[next] [prev] [prev-tail] [tail] [up]

Chapter 2
detailed summary tables of results

 2.1 List of integrals sorted by grade for each CAS
  2.1.1 Rubi
  2.1.2 Mathematica
  2.1.3 Maple
  2.1.4 Maxima
  2.1.5 FriCAS
  2.1.6 Sympy
  2.1.7 Giac
  2.1.8 Mupad
 2.2 Detailed conclusion table per each integral for all CAS systems
 2.3 Detailed conclusion table specific for Rubi results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88 }

B grade: { 10, 11 }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57 }

B grade: { }

C grade: { 15, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88 }

F grade: { }

2.1.3 Maple

A grade: { 2, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 66 }

B grade: { 1, 3, 11, 24, 26, 44, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88 }

C grade: { }

F grade: { }

2.1.4 Maxima

A grade: { 2, 4, 5, 6, 8, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 27, 29, 31 }

B grade: { 1, 3, 7, 9, 11 }

C grade: { }

F grade: { 24, 26, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 }

B grade: { 10, 11, 31, 32 }

C grade: { }

F grade: { 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88 }

2.1.6 Sympy

A grade: { 4, 5, 10, 12, 13, 14, 15, 18, 19, 20, 21, 26, 27, 28 }

B grade: { 1, 2, 3, 11, 16, 17, 22, 23 }

C grade: { }

F grade: { 6, 7, 8, 9, 24, 25, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31 }

B grade: { 11, 24, 32 }

C grade: { }

F grade: { 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88 }

2.1.8 Mupad

A grade: { }

B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 37 }

C grade: { }

F grade: { 33, 34, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88 }

2.2 Detailed conclusion table per each integral for all CAS systems

Detailed conclusion table per each integral is given by table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given just an F.

In this table,the column normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 25 68 94 24 294 45 34
normalized size 1 1.00 0.81 2.19 3.03 0.77 9.48 1.45 1.10
time (sec) N/A 0.043 0.041 0.049 0.625 0.776 1.244 0.376 0.382
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 13 16 14 14 51 14 11
normalized size 1 1.00 0.68 0.84 0.74 0.74 2.68 0.74 0.58
time (sec) N/A 0.040 0.012 0.037 0.614 1.339 0.664 2.407 0.249
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 17 31 42 10 46 25 10
normalized size 1 1.00 1.31 2.38 3.23 0.77 3.54 1.92 0.77
time (sec) N/A 0.038 0.008 0.043 0.843 0.848 0.373 0.508 0.292
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 12 13 12 12 8 10 10
normalized size 1 1.00 1.20 1.30 1.20 1.20 0.80 1.00 1.00
time (sec) N/A 0.024 0.006 0.028 0.633 0.759 0.123 0.365 0.057
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 10 9 12 11 5 8 8
normalized size 1 1.00 0.91 0.82 1.09 1.00 0.45 0.73 0.73
time (sec) N/A 0.010 0.005 0.024 0.678 0.895 0.177 0.348 0.293
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 42 33 31 37 0 34 20
normalized size 1 1.00 1.83 1.43 1.35 1.61 0.00 1.48 0.87
time (sec) N/A 0.050 0.034 0.053 0.675 0.801 0.000 0.372 0.285
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 30 29 41 26 0 37 35
normalized size 1 1.00 1.25 1.21 1.71 1.08 0.00 1.54 1.46
time (sec) N/A 0.046 0.049 0.051 0.618 0.859 0.000 0.416 0.320
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 60 55 58 83 0 52 45
normalized size 1 1.00 1.22 1.12 1.18 1.69 0.00 1.06 0.92
time (sec) N/A 0.074 0.112 0.062 1.160 0.938 0.000 0.595 0.289
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 38 45 70 53 0 59 45
normalized size 1 1.00 1.03 1.22 1.89 1.43 0.00 1.59 1.22
time (sec) N/A 0.048 0.058 0.062 0.544 0.775 0.000 1.015 0.372
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 5 11 5 10 9 11 10 9 7
normalized size 1 2.20 1.00 2.00 1.80 2.20 2.00 1.80 1.40
time (sec) N/A 0.021 0.003 0.021 0.470 0.877 0.106 0.300 0.264
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 3 13 3 12 9 11 8 11 9
normalized size 1 4.33 1.00 4.00 3.00 3.67 2.67 3.67 3.00
time (sec) N/A 0.022 0.004 0.024 0.307 0.970 0.110 0.411 0.077
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 6 6 12 7 6 6 5 6 6
normalized size 1 1.00 2.00 1.17 1.00 1.00 0.83 1.00 1.00
time (sec) N/A 0.019 0.008 0.024 0.603 0.980 0.320 0.484 0.251
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 12 11 6 6 5 6 6
normalized size 1 1.00 1.20 1.10 0.60 0.60 0.50 0.60 0.60
time (sec) N/A 0.019 0.009 0.035 0.759 1.221 0.323 0.527 0.248
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 18 11 23 18 7 10 10
normalized size 1 1.00 1.29 0.79 1.64 1.29 0.50 0.71 0.71
time (sec) N/A 0.031 0.006 0.044 0.910 1.104 0.464 0.461 0.298
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 26 13 23 16 8 12 10
normalized size 1 1.00 1.62 0.81 1.44 1.00 0.50 0.75 0.62
time (sec) N/A 0.031 0.011 0.070 1.137 1.409 0.875 0.372 0.305
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 13 11 10 12 58 10 10
normalized size 1 1.00 1.30 1.10 1.00 1.20 5.80 1.00 1.00
time (sec) N/A 0.036 0.019 0.040 0.569 1.519 0.461 0.441 0.247
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 13 11 10 12 58 12 10
normalized size 1 1.00 1.08 0.92 0.83 1.00 4.83 1.00 0.83
time (sec) N/A 0.036 0.017 0.056 0.295 1.031 0.471 0.404 0.044
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 12 9 8 14 14 8 8
normalized size 1 1.00 1.20 0.90 0.80 1.40 1.40 0.80 0.80
time (sec) N/A 0.019 0.008 0.025 1.209 0.823 0.548 1.053 0.035
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 11 8 14 15 8 8
normalized size 1 1.00 1.00 0.92 0.67 1.17 1.25 0.67 0.67
time (sec) N/A 0.019 0.011 0.039 0.498 0.945 0.551 0.478 0.036
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 12 9 12 20 7 8 8
normalized size 1 1.00 0.86 0.64 0.86 1.43 0.50 0.57 0.57
time (sec) N/A 0.031 0.027 0.050 0.618 1.068 0.794 0.426 0.259
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 12 9 12 22 10 8 8
normalized size 1 1.00 0.75 0.56 0.75 1.38 0.62 0.50 0.50
time (sec) N/A 0.031 0.032 0.073 0.297 0.787 1.332 0.980 0.353
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 18 15 14 21 126 14 14
normalized size 1 1.00 1.29 1.07 1.00 1.50 9.00 1.00 1.00
time (sec) N/A 0.038 0.008 0.053 0.457 0.812 0.585 0.355 0.043
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 29 17 16 22 126 18 16
normalized size 1 1.00 1.45 0.85 0.80 1.10 6.30 0.90 0.80
time (sec) N/A 0.037 0.011 0.073 0.765 0.667 0.584 0.409 0.044
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 96 315 0 243 0 194 1677
normalized size 1 1.00 0.92 3.03 0.00 2.34 0.00 1.87 16.12
time (sec) N/A 0.256 0.210 0.041 0.000 1.055 0.000 0.524 1.112
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 40 45 38 41 0 39 38
normalized size 1 1.00 1.00 1.12 0.95 1.02 0.00 0.98 0.95
time (sec) N/A 0.061 0.056 0.025 0.294 0.663 0.000 0.446 0.092
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 54 108 0 154 991 90 74
normalized size 1 1.00 0.92 1.83 0.00 2.61 16.80 1.53 1.25
time (sec) N/A 0.109 0.081 0.036 0.000 1.211 88.657 0.353 0.488
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 13 12 15 17 13 12
normalized size 1 1.00 1.00 1.08 1.00 1.25 1.42 1.08 1.00
time (sec) N/A 0.025 0.015 0.018 0.473 0.949 0.289 0.423 0.043
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 41 36 0 137 144 61 38
normalized size 1 1.00 0.98 0.86 0.00 3.26 3.43 1.45 0.90
time (sec) N/A 0.026 0.023 0.022 0.000 1.033 3.394 0.925 0.483
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 50 54 47 52 0 54 52
normalized size 1 1.00 0.94 1.02 0.89 0.98 0.00 1.02 0.98
time (sec) N/A 0.072 0.043 0.038 0.334 0.964 0.000 0.370 0.212
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 66 78 0 230 0 91 86
normalized size 1 1.00 0.99 1.16 0.00 3.43 0.00 1.36 1.28
time (sec) N/A 0.095 0.323 0.047 0.000 1.092 0.000 0.433 0.472
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 99 114 115 181 0 136 112
normalized size 1 1.00 1.08 1.24 1.25 1.97 0.00 1.48 1.22
time (sec) N/A 0.154 0.429 0.056 0.698 1.058 0.000 0.441 0.508
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 112 153 0 459 0 206 184
normalized size 1 1.00 1.02 1.39 0.00 4.17 0.00 1.87 1.67
time (sec) N/A 0.271 0.637 0.056 0.000 1.081 0.000 1.406 0.558
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 129 129 108 127 0 0 0 0 -1
normalized size 1 1.00 0.84 0.98 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.097 0.852 0.224 0.000 0.865 0.000 0.000 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 80 171 0 0 0 0 -1
normalized size 1 1.00 0.80 1.71 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.070 0.516 0.237 0.000 0.696 0.000 0.000 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 80 116 0 0 0 0 -1
normalized size 1 1.00 0.80 1.16 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.071 0.462 0.208 0.000 1.674 0.000 0.000 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 60 117 0 0 0 0 60
normalized size 1 1.00 0.88 1.72 0.00 0.00 0.00 0.00 0.88
time (sec) N/A 0.049 0.098 0.229 0.000 1.002 0.000 0.000 0.494
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 54 92 0 0 0 0 50
normalized size 1 1.00 0.82 1.39 0.00 0.00 0.00 0.00 0.76
time (sec) N/A 0.051 0.202 0.156 0.000 1.121 0.000 0.000 0.724
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 96 96 58 153 0 0 0 0 -1
normalized size 1 1.00 0.60 1.59 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.073 0.117 0.218 0.000 1.656 0.000 0.000 0.000
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 59 124 0 0 0 0 -1
normalized size 1 1.00 0.58 1.22 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.071 0.152 0.242 0.000 1.629 0.000 0.000 0.000
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 131 131 74 187 0 0 0 0 -1
normalized size 1 1.00 0.56 1.43 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.091 0.245 0.299 0.000 0.596 0.000 0.000 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 157 228 0 0 0 0 -1
normalized size 1 1.00 0.81 1.18 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.190 1.667 0.240 0.000 1.130 0.000 0.000 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 116 332 0 0 0 0 -1
normalized size 1 1.00 0.75 2.16 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.161 0.802 0.265 0.000 1.149 0.000 0.000 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 117 229 0 0 0 0 -1
normalized size 1 1.00 0.76 1.49 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.168 0.816 0.242 0.000 0.849 0.000 0.000 0.000
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 83 294 0 0 0 0 -1
normalized size 1 1.00 0.73 2.58 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.131 0.269 0.247 0.000 1.073 0.000 0.000 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 79 170 0 0 0 0 -1
normalized size 1 1.00 0.69 1.49 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.129 0.379 0.216 0.000 1.172 0.000 0.000 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 75 277 0 0 0 0 -1
normalized size 1 1.00 0.64 2.35 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.138 0.235 0.229 0.000 0.734 0.000 0.000 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 76 190 0 0 0 0 -1
normalized size 1 1.00 0.61 1.53 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.139 0.264 0.228 0.000 0.886 0.000 0.000 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 165 165 109 327 0 0 0 0 -1
normalized size 1 1.00 0.66 1.98 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.171 0.474 0.262 0.000 0.685 0.000 0.000 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 242 242 205 252 0 0 0 0 -1
normalized size 1 1.00 0.85 1.04 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.320 2.485 0.318 0.000 1.051 0.000 0.000 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 202 202 149 356 0 0 0 0 -1
normalized size 1 1.00 0.74 1.76 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.293 1.389 0.434 0.000 1.138 0.000 0.000 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 202 202 147 226 0 0 0 0 -1
normalized size 1 1.00 0.73 1.12 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.298 1.200 0.298 0.000 1.148 0.000 0.000 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 161 105 315 0 0 0 0 -1
normalized size 1 1.00 0.65 1.96 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.250 0.551 0.399 0.000 0.874 0.000 0.000 0.000
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 157 98 210 0 0 0 0 -1
normalized size 1 1.00 0.62 1.34 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.243 0.711 0.268 0.000 1.077 0.000 0.000 0.000
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 165 165 101 313 0 0 0 0 -1
normalized size 1 1.00 0.61 1.90 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.253 0.319 0.322 0.000 1.121 0.000 0.000 0.000
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 169 169 102 214 0 0 0 0 -1
normalized size 1 1.00 0.60 1.27 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.260 0.824 0.312 0.000 0.869 0.000 0.000 0.000
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 192 192 130 351 0 0 0 0 -1
normalized size 1 1.00 0.68 1.83 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.271 0.610 0.340 0.000 1.291 0.000 0.000 0.000
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 144 241 0 0 0 0 -1
normalized size 1 1.00 0.75 1.25 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.274 0.622 0.334 0.000 1.095 0.000 0.000 0.000
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 544 544 2035 2930 0 0 0 0 -1
normalized size 1 1.00 3.74 5.39 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.899 17.628 1.112 0.000 0.000 0.000 0.000 0.000
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 461 461 834 2051 0 0 0 0 -1
normalized size 1 1.00 1.81 4.45 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.336 14.992 1.068 0.000 0.000 0.000 0.000 0.000
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 474 474 1955 2087 0 0 0 0 -1
normalized size 1 1.00 4.12 4.40 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.337 15.526 0.849 0.000 0.000 0.000 0.000 0.000
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 399 399 757 1247 0 0 0 0 -1
normalized size 1 1.00 1.90 3.13 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.898 14.529 0.866 0.000 0.000 0.000 0.000 0.000
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 410 410 434 1314 0 0 0 0 -1
normalized size 1 1.00 1.06 3.20 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.904 5.818 0.868 0.000 0.000 0.000 0.000 0.000
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 302 302 361 815 0 0 0 0 -1
normalized size 1 1.00 1.20 2.70 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.607 1.802 0.870 0.000 0.000 0.000 0.000 0.000
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 307 307 261 855 0 0 0 0 -1
normalized size 1 1.00 0.85 2.79 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.588 1.605 0.825 0.000 0.000 0.000 0.000 0.000
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 426 426 791 1248 0 0 0 0 -1
normalized size 1 1.00 1.86 2.93 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.964 14.747 0.868 0.000 0.000 0.000 0.000 0.000
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-1) F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 447 447 1192 845 0 0 0 0 -1
normalized size 1 1.00 2.67 1.89 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.013 11.252 0.984 0.000 0.000 0.000 0.000 0.000
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 501 501 881 1807 0 0 0 0 -1
normalized size 1 1.00 1.76 3.61 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.355 6.576 0.790 0.000 0.000 0.000 0.000 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 557 557 2029 4706 0 0 0 0 -1
normalized size 1 1.00 3.64 8.45 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.557 15.365 1.596 0.000 0.000 0.000 0.000 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 473 473 835 3595 0 0 0 0 -1
normalized size 1 1.00 1.77 7.60 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.157 14.708 1.724 0.000 0.000 0.000 0.000 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 487 487 1956 3396 0 0 0 0 -1
normalized size 1 1.00 4.02 6.97 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.151 14.597 1.543 0.000 0.000 0.000 0.000 0.000
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 404 404 366 3174 0 0 0 0 -1
normalized size 1 1.00 0.91 7.86 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.842 20.200 0.919 0.000 0.000 0.000 0.000 0.000
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 418 418 614 2148 0 0 0 0 -1
normalized size 1 1.00 1.47 5.14 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.907 9.221 1.556 0.000 0.000 0.000 0.000 0.000
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 438 438 786 1384 0 0 0 0 -1
normalized size 1 1.00 1.79 3.16 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.905 13.938 1.210 0.000 0.000 0.000 0.000 0.000
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 445 445 1182 1351 0 0 0 0 -1
normalized size 1 1.00 2.66 3.04 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.933 10.122 1.256 0.000 0.000 0.000 0.000 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 507 507 865 4318 0 0 0 0 -1
normalized size 1 1.00 1.71 8.52 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.271 6.486 1.132 0.000 0.000 0.000 0.000 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 530 530 1257 2143 0 0 0 0 -1
normalized size 1 1.00 2.37 4.04 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.367 13.169 1.671 0.000 0.000 0.000 0.000 0.000
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 590 590 950 2888 0 0 0 0 -1
normalized size 1 1.00 1.61 4.89 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.680 6.609 2.082 0.000 0.000 0.000 0.000 0.000
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 590 590 930 7803 0 0 0 0 -1
normalized size 1 1.00 1.58 13.23 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.473 15.022 2.882 0.000 0.000 0.000 0.000 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 604 604 2024 7238 0 0 0 0 -1
normalized size 1 1.00 3.35 11.98 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.582 14.577 2.677 0.000 0.000 0.000 0.000 0.000
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 498 498 837 5791 0 0 0 0 -1
normalized size 1 1.00 1.68 11.63 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.115 14.363 2.385 0.000 0.000 0.000 0.000 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 512 512 1954 5404 0 0 0 0 -1
normalized size 1 1.00 3.82 10.55 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.138 14.556 2.458 0.000 0.000 0.000 0.000 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 520 520 831 4303 0 0 0 0 -1
normalized size 1 1.00 1.60 8.28 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.120 14.356 2.227 0.000 0.000 0.000 0.000 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 534 534 1211 4116 0 0 0 0 -1
normalized size 1 1.00 2.27 7.71 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.210 10.388 2.240 0.000 0.000 0.000 0.000 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 529 529 837 2986 0 0 0 0 -1
normalized size 1 1.00 1.58 5.64 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.212 14.333 1.947 0.000 0.000 0.000 0.000 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 535 535 1226 2918 0 0 0 0 -1
normalized size 1 1.00 2.29 5.45 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.229 11.369 2.118 0.000 0.000 0.000 0.000 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 611 611 922 4913 0 0 0 0 -1
normalized size 1 1.00 1.51 8.04 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.647 6.536 2.845 0.000 0.000 0.000 0.000 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 629 629 1308 4661 0 0 0 0 -1
normalized size 1 1.00 2.08 7.41 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.775 14.488 3.143 0.000 0.000 0.000 0.000 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 700 700 1014 5638 0 0 0 0 -1
normalized size 1 1.00 1.45 8.05 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.118 6.709 3.374 0.000 0.000 0.000 0.000 0.000

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [78] had the largest ratio of [.5200]

Table 2.1:Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 3 3 1.00 13 0.231
2 A 2 1 1.00 13 0.077
3 A 2 2 1.00 13 0.154
4 A 2 2 1.00 11 0.182
5 A 1 1 1.00 8 0.125
6 A 4 3 1.00 11 0.273
7 A 3 3 1.00 13 0.231
8 A 4 3 1.00 13 0.231
9 A 3 2 1.00 13 0.154
10 B 2 2 2.20 13 0.154
11 B 2 2 4.33 15 0.133
12 A 2 2 1.00 9 0.222
13 A 2 2 1.00 11 0.182
14 A 2 2 1.00 11 0.182
15 A 2 2 1.00 13 0.154
16 A 3 2 1.00 11 0.182
17 A 3 2 1.00 13 0.154
18 A 2 2 1.00 9 0.222
19 A 2 2 1.00 11 0.182
20 A 1 1 1.00 11 0.091
21 A 1 1 1.00 13 0.077
22 A 3 2 1.00 11 0.182
23 A 3 2 1.00 13 0.154
24 A 5 5 1.00 13 0.385
25 A 3 2 1.00 13 0.154
26 A 4 4 1.00 13 0.308
27 A 2 2 1.00 11 0.182
28 A 2 2 1.00 8 0.250
29 A 6 4 1.00 11 0.364
30 A 4 4 1.00 13 0.308
31 A 4 3 1.00 13 0.231
32 A 5 5 1.00 13 0.385
33 A 5 4 1.00 23 0.174
34 A 4 4 1.00 23 0.174
35 A 4 4 1.00 23 0.174
36 A 3 3 1.00 23 0.130
37 A 3 3 1.00 23 0.130
38 A 4 4 1.00 23 0.174
39 A 4 4 1.00 23 0.174
40 A 5 4 1.00 23 0.174
41 A 6 5 1.00 25 0.200
42 A 5 5 1.00 25 0.200
43 A 5 5 1.00 25 0.200
44 A 4 4 1.00 25 0.160
45 A 4 4 1.00 25 0.160
46 A 4 4 1.00 25 0.160
47 A 4 4 1.00 25 0.160
48 A 5 5 1.00 25 0.200
49 A 7 6 1.00 25 0.240
50 A 6 6 1.00 25 0.240
51 A 6 6 1.00 25 0.240
52 A 5 5 1.00 25 0.200
53 A 5 5 1.00 25 0.200
54 A 5 5 1.00 25 0.200
55 A 5 5 1.00 25 0.200
56 A 5 5 1.00 25 0.200
57 A 5 5 1.00 25 0.200
58 A 15 12 1.00 25 0.480
59 A 14 12 1.00 25 0.480
60 A 14 12 1.00 25 0.480
61 A 13 11 1.00 25 0.440
62 A 13 11 1.00 25 0.440
63 A 9 7 1.00 25 0.280
64 A 9 7 1.00 25 0.280
65 A 13 11 1.00 25 0.440
66 A 13 11 1.00 25 0.440
67 A 14 12 1.00 25 0.480
68 A 15 12 1.00 25 0.480
69 A 14 12 1.00 25 0.480
70 A 14 12 1.00 25 0.480
71 A 13 11 1.00 25 0.440
72 A 13 11 1.00 25 0.440
73 A 13 11 1.00 25 0.440
74 A 13 11 1.00 25 0.440
75 A 14 12 1.00 25 0.480
76 A 14 12 1.00 25 0.480
77 A 15 12 1.00 25 0.480
78 A 15 13 1.00 25 0.520
79 A 15 13 1.00 25 0.520
80 A 14 12 1.00 25 0.480
81 A 14 12 1.00 25 0.480
82 A 14 12 1.00 25 0.480
83 A 14 12 1.00 25 0.480
84 A 14 12 1.00 25 0.480
85 A 14 12 1.00 25 0.480
86 A 15 13 1.00 25 0.520
87 A 15 13 1.00 25 0.520
88 A 16 13 1.00 25 0.520

[next] [prev] [prev-tail] [front] [up]