22 December 2011 04:46:43 PM

LYNESS_RULE_PRB:
  C++ version
  Test the LYNESS_RULE library.

TEST01
  LYNESS_RULE_NUM returns the number of rules;
  LYNESS_DEGREE returns the degree of a rule;
  LYNESS_ORDER_NUM returns the order of a rule.

  Number of available rules = 21

      Rule     Order  Precision

         0         1         1
         1         3         2
         2         4         2
         3         4         3
         4         7         3
         5         6         4
         6        10         4
         7         9         4
         8         7         5
         9        10         5
        10        12         6
        11        16         6
        12        13         6
        13        13         7
        14        16         7
        15        16         8
        16        21         8
        17        16         8
        18        19         9
        19        22         9
        20        27        11
        21        28        11

TEST02
  LYNESS_RULE returns the points and weights
  of a Lyness rule for the triangle.

  In this test, we simply check that the weights
  sum to 1.

  Number of available rules = 21

      Rule    Sum of weights

         0                          1
         1                          1
         2                          1
         3                          1
         4                          1
         5                          1
         6                          1
         7                          1
         8                          1
         9                          1
        10                          1
        11                          1
        12                          1
        13                          1
        14                          1
        15                          1
        16                          1
        17                          1
        18                          1
        19                          1
        20                          1
        21                          1

TEST03
  LYNESS_RULE returns the points and weights
  of a Lyness rule for the triangle.

  In this test, we simply check that, for each
  quadrature point, the barycentric coordinates
  sum to 1.

      Rule   Suborder    Sum of coordinates

         0         1
                           1

         1         1
                           1

         2         2
                           1
                           1

         3         2
                           1
                           1

         4         3
                           1
                           1
                           1

         5         2
                           1
                           1

         6         3
                           1
                           1
                           1

         7         3
                           1
                           1
                           1

         8         3
                           1
                           1
                           1

         9         4
                           1
                           1
                           1
                           1

        10         3
                           1
                           1
                           1

        11         5
                           1
                           1
                           1
                           1
                           1

        12         4
                           1
                           1
                           1
                           1

        13         4
                           1
                           1
                           1
                           1

        14         5
                           1
                           1
                           1
                           1
                           1

        15         5
                           1
                           1
                           1
                           1
                           1

        16         6
                           1
                           1
                           1
                           1
                           1
                           1

        17         5
                           1
                           1
                           1
                           1
                           1

        18         6
                           1
                           1
                           1
                           1
                           1
                           1

        19         7
                           1
                           1
                           1
                           1
                           1
                           1
                           1

        20         7
                           1
                           1
                           1
                           1
                           1
                           1
                           1

TEST04
  LYNESS_RULE returns the points and weights
  of a Lyness rule for the triangle.

  In this test, we simply print a rule.

  Rule =      18
  Order =     19
  Precision = 9

     I      W                   X                   Y

     0        0.0971357962827961        0.3333333333333333        0.3333333333333333
     1       0.03133470022713983       0.02063496160252593         0.489682519198737
     2       0.03133470022713983         0.489682519198737         0.489682519198737
     3       0.03133470022713983         0.489682519198737       0.02063496160252593
     4       0.07782754100477543         0.125820817014129        0.4370895914929355
     5       0.07782754100477543        0.4370895914929355        0.4370895914929354
     6       0.07782754100477543        0.4370895914929354         0.125820817014129
     7        0.0796477389272091        0.6235929287619356        0.1882035356190322
     8        0.0796477389272091        0.1882035356190322        0.1882035356190322
     9        0.0796477389272091        0.1882035356190322        0.6235929287619356
    10        0.0255776756586981        0.9105409732110941       0.04472951339445297
    11        0.0255776756586981       0.04472951339445297       0.04472951339445297
    12        0.0255776756586981       0.04472951339445297        0.9105409732110941
    13        0.0432835393772894       0.03683841205473626         0.741198598784498
    14        0.0432835393772894         0.741198598784498        0.2219629891607657
    15        0.0432835393772894        0.2219629891607657       0.03683841205473626
    16        0.0432835393772894         0.741198598784498       0.03683841205473626
    17        0.0432835393772894        0.2219629891607657         0.741198598784498
    18        0.0432835393772894       0.03683841205473626        0.2219629891607657

TEST05
  LYNESS_RULE returns the points and weights
  of a Lyness rule for the triangle.

  In this test, we simply print a rule.

  Rule =      18
  Order =     19
  Precision = 9

  Wrote the region file "lyness_18_r.txt".
  Wrote the weight file "lyness_18_w.txt".
  Wrote the point file "lyness_18_x.txt".

TEST06
  LYNESS_RULE returns the points and weights of
  a Lyness rule for the unit triangle.

  This routine uses those rules to estimate the
  integral of monomomials in the unit triangle.

  Integrate 2 * X^0 * Y^0

      Rule       QUAD           ERROR

         0               1           0
         1               1           0
         2               1           0
         3               1           0
         4               1           0
         5               1     1.1e-16
         6               1     1.1e-16
         7               1           0
         8               1           0
         9               1           0
        10               1     4.1e-15
        11               1     2.2e-16
        12               1     2.2e-16
        13               1           0
        14               1     1.1e-16
        15               1     1.1e-16
        16               1     1.4e-15
        17               1     2.2e-16
        18               1           0
        19               1     2.2e-16
        20               1     8.9e-16
        21               1     2.2e-16

  Integrate 6 * X^0 * Y^1

      Rule       QUAD           ERROR

         0               1       1e-10
         1               1           0
         2               1     7.5e-11
         3               1     5.6e-11
         4               1           0
         5               1           0
         6               1           0
         7               1           0
         8               1     1.1e-16
         9               1     1.1e-16
        10               1     3.8e-15
        11               1           0
        12               1     2.2e-16
        13               1           0
        14               1           0
        15               1     1.1e-16
        16               1     1.8e-15
        17               1     2.2e-16
        18               1     2.2e-16
        19               1     2.2e-16
        20               1     8.9e-16
        21               1           0

  Integrate 6 * X^1 * Y^0

      Rule       QUAD           ERROR

         0               1       1e-10
         1               1           0
         2               1     7.5e-11
         3               1     5.6e-11
         4               1           0
         5               1           0
         6               1           0
         7               1           0
         8               1     1.1e-16
         9               1     1.1e-16
        10               1     3.8e-15
        11               1           0
        12               1     2.2e-16
        13               1           0
        14               1           0
        15               1     2.2e-16
        16               1     1.8e-15
        17               1     4.4e-16
        18               1     2.2e-16
        19               1           0
        20               1     1.1e-15
        21               1           0

  Integrate 12 * X^0 * Y^2

      Rule       QUAD           ERROR

         0        0.666667        0.33
         1               1           0
         2               1       1e-10
         3               1     7.5e-11
         4               1           0
         5               1     2.2e-16
         6               1     2.2e-16
         7               1           0
         8               1     3.3e-16
         9               1           0
        10               1     2.6e-15
        11               1     1.1e-16
        12               1     2.2e-16
        13               1           0
        14               1     2.2e-16
        15               1     1.1e-16
        16               1     1.3e-15
        17               1     2.2e-16
        18               1           0
        19               1           0
        20               1     4.4e-16
        21               1     3.3e-16

  Integrate 24 * X^1 * Y^1

      Rule       QUAD           ERROR

         0         1.33333        0.33
         1               1           0
         2               1       2e-10
         3               1     1.5e-10
         4               1           0
         5               1           0
         6               1           0
         7               1     2.2e-16
         8               1     2.2e-16
         9               1     2.2e-16
        10               1     5.1e-15
        11               1     2.2e-16
        12               1           0
        13               1           0
        14               1           0
        15               1           0
        16               1     2.2e-15
        17               1     2.2e-16
        18               1           0
        19               1     2.2e-16
        20               1     1.1e-15
        21               1     2.2e-16

  Integrate 12 * X^2 * Y^0

      Rule       QUAD           ERROR

         0        0.666667        0.33
         1               1           0
         2               1       1e-10
         3               1     7.5e-11
         4               1           0
         5               1     2.2e-16
         6               1     2.2e-16
         7               1     2.2e-16
         8               1     2.2e-16
         9               1           0
        10               1     2.6e-15
        11               1     1.1e-16
        12               1     1.1e-16
        13               1           0
        14               1     2.2e-16
        15               1     1.1e-16
        16               1     1.2e-15
        17               1     2.2e-16
        18               1     1.1e-16
        19               1     2.2e-16
        20               1     4.4e-16
        21               1     3.3e-16

  Integrate 20 * X^0 * Y^3

      Rule       QUAD           ERROR

         0         0.37037        0.63
         1        0.833333        0.17
         2         1.11111        0.11
         3               1     6.3e-11
         4               1     1.1e-16
         5               1     1.1e-16
         6               1     6.7e-16
         7               1     2.2e-16
         8               1     2.2e-16
         9               1           0
        10               1     1.6e-15
        11               1     2.2e-16
        12               1           0
        13               1     1.1e-16
        14               1     2.2e-16
        15               1     3.3e-16
        16               1     8.9e-16
        17               1           0
        18               1     3.3e-16
        19               1     1.1e-16
        20               1     2.2e-16
        21               1     3.3e-16

  Integrate 60 * X^1 * Y^2

      Rule       QUAD           ERROR

         0         1.11111        0.11
         1            1.25        0.25
         2        0.833333        0.17
         3               1     1.9e-10
         4               1           0
         5               1     1.1e-16
         6               1           0
         7               1     2.2e-16
         8               1     3.3e-16
         9               1     1.1e-16
        10               1     4.3e-15
        11               1           0
        12               1     2.2e-16
        13               1     2.2e-16
        14               1     1.1e-16
        15               1     2.2e-16
        16               1     1.4e-15
        17               1     2.2e-16
        18               1     1.1e-16
        19               1           0
        20               1     1.1e-15
        21               1     1.1e-16

  Integrate 60 * X^2 * Y^1

      Rule       QUAD           ERROR

         0         1.11111        0.11
         1            1.25        0.25
         2        0.833333        0.17
         3               1     1.9e-10
         4               1           0
         5               1     1.1e-16
         6               1           0
         7               1     2.2e-16
         8               1     2.2e-16
         9               1     2.2e-16
        10               1     4.2e-15
        11               1     2.2e-16
        12               1           0
        13               1           0
        14               1     1.1e-16
        15               1           0
        16               1     1.8e-15
        17               1     2.2e-16
        18               1           0
        19               1           0
        20               1     1.1e-15
        21               1           0

  Integrate 20 * X^3 * Y^0

      Rule       QUAD           ERROR

         0         0.37037        0.63
         1        0.833333        0.17
         2         1.11111        0.11
         3               1     6.3e-11
         4               1     1.1e-16
         5               1     2.2e-16
         6               1     6.7e-16
         7               1     2.2e-16
         8               1     2.2e-16
         9               1           0
        10               1     1.6e-15
        11               1     2.2e-16
        12               1     1.1e-16
        13               1     2.2e-16
        14               1     2.2e-16
        15               1     3.3e-16
        16               1     6.7e-16
        17               1     2.2e-16
        18               1     2.2e-16
        19               1     2.2e-16
        20               1     2.2e-16
        21               1     3.3e-16

  Integrate 30 * X^0 * Y^4

      Rule       QUAD           ERROR

         0        0.185185        0.81
         1           0.625        0.38
         2         1.38889        0.39
         3        0.933333       0.067
         4         1.08333       0.083
         5               1     3.3e-16
         6               1     7.8e-16
         7               1     4.4e-16
         8               1     4.4e-16
         9               1           0
        10               1     6.7e-16
        11               1     1.1e-16
        12               1     2.2e-16
        13               1     2.2e-16
        14               1           0
        15               1     4.4e-16
        16               1     2.2e-16
        17               1     2.2e-16
        18               1     3.3e-16
        19               1     1.1e-16
        20               1     3.3e-16
        21               1     1.1e-16

  Integrate 1.2e+02 * X^1 * Y^3

      Rule       QUAD           ERROR

         0        0.740741        0.26
         1            1.25        0.25
         2        0.555556        0.44
         3         1.13333        0.13
         4        0.833333        0.17
         5               1           0
         6               1     2.2e-16
         7               1     4.4e-16
         8               1     4.4e-16
         9               1           0
        10               1     3.4e-15
        11               1     2.2e-16
        12               1     2.2e-16
        13               1           0
        14               1           0
        15               1     2.2e-16
        16               1       1e-15
        17               1     2.2e-16
        18               1     1.1e-16
        19               1           0
        20               1     8.9e-16
        21               1     1.1e-16

  Integrate 1.8e+02 * X^2 * Y^2

      Rule       QUAD           ERROR

         0         1.11111        0.11
         1           1.875        0.88
         2        0.833333        0.17
         3             0.8         0.2
         4            1.25        0.25
         5               1           0
         6               1           0
         7               1     4.4e-16
         8               1     2.2e-16
         9               1           0
        10               1     3.8e-15
        11               1     2.2e-16
        12               1     2.2e-16
        13               1     2.2e-16
        14               1     2.2e-16
        15               1           0
        16               1     1.8e-15
        17               1     2.2e-16
        18               1           0
        19               1     2.2e-16
        20               1     1.6e-15
        21               1     3.3e-16

  Integrate 1.2e+02 * X^3 * Y^1

      Rule       QUAD           ERROR

         0        0.740741        0.26
         1            1.25        0.25
         2        0.555556        0.44
         3         1.13333        0.13
         4        0.833333        0.17
         5               1           0
         6               1     1.1e-16
         7               1     4.4e-16
         8               1     5.6e-16
         9               1           0
        10               1     3.2e-15
        11               1           0
        12               1           0
        13               1     2.2e-16
        14               1           0
        15               1     2.2e-16
        16               1     1.3e-15
        17               1     2.2e-16
        18               1           0
        19               1     1.1e-16
        20               1     8.9e-16
        21               1     1.1e-16

  Integrate 30 * X^4 * Y^0

      Rule       QUAD           ERROR

         0        0.185185        0.81
         1           0.625        0.38
         2         1.38889        0.39
         3        0.933333       0.067
         4         1.08333       0.083
         5               1     2.2e-16
         6               1     7.8e-16
         7               1     4.4e-16
         8               1     4.4e-16
         9               1     2.2e-16
        10               1     6.7e-16
        11               1     2.2e-16
        12               1     1.1e-16
        13               1     3.3e-16
        14               1           0
        15               1     4.4e-16
        16               1     2.2e-16
        17               1           0
        18               1     4.4e-16
        19               1     2.2e-16
        20               1     2.2e-16
        21               1     4.4e-16

  Integrate 42 * X^0 * Y^5

      Rule       QUAD           ERROR

         0       0.0864198        0.91
         1          0.4375        0.56
         2         1.81481        0.81
         3        0.808889        0.19
         4         1.26389        0.26
         5         1.00527      0.0053
         6        0.972222       0.028
         7         1.00889      0.0089
         8               1     4.4e-16
         9               1           0
        10               1     6.7e-16
        11               1     2.2e-16
        12               1     3.3e-16
        13               1     2.2e-16
        14               1     2.2e-16
        15               1     4.4e-16
        16               1     3.3e-16
        17               1     2.2e-16
        18               1     4.4e-16
        19               1     2.2e-16
        20               1     3.3e-16
        21               1     1.1e-16

  Integrate 2.1e+02 * X^1 * Y^4

      Rule       QUAD           ERROR

         0        0.432099        0.57
         1         1.09375       0.094
         2        0.324074        0.68
         3         1.24444        0.24
         4        0.631944        0.37
         5        0.986815       0.013
         6         1.06944       0.069
         7        0.977773       0.022
         8               1     4.4e-16
         9               1           0
        10               1     2.9e-15
        11               1           0
        12               1           0
        13               1     1.1e-16
        14               1     2.2e-16
        15               1     2.2e-16
        16               1     3.3e-16
        17               1     2.2e-16
        18               1     2.2e-16
        19               1     1.1e-16
        20               1     2.2e-16
        21               1     3.3e-16

  Integrate 4.2e+02 * X^2 * Y^3

      Rule       QUAD           ERROR

         0        0.864198        0.14
         1          2.1875         1.2
         2        0.648148        0.35
         3        0.808889        0.19
         4         1.26389        0.26
         5         1.00527      0.0053
         6        0.972222       0.028
         7         1.00889      0.0089
         8               1     5.6e-16
         9               1           0
        10               1     2.7e-15
        11               1     2.2e-16
        12               1     4.4e-16
        13               1     2.2e-16
        14               1     2.2e-16
        15               1           0
        16               1     1.6e-15
        17               1     4.4e-16
        18               1           0
        19               1     2.2e-16
        20               1     8.9e-16
        21               1     3.3e-16

  Integrate 4.2e+02 * X^3 * Y^2

      Rule       QUAD           ERROR

         0        0.864198        0.14
         1          2.1875         1.2
         2        0.648148        0.35
         3        0.808889        0.19
         4         1.26389        0.26
         5         1.00527      0.0053
         6        0.972222       0.028
         7         1.00889      0.0089
         8               1     5.6e-16
         9               1           0
        10               1     2.7e-15
        11               1     2.2e-16
        12               1     2.2e-16
        13               1     4.4e-16
        14               1           0
        15               1           0
        16               1     1.6e-15
        17               1     4.4e-16
        18               1           0
        19               1           0
        20               1     1.1e-15
        21               1     3.3e-16

  Integrate 2.1e+02 * X^4 * Y^1

      Rule       QUAD           ERROR

         0        0.432099        0.57
         1         1.09375       0.094
         2        0.324074        0.68
         3         1.24444        0.24
         4        0.631944        0.37
         5        0.986815       0.013
         6         1.06944       0.069
         7        0.977773       0.022
         8               1     5.6e-16
         9               1           0
        10               1     2.7e-15
        11               1     2.2e-16
        12               1           0
        13               1     3.3e-16
        14               1           0
        15               1     3.3e-16
        16               1     6.7e-16
        17               1     2.2e-16
        18               1     2.2e-16
        19               1     1.1e-16
        20               1           0
        21               1     3.3e-16

  Integrate 42 * X^5 * Y^0

      Rule       QUAD           ERROR

         0       0.0864198        0.91
         1          0.4375        0.56
         2         1.81481        0.81
         3        0.808889        0.19
         4         1.26389        0.26
         5         1.00527      0.0053
         6        0.972222       0.028
         7         1.00889      0.0089
         8               1     4.4e-16
         9               1     2.2e-16
        10               1     4.4e-16
        11               1     3.3e-16
        12               1     2.2e-16
        13               1     2.2e-16
        14               1     2.2e-16
        15               1     6.7e-16
        16               1     2.2e-16
        17               1           0
        18               1     5.6e-16
        19               1     3.3e-16
        20               1     2.2e-16
        21               1     1.1e-16

  Integrate 56 * X^0 * Y^6

      Rule       QUAD           ERROR

         0       0.0384088        0.96
         1        0.291667        0.71
         2         2.36214         1.4
         3        0.660662        0.34
         4         1.53395        0.53
         5         1.01295       0.013
         6        0.898765         0.1
         7         1.03997        0.04
         8        0.995414      0.0046
         9         1.00317      0.0032
        10               1     8.9e-16
        11               1     3.3e-16
        12               1     1.1e-16
        13               1     4.4e-16
        14               1     4.4e-16
        15               1     4.4e-16
        16               1     2.2e-16
        17               1     1.1e-16
        18               1     2.2e-16
        19               1           0
        20               1     1.1e-16
        21               1     1.1e-16

  Integrate 3.4e+02 * X^1 * Y^5

      Rule       QUAD           ERROR

         0        0.230453        0.77
         1           0.875        0.12
         2         0.17284        0.83
         3         1.25357        0.25
         4        0.453704        0.55
         5        0.982247       0.018
         6         1.19259        0.19
         7        0.915646       0.084
         8         1.01376       0.014
         9        0.990476      0.0095
        10               1     7.8e-16
        11               1     2.2e-16
        12               1           0
        13               1     2.2e-16
        14               1     2.2e-16
        15               1     2.2e-16
        16               1     1.1e-16
        17               1           0
        18               1     1.1e-16
        19               1     1.1e-16
        20               1     2.2e-16
        21               1     3.3e-16

  Integrate 8.4e+02 * X^2 * Y^4

      Rule       QUAD           ERROR

         0        0.576132        0.42
         1          2.1875         1.2
         2        0.432099        0.57
         3        0.949926        0.05
         4         1.13426        0.13
         5        0.958434       0.042
         6         1.03704       0.037
         7         1.02691       0.027
         8        0.962963       0.037
         9               1           0
        10               1     5.6e-15
        11               1     2.2e-16
        12               1     4.4e-16
        13               1     2.2e-16
        14               1     2.2e-16
        15               1     6.7e-16
        16               1     5.6e-16
        17               1     2.2e-16
        18               1     2.2e-16
        19               1           0
        20               1     8.9e-16
        21               1     3.3e-16

  Integrate 1.1e+03 * X^3 * Y^3

      Rule       QUAD           ERROR

         0        0.768176        0.23
         1         2.91667         1.9
         2        0.576132        0.42
         3        0.594568        0.41
         4         1.51235        0.51
         5          1.0635       0.063
         6        0.864198        0.14
         7         1.00379      0.0038
         8         1.05115       0.051
         9         1.01587       0.016
        10               1     1.8e-15
        11               1     2.2e-16
        12               1     4.4e-16
        13               1     8.9e-16
        14               1     4.4e-16
        15               1     4.4e-16
        16               1       2e-15
        17               1     2.2e-16
        18               1           0
        19               1           0
        20               1     8.9e-16
        21               1     3.3e-16

  Integrate 8.4e+02 * X^4 * Y^2

      Rule       QUAD           ERROR

         0        0.576132        0.42
         1          2.1875         1.2
         2        0.432099        0.57
         3        0.949926        0.05
         4         1.13426        0.13
         5        0.958434       0.042
         6         1.03704       0.037
         7         1.02691       0.027
         8        0.962963       0.037
         9               1           0
        10               1     5.6e-15
        11               1     2.2e-16
        12               1     2.2e-16
        13               1     3.3e-16
        14               1     2.2e-16
        15               1           0
        16               1       1e-15
        17               1     4.4e-16
        18               1     2.2e-16
        19               1           0
        20               1     6.7e-16
        21               1     3.3e-16

  Integrate 3.4e+02 * X^5 * Y^1

      Rule       QUAD           ERROR

         0        0.230453        0.77
         1           0.875        0.12
         2         0.17284        0.83
         3         1.25357        0.25
         4        0.453704        0.55
         5        0.982247       0.018
         6         1.19259        0.19
         7        0.915646       0.084
         8         1.01376       0.014
         9        0.990476      0.0095
        10               1     6.7e-16
        11               1     2.2e-16
        12               1           0
        13               1     3.3e-16
        14               1     1.1e-16
        15               1     4.4e-16
        16               1     4.4e-16
        17               1           0
        18               1           0
        19               1     2.2e-16
        20               1     1.1e-16
        21               1     2.2e-16

  Integrate 56 * X^6 * Y^0

      Rule       QUAD           ERROR

         0       0.0384088        0.96
         1        0.291667        0.71
         2         2.36214         1.4
         3        0.660662        0.34
         4         1.53395        0.53
         5         1.01295       0.013
         6        0.898765         0.1
         7         1.03997        0.04
         8        0.995414      0.0046
         9         1.00317      0.0032
        10               1     8.9e-16
        11               1     3.3e-16
        12               1     1.1e-16
        13               1     3.3e-16
        14               1     4.4e-16
        15               1     4.4e-16
        16               1     2.2e-16
        17               1     1.1e-16
        18               1     2.2e-16
        19               1           0
        20               1     2.2e-16
        21               1     1.1e-16

  Integrate 72 * X^0 * Y^7

      Rule       QUAD           ERROR

         0       0.0164609        0.98
         1          0.1875        0.81
         2         3.01235           2
         3        0.516101        0.48
         4         1.88241        0.88
         5          1.0169       0.017
         6        0.774074        0.23
         7         1.10277         0.1
         8        0.981708       0.018
         9         1.01361       0.014
        10          1.0002      0.0002
        11        0.995833      0.0042
        12         0.99932     0.00068
        13               1     4.4e-16
        14               1     2.2e-16
        15               1     4.4e-16
        16               1     4.4e-16
        17               1           0
        18               1     7.8e-16
        19               1           0
        20               1     1.1e-16
        21               1           0

  Integrate 5e+02 * X^1 * Y^6

      Rule       QUAD           ERROR

         0        0.115226        0.88
         1         0.65625        0.34
         2       0.0864198        0.91
         3         1.16663        0.17
         4        0.314352        0.69
         5        0.999117     0.00088
         6         1.33519        0.34
         7        0.820163        0.18
         8         1.04339       0.043
         9        0.966667       0.033
        10        0.999307     0.00069
        11         1.01458       0.015
        12         1.00238      0.0024
        13               1     8.9e-16
        14               1     2.2e-16
        15               1     2.2e-16
        16               1     1.1e-16
        17               1     2.2e-16
        18               1     2.2e-16
        19               1     1.1e-16
        20               1     4.4e-16
        21               1     3.3e-16

  Integrate 1.5e+03 * X^2 * Y^5

      Rule       QUAD           ERROR

         0        0.345679        0.65
         1         1.96875        0.97
         2        0.259259        0.74
         3         1.08068       0.081
         4        0.943056       0.057
         5        0.881502        0.12
         6         1.20556        0.21
         7         1.01725       0.017
         8        0.909751        0.09
         9        0.989796        0.01
        10         1.00089     0.00089
        11         0.98125       0.019
        12        0.996939      0.0031
        13               1       1e-15
        14               1     4.4e-16
        15               1     4.4e-16
        16               1     1.1e-16
        17               1     2.2e-16
        18               1     4.4e-16
        19               1     2.2e-16
        20               1     1.3e-15
        21               1     5.6e-16

  Integrate 2.5e+03 * X^3 * Y^4

      Rule       QUAD           ERROR

         0        0.576132        0.42
         1         3.28125         2.3
         2        0.432099        0.57
         3        0.591526        0.41
         4         1.57176        0.57
         5         1.05737       0.057
         6        0.842593        0.16
         7         1.02827       0.028
         8         1.05367       0.054
         9         1.03741       0.037
        10        0.999505      0.0005
        11         1.01042        0.01
        12          1.0017      0.0017
        13               1     6.7e-16
        14               1     4.4e-16
        15               1     4.4e-16
        16               1     7.8e-16
        17               1     4.4e-16
        18               1     1.1e-16
        19               1           0
        20               1     2.2e-16
        21               1     3.3e-16

  Integrate 2.5e+03 * X^4 * Y^3

      Rule       QUAD           ERROR

         0        0.576132        0.42
         1         3.28125         2.3
         2        0.432099        0.57
         3        0.591526        0.41
         4         1.57176        0.57
         5         1.05737       0.057
         6        0.842593        0.16
         7         1.02827       0.028
         8         1.05367       0.054
         9         1.03741       0.037
        10        0.999505      0.0005
        11         1.01042        0.01
        12          1.0017      0.0017
        13               1     6.7e-16
        14               1     2.2e-16
        15               1     2.2e-16
        16               1     1.3e-15
        17               1     6.7e-16
        18               1     1.1e-16
        19               1           0
        20               1     2.2e-16
        21               1     1.1e-16

  Integrate 1.5e+03 * X^5 * Y^2

      Rule       QUAD           ERROR

         0        0.345679        0.65
         1         1.96875        0.97
         2        0.259259        0.74
         3         1.08068       0.081
         4        0.943056       0.057
         5        0.881502        0.12
         6         1.20556        0.21
         7         1.01725       0.017
         8        0.909751        0.09
         9        0.989796        0.01
        10         1.00089     0.00089
        11         0.98125       0.019
        12        0.996939      0.0031
        13               1     1.3e-15
        14               1     2.2e-16
        15               1     1.1e-16
        16               1     6.7e-16
        17               1     4.4e-16
        18               1     3.3e-16
        19               1           0
        20               1     8.9e-16
        21               1     6.7e-16

  Integrate 5e+02 * X^6 * Y^1

      Rule       QUAD           ERROR

         0        0.115226        0.88
         1         0.65625        0.34
         2       0.0864198        0.91
         3         1.16663        0.17
         4        0.314352        0.69
         5        0.999117     0.00088
         6         1.33519        0.34
         7        0.820163        0.18
         8         1.04339       0.043
         9        0.966667       0.033
        10        0.999307     0.00069
        11         1.01458       0.015
        12         1.00238      0.0024
        13               1     4.4e-16
        14               1           0
        15               1     2.2e-16
        16               1     4.4e-16
        17               1     2.2e-16
        18               1     2.2e-16
        19               1     2.2e-16
        20               1     7.8e-16
        21               1     4.4e-16

  Integrate 72 * X^7 * Y^0

      Rule       QUAD           ERROR

         0       0.0164609        0.98
         1          0.1875        0.81
         2         3.01235           2
         3        0.516101        0.48
         4         1.88241        0.88
         5          1.0169       0.017
         6        0.774074        0.23
         7         1.10277         0.1
         8        0.981708       0.018
         9         1.01361       0.014
        10          1.0002      0.0002
        11        0.995833      0.0042
        12         0.99932     0.00068
        13               1     4.4e-16
        14               1     2.2e-16
        15               1     4.4e-16
        16               1     5.6e-16
        17               1     2.2e-16
        18               1     6.7e-16
        19               1           0
        20               1     1.1e-16
        21               1     2.2e-16

  Integrate 90 * X^0 * Y^8

      Rule       QUAD           ERROR

         0      0.00685871        0.99
         1        0.117188        0.88
         2         3.75514         2.8
         3        0.389922        0.61
         4         2.29996         1.3
         5         1.01216       0.012
         6        0.600309         0.4
         7         1.20174         0.2
         8        0.956602       0.043
         9         1.03515       0.035
        10         1.00044     0.00044
        11        0.980221        0.02
        12        0.996936      0.0031
        13        0.999572     0.00043
        14         1.00032     0.00032
        15               1     1.2e-15
        16               1     4.4e-16
        17               1     1.1e-16
        18               1     1.2e-15
        19               1     1.1e-16
        20               1           0
        21               1     2.2e-16

  Integrate 7.2e+02 * X^1 * Y^7

      Rule       QUAD           ERROR

         0       0.0548697        0.95
         1         0.46875        0.53
         2       0.0411523        0.96
         3         1.02082       0.021
         4        0.212191        0.79
         5         1.03586       0.036
         6         1.46914        0.47
         7        0.706913        0.29
         8         1.08213       0.082
         9        0.927415       0.073
        10        0.999233     0.00077
        11         1.05828       0.058
        12         1.00885      0.0089
        13         1.00171      0.0017
        14        0.998702      0.0013
        15               1     2.2e-16
        16               1           0
        17               1     2.2e-16
        18               1     2.2e-16
        19               1     2.2e-16
        20               1     2.1e-15
        21               1           0

  Integrate 2.5e+03 * X^2 * Y^6

      Rule       QUAD           ERROR

         0        0.192044        0.81
         1         1.64062        0.64
         2        0.144033        0.86
         3          1.1335        0.13
         4         0.74267        0.26
         5        0.811392        0.19
         6         1.44753        0.45
         7        0.967166       0.033
         8        0.866501        0.13
         9        0.968983       0.031
        10        0.996224      0.0038
        11        0.948785       0.051
        12         0.99662      0.0034
        13        0.994117      0.0059
        14         1.00622      0.0062
        15               1     6.7e-16
        16               1     2.2e-16
        17               1     2.2e-16
        18               1     3.3e-16
        19               1     2.2e-16
        20               1     2.4e-15
        21               1     7.8e-16

  Integrate 5e+03 * X^3 * Y^5

      Rule       QUAD           ERROR

         0        0.384088        0.62
         1         3.28125         2.3
         2        0.288066        0.71
         3        0.694511        0.31
         4         1.48534        0.49
         5        0.972131       0.028
         6        0.950617       0.049
         7         1.04481       0.045
         8        0.992477      0.0075
         9         1.03418       0.034
        10         1.01154       0.012
        11         1.00174      0.0017
        12        0.987653       0.012
        13         1.01166       0.012
        14        0.985894       0.014
        15               1     6.7e-16
        16               1     4.4e-16
        17               1     2.2e-16
        18               1     5.6e-16
        19               1     2.2e-16
        20               1     5.6e-16
        21               1     2.2e-16

  Integrate 6.3e+03 * X^4 * Y^4

      Rule       QUAD           ERROR

         0         0.48011        0.52
         1         4.10156         3.1
         2        0.360082        0.64
         3        0.414538        0.59
         4         1.85667        0.86
         5         1.12991        0.13
         6         0.70216         0.3
         7         1.06459       0.065
         8         1.13775        0.14
         9          1.1105        0.11
        10        0.983592       0.016
        11         1.04384       0.044
        12         1.02361       0.024
        13        0.985455       0.015
        14         1.01805       0.018
        15               1     4.4e-16
        16               1     4.4e-16
        17               1     4.4e-16
        18               1           0
        19               1     2.2e-16
        20               1     1.1e-16
        21               1     1.1e-16

  Integrate 5e+03 * X^5 * Y^3

      Rule       QUAD           ERROR

         0        0.384088        0.62
         1         3.28125         2.3
         2        0.288066        0.71
         3        0.694511        0.31
         4         1.48534        0.49
         5        0.972131       0.028
         6        0.950617       0.049
         7         1.04481       0.045
         8        0.992477      0.0075
         9         1.03418       0.034
        10         1.01154       0.012
        11         1.00174      0.0017
        12        0.987653       0.012
        13         1.01166       0.012
        14        0.985894       0.014
        15               1           0
        16               1     1.2e-15
        17               1     2.2e-16
        18               1     3.3e-16
        19               1     2.2e-16
        20               1     5.6e-16
        21               1     2.2e-16

  Integrate 2.5e+03 * X^6 * Y^2

      Rule       QUAD           ERROR

         0        0.192044        0.81
         1         1.64062        0.64
         2        0.144033        0.86
         3          1.1335        0.13
         4         0.74267        0.26
         5        0.811392        0.19
         6         1.44753        0.45
         7        0.967166       0.033
         8        0.866501        0.13
         9        0.968983       0.031
        10        0.996224      0.0038
        11        0.948785       0.051
        12         0.99662      0.0034
        13        0.994117      0.0059
        14         1.00622      0.0062
        15               1     2.2e-16
        16               1     3.3e-16
        17               1     4.4e-16
        18               1     4.4e-16
        19               1           0
        20               1     2.2e-15
        21               1     7.8e-16

  Integrate 7.2e+02 * X^7 * Y^1

      Rule       QUAD           ERROR

         0       0.0548697        0.95
         1         0.46875        0.53
         2       0.0411523        0.96
         3         1.02082       0.021
         4        0.212191        0.79
         5         1.03586       0.036
         6         1.46914        0.47
         7        0.706913        0.29
         8         1.08213       0.082
         9        0.927415       0.073
        10        0.999233     0.00077
        11         1.05828       0.058
        12         1.00885      0.0089
        13         1.00171      0.0017
        14        0.998702      0.0013
        15               1     6.7e-16
        16               1     3.3e-16
        17               1           0
        18               1     6.7e-16
        19               1     3.3e-16
        20               1     2.7e-15
        21               1     2.2e-16

  Integrate 90 * X^8 * Y^0

      Rule       QUAD           ERROR

         0      0.00685871        0.99
         1        0.117188        0.88
         2         3.75514         2.8
         3        0.389922        0.61
         4         2.29996         1.3
         5         1.01216       0.012
         6        0.600309         0.4
         7         1.20174         0.2
         8        0.956602       0.043
         9         1.03515       0.035
        10         1.00044     0.00044
        11        0.980221        0.02
        12        0.996936      0.0031
        13        0.999572     0.00043
        14         1.00032     0.00032
        15               1     1.1e-15
        16               1     4.4e-16
        17               1     2.2e-16
        18               1     1.2e-15
        19               1     1.1e-16
        20               1     2.2e-16
        21               1     3.3e-16

  Integrate 1.1e+02 * X^0 * Y^9

      Rule       QUAD           ERROR

         0      0.00279429           1
         1       0.0716146        0.93
         2         4.58543         3.6
         3        0.287142        0.71
         4          2.7799         1.8
         5        0.996255      0.0037
         6        0.383202        0.62
         7         1.33761        0.34
         8        0.920084        0.08
         9         1.07095       0.071
        10         1.00009     8.6e-05
        11         0.94523       0.055
        12        0.991867      0.0081
        13        0.997886      0.0021
        14         1.00164      0.0016
        15        0.999942     5.8e-05
        16          1.0002      0.0002
        17         1.00013     0.00013
        18               1     1.7e-15
        19               1     1.1e-16
        20               1     1.3e-15
        21               1     5.6e-16

  Integrate 9.9e+02 * X^1 * Y^8

      Rule       QUAD           ERROR

         0       0.0251486        0.97
         1        0.322266        0.68
         2       0.0188615        0.98
         3        0.852434        0.15
         4        0.140223        0.86
         5         1.08374       0.084
         6         1.57729        0.58
         7        0.590312        0.41
         8         1.12094        0.12
         9        0.874065        0.13
        10         1.00203       0.002
        11         1.13768        0.14
        12         1.01975        0.02
        13         1.00716      0.0072
        14        0.994392      0.0056
        15         1.00026     0.00026
        16        0.999113     0.00089
        17        0.999431     0.00057
        18               1     8.9e-16
        19               1     2.2e-16
        20               1     5.1e-15
        21               1     8.9e-16

  Integrate 4e+03 * X^2 * Y^7

      Rule       QUAD           ERROR

         0        0.100594         0.9
         1         1.28906        0.29
         2       0.0754458        0.92
         3         1.10343         0.1
         4        0.560892        0.44
         5        0.769683        0.23
         6         1.72582        0.73
         7        0.883621        0.12
         8         0.84609        0.15
         9        0.939825        0.06
        10        0.981678       0.018
        11        0.922919       0.077
        12         1.00607      0.0061
        13        0.979223       0.021
        14         1.02298       0.023
        15        0.999209     0.00079
        16         1.00132      0.0013
        17         1.00121      0.0012
        18               1     5.6e-16
        19               1     1.1e-16
        20               1     4.7e-15
        21               1     1.6e-15

  Integrate 9.2e+03 * X^3 * Y^6

      Rule       QUAD           ERROR

         0         0.23472        0.77
         1         3.00781           2
         2         0.17604        0.82
         3        0.800594         0.2
         4         1.30875        0.31
         5        0.846318        0.15
         6         1.17507        0.18
         7         1.02585       0.026
         8        0.896388         0.1
         9         1.00176      0.0018
        10         1.03039        0.03
        11        0.959901        0.04
        12        0.959792        0.04
        13         1.02893       0.029
        14        0.963277       0.037
        15         1.00155      0.0016
        16        0.999523     0.00048
        17        0.998423      0.0016
        18               1     8.9e-16
        19               1     2.2e-16
        20               1     4.4e-16
        21               1     6.7e-16

  Integrate 1.4e+04 * X^4 * Y^5

      Rule       QUAD           ERROR

         0         0.35208        0.65
         1         4.51172         3.5
         2         0.26406        0.74
         3        0.402555         0.6
         4         1.96312        0.96
         5          1.1061        0.11
         6        0.693158        0.31
         7          1.1078        0.11
         8         1.14249        0.14
         9         1.15903        0.16
        10        0.982741       0.017
        11         1.06746       0.067
        12         1.02844       0.028
        13        0.985505       0.014
        14         1.01867       0.019
        15        0.999065     0.00093
        16         0.99975     0.00025
        17         1.00075     0.00075
        18               1     4.4e-16
        19               1     1.1e-16
        20               1     7.8e-16
        21               1     2.2e-16

  Integrate 1.4e+04 * X^5 * Y^4

      Rule       QUAD           ERROR

         0         0.35208        0.65
         1         4.51172         3.5
         2         0.26406        0.74
         3        0.402555         0.6
         4         1.96312        0.96
         5          1.1061        0.11
         6        0.693158        0.31
         7          1.1078        0.11
         8         1.14249        0.14
         9         1.15903        0.16
        10        0.982741       0.017
        11         1.06746       0.067
        12         1.02844       0.028
        13        0.985505       0.014
        14         1.01867       0.019
        15        0.999065     0.00093
        16         0.99975     0.00025
        17         1.00075     0.00075
        18               1     2.2e-16
        19               1     1.1e-16
        20               1     6.7e-16
        21               1     2.2e-16

  Integrate 9.2e+03 * X^6 * Y^3

      Rule       QUAD           ERROR

         0         0.23472        0.77
         1         3.00781           2
         2         0.17604        0.82
         3        0.800594         0.2
         4         1.30875        0.31
         5        0.846318        0.15
         6         1.17507        0.18
         7         1.02585       0.026
         8        0.896388         0.1
         9         1.00176      0.0018
        10         1.03039        0.03
        11        0.959901        0.04
        12        0.959792        0.04
        13         1.02893       0.029
        14        0.963277       0.037
        15         1.00155      0.0016
        16        0.999523     0.00048
        17        0.998423      0.0016
        18               1     7.8e-16
        19               1     2.2e-16
        20               1     6.7e-16
        21               1     4.4e-16

  Integrate 4e+03 * X^7 * Y^2

      Rule       QUAD           ERROR

         0        0.100594         0.9
         1         1.28906        0.29
         2       0.0754458        0.92
         3         1.10343         0.1
         4        0.560892        0.44
         5        0.769683        0.23
         6         1.72582        0.73
         7        0.883621        0.12
         8         0.84609        0.15
         9        0.939825        0.06
        10        0.981678       0.018
        11        0.922919       0.077
        12         1.00607      0.0061
        13        0.979223       0.021
        14         1.02298       0.023
        15        0.999209     0.00079
        16         1.00132      0.0013
        17         1.00121      0.0012
        18               1     4.4e-16
        19               1     2.2e-16
        20               1     4.2e-15
        21               1     1.4e-15

  Integrate 9.9e+02 * X^8 * Y^1

      Rule       QUAD           ERROR

         0       0.0251486        0.97
         1        0.322266        0.68
         2       0.0188615        0.98
         3        0.852434        0.15
         4        0.140223        0.86
         5         1.08374       0.084
         6         1.57729        0.58
         7        0.590312        0.41
         8         1.12094        0.12
         9        0.874065        0.13
        10         1.00203       0.002
        11         1.13768        0.14
        12         1.01975        0.02
        13         1.00716      0.0072
        14        0.994392      0.0056
        15         1.00026     0.00026
        16        0.999113     0.00089
        17        0.999431     0.00057
        18               1     6.7e-16
        19               1     3.3e-16
        20               1     5.7e-15
        21               1     6.7e-16

  Integrate 1.1e+02 * X^9 * Y^0

      Rule       QUAD           ERROR

         0      0.00279429           1
         1       0.0716146        0.93
         2         4.58543         3.6
         3        0.287142        0.71
         4          2.7799         1.8
         5        0.996255      0.0037
         6        0.383202        0.62
         7         1.33761        0.34
         8        0.920084        0.08
         9         1.07095       0.071
        10         1.00009     8.6e-05
        11         0.94523       0.055
        12        0.991867      0.0081
        13        0.997886      0.0021
        14         1.00164      0.0016
        15        0.999942     5.8e-05
        16          1.0002      0.0002
        17         1.00013     0.00013
        18               1     1.6e-15
        19               1           0
        20               1     1.3e-15
        21               1     5.6e-16

  Integrate 1.3e+02 * X^0 * Y^10

      Rule       QUAD           ERROR

         0      0.00111772           1
         1       0.0429688        0.96
         2         5.50084         4.5
         3        0.207231        0.79
         4         3.31769         2.3
         5        0.968918       0.031
         6        0.129515        0.87
         7         1.50907        0.51
         8        0.873671        0.13
         9         1.12323        0.12
        10        0.998219      0.0018
        11         0.88397        0.12
        12         0.98336       0.017
        13        0.993975       0.006
        14         1.00481      0.0048
        15        0.999662     0.00034
        16         1.00109      0.0011
        17         1.00066     0.00066
        18         0.99997       3e-05
        19        0.999979     2.1e-05
        20               1     3.8e-15
        21               1     8.9e-16

  Integrate 1.3e+03 * X^1 * Y^9

      Rule       QUAD           ERROR

         0       0.0111772        0.99
         1        0.214844        0.79
         2      0.00838287        0.99
         3        0.686695        0.31
         4       0.0909672        0.91
         5         1.13294        0.13
         6         1.65163        0.65
         7        0.480319        0.52
         8         1.15215        0.15
         9        0.809557        0.19
        10         1.00942      0.0094
        11         1.25153        0.25
        12          1.0344       0.034
        13         1.01744       0.017
        14        0.985803       0.014
        15         1.00134      0.0013
        16        0.995717      0.0043
        17        0.997466      0.0025
        18         1.00015     0.00015
        19          1.0001      0.0001
        20               1     9.4e-15
        21               1     1.8e-15

  Integrate 5.9e+03 * X^2 * Y^8

      Rule       QUAD           ERROR

         0       0.0502972        0.95
         1        0.966797       0.033
         2       0.0377229        0.96
         3         1.01255       0.013
         4        0.409352        0.59
         5        0.761318        0.24
         6         2.00874           1
         7        0.780207        0.22
         8        0.849523        0.15
         9         0.90383       0.096
        10        0.957945       0.042
        11        0.924013       0.076
        12         1.02938       0.029
        13        0.956754       0.043
        14         1.05042        0.05
        15        0.996306      0.0037
        16         1.00487      0.0049
        17         1.00396       0.004
        18        0.999303      0.0007
        19        0.999414     0.00059
        20               1       6e-15
        21               1     1.3e-15

  Integrate 1.6e+04 * X^3 * Y^7

      Rule       QUAD           ERROR

         0        0.134126        0.87
         1         2.57812         1.6
         2        0.100594         0.9
         3         0.86017        0.14
         4         1.09161       0.092
         5        0.720497        0.28
         6         1.48628        0.49
         7        0.967926       0.032
         8         0.79708         0.2
         9        0.949768        0.05
        10         1.04271       0.043
        11         0.89397        0.11
        12        0.931119       0.069
        13         1.03934       0.039
        14        0.945921       0.054
        15         1.00613      0.0061
        16        0.999956     4.4e-05
        17        0.997525      0.0025
        18         1.00188      0.0019
        19         1.00173      0.0017
        20               1     8.9e-16
        21               1     1.1e-15

  Integrate 2.8e+04 * X^4 * Y^6

      Rule       QUAD           ERROR

         0         0.23472        0.77
         1         4.51172         3.5
         2         0.17604        0.82
         3        0.467461        0.53
         4         1.91031        0.91
         5        0.998828      0.0012
         6        0.818587        0.18
         7         1.11924        0.12
         8         1.06917       0.069
         9         1.15486        0.15
        10         1.00786      0.0079
        11          1.0536       0.054
        12        0.999566     0.00043
        13         1.01024        0.01
        14        0.989214       0.011
        15         0.99789      0.0021
        16        0.999336     0.00066
        17        0.996401      0.0036
        18        0.996691      0.0033
        19        0.996853      0.0031
        20               1     2.3e-15
        21               1           0

  Integrate 3.3e+04 * X^5 * Y^5

      Rule       QUAD           ERROR

         0        0.281664        0.72
         1         5.41406         4.4
         2        0.211248        0.79
         3        0.273552        0.73
         4         2.29237         1.3
         5         1.16618        0.17
         6        0.554527        0.45
         7         1.19336        0.19
         8         1.23958        0.24
         9         1.28766        0.29
        10        0.950326        0.05
        11         1.13827        0.14
        12         1.07273       0.073
        13        0.955574       0.044
        14         1.05418       0.054
        15        0.997684      0.0023
        16        0.996791      0.0032
        17         1.00713      0.0071
        18         1.00398       0.004
        19         1.00383      0.0038
        20               1     8.9e-16
        21               1     4.4e-16

  Integrate 2.8e+04 * X^6 * Y^4

      Rule       QUAD           ERROR

         0         0.23472        0.77
         1         4.51172         3.5
         2         0.17604        0.82
         3        0.467461        0.53
         4         1.91031        0.91
         5        0.998828      0.0012
         6        0.818587        0.18
         7         1.11924        0.12
         8         1.06917       0.069
         9         1.15486        0.15
        10         1.00786      0.0079
        11          1.0536       0.054
        12        0.999566     0.00043
        13         1.01024        0.01
        14        0.989214       0.011
        15         0.99789      0.0021
        16        0.999336     0.00066
        17        0.996401      0.0036
        18        0.996691      0.0033
        19        0.996853      0.0031
        20               1     2.3e-15
        21               1           0

  Integrate 1.6e+04 * X^7 * Y^3

      Rule       QUAD           ERROR

         0        0.134126        0.87
         1         2.57812         1.6
         2        0.100594         0.9
         3         0.86017        0.14
         4         1.09161       0.092
         5        0.720497        0.28
         6         1.48628        0.49
         7        0.967926       0.032
         8         0.79708         0.2
         9        0.949768        0.05
        10         1.04271       0.043
        11         0.89397        0.11
        12        0.931119       0.069
        13         1.03934       0.039
        14        0.945921       0.054
        15         1.00613      0.0061
        16        0.999956     4.4e-05
        17        0.997525      0.0025
        18         1.00188      0.0019
        19         1.00173      0.0017
        20               1     4.4e-16
        21               1     8.9e-16

  Integrate 5.9e+03 * X^8 * Y^2

      Rule       QUAD           ERROR

         0       0.0502972        0.95
         1        0.966797       0.033
         2       0.0377229        0.96
         3         1.01255       0.013
         4        0.409352        0.59
         5        0.761318        0.24
         6         2.00874           1
         7        0.780207        0.22
         8        0.849523        0.15
         9         0.90383       0.096
        10        0.957945       0.042
        11        0.924013       0.076
        12         1.02938       0.029
        13        0.956754       0.043
        14         1.05042        0.05
        15        0.996306      0.0037
        16         1.00487      0.0049
        17         1.00396       0.004
        18        0.999303      0.0007
        19        0.999414     0.00059
        20               1     5.8e-15
        21               1     1.2e-15

  Integrate 1.3e+03 * X^9 * Y^1

      Rule       QUAD           ERROR

         0       0.0111772        0.99
         1        0.214844        0.79
         2      0.00838287        0.99
         3        0.686695        0.31
         4       0.0909672        0.91
         5         1.13294        0.13
         6         1.65163        0.65
         7        0.480319        0.52
         8         1.15215        0.15
         9        0.809557        0.19
        10         1.00942      0.0094
        11         1.25153        0.25
        12          1.0344       0.034
        13         1.01744       0.017
        14        0.985803       0.014
        15         1.00134      0.0013
        16        0.995717      0.0043
        17        0.997466      0.0025
        18         1.00015     0.00015
        19          1.0001      0.0001
        20               1       1e-14
        21               1     1.6e-15

  Integrate 1.3e+02 * X^10 * Y^0

      Rule       QUAD           ERROR

         0      0.00111772           1
         1       0.0429688        0.96
         2         5.50084         4.5
         3        0.207231        0.79
         4         3.31769         2.3
         5        0.968918       0.031
         6        0.129515        0.87
         7         1.50907        0.51
         8        0.873671        0.13
         9         1.12323        0.12
        10        0.998219      0.0018
        11         0.88397        0.12
        12         0.98336       0.017
        13        0.993975       0.006
        14         1.00481      0.0048
        15        0.999662     0.00034
        16         1.00109      0.0011
        17         1.00066     0.00066
        18         0.99997       3e-05
        19        0.999979     2.1e-05
        20               1     3.8e-15
        21               1       1e-15

LYNESS_RULE_PRB:
  Normal end of execution.

22 December 2011 04:46:43 PM