[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, 10, 11, 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, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 8, 10, 13, 14, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 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, 71, 73, 81, 85, 86, 87, 89, 90, 93, 94, 95, 96, 97, 98 }

B grade: { 6, 7, 9, 11, 12, 15, 16, 33, 34, 88, 91 }

C grade: { 70, 72, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 92 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 6, 8, 11, 12, 13, 14, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 57, 59, 60, 62, 63, 65, 66, 71, 72, 73, 81, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98 }

B grade: { 7, 9, 10, 15, 16, 17, 18, 34, 52, 55, 56, 58, 61, 64, 67, 68, 69, 70, 84, 85 }

C grade: { 5, 74, 75, 76, 77, 78, 79, 80, 82, 83 }

F grade: { }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 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, 52, 67, 68, 69, 73, 81, 86, 92, 93, 94, 95, 97, 98 }

B grade: { 6, 7, 15, 16, 51, 53, 54, 87, 88, 89, 90, 91 }

C grade: { }

F grade: { 50, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 96 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 8, 10, 11, 12, 13, 14, 17, 18, 19, 24, 25, 28, 29, 30, 32, 33, 34, 35, 36, 37, 44, 45, 46, 47, 48, 49, 50, 51, 53, 73, 86, 87, 88, 89, 90, 93, 95, 96, 97, 98 }

B grade: { 6, 7, 9, 15, 16, 20, 21, 22, 23, 26, 27, 31, 38, 39, 40, 41, 42, 43, 67, 68, 69, 70, 71, 72, 81, 85, 91 }

C grade: { 92 }

F grade: { 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 94 }

2.1.6 Sympy

A grade: { 5, 13, 20, 24, 38, 44, 73 }

B grade: { 1, 2, 3, 4, 6, 25, 26, 27, 45, 46, 84 }

C grade: { }

F grade: { 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 22, 23, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 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, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 67, 68, 69, 70, 72, 73, 86, 87, 89, 92, 93, 94, 95, 96, 97, 98 }

B grade: { 6, 7, 15, 16, 23, 47, 49, 53, 71, 81, 84, 85, 88, 90, 91 }

C grade: { 48, 50, 54 }

F grade: { 51, 52, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 74, 75, 76, 77, 78, 79, 80, 82, 83 }

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, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 55, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 92 }

C grade: { }

F grade: { 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 87, 88, 89, 90, 91, 93, 94, 95, 96, 97, 98 }

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 A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 26 42 37 23 473 31 25
normalized size 1 1.00 0.79 1.27 1.12 0.70 14.33 0.94 0.76
time (sec) N/A 0.052 0.005 0.080 0.854 0.673 6.362 0.179 2.114
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 19 16 14 14 78 14 16
normalized size 1 1.00 1.00 0.84 0.74 0.74 4.11 0.74 0.84
time (sec) N/A 0.045 0.003 0.069 0.574 1.085 3.745 0.198 2.035
Problem 3 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 18 25 21 14 153 22 15
normalized size 1 1.00 0.90 1.25 1.05 0.70 7.65 1.10 0.75
time (sec) N/A 0.045 0.003 0.078 0.862 1.137 2.268 0.173 2.037
Problem 4 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 7 7 7 8 7 7 12 7 7
normalized size 1 1.00 1.00 1.14 1.00 1.00 1.71 1.00 1.00
time (sec) N/A 0.041 0.002 0.062 0.659 0.633 1.237 0.158 0.024
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 5 5 5 8 5 5 2 5 5
normalized size 1 1.00 1.00 1.60 1.00 1.00 0.40 1.00 1.00
time (sec) N/A 0.040 0.001 0.086 0.884 0.626 0.707 0.217 2.050
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 21 9 21 22 19 23 8
normalized size 1 1.00 2.62 1.12 2.62 2.75 2.38 2.88 1.00
time (sec) N/A 0.025 0.006 0.052 0.312 0.629 0.224 0.156 2.112
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 51 44 37 48 0 38 26
normalized size 1 1.00 2.32 2.00 1.68 2.18 0.00 1.73 1.18
time (sec) N/A 0.044 0.008 0.103 0.484 1.452 0.000 0.147 0.077
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 19 19 21 18 17 29 0 17 13
normalized size 1 1.00 1.11 0.95 0.89 1.53 0.00 0.89 0.68
time (sec) N/A 0.048 0.004 0.109 0.321 0.465 0.000 0.317 2.029
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 75 66 51 72 0 47 39
normalized size 1 1.00 2.14 1.89 1.46 2.06 0.00 1.34 1.11
time (sec) N/A 0.055 0.007 0.120 0.703 0.583 0.000 0.825 0.082
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 143 138 87 225 0 99 100
normalized size 1 1.00 1.83 1.77 1.12 2.88 0.00 1.27 1.28
time (sec) N/A 0.090 0.256 0.076 0.881 0.712 0.000 0.152 2.132
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 116 86 53 152 0 59 65
normalized size 1 1.00 2.15 1.59 0.98 2.81 0.00 1.09 1.20
time (sec) N/A 0.073 0.182 0.066 0.826 1.298 0.000 0.166 0.097
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 90 46 30 95 0 30 28
normalized size 1 1.00 2.50 1.28 0.83 2.64 0.00 0.83 0.78
time (sec) N/A 0.053 0.181 0.064 2.343 0.548 0.000 0.177 0.085
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 26 26 26 18 17 73 87 17 18
normalized size 1 1.00 1.00 0.69 0.65 2.81 3.35 0.65 0.69
time (sec) N/A 0.027 0.021 0.043 0.923 0.739 1.067 0.182 2.227
Problem 14 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 42 42 50 56 48 113 0 50 853
normalized size 1 1.00 1.19 1.33 1.14 2.69 0.00 1.19 20.31
time (sec) N/A 0.049 0.048 0.102 1.720 0.745 0.000 0.220 2.666
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 140 111 105 274 0 103 1138
normalized size 1 1.00 2.26 1.79 1.69 4.42 0.00 1.66 18.35
time (sec) N/A 0.086 0.550 0.121 1.183 0.666 0.000 0.175 2.589
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 204 205 200 592 0 178 833
normalized size 1 1.00 2.17 2.18 2.13 6.30 0.00 1.89 8.86
time (sec) N/A 0.138 1.466 0.126 0.726 0.871 0.000 0.194 5.277
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 77 194 112 285 0 119 681
normalized size 1 1.00 0.88 2.20 1.27 3.24 0.00 1.35 7.74
time (sec) N/A 0.181 0.196 0.087 1.026 2.474 0.000 1.614 2.683
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 52 105 62 211 0 80 126
normalized size 1 1.00 0.87 1.75 1.03 3.52 0.00 1.33 2.10
time (sec) N/A 0.105 0.103 0.075 0.772 0.616 0.000 0.190 2.453
Problem 19 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 37 54 33 177 0 50 108
normalized size 1 1.00 0.92 1.35 0.82 4.42 0.00 1.25 2.70
time (sec) N/A 0.059 0.072 0.072 1.735 0.746 0.000 0.193 2.370
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 29 21 20 163 12026 37 24
normalized size 1 1.00 0.97 0.70 0.67 5.43 400.87 1.23 0.80
time (sec) N/A 0.019 0.059 0.056 0.953 0.577 38.278 0.162 2.384
Problem 21 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 41 41 40 39 38 228 0 55 34
normalized size 1 1.00 0.98 0.95 0.93 5.56 0.00 1.34 0.83
time (sec) N/A 0.056 0.093 0.111 0.739 0.670 0.000 0.343 2.302
Problem 22 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 61 61 59 65 70 396 0 90 67
normalized size 1 1.00 0.97 1.07 1.15 6.49 0.00 1.48 1.10
time (sec) N/A 0.080 0.215 0.116 1.092 0.626 0.000 0.869 2.335
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 90 106 127 610 0 156 101
normalized size 1 1.00 1.01 1.19 1.43 6.85 0.00 1.75 1.13
time (sec) N/A 0.102 0.382 0.126 0.847 0.864 0.000 0.599 2.367
Problem 24 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 98 98 79 80 89 71 85 60 75
normalized size 1 1.00 0.81 0.82 0.91 0.72 0.87 0.61 0.77
time (sec) N/A 0.090 0.091 0.053 0.917 0.572 1.649 0.198 0.307
Problem 25 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 4 4 4 7 6 8 14 6 4
normalized size 1 1.00 1.00 1.75 1.50 2.00 3.50 1.50 1.00
time (sec) N/A 0.014 0.003 0.064 0.498 0.441 0.429 0.269 2.244
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 17 14 14 25 34 14 10
normalized size 1 1.00 1.31 1.08 1.08 1.92 2.62 1.08 0.77
time (sec) N/A 0.015 0.004 0.072 0.866 1.004 1.137 0.168 2.249
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 27 20 20 37 54 20 17
normalized size 1 1.00 1.29 0.95 0.95 1.76 2.57 0.95 0.81
time (sec) N/A 0.017 0.004 0.071 0.306 0.582 3.010 0.587 2.237
Problem 28 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 78 78 111 78 91 259 0 96 86
normalized size 1 1.00 1.42 1.00 1.17 3.32 0.00 1.23 1.10
time (sec) N/A 0.084 0.422 0.065 1.081 2.131 0.000 0.180 0.134
Problem 29 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 56 56 86 50 67 191 0 65 51
normalized size 1 1.00 1.54 0.89 1.20 3.41 0.00 1.16 0.91
time (sec) N/A 0.071 0.196 0.058 0.693 0.652 0.000 0.162 2.312
Problem 30 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 38 38 38 33 50 134 0 41 30
normalized size 1 1.00 1.00 0.87 1.32 3.53 0.00 1.08 0.79
time (sec) N/A 0.055 0.033 0.059 0.543 0.629 0.000 0.176 0.101
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 29 21 39 95 0 31 21
normalized size 1 1.00 1.00 0.72 1.34 3.28 0.00 1.07 0.72
time (sec) N/A 0.031 0.012 0.046 0.850 0.562 0.000 0.182 0.091
Problem 32 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 41 41 38 47 64 119 0 57 414
normalized size 1 1.00 0.93 1.15 1.56 2.90 0.00 1.39 10.10
time (sec) N/A 0.052 0.057 0.096 0.924 0.596 0.000 0.187 2.500
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 152 92 92 186 0 85 483
normalized size 1 1.00 2.58 1.56 1.56 3.15 0.00 1.44 8.19
time (sec) N/A 0.098 0.388 0.116 1.261 0.674 0.000 0.191 2.527
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 215 165 145 270 0 127 969
normalized size 1 1.00 2.39 1.83 1.61 3.00 0.00 1.41 10.77
time (sec) N/A 0.166 1.184 0.126 1.994 0.937 0.000 0.194 2.639
Problem 35 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 87 87 76 122 97 273 0 104 1036
normalized size 1 1.00 0.87 1.40 1.11 3.14 0.00 1.20 11.91
time (sec) N/A 0.196 0.227 0.070 1.049 1.015 0.000 0.187 2.694
Problem 36 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 60 60 52 60 54 213 0 72 291
normalized size 1 1.00 0.87 1.00 0.90 3.55 0.00 1.20 4.85
time (sec) N/A 0.098 0.127 0.071 0.910 0.698 0.000 0.219 2.612
Problem 37 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 38 38 36 32 31 183 0 48 425
normalized size 1 1.00 0.95 0.84 0.82 4.82 0.00 1.26 11.18
time (sec) N/A 0.060 0.085 0.061 1.395 0.623 0.000 1.176 2.549
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 29 21 20 163 12026 37 24
normalized size 1 1.00 0.97 0.70 0.67 5.43 400.87 1.23 0.80
time (sec) N/A 0.019 0.052 0.053 1.431 0.501 38.680 0.376 0.002
Problem 39 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 37 37 38 33 32 216 0 36 30
normalized size 1 1.00 1.03 0.89 0.86 5.84 0.00 0.97 0.81
time (sec) N/A 0.061 0.083 0.099 0.888 0.734 0.000 0.242 2.379
Problem 40 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 56 56 55 51 48 276 0 71 51
normalized size 1 1.00 0.98 0.91 0.86 4.93 0.00 1.27 0.91
time (sec) N/A 0.086 0.150 0.109 0.870 0.950 0.000 0.166 2.309
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 80 80 74 348 0 104 84
normalized size 1 1.00 1.01 1.01 0.94 4.41 0.00 1.32 1.06
time (sec) N/A 0.101 0.347 0.108 0.862 1.201 0.000 0.182 2.304
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 70 81 72 326 0 69 52
normalized size 1 1.00 1.08 1.25 1.11 5.02 0.00 1.06 0.80
time (sec) N/A 0.049 0.243 0.069 1.090 0.744 0.000 0.178 2.341
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 106 175 186 616 0 149 123
normalized size 1 1.00 0.99 1.64 1.74 5.76 0.00 1.39 1.15
time (sec) N/A 0.117 0.698 0.070 1.132 0.765 0.000 0.159 2.440
Problem 44 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 34 34 15 14 13 31 63 46 26
normalized size 1 1.00 0.44 0.41 0.38 0.91 1.85 1.35 0.76
time (sec) N/A 0.013 0.025 0.052 0.820 2.582 0.666 0.192 2.325
Problem 45 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 55 55 35 27 26 57 218 59 40
normalized size 1 1.00 0.64 0.49 0.47 1.04 3.96 1.07 0.73
time (sec) N/A 0.026 0.079 0.059 0.960 0.619 3.444 1.295 2.170
Problem 46 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 71 71 51 35 41 81 439 68 53
normalized size 1 1.00 0.72 0.49 0.58 1.14 6.18 0.96 0.75
time (sec) N/A 0.052 0.129 0.060 1.569 1.754 13.610 0.145 2.149
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 13 10 4 0 24 10
normalized size 1 1.00 1.00 1.08 0.83 0.33 0.00 2.00 0.83
time (sec) N/A 0.016 0.007 0.863 0.886 0.689 0.000 1.710 0.035
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 14 12 1 0 28 39
normalized size 1 1.00 1.00 1.00 0.86 0.07 0.00 2.00 2.79
time (sec) N/A 0.016 0.006 0.535 0.877 1.466 0.000 1.247 2.295
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 23 19 11 11 0 45 -1
normalized size 1 1.00 0.79 0.66 0.38 0.38 0.00 1.55 -0.03
time (sec) N/A 0.022 0.027 1.432 0.977 0.680 0.000 0.228 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 25 21 0 1 0 55 -1
normalized size 1 1.00 0.76 0.64 0.00 0.03 0.00 1.67 -0.03
time (sec) N/A 0.025 0.028 0.990 0.000 0.447 0.000 0.647 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 28 14 35 19 0 0 -1
normalized size 1 1.00 1.87 0.93 2.33 1.27 0.00 0.00 -0.07
time (sec) N/A 0.020 0.017 0.709 1.129 1.349 0.000 0.000 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 30 34 17 0 0 0 -1
normalized size 1 1.00 1.76 2.00 1.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.018 0.010 0.412 0.900 0.000 0.000 0.000 0.000
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 51 37 300 44 0 78 -1
normalized size 1 1.00 1.59 1.16 9.38 1.38 0.00 2.44 -0.03
time (sec) N/A 0.027 0.050 1.565 1.835 0.603 0.000 0.256 0.000
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B F(-2) F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 53 51 284 0 0 90 -1
normalized size 1 1.00 1.47 1.42 7.89 0.00 0.00 2.50 -0.03
time (sec) N/A 0.026 0.033 1.176 1.053 0.000 0.000 0.686 0.000
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 11 41 0 0 0 0 7
normalized size 1 1.00 1.22 4.56 0.00 0.00 0.00 0.00 0.78
time (sec) N/A 0.008 0.023 1.556 0.000 0.626 0.000 0.000 0.009
Problem 56 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 32 32 34 75 0 0 0 0 -1
normalized size 1 1.00 1.06 2.34 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.022 0.039 2.405 0.000 0.829 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 F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 46 49 0 0 0 0 -1
normalized size 1 1.00 1.10 1.17 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.035 0.078 0.974 0.000 0.593 0.000 0.000 0.000
Problem 58 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 43 43 39 101 0 0 0 0 -1
normalized size 1 1.00 0.91 2.35 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.054 0.052 2.339 0.000 0.574 0.000 0.000 0.000
Problem 59 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 89 89 66 110 0 0 0 0 -1
normalized size 1 1.00 0.74 1.24 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.094 0.073 2.622 0.000 0.630 0.000 0.000 0.000
Problem 60 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 121 121 123 192 0 0 0 0 -1
normalized size 1 1.00 1.02 1.59 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.162 0.481 1.793 0.000 0.512 0.000 0.000 0.000
Problem 61 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 9 9 11 41 0 0 0 0 -1
normalized size 1 1.00 1.22 4.56 0.00 0.00 0.00 0.00 -0.11
time (sec) N/A 0.008 0.035 1.813 0.000 0.470 0.000 0.000 0.000
Problem 62 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 32 32 33 62 0 0 0 0 -1
normalized size 1 1.00 1.03 1.94 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.018 0.040 2.138 0.000 0.509 0.000 0.000 0.000
Problem 63 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 42 42 46 48 0 0 0 0 -1
normalized size 1 1.00 1.10 1.14 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.029 0.071 0.695 0.000 0.531 0.000 0.000 0.000
Problem 64 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 32 32 35 70 0 0 0 0 -1
normalized size 1 1.00 1.09 2.19 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.018 0.063 2.338 0.000 0.681 0.000 0.000 0.000
Problem 65 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 56 56 43 101 0 0 0 0 -1
normalized size 1 1.00 0.77 1.80 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.033 0.044 2.820 0.000 0.580 0.000 0.000 0.000
Problem 66 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 78 78 75 73 0 0 0 0 -1
normalized size 1 1.00 0.96 0.94 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.047 0.185 1.851 0.000 0.569 0.000 0.000 0.000
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 33 8 49 0 8 -1
normalized size 1 1.00 1.00 3.67 0.89 5.44 0.00 0.89 -0.11
time (sec) N/A 0.021 0.008 0.875 1.608 0.628 0.000 0.234 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 57 11 89 0 11 -1
normalized size 1 1.00 1.00 3.80 0.73 5.93 0.00 0.73 -0.07
time (sec) N/A 0.027 0.026 1.043 0.699 1.390 0.000 0.424 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 53 8 39 0 16 -1
normalized size 1 1.00 1.00 5.89 0.89 4.33 0.00 1.78 -0.11
time (sec) N/A 0.026 0.010 2.153 1.741 1.211 0.000 1.422 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 487 487 121 3350 0 809 0 307 926
normalized size 1 1.00 0.25 6.88 0.00 1.66 0.00 0.63 1.90
time (sec) N/A 1.101 0.242 0.227 0.000 0.861 0.000 1.025 2.655
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 109 64 0 817 0 299 938
normalized size 1 1.00 1.08 0.63 0.00 8.09 0.00 2.96 9.29
time (sec) N/A 0.116 0.198 0.089 0.000 0.713 0.000 1.127 2.596
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 292 292 45 227 0 3830 0 170 214
normalized size 1 1.00 0.15 0.78 0.00 13.12 0.00 0.58 0.73
time (sec) N/A 0.191 0.077 0.216 0.000 42.423 0.000 0.665 2.730
Problem 73 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 45 45 24 21 20 43 78 53 20
normalized size 1 1.00 0.53 0.47 0.44 0.96 1.73 1.18 0.44
time (sec) N/A 0.018 0.058 0.081 1.639 0.681 1.985 0.559 2.164
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-2) F F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 494 494 130 150 0 0 0 0 1520
normalized size 1 1.00 0.26 0.30 0.00 0.00 0.00 0.00 3.08
time (sec) N/A 0.918 0.249 0.099 0.000 0.000 0.000 0.000 8.818
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 171 171 146 60 0 0 0 0 184
normalized size 1 1.00 0.85 0.35 0.00 0.00 0.00 0.00 1.08
time (sec) N/A 0.238 0.228 0.464 0.000 0.000 0.000 0.000 3.081
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 245 245 172 76 0 0 0 0 216
normalized size 1 1.00 0.70 0.31 0.00 0.00 0.00 0.00 0.88
time (sec) N/A 0.486 0.274 0.218 0.000 0.000 0.000 0.000 3.421
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-2) F F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 494 494 130 148 0 0 0 0 1518
normalized size 1 1.00 0.26 0.30 0.00 0.00 0.00 0.00 3.07
time (sec) N/A 0.589 0.185 0.095 0.000 0.000 0.000 0.000 7.832
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 175 175 146 62 0 0 0 0 184
normalized size 1 1.00 0.83 0.35 0.00 0.00 0.00 0.00 1.05
time (sec) N/A 0.249 0.180 0.429 0.000 0.000 0.000 0.000 3.120
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 213 213 172 78 0 0 0 0 216
normalized size 1 1.00 0.81 0.37 0.00 0.00 0.00 0.00 1.01
time (sec) N/A 0.216 0.224 0.221 0.000 0.000 0.000 0.000 3.416
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 223 223 378 62 0 0 0 0 535
normalized size 1 1.00 1.70 0.28 0.00 0.00 0.00 0.00 2.40
time (sec) N/A 0.562 0.127 0.071 0.000 0.000 0.000 0.000 2.778
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 103 79 73 72 138 0 185 99
normalized size 1 1.24 0.95 0.88 0.87 1.66 0.00 2.23 1.19
time (sec) N/A 0.104 0.175 0.069 0.775 3.086 0.000 0.379 2.389
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 129 129 141 67 0 0 0 0 1025
normalized size 1 1.00 1.09 0.52 0.00 0.00 0.00 0.00 7.95
time (sec) N/A 0.180 0.152 0.071 0.000 0.000 0.000 0.000 3.108
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 205 205 378 62 0 0 0 0 403
normalized size 1 1.00 1.84 0.30 0.00 0.00 0.00 0.00 1.97
time (sec) N/A 0.473 0.122 0.076 0.000 0.000 0.000 0.000 2.447
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 117 233 0 0 728 199 95
normalized size 1 1.00 1.65 3.28 0.00 0.00 10.25 2.80 1.34
time (sec) N/A 0.119 0.294 0.237 0.000 0.000 23.606 0.543 2.293
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 64 246 0 3963 0 222 241
normalized size 1 1.00 0.72 2.76 0.00 44.53 0.00 2.49 2.71
time (sec) N/A 0.077 0.162 0.112 0.000 63.662 0.000 0.881 2.267
Problem 86 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 17 17 17 16 19 19 0 16 9
normalized size 1 1.00 1.00 0.94 1.12 1.12 0.00 0.94 0.53
time (sec) N/A 0.029 0.009 0.101 0.303 0.528 0.000 0.454 2.163
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 40 43 95 90 0 38 -1
normalized size 1 1.00 1.00 1.08 2.38 2.25 0.00 0.95 -0.02
time (sec) N/A 0.063 0.029 0.085 1.139 2.084 0.000 0.401 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 47 17 47 21 0 45 -1
normalized size 1 1.00 2.35 0.85 2.35 1.05 0.00 2.25 -0.05
time (sec) N/A 0.051 0.037 0.987 0.959 0.497 0.000 0.370 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 30 81 67 0 24 -1
normalized size 1 1.00 1.00 1.20 3.24 2.68 0.00 0.96 -0.04
time (sec) N/A 0.060 0.016 0.095 0.893 0.801 0.000 0.311 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 10 60 16 0 27 -1
normalized size 1 1.00 1.00 0.91 5.45 1.45 0.00 2.45 -0.09
time (sec) N/A 0.035 0.009 0.087 0.884 0.675 0.000 0.366 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 44 8 39 17 0 33 -1
normalized size 1 1.00 4.89 0.89 4.33 1.89 0.00 3.67 -0.11
time (sec) N/A 0.053 0.024 0.440 0.582 0.641 0.000 0.335 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A C F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 153 153 217 125 151 1690 0 143 1281
normalized size 1 1.00 1.42 0.82 0.99 11.05 0.00 0.93 8.37
time (sec) N/A 0.197 0.301 0.109 1.593 46.276 0.000 2.134 5.211
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 45 34 52 123 0 38 -1
normalized size 1 1.00 1.00 0.76 1.16 2.73 0.00 0.84 -0.02
time (sec) N/A 0.073 0.027 0.697 0.769 5.093 0.000 0.511 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 28 21 39 0 0 24 -1
normalized size 1 1.00 1.00 0.75 1.39 0.00 0.00 0.86 -0.04
time (sec) N/A 0.067 0.017 0.125 1.760 0.000 0.000 0.409 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 45 44 43 90 0 38 -1
normalized size 1 1.00 1.00 0.98 0.96 2.00 0.00 0.84 -0.02
time (sec) N/A 0.077 0.034 0.121 2.064 0.910 0.000 0.467 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 28 31 0 67 0 24 -1
normalized size 1 1.00 1.00 1.11 0.00 2.39 0.00 0.86 -0.04
time (sec) N/A 0.071 0.018 0.122 0.000 0.910 0.000 0.423 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 46 39 58 97 0 46 -1
normalized size 1 1.00 0.98 0.83 1.23 2.06 0.00 0.98 -0.02
time (sec) N/A 0.079 0.032 0.050 0.806 0.528 0.000 0.563 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 29 24 42 74 0 27 -1
normalized size 1 1.00 1.00 0.83 1.45 2.55 0.00 0.93 -0.03
time (sec) N/A 0.077 0.017 0.061 1.039 0.535 0.000 0.560 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 [72] had the largest ratio of [.7500]

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 4 3 1.00 16 0.188
2 A 3 2 1.00 16 0.125
3 A 3 3 1.00 16 0.188
4 A 2 2 1.00 16 0.125
5 A 2 2 1.00 16 0.125
6 A 2 2 1.00 14 0.143
7 A 3 3 1.00 14 0.214
8 A 3 2 1.00 16 0.125
9 A 4 3 1.00 16 0.188
10 A 4 3 1.00 15 0.200
11 A 4 3 1.00 15 0.200
12 A 3 3 1.00 15 0.200
13 A 2 2 1.00 13 0.154
14 A 4 4 1.00 13 0.308
15 A 5 5 1.00 15 0.333
16 A 6 6 1.00 15 0.400
17 A 6 6 1.00 15 0.400
18 A 5 5 1.00 15 0.333
19 A 4 4 1.00 15 0.267
20 A 2 2 1.00 10 0.200
21 A 3 3 1.00 15 0.200
22 A 4 3 1.00 15 0.200
23 A 4 3 1.00 15 0.200
24 A 7 7 1.00 13 0.538
25 A 3 3 1.00 10 0.300
26 A 3 2 1.00 10 0.200
27 A 3 2 1.00 10 0.200
28 A 4 3 1.00 15 0.200
29 A 4 3 1.00 15 0.200
30 A 3 3 1.00 15 0.200
31 A 2 2 1.00 13 0.154
32 A 4 4 1.00 13 0.308
33 A 5 5 1.00 15 0.333
34 A 6 6 1.00 15 0.400
35 A 6 6 1.00 15 0.400
36 A 5 5 1.00 15 0.333
37 A 3 3 1.00 15 0.200
38 A 2 2 1.00 10 0.200
39 A 3 3 1.00 15 0.200
40 A 4 3 1.00 15 0.200
41 A 4 3 1.00 15 0.200
42 A 4 4 1.00 10 0.400
43 A 5 5 1.00 10 0.500
44 A 2 2 1.00 8 0.250
45 A 4 4 1.00 8 0.500
46 A 5 5 1.00 8 0.625
47 A 3 3 1.00 12 0.250
48 A 3 3 1.00 10 0.300
49 A 4 4 1.00 12 0.333
50 A 4 4 1.00 10 0.400
51 A 3 3 1.00 12 0.250
52 A 3 3 1.00 10 0.300
53 A 4 4 1.00 12 0.333
54 A 4 4 1.00 10 0.400
55 A 1 1 1.00 10 0.100
56 A 2 2 1.00 12 0.167
57 A 2 2 1.00 12 0.167
58 A 4 4 1.00 10 0.400
59 A 6 6 1.00 12 0.500
60 A 6 6 1.00 12 0.500
61 A 1 1 1.00 10 0.100
62 A 2 2 1.00 12 0.167
63 A 2 2 1.00 12 0.167
64 A 3 3 1.00 10 0.300
65 A 4 4 1.00 12 0.333
66 A 4 4 1.00 12 0.333
67 A 2 2 1.00 13 0.154
68 A 2 2 1.00 21 0.095
69 A 2 2 1.00 15 0.133
70 A 10 6 1.00 10 0.600
71 A 4 3 1.00 11 0.273
72 A 10 6 1.00 8 0.750
73 A 3 3 1.00 10 0.300
74 A 12 3 1.00 10 0.300
75 A 7 3 1.00 10 0.300
76 A 9 3 1.00 10 0.300
77 A 12 3 1.00 11 0.273
78 A 7 3 1.00 11 0.273
79 A 9 3 1.00 11 0.273
80 A 11 5 1.00 8 0.625
81 A 7 3 1.24 8 0.375
82 A 9 3 1.00 8 0.375
83 A 11 5 1.00 10 0.500
84 A 8 6 1.00 10 0.600
85 A 10 6 1.00 10 0.600
86 A 4 4 1.00 11 0.364
87 A 4 4 1.00 15 0.267
88 A 5 5 1.00 15 0.333
89 A 3 3 1.00 15 0.200
90 A 3 3 1.00 13 0.231
91 A 4 4 1.00 15 0.267
92 A 11 10 1.00 15 0.667
93 A 5 5 1.00 15 0.333
94 A 4 4 1.00 15 0.267
95 A 5 5 1.00 15 0.333
96 A 4 4 1.00 15 0.267
97 A 5 5 1.00 15 0.333
98 A 4 4 1.00 15 0.267

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