = t18 * t50;
  number t135 = t133 * t134;
  number t138 = t10 * t78 * t18;
  number t140 = 6720.0 * t107 * t94 - 56.0 * t35 * t90 + 60480.0 * t110 * t65 + 168.0 * t60 * t83 + 1680.0
  * t113 * t115 + 30240.0 * t87 * t80 - 1680.0 * t73 * t119 - 2100.0 * t85 * t122 - 16128.0 * t124 * t51
  + 46200.0 * t103 * t127 - 15400.0 * t98 * t130 + 40320.0 * t87 * t10 * t135 + 12600.0 * t124 * t138;
  number t141 = l * t7;
  number t143 = t75 * t134;
  number t145 = t48 * x;
  number t147 = t42 * x;
  number t155 = t99 * t50;
  number t160 = -107520.0 * t141 * t69 * t143 + 14112.0 * t21 * t145 + 12992.0 * t85 * t147 + 5760.0
  * t113 * t147 + 5880.0 * t30 * t145 - 5880.0 * t55 * t147 + 7840.0 * t85 * t57 + 1400.0 * t60 * t147
  - 14112.0 * t82 * t147 + 2800.0 * t21 * t155 - 56.0 * t33 * t155 + 33600.0 * t98 * t51 - 1680.0 * t55 * t83;
  number t163 = t4 * t12;
  number t166 = f5 (x);
  number t167 = t48 * t166;
  number t168 = t18 * t17;
  number t169 = t167 * t168;
  number t175 = t124 * t10;
  number t178 = t166 * t10 * t64;
  number t181 = t43 * t10;
  number t182 = t181 * t18;
  number t185 = t75 * t18;
  number t187 = 6720.0 * t163 * t51 + 560.0 * t30 * t155 - 588.0 * t113 * t169 + 1120.0 * t113 * t96
  + 5040.0 * t98 * t119 - 2520.0 * t82 * t115 - 3360.0 * t124 * t119 - 13440.0 * t175 * t76 + 672.0 * t113
  * t178 - 12992.0 * t35 * t145 - 18480.0 * t110 * t182 + 3850.0 * t82 * t122 + 700.0 * t55 * t185;
  number t191 = l * t53;
  number t193 = t166 * t18;
  number t196 = l * t1;
  number t197 = t44 * t134;
  number t200 = t13 * t43 * t168;
  number t203 = t10 * t118 * t168;
  number t206 = t69 * t78 * t168;
  number t208 = t133 * t168;
  number t210 = t78 * t99;
  number t211 = t210 * t134;
  number t214 = t48 * t10 * t17;
  number t216 = -3360.0 * t124 * t101 + 7700.0 * t82 * t185 - 112.0 * t37 * t90 + 13440.0 * t191 * t94
  - 770.0 * t21 * t193 - 1008.0 * t82 * t178 + 40320.0 * t196 * t197 + 23520.0 * t141 * t200 - 17640.0 * t87
  * t203 + 70560.0 * t141 * t206 - 5880.0 * t98 * t208 - 3360.0 * t124 * t211 - 18900.0 * t85 * t214;
  number t219 = t69 * t17;
  number t222 = t43 * t50;
  number t224 = t13 * t99;
  number t225 = t224 * t168;
  number t233 = t32 * t67;
  number t236 = 7140.0 * t55 * t214 + 12600.0 * t73 * t219 - 10080.0 * t113 * t214 + 8064.0 * t87 * t222
  - 980.0 * t113 * t225 + 5376.0 * t113 * t57 + 4032.0 * t113 * t83 - 1344.0 * t37 * t155 - 16800.0 * t103
  * t222 - 23520.0 * t73 * t51 - 11200.0 * t82 * t57 + 336.0 * t233 * t222 - 15344.0 * t98 * t219;
  number t238 = t99 * t43 * t134;
  number t240 = t98 * t10;
  number t244 = t27 * t54;
  number t246 = t13 * t17;
  number t248 = t99 * t99;
  number t249 = t248 * t134;
  number t252 = t43 * t78 * t134;
  number t255 = t13 * t181 * t134;
  number t258 = t166 * t42 * t168;
  number t260 = t87 * t42;
  number t261 = t75 * t168;
  number t263 = t167 * t134;
  number t265 = t53 * t99;
  number t268 = -13440.0 * t141 * t238 + 20160.0 * t240 * t76 - 1260.0 * t60 * t214 - 4760.0 * t163
  * t219 + 84.0 * t244 * t214 + 6300.0 * t35 * t246 + 280.0 * t113 * t249 + 201600.0 * t191 * t252 + 53760.0
  * t191 * t255 + 1176.0 * t124 * t258 - 35280.0 * t260 * t261 - 2688.0 * t175 * t263 + 15120.0 * t265 * t181
  * t19;
  number t273 = t78 * t78;
  number t276 = t7 * t166;
  number t279 = t6 * t13;
  number t294 = -22680.0 * t10 * t7 * t273 * t19 - 3024.0 * t276 * t43 * t19 - 60480.0 * t279 * t93 * t19
  - 272160.0 * t181 * t6 * t78 * t19 - 2100.0 * t113 * t122 + 10080.0 * t141 * t182 - 25200.0 * t87 * t127
  + 840.0 * t85 * t115 + 336.0 * t85 * t178 - 20160.0 * t103 * t71 - 2380.0 * t30 * t246 + 23016.0 * t82 * t214
  + 6720.0 * t124 * t219;
  number t295 = t27 * t12;
  number t299 = t24 * t54;
  number t307 = t273 * t134;
  number t310 = t48 * t181 * t168;
  number t313 = -56.0 * t295 * t219 - 7672.0 * t21 * t246 + 3360.0 * t37 * t246 + 8.0 * t299 * t147
  - 1680.0 * t82 * t96 - 8.0 * t25 * t145 - 28.0 * t28 * t246 + 420.0 * t33 * t246 - 40320.0 * t141 * t65
  + 840.0 * t47 * t219 + 5040.0 * t87 * t307 - 70560.0 * t191 * t310 - 5760.0 * t37 * t145;
  number t315 = t4 * t67;
  number t319 = t114 * t168;
  number t323 = t42 * t14 * t134;
  number t328 = t42 * t118 * t134;
  number t330 = l * t6;
  number t332 = t48 * t93 * t134;
  number t337 = t10 * t12;
  number t340 = t12 * t78;
  number t341 = t166 * t19;
  number t343 = -3360.0 * t315 * t222 - 4200.0 * t85 * t185 - 23100.0 * t98 * t138 + 5880.0 * t175
  * t319 + 11760.0 * t68 * t222 + 13440.0 * t87 * t323 - 1400.0 * t33 * t145 + 168.0 * t28 * t145 - 80640.0
  * t141 * t328 - 161280.0 * t330 * t332 + 7560.0 * t67 * t118 * t13 * t19 - 630.0 * t337 * t248 * t19 - 756.0
  * t340 * t341;
  number t344 = t10 * t67;
  number t345 = t210 * t19;
  number t348 = t224 * t19;
  number t352 = f8 (x);
  number t353 = t54 * t352;
  number t356 = f7 (x);
  number t357 = t12 * t356;
  number t364 = t54 * t48;
  number t370 = t69 * t7;
  number t373 = t42 * t67;
  number t375 = t114 * t19;
  number t377 = t13 * t166;
  number t378 = t377 * t19;
  number t380 = 11340.0 * t344 * t345 - 2520.0 * t12 * t48 * t348 + 126.0 * t54 * t99 * t341 + 9.0 * t353
  * t10 * t19 - 72.0 * t357 * t42 * t19 - 70.0 * t30 * t193 + 151200.0 * t69 * t53 * t118 * t19 + 36.0 * t364
  * t356 * t19 + 84.0 * t54 * t13 * t89 * t19 - 20160.0 * t370 * t14 * t19 + 7560.0 * t373 * t348 - 30240.0
  * t370 * t375 - 1008.0 * t337 * t378;
  number t383 = t43 * t53;
  number t384 = t75 * t19;
  number t386 = t67 * t89;
  number t389 = t48 * t14;
  number t390 = t389 * t19;
  number t392 = t42 * t7;
  number t393 = t133 * t19;
  number t395 = t48 * t89;
  number t396 = t395 * t19;
  number t398 = t167 * t19;
  number t403 = t99 * t69 * t168;
  number t406 = t10 * t14 * t168;
  number t412 = t89 * t10 * t168;
  number t414 = 151200.0 * t383 * t384 + 504.0 * t386 * t69 * t19 + 15120.0 * t344 * t390 - 90720.0
  * t392 * t393 - 504.0 * t337 * t396 + 4536.0 * t373 * t398 + 35280.0 * t103 * t42 * t261 - 5880.0 * t87
  * t403 - 3920.0 * t98 * t406 + 588.0 * t82 * t169 + 3920.0 * t124 * t406 + 5880.0 * t124 * t208 - 196.0
  * t113 * t412;
  number t420 = t114 * t134;
  number t422 = t224 * t134;
  number t428 = t43 * t69;
  number t429 = t428 * t168;
  number t432 = 980.0 * t82 * t225 + 10080.0 * t62 * t182 + 350.0 * t55 * t122 + 4200.0 * t315 * t127
  + 5880.0 * t103 * t403 + 20160.0 * t260 * t420 - 4480.0 * t175 * t422 + 70560.0 * t92 * t310 - 4200.0
  * t113 * t185 - 23520.0 * t110 * t200 + 196.0 * t82 * t412 + 20160.0 * t330 * t429 - 5880.0 * t240 * t319;
  number t438 = t89 * t42 * t134;
  number t440 = t352 * t134;
  number t446 = t356 * t10 * t134;
  number t448 = t389 * t134;
  number t450 = t377 * t134;
  number t452 = t356 * t168;
  number t454 = t3 * t6;
  number t456 = -1960.0 * t35 * t155 - 168.0 * t244 * t147 - 1680.0 * t73 * t101 - 448.0 * t124 * t438
  - 8.0 * t37 * t440 + 12600.0 * t73 * t138 - 25200.0 * t68 * t127 + 420.0 * t37 * t193 + 64.0 * t113 * t446
  - 4480.0 * t124 * t448 + 448.0 * t113 * t450 - 28.0 * t21 * t452 - 20160.0 * t454 * t429;
  number t461 = t1 * t48;
  number t465 = t395 * t134;
  number t472 = t166 * t69 * t134;
  number t474 = t4 * t7;
  number t476 = -1176.0 * t98 * t258 + 28.0 * t37 * t452 - 70560.0 * t110 * t206 + 17640.0 * t103 * t203
  + 181440.0 * t461 * t428 * t19 + 8400.0 * t124 * t130 + 224.0 * t113 * t465 - 1400.0 * t163 * t130
  - 2100.0 * t163 * t138 + 8400.0 * t73 * t130 + 420.0 * t35 * t193 + 2688.0 * t87 * t472 - 1680.0 * t474
  * t182;
  number t487 = t8 * t1;
  number t488 = t3 * t487;
  number t490 = t42 * t12;
  number t491 = t19 * x;
  number t492 = t248 * t491;
  number t494 = t113 * t10;
  number t499 = t32 * t487;
  number t501 = t4 * t487;
  number t503 = l * t487;
  number t505 = t166 * t166;
  number t508 = t27 * t487;
  number t516 = t224 * t491;
  number t520 = t24 * t487;
  number t523 = 648.0 * t113 * t356 * t42 * t19 - 1360800.0 * t141 * t43 * t384 + 60480.0 * t124 * t323
  - 109584.0 * t488 * t10 - 9450.0 * t490 * t492 + 9072.0 * t494 * t378 + t5 * l * t487 * t10 + 22449.0 * t499
  * t10 - 67284.0 * t501 * t10 + 40320.0 * t503 * t10 - 126.0 * t8 * t505 * t491 - 4536.0 * t508 * t10
  + 22680.0 * t113 * t48 * t348 + 27216.0 * t87 * t166 * t43 * t19 - 75600.0 * t337 * t48 * t516 - 22050.0
  * t35 * t122 - 44100.0 * t35 * t185 - 252.0 * t520 * t145 - 63504.0 * t488 * t246;
  number t530 = t87 * t69;
  number t539 = t23 * t487;
  number t549 = 288.0 * t37 * t446 + 12096.0 * t124 * t472 - 1008.0 * t21 * t465 - 2016.0 * t21 * t450
  + 2898.0 * t508 * t145 - 20160.0 * t494 * t422 - 483840.0 * t530 * t143 + 45360.0 * t37 * t147 - 30240.0
  * t276 * t181 * t491 + 816480.0 * t260 * t393
  + t487 * f10 (x) * t491
  + 118124.0 * t539 * t10 - 20160.0
  * t113 * t448 + 546.0 * t520 * t10 + 272160.0 * t530 * t375 + 15120.0 * t82 * t211 + 120960.0 * t191 * t429
  + 1386.0 * t488 * t90 + 2016.0 * t37 * t450 - 288.0 * t21 * t446;
  number t556 = t82 * t10;
  number t562 = t98 * t42;
  number t569 = t124 * t42;
  number t578 = 7560.0 * t47 * t222 - 181440.0 * t92 * t429 - 604800.0 * t279 * t428 * t491 + 60480.0
  * t103 * t238 + 12096.0 * t556 * t263 - 120.0 * t8 * t13 * t356 * t491 - 907200.0 * t110 * t252 - 90720.0
  * t562 * t420 - 138096.0 * t98 * t222 + 483840.0 * t103 * t69 * t143 + 20160.0 * t556 * t422 - 252.0 * t488
  * t452 - 40824.0 * t569 * t398 + 90720.0 * t124 * t71 + 70560.0 * t68 * t200 - 1764.0 * t35 * t169
  + 204120.0 * t124 * t80 + 4536.0 * t35 * t178 - 272160.0 * t87 * t65 - 272160.0 * t68 * t65;
  number t583 = t89 * t491;
  number t587 = t14 * t491;
  number t603 = 90720.0 * t73 * t71 + 190512.0 * t21 * t214 + 85680.0 * t55 * t51 - 210.0 * t8 * t99
  * t583 - 567000.0 * t392 * t273 * t491 - 37800.0 * t340 * t587 - 336.0 * t28 * t57 + 211680.0 * t68 * t206
  - 92064.0 * t21 * t57 + 1764.0 * t21 * t412 + 635040.0 * t110 * t310 - 22680.0 * t85 * t101 - 362880.0
  * t87 * t328 + 5040.0 * t33 * t57 + 1008.0 * t244 * t51 + 79380.0 * t30 * t214 - 15120.0 * t474 * t94
  + 423360.0 * t87 * t206 + 6300.0 * t499 * t246 - 756.0 * t30 * t178;
  number t607 = t85 * t10;
  number t630 = -18900.0 * t33 * t214 - 90720.0 * t607 * t76 + 2268.0 * t28 * t214 - 108.0 * t25 * t214
  - 15120.0 * t60 * t51 + 544320.0 * t191 * t13 * t93 * t19 + 17640.0 * t85 * t208 + 317520.0 * t562 * t261
  - 52920.0 * t82 * t208 - 1890.0 * t30 * t115 + 204120.0 * t73 * t80 - 9.0 * t9 * t147 + 5292.0 * t21 * t169
  - 252.0 * t28 * t83 - 35280.0 * t124 * t403 + 17640.0 * t607 * t319 - 1632960.0 * t330 * t48 * t428 * t19
  - 241920.0 * t110 * t255 - 60480.0 * t87 * t238;
  number t644 = t377 * t491;
  number t654 = -181440.0 * t124 * t127 + 117612.0 * t488 * t145 + 60480.0 * t113 * t130 + 1008.0
  * t37 * t465 - 12096.0 * t98 * t472 - 30240.0 * t37 * t185 - 15120.0 * t113 * t211 + 7056.0 * t113 * t258
  + 6300.0 * t30 * t122 + 4536.0 * t37 * t178 - 2016.0 * t113 * t438 - 28560.0 * t30 * t57 - 21420.0 * t30
  * t83 + 5040.0 * t364 * t644 + 90720.0 * t113 * t138 - 35280.0 * t82 * t406 - 136080.0 * t141 * t99 * t181
  * t19 + 181440.0 * t175 * t135 - 10584.0 * t82 * t258 - 725760.0 * t191 * t332;
  number t663 = t5 * t487;
  number t680 = -105840.0 * t124 * t203 + 907200.0 * t141 * t252 + 241920.0 * t141 * t255 - 22680.0
  * t113 * t101 - 45.0 * t8 * t48 * t352 * t491 - 36.0 * t663 * t10 - 120960.0 * t113 * t51 + 3024.0 * t233
  * t182 - 12096.0 * t494 * t263 + 276192.0 * t82 * t51 + 141120.0 * t87 * t200 + 23520.0 * t113 * t406
  + 35280.0 * t494 * t319 - 211680.0 * t569 * t261 + 302400.0 * t373 * t389 * t491 - 423360.0 * t141 * t310
  - 5880.0 * t37 * t225 - 2940.0 * t35 * t225 + 35280.0 * t113 * t208 - 3528.0 * t37 * t169;
  number t704 = 362880.0 * t196 * t46 - 77760.0 * t37 * t214 - 117612.0 * t21 * t147 - 52920.0 * t556
  * t319 - 226800.0 * t85 * t51 + 11340.0 * t37 * t115 + 11760.0 * t85 * t406 - 105840.0 * t73 * t42 * t261
  - 151200.0 * t103 * t182 + 40320.0 * t37 * t57 - 10080.0 * t503 * t155 + 88200.0 * t85 * t130 - 60480.0
  * t98 * t323 + 3528.0 * t85 * t258 - 166320.0 * t98 * t71 + 30240.0 * t37 * t83 + 11340.0 * t35 * t115
  - 175392.0 * t35 * t214 + 2449440.0 * t191 * t181 * t78 * t19 + 498960.0 * t103 * t65;
  number t710 = t10 * t54;
  number t711 = t13 * t89;
  number t719 = t99 * t166;
  number t723 = t69 * t67;
  number t726 = t48 * t356;
  number t733 = t118 * t13;
  number t743 = 41580.0 * t82 * t119 - 20790.0 * t21 * t115 + 1680.0 * t710 * t711 * t491 - 118188.0
  * t539 * t145 + 2016.0 * t82 * t438 + 362880.0 * t103 * t328 + 90720.0 * t569 * t420 - 181440.0 * t240
  * t135 + 2520.0 * t710 * t719 * t491 + 725760.0 * t92 * t332 + 60480.0 * t723 * t167 * t491 + 720.0 * t710
  * t726 * t491 - 15120.0 * t490 * t644 + 151200.0 * t265 * t93 * t491 - 1260.0 * t30 * t96 + 302400.0 * t344
  * t733 * t491 - 10.0 * t40 * t10 * t491 + 90.0 * t353 * t42 * t491 - 3175200.0 * t93 * t6 * t78 * t491;
  number t744 = t43 * t7;
  number t747 = t78 * t166;
  number t759 = t99 * t491;
  number t778 = -378000.0 * t744 * t114 * t491 - 22680.0 * t337 * t747 * t491 - 362880.0 * t44 * t42
  * t491 - 69048.0 * t21 * t83 - 1512000.0 * t370 * t133 * t491 + 1814400.0 * t181 * t53 * t75 * t491
  - 18900.0 * t12 * t118 * t759 - 1512.0 * t244 * t219 + 7560.0 * t37 * t96 - 52920.0 * t55 * t219 - 16800.0
  * t337 * t15 * t491 + 60480.0 * t107 * t429 + 226800.0 * t373 * t210 * t491 + 158760.0 * t98 * t203
  - 7560.0 * t490 * t395 * t491 - 68040.0 * t124 * t733 * t19 - 2898.0 * t28 * t147 + 113400.0 * t73 * t222
  + 72576.0 * t87 * t182 + 252.0 * t25 * t147;
  number t808 = 36.0 * t488 * t440 + 3024.0 * t503 * t193 + 22680.0 * t124 * t307 + 1260.0 * t37 * t249
  + 58464.0 * t539 * t246 - 30240.0 * t315 * t182 + 105840.0 * t68 * t182 + 60480.0 * t124 * t222 + 17640.0
  * t33 * t147 + 23016.0 * t488 * t155 - 13860.0 * t21 * t96 + 56700.0 * t35 * t83 - 324.0 * t37 * t726 * t19
  - 18900.0 * t539 * t155 - 504.0 * t295 * t222 + 1814400.0 * t461 * t44 * t491 + 1260.0 * t54 * t78 * t583
  + 15120.0 * t55 * t10 * t76 + 22680.0 * t67 * t273 * t48 * t491 - 81.0 * t37 * t352 * t10 * t19;
  number t837 = -1134.0 * t37 * t719 * t19 - 756.0 * t37 * t711 * t19 - 1360800.0 * t141 * t69 * t118
  * t19 - 34020.0 * t163 * t80 + 181440.0 * t87 * t69 * t14 * t19 - 60921.0 * t30 * t147 + 3150.0 * t364 * t492
  + 3780.0 * t33 * t83 + 100800.0 * t723 * t516 - 4536.0 * t124 * t89 * t69 * t19 - 36.0 * t503 * t440 - 588.0
  * t35 * t412 - 211680.0 * t103 * t200 + 52920.0 * t98 * t403 - 8316.0 * t21 * t178 - 635040.0 * t103
  * t206 - 211680.0 * t62 * t310 + 20160.0 * t82 * t448 + 72.0 * t299 * t219 - 52920.0 * t73 * t203;
  number t863 = -17640.0 * t73 * t403 + 4536.0 * t494 * t396 - 720.0 * t357 * t69 * t491 - 136080.0
  * t175 * t390 - 102060.0 * t175 * t345 + 166320.0 * t556 * t76 + 378000.0 * t98 * t127 + 6804.0 * t113
  * t747 * t19 + 132300.0 * t85 * t138 + 63000.0 * t21 * t185 + 31500.0 * t21 * t122 + 3780.0 * t55 * t101
  - 374220.0 * t98 * t80 + 204120.0 * t87 * t10 * t273 * t19 + 36.0 * t520 * t246 + 41580.0 * t82 * t101
  - 15120.0 * t37 * t122 - 15120.0 * t163 * t71 - 1176.0 * t37 * t412;
  number t886 = -6300.0 * t488 * t193 - 25200.0 * t55 * t130 + 4410.0 * t539 * t193 + 7560.0 * t35 * t96
  + 118188.0 * t35 * t147 - 17640.0 * t499 * t145 - 252000.0 * t744 * t587 + 2268000.0 * t383 * t118
  * t491 + 5040.0 * t386 * t43 * t491 - 42840.0 * t163 * t222 + 168.0 * t503 * t452 + 126.0 * t501 * t90
  - 756.0 * t508 * t246 - 181440.0 * t454 * t197 + 12600.0 * t60 * t219 + 9.0 * t663 * t145 + 181440.0
  * t330 * t197 - 127008.0 * t82 * t219 - 1260.0 * t21 * t249 - 26460.0 * t501 * t246;
  number t910 = -37800.0 * t55 * t138 + 7140.0 * t501 * t155 + 8820.0 * t21 * t225 - 630.0 * t33 * t122
  - 1260.0 * t33 * t185 + 3780.0 * t60 * t138 + 2520.0 * t60 * t130 + 5670.0 * t113 * t10 * t248 * t19
  + 75600.0 * t163 * t127 + 25920.0 * t503 * t246 - 7560.0 * t47 * t127 - 45360.0 * t503 * t145 + 12600.0
  * t30 * t185 - 1260.0 * t499 * t155 - 189000.0 * t82 * t138 - 756.0 * t539 * t90 - 126000.0 * t82 * t130
  + 75600.0 * t35 * t57 - 264600.0 * t73 * t127 + 116928.0 * t85 * t219;
  number t934 = 45360.0 * t315 * t65 + 90720.0 * t62 * t94 - 90720.0 * t494 * t76 + 3780.0 * t55 * t119
  + 126.0 * t499 * t193 + 90720.0 * t141 * t94 - 22680.0 * t113 * t119 + 84.0 * t508 * t155 - 1260.0 * t501
  * t193 + 5040.0 * t113 * t15 * t19 - 22680.0 * t98 * t307 + 9.0 * t503 * t39 * t19 + 84.0 * t539 * t452 - 756.0
  * t503 * t90 - 166320.0 * t110 * t94 - 22680.0 * t85 * t119 + 4200.0 * t54 * t14 * t759 + 60921.0 * t501
  * t145 + 51840.0 * t113 * t219 - 68040.0 * t569 * t348;
  return x - 9.0 * t1 * x * (t59 + t105 + t140 + t160 + t187 + t216 + t236 + t268 + t294 + t313 + t343 + t380 + t414 + t432 + t456 + t476) /
    (t523 + t549 + t578 + t603 + t630 + t654 + t680 + t704 + t743 + t778 + t808 + t837 + t863 + t886 + t910 + t934);
}