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2 detailed summary tables of results

 2.1 Detailed conclusion table per each integral for all CAS systems
 2.2 Detailed conclusion table specific for Rubi results

2.1 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 Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 13 16 1 10 16 0
normalized size 1 1. 1. 0.81 1. 0.06 0.62 1. 0.
time (sec) N/A 0.008 0. 0.01 1.398 0.2 0.025 0.211 0.
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 17 22 1 17 22 17
normalized size 1 1. 1. 0.77 1. 0.05 0.77 1. 0.77
time (sec) N/A 0.023 0.006 0.001 1.368 0.169 0.033 0.214 2.091
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 17 22 1 15 22 0
normalized size 1 1. 1. 0.77 1. 0.05 0.68 1. 0.
time (sec) N/A 0.011 0.024 0.001 1.409 0.187 0.038 0.212 0.
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 2 2 2 3 3 3 2 4 2
normalized size 1 1. 1. 1.5 1.5 1.5 1. 2. 1.
time (sec) N/A 0.002 0. 0.004 1.387 0.199 0.023 0.211 0.024
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 24 27 43 62 29 31 24
normalized size 1 1. 0.67 0.75 1.19 1.72 0.81 0.86 0.67
time (sec) N/A 0.027 0.04 0.026 1.412 0.208 0.122 0.211 2.229
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 28 25 32 45 24 46 24
normalized size 1 1. 0.88 0.78 1. 1.41 0.75 1.44 0.75
time (sec) N/A 0.033 0.025 0.008 1.376 0.21 0.154 0.214 2.063
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 34 66 54 46 144 57 26
normalized size 1 1. 0.85 1.65 1.35 1.15 3.6 1.42 0.65
time (sec) N/A 0.064 0.023 0.005 1.374 0.202 1.033 0.21 4.942
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 38 35 0 1 124 46 34
normalized size 1 1. 1.12 1.03 0. 0.03 3.65 1.35 1.
time (sec) N/A 0.038 0.053 0.005 0. 0.198 0.258 0.213 2.058
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 15 19 19 26 19 14
normalized size 1 1. 1. 0.94 1.19 1.19 1.62 1.19 0.88
time (sec) N/A 0.016 0.034 0.002 1.513 0.198 0.201 0.211 1.672
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 16 17 19 19 22 19 19
normalized size 1 1. 0.84 0.89 1. 1. 1.16 1. 1.
time (sec) N/A 0.025 0.056 0.002 1.518 0.194 0.093 0.21 0.67
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 35 36 53 96 39 108 34
normalized size 1 1. 0.71 0.73 1.08 1.96 0.8 2.2 0.69
time (sec) N/A 0.07 0.031 0.012 1.513 0.198 0.199 0.212 4.58
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 62 69 105 109 4216 109 39
normalized size 1 1. 0.91 1.01 1.54 1.6 62. 1.6 0.57
time (sec) N/A 0.117 0.043 0.007 1.372 0.281 145.64 0.21 9.139
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 34 44 58 43 121 88 36
normalized size 1 1. 0.72 0.94 1.23 0.91 2.57 1.87 0.77
time (sec) N/A 0.051 0.013 0.005 1.39 0.207 0.842 0.225 4.791
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 30 41 54 41 393 54 26
normalized size 1 1. 0.75 1.02 1.35 1.02 9.82 1.35 0.65
time (sec) N/A 0.055 0.02 0.009 1.49 0.217 1.522 0.212 6.194
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 20 26 26 19 27 19
normalized size 1 1. 1. 0.74 0.96 0.96 0.7 1. 0.7
time (sec) N/A 0.045 0.006 0.003 1.501 0.221 0.13 0.222 2.531
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 40 35 46 55 41 47 37
normalized size 1 1. 0.98 0.85 1.12 1.34 1. 1.15 0.9
time (sec) N/A 0.048 0.015 0.006 1.532 0.213 0.172 0.216 3.22
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 34 32 42 54 31 49 31
normalized size 1 1. 0.79 0.74 0.98 1.26 0.72 1.14 0.72
time (sec) N/A 0.2 0.027 0.006 1.562 0.223 0.162 0.216 11.235
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 64 58 97 131 73 97 73
normalized size 1 1. 0.75 0.68 1.14 1.54 0.86 1.14 0.86
time (sec) N/A 0.077 0.057 0.004 1.552 0.223 0.193 0.21 5.899
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 64 58 97 131 73 97 73
normalized size 1 1. 0.75 0.68 1.14 1.54 0.86 1.14 0.86
time (sec) N/A 0.079 0.014 0.002 1.555 0.22 0.192 0.212 6.412
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A A A A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 67 67 73 54 72 77 70 72 63
normalized size 1 1. 1.09 0.81 1.07 1.15 1.04 1.07 0.94
time (sec) N/A 0.072 0.154 0.004 1.544 0.21 0.237 0.209 4.831
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 17 19 0 27 20 24 12
normalized size 1 1. 0.94 1.06 0. 1.5 1.11 1.33 0.67
time (sec) N/A 0.011 0.012 0.004 0. 0.227 0.035 0.209 0.861
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 33 36 57 72 201 113 31
normalized size 1 1. 0.85 0.92 1.46 1.85 5.15 2.9 0.79
time (sec) N/A 0.031 0.018 0.002 1.383 0.223 0.836 0.206 3.559
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 57 73 92 130 597 208 51
normalized size 1 1. 0.95 1.22 1.53 2.17 9.95 3.47 0.85
time (sec) N/A 0.049 0.03 0.006 1.406 0.23 1.574 0.208 6.073
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 11 14 14 7 15 7
normalized size 1 1. 1. 1.1 1.4 1.4 0.7 1.5 0.7
time (sec) N/A 0.006 0.001 0.001 1.376 0.197 0.037 0.203 0.654
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 13 16 18 10 16 8
normalized size 1 1. 1. 1.08 1.33 1.5 0.83 1.33 0.67
time (sec) N/A 0.005 0.004 0. 1.396 0.214 0.518 0.202 0.638
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 19 24 23 14 26 0
normalized size 1 1. 1. 1.06 1.33 1.28 0.78 1.44 0.
time (sec) N/A 0.022 0.003 0.003 1.422 0.202 0.477 0.203 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 31 30 39 39 26 41 0
normalized size 1 1. 1. 0.97 1.26 1.26 0.84 1.32 0.
time (sec) N/A 0.034 0.005 0.002 1.43 0.192 0.502 0.2 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 19 24 22 10 27 12
normalized size 1 1. 1. 1.06 1.33 1.22 0.56 1.5 0.67
time (sec) N/A 0.012 0.005 0.003 1.377 0.213 0.165 0.199 1.706
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 28 29 38 35 19 41 24
normalized size 1 1. 1. 1.04 1.36 1.25 0.68 1.46 0.86
time (sec) N/A 0.03 0.006 0.008 1.412 0.214 0.598 0.199 2.834
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 35 43 61 85 36 70 39
normalized size 1 1. 0.83 1.02 1.45 2.02 0.86 1.67 0.93
time (sec) N/A 0.048 0.054 0.008 1.376 0.21 0.746 0.202 4.268
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 11 14 14 20 14 5
normalized size 1 1. 1. 1.1 1.4 1.4 2. 1.4 0.5
time (sec) N/A 0.007 0.003 0.003 1.52 0.231 0.103 0.2 0.726
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 22 28 24 15 31 5
normalized size 1 1. 1. 2.2 2.8 2.4 1.5 3.1 0.5
time (sec) N/A 0.008 0.004 0.003 1.408 0.225 0.115 0.198 0.898
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 66 58 89 77 78 0 73
normalized size 1 1. 0.85 0.74 1.14 0.99 1. 0. 0.94
time (sec) N/A 0.095 0.075 0.004 1.575 0.214 0.652 0. 4.751
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 65 54 76 81 71 0 68
normalized size 1 1. 0.88 0.73 1.03 1.09 0.96 0. 0.92
time (sec) N/A 0.075 0.025 0.003 1.562 0.239 0.603 0. 3.973
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 89 92 0 120 20 140 109
normalized size 1 1. 0.77 0.8 0. 1.04 0.17 1.22 0.95
time (sec) N/A 0.129 0.038 0.002 0. 0.212 0.168 0.211 9.59
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 43 35 50 80 46 53 34
normalized size 1 1. 1.23 1. 1.43 2.29 1.31 1.51 0.97
time (sec) N/A 0.027 0.025 0.002 1.517 0.22 0.623 0.213 0.933
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 43 36 55 77 48 53 31
normalized size 1 1. 1.23 1.03 1.57 2.2 1.37 1.51 0.89
time (sec) N/A 0.031 0.022 0.002 1.573 0.228 0.625 0.213 0.959
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 169 171 120 111 204 219 151 128 168
normalized size 1 1.01 0.71 0.66 1.21 1.3 0.89 0.76 0.99
time (sec) N/A 0.21 0.075 0.004 1.548 0.223 0.769 0.21 11.799
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 68 56 0 238 24 100 71
normalized size 1 1. 0.93 0.77 0. 3.26 0.33 1.37 0.97
time (sec) N/A 0.129 0.08 0.031 0. 0.226 0.629 0.23 1.77
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 68 56 0 240 24 100 71
normalized size 1 1. 0.93 0.77 0. 3.29 0.33 1.37 0.97
time (sec) N/A 0.052 0.04 0.019 0. 0.226 0.63 0.255 1.704
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 83 54 101 128 158 109 70
normalized size 1 1. 1.15 0.75 1.4 1.78 2.19 1.51 0.97
time (sec) N/A 0.127 0.056 0.004 1.501 0.245 0.781 0.225 2.011
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 67 60 0 225 24 136 60
normalized size 1 1. 1. 0.9 0. 3.36 0.36 2.03 0.9
time (sec) N/A 0.102 0.049 0.022 0. 0.212 0.788 0.25 1.478
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 67 60 0 182 92 69 60
normalized size 1 1. 1. 0.9 0. 2.72 1.37 1.03 0.9
time (sec) N/A 0.03 0.027 0.019 0. 0.223 0.291 0.204 1.106
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 196 196 91 386 0 501 24 0 178
normalized size 1 1. 0.46 1.97 0. 2.56 0.12 0. 0.91
time (sec) N/A 0.305 0.091 0.065 0. 0.215 0.818 0. 8.221
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 196 196 91 386 0 501 24 0 178
normalized size 1 1. 0.46 1.97 0. 2.56 0.12 0. 0.91
time (sec) N/A 0.286 0.12 0.039 0. 0.212 0.844 0. 8.097
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 75 66 88 101 83 90 68
normalized size 1 1. 1.03 0.9 1.21 1.38 1.14 1.23 0.93
time (sec) N/A 0.187 0.021 0.005 1.539 0.216 0.349 0.199 16.738
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 138 138 122 111 151 207 14 0 131
normalized size 1 1. 0.88 0.8 1.09 1.5 0.1 0. 0.95
time (sec) N/A 0.405 0.054 0.056 1.575 0.225 0.989 0. 23.235
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 138 138 115 95 144 244 14 0 138
normalized size 1 1. 0.83 0.69 1.04 1.77 0.1 0. 1.
time (sec) N/A 0.564 0.037 0.083 1.501 0.218 0.388 0. 38.371
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 339 339 209 22 0 1345 14 323 529
normalized size 1 1. 0.62 0.06 0. 3.97 0.04 0.95 1.56
time (sec) N/A 0.681 0.008 0.01 0. 0.233 1.937 0.204 25.612
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 98 66 119 151 0 122 83
normalized size 1 1. 1.01 0.68 1.23 1.56 0. 1.26 0.86
time (sec) N/A 0.096 0.036 0.001 1.569 0.219 0. 0.199 6.336
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 275 275 42 30 0 257 165 277 529
normalized size 1 1. 0.15 0.11 0. 0.93 0.6 1.01 1.92
time (sec) N/A 0.59 0.017 0.009 0. 0.23 0.289 0.208 26.032
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 260 41 54 63 46 54 42
normalized size 1 1. 5.31 0.84 1.1 1.29 0.94 1.1 0.86
time (sec) N/A 0.075 0.164 0.003 1.574 0.221 0.24 0.206 4.007
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 9 11 11 5 11 5
normalized size 1 1. 1. 1.12 1.38 1.38 0.62 1.38 0.62
time (sec) N/A 0.004 0.013 0.001 1.375 0.22 0.061 0.2 0.461
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 14 18 18 12 18 0
normalized size 1 1. 1. 0.82 1.06 1.06 0.71 1.06 0.
time (sec) N/A 0.007 0.001 0.006 1.367 0.219 0.068 0.198 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 14 18 18 12 18 12
normalized size 1 1. 1. 0.82 1.06 1.06 0.71 1.06 0.71
time (sec) N/A 0.011 0.002 0.001 1.366 0.234 0.07 0.2 1.05
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 19 34 0 34 0 0 20
normalized size 1 1. 0.73 1.31 0. 1.31 0. 0. 0.77
time (sec) N/A 0.019 0.012 0.01 0. 0.22 0. 0. 1.622
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 16 16 20 15 20 15
normalized size 1 1. 1. 1.07 1.07 1.33 1. 1.33 1.
time (sec) N/A 0.008 0.002 0.001 1.404 0.22 0.08 0.199 0.543
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 127 104 96 139 133 139 0
normalized size 1 1. 1. 0.82 0.76 1.09 1.05 1.09 0.
time (sec) N/A 0.205 0.003 0.001 1.411 0.224 0.315 0.208 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 7 8 8 5 8 5
normalized size 1 1. 1. 0.88 1. 1. 0.62 1. 0.62
time (sec) N/A 0.018 0.001 0.001 1.4 0.223 0.068 0.203 1.427
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 2 2 2 9 4 0 0 4 2
normalized size 1 1. 1. 4.5 2. 0. 0. 2. 1.
time (sec) N/A 0.004 0.088 0.004 1.445 0. 0. 0.214 0.024
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 4 4 4 11 7 0 0 7 3
normalized size 1 1. 1. 2.75 1.75 0. 0. 1.75 0.75
time (sec) N/A 0.006 0.003 0.001 1.514 0. 0. 0.215 0.477
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 3 3 3 4 4 4 3 5 3
normalized size 1 1. 1. 1.33 1.33 1.33 1. 1.67 1.
time (sec) N/A 0.018 0.001 0. 1.45 0.22 0.076 0.215 1.004
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 15 8 0 0 0 14
normalized size 1 1. 1. 0.88 0.47 0. 0. 0. 0.82
time (sec) N/A 0.049 0.01 0.006 1.483 0. 0. 0. 2.33
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 13 0 16 15 16 8
normalized size 1 1. 1. 1.08 0. 1.33 1.25 1.33 0.67
time (sec) N/A 0.025 0.004 0.001 0. 0.219 1.174 0.199 1.635
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 28 25 34 34 22 32 0
normalized size 1 1. 0.97 0.86 1.17 1.17 0.76 1.1 0.
time (sec) N/A 0.021 0.002 0.001 1.401 0.238 0.103 0.204 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 46 48 63 63 44 63 0
normalized size 1 1. 0.85 0.89 1.17 1.17 0.81 1.17 0.
time (sec) N/A 0.052 0.014 0.001 1.427 0.204 0.132 0.199 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 27 30 51 46 24 49 26
normalized size 1 1. 0.93 1.03 1.76 1.59 0.83 1.69 0.9
time (sec) N/A 0.025 0.019 0.008 1.415 0.217 0.654 0.199 3.358
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 46 47 59 53 42 78 0
normalized size 1 1. 1. 1.02 1.28 1.15 0.91 1.7 0.
time (sec) N/A 0.047 0.005 0.002 1.38 0.219 0.619 0.201 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 59 58 77 66 54 127 0
normalized size 1 1. 1. 0.98 1.31 1.12 0.92 2.15 0.
time (sec) N/A 0.063 0.005 0.002 1.379 0.22 0.598 0.201 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 23 24 31 31 36 31 20
normalized size 1 1. 1. 1.04 1.35 1.35 1.57 1.35 0.87
time (sec) N/A 0.02 0.004 0.003 1.55 0.222 0.552 0.2 2.325
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 38 29 38 31 31 38 31
normalized size 1 1. 1.41 1.07 1.41 1.15 1.15 1.41 1.15
time (sec) N/A 0.071 0.003 0.001 1.385 0.216 0.554 0.199 1.227
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 44 37 49 49 53 49 0
normalized size 1 1. 1. 0.84 1.11 1.11 1.2 1.11 0.
time (sec) N/A 0.047 0.004 0.003 1.571 0.228 0.583 0.202 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 45 59 59 63 59 0
normalized size 1 1. 1. 0.83 1.09 1.09 1.17 1.09 0.
time (sec) N/A 0.053 0.005 0.002 1.533 0.218 0.595 0.204 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 32 42 42 29 45 20
normalized size 1 1. 1. 1.28 1.68 1.68 1.16 1.8 0.8
time (sec) N/A 0.024 0.005 0.005 1.404 0.223 0.554 0.2 2.811
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 8 0 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.01 0.251 0.018 0. 0. 0. 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 4 4 4 5 5 5 3 5 3
normalized size 1 1. 1. 1.25 1.25 1.25 0.75 1.25 0.75
time (sec) N/A 0.005 0.004 0.001 1.401 0.227 0.03 0.198 0.027
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 2 2 2 3 3 3 2 3 2
normalized size 1 1. 1. 1.5 1.5 1.5 1. 1.5 1.
time (sec) N/A 0.004 0.004 0. 1.386 0.224 0.031 0.199 0.023
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 5 5 5 6 4 15 5 8 5
normalized size 1 1. 1. 1.2 0.8 3. 1. 1.6 1.
time (sec) N/A 0.004 0.007 0.001 1.382 0.232 0.039 0.2 0.034
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 3 3 3 4 4 22 3 23 3
normalized size 1 1. 1. 1.33 1.33 7.33 1. 7.67 1.
time (sec) N/A 0.005 0.007 0. 1.388 0.219 0.048 0.203 0.031
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 27 26 34 50 75 35 17
normalized size 1 1. 1.29 1.24 1.62 2.38 3.57 1.67 0.81
time (sec) N/A 0.041 0.043 0.019 1.546 0.228 0.653 0.203 1.998
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 3 3 33 7 20 23 15 23 3
normalized size 1 1. 11. 2.33 6.67 7.67 5. 7.67 1.
time (sec) N/A 0.006 0.007 0.006 1.409 0.214 0.09 0.201 0.027
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 5 5 17 9 20 26 15 23 5
normalized size 1 1. 3.4 1.8 4. 5.2 3. 4.6 1.
time (sec) N/A 0.005 0.007 0.003 1.405 0.228 0.092 0.201 0.03
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 11 14 14 10 14 10
normalized size 1 1. 1. 0.79 1. 1. 0.71 1. 0.71
time (sec) N/A 0.011 0.003 0.006 1.397 0.228 0.035 0.199 0.495
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 17 22 22 15 22 15
normalized size 1 1. 1. 0.85 1.1 1.1 0.75 1.1 0.75
time (sec) N/A 0.028 0.005 0.005 1.391 0.24 0.768 0.21 1.366
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 15 11 15 15 8 15 8
normalized size 1 1. 1.15 0.85 1.15 1.15 0.62 1.15 0.62
time (sec) N/A 0.011 0.003 0.036 1.398 0.232 0.04 0.209 0.643
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 44 0 0 0 0 0 39
normalized size 1 1. 1. 0. 0. 0. 0. 0. 0.89
time (sec) N/A 0.018 0.236 0.299 0. 0. 0. 0. 0.724
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 16 20 24 17 20 17
normalized size 1 1. 1. 0.84 1.05 1.26 0.89 1.05 0.89
time (sec) N/A 0.034 0.006 0.009 1.388 0.229 1.59 0.206 2.29
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 11 14 14 10 14 10
normalized size 1 1. 1. 0.79 1. 1. 0.71 1. 0.71
time (sec) N/A 0.011 0.003 0.005 1.363 0.264 0.034 0.211 0.502
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 15 11 12 14 8 12 8
normalized size 1 1. 1.36 1. 1.09 1.27 0.73 1.09 0.73
time (sec) N/A 0.011 0.003 0.019 1.398 0.248 0.039 0.217 0.648
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 2 2 2 3 3 9 5 3 5
normalized size 1 1. 1. 1.5 1.5 4.5 2.5 1.5 2.5
time (sec) N/A 0.01 0.003 0.02 1.423 0.232 0.033 0.231 0.481
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 7 15 14 20 15 10
normalized size 1 1. 1. 0.47 1. 0.93 1.33 1. 0.67
time (sec) N/A 0.013 0.008 0.008 1.388 0.237 0.76 0.221 0.966
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 9 11 11 7 11 7
normalized size 1 1. 1. 1.12 1.38 1.38 0.88 1.38 0.88
time (sec) N/A 0.014 0.003 0. 1.369 0.22 0.175 0.21 0.785
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 15 18 20 20 17 20 17
normalized size 1 1. 0.88 1.06 1.18 1.18 1. 1.18 1.
time (sec) N/A 0.033 0.01 0.003 1.372 0.221 0.384 0.203 1.446
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 25 26 26 36 26 0
normalized size 1 1. 1. 1. 1.04 1.04 1.44 1.04 0.
time (sec) N/A 0.023 0.005 0.003 1.399 0.216 0.405 0.199 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 29 37 35 39 56 35 36
normalized size 1 1. 0.71 0.9 0.85 0.95 1.37 0.85 0.88
time (sec) N/A 0.048 0.037 0.019 1.345 0.251 0.84 0.202 1.651
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 31 23 31 31 39 31 32
normalized size 1 1. 0.94 0.7 0.94 0.94 1.18 0.94 0.97
time (sec) N/A 0.034 0.006 0.02 1.427 0.228 0.818 0.201 1.363
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 7 7 7 8 9 9 7 9 7
normalized size 1 1. 1. 1.14 1.29 1.29 1. 1.29 1.
time (sec) N/A 0.014 0.004 0.005 1.419 0.217 0.17 0.199 0.763
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 14 17 19 19 17 19 17
normalized size 1 1. 0.88 1.06 1.19 1.19 1.06 1.19 1.06
time (sec) N/A 0.035 0.009 0.004 1.396 0.213 0.387 0.199 1.34
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 25 26 26 36 26 0
normalized size 1 1. 1. 1. 1.04 1.04 1.44 1.04 0.
time (sec) N/A 0.025 0.005 0.005 1.411 0.219 0.405 0.2 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 29 37 35 39 56 35 36
normalized size 1 1. 0.71 0.9 0.85 0.95 1.37 0.85 0.88
time (sec) N/A 0.051 0.035 0.016 1.411 0.245 0.843 0.2 1.606
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 31 23 31 34 39 31 32
normalized size 1 1. 0.94 0.7 0.94 1.03 1.18 0.94 0.97
time (sec) N/A 0.036 0.007 0.009 1.419 0.221 0.817 0.199 1.34
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 2 2 2 3 18 0 2 3 2
normalized size 1 1. 1. 1.5 9. 0. 1. 1.5 1.
time (sec) N/A 0.017 0.006 0.002 1.502 0. 0.833 0.198 0.636
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 2 2 2 3 18 0 12 3 2
normalized size 1 1. 1. 1.5 9. 0. 6. 1.5 1.
time (sec) N/A 0.019 0.005 0.004 1.501 0. 1.836 0.202 0.641
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 11 20 0 17 18 7
normalized size 1 1. 1. 1.1 2. 0. 1.7 1.8 0.7
time (sec) N/A 0.036 0.007 0.003 1.528 0. 2.469 0.198 1.612
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 12 23 0 10 15 10
normalized size 1 1. 1. 0.8 1.53 0. 0.67 1. 0.67
time (sec) N/A 0.055 0.007 0.008 1.479 0. 2.231 0.199 2.14
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 17 27 24 12 22 10
normalized size 1 1. 1. 1.42 2.25 2. 1. 1.83 0.83
time (sec) N/A 0.01 0.005 0.002 1.414 0.222 0.083 0.199 0.493
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 22 12 15 15 14 15 8
normalized size 1 1. 2. 1.09 1.36 1.36 1.27 1.36 0.73
time (sec) N/A 0.009 0.009 0.002 1.391 0.211 0.135 0.199 0.614
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 21 11 14 14 12 14 7
normalized size 1 1. 2.1 1.1 1.4 1.4 1.2 1.4 0.7
time (sec) N/A 0.008 0.009 0.004 1.39 0.209 0.139 0.205 0.612
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 17 15 24 19 18 10
normalized size 1 1. 1. 1.42 1.25 2. 1.58 1.5 0.83
time (sec) N/A 0.009 0.043 0.001 1.39 0.216 0.136 0.204 0.635
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 29 15 36 29 76 8
normalized size 1 1. 1. 2.64 1.36 3.27 2.64 6.91 0.73
time (sec) N/A 0.009 0.047 0.003 1.406 0.223 0.614 0.219 0.644
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 38 21 35 41 17 69 10
normalized size 1 1. 3.17 1.75 2.92 3.42 1.42 5.75 0.83
time (sec) N/A 0.009 0.016 0.004 1.39 0.233 0.908 0.212 0.613
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 68 19 35 38 34 38 8
normalized size 1 1. 6.18 1.73 3.18 3.45 3.09 3.45 0.73
time (sec) N/A 0.009 0.018 0.003 1.378 0.232 1.031 0.216 0.611
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 23 27 32 31 46 24 19
normalized size 1 1. 0.92 1.08 1.28 1.24 1.84 0.96 0.76
time (sec) N/A 0.018 0.033 0.003 1.4 0.215 0.272 0.201 0.71
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 29 22 30 30 37 34 19
normalized size 1 1. 1.07 0.81 1.11 1.11 1.37 1.26 0.7
time (sec) N/A 0.021 0.01 0.002 1.413 0.227 0.611 0.204 1.179
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 23 27 30 30 46 24 19
normalized size 1 1. 0.92 1.08 1.2 1.2 1.84 0.96 0.76
time (sec) N/A 0.018 0.022 0.004 1.382 0.244 0.263 0.2 0.712
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 29 22 30 28 36 30 19
normalized size 1 1. 1.12 0.85 1.15 1.08 1.38 1.15 0.73
time (sec) N/A 0.021 0.009 0.004 1.388 0.224 0.609 0.202 1.14
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 11 14 24 58 14 14
normalized size 1 1. 1. 1.1 1.4 2.4 5.8 1.4 1.4
time (sec) N/A 0.016 0.006 0.004 1.385 0.208 2.197 0.199 0.7
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 6 5 12 12 3 41 7
normalized size 1 1. 0.67 0.56 1.33 1.33 0.33 4.56 0.78
time (sec) N/A 0.016 0.006 0.004 1.386 0.22 0.216 0.197 0.488
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 8 9 14 14 7 11 8
normalized size 1 1. 0.67 0.75 1.17 1.17 0.58 0.92 0.67
time (sec) N/A 0.015 0.008 0.007 1.396 0.217 0.645 0.201 0.504
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 23 11 20 24 8 14 8
normalized size 1 1. 2.3 1.1 2. 2.4 0.8 1.4 0.8
time (sec) N/A 0.013 0.008 0.007 1.352 0.222 0.664 0.201 0.506
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 25 11 20 23 8 14 7
normalized size 1 1. 2.27 1. 1.82 2.09 0.73 1.27 0.64
time (sec) N/A 0.015 0.009 0.014 1.351 0.215 0.683 0.203 0.502
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 40 39 0 1 114 65 31
normalized size 1 1. 1. 0.98 0. 0.02 2.85 1.62 0.78
time (sec) N/A 0.071 0.047 0.014 0. 0.235 27.066 0.202 3.28
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 44 43 0 1 0 81 37
normalized size 1 1. 0.94 0.91 0. 0.02 0. 1.72 0.79
time (sec) N/A 0.1 0.079 0.033 0. 0.242 0. 0.204 3.613
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 47 158 158 73 105 61 65
normalized size 1 1. 0.64 2.16 2.16 1. 1.44 0.84 0.89
time (sec) N/A 0.078 0.133 0.004 1.401 0.241 1.528 0.2 2.628
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 12 15 16 20 15 10
normalized size 1 1. 1. 0.8 1. 1.07 1.33 1. 0.67
time (sec) N/A 0.015 0.007 0.015 1.39 0.247 0.748 0.198 0.948
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 47 158 153 73 105 61 65
normalized size 1 1. 0.64 2.16 2.1 1. 1.44 0.84 0.89
time (sec) N/A 0.075 0.134 0.007 1.421 0.229 1.601 0.202 2.713
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 22 19 42 14 39 14
normalized size 1 1. 1. 1.57 1.36 3. 1. 2.79 1.
time (sec) N/A 0.013 0.005 0.004 1.364 0.215 0.086 0.203 0.496
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 101 138 655 181 0 0 0
normalized size 1 1. 0.97 1.33 6.3 1.74 0. 0. 0.
time (sec) N/A 0.336 0.185 0.036 1.688 0.247 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 153 153 133 237 1034 221 0 0 0
normalized size 1 1. 0.87 1.55 6.76 1.44 0. 0. 0.
time (sec) N/A 0.62 0.435 0.043 2.2 0.262 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 20 144 28 19 31 0
normalized size 1 1. 1. 1.33 9.6 1.87 1.27 2.07 0.
time (sec) N/A 0.023 0.008 0.005 1.561 0.255 0.188 0.208 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 12 15 18 26 15 10
normalized size 1 1. 1. 0.8 1. 1.2 1.73 1. 0.67
time (sec) N/A 0.014 0.009 0.025 1.378 0.225 0.696 0.2 1.052
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 14 19 14 26 14 14 20
normalized size 1 1. 0.58 0.79 0.58 1.08 0.58 0.58 0.83
time (sec) N/A 0.039 0.007 0.004 1.416 0.221 0.053 0.199 1.621
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 7 7 6 15 12 24 12 12 15
normalized size 1 1. 0.86 2.14 1.71 3.43 1.71 1.71 2.14
time (sec) N/A 0.034 0.005 0.02 1.397 0.23 0.055 0.201 1.577
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 22 69 34 30 104 454 29
normalized size 1 1. 0.69 2.16 1.06 0.94 3.25 14.19 0.91
time (sec) N/A 0.021 0.018 0.014 1.426 0.222 1.885 0.219 1.553
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 20 71 32 27 107 455 29
normalized size 1 1. 0.65 2.29 1.03 0.87 3.45 14.68 0.94
time (sec) N/A 0.018 0.016 0.012 1.43 0.242 1.89 0.215 1.562
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 50 137 81 81 308 1 88
normalized size 1 1. 0.6 1.63 0.96 0.96 3.67 0.01 1.05
time (sec) N/A 0.083 0.06 0.016 1.45 0.25 5.818 0.22 6.05
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 49 142 78 78 304 1 88
normalized size 1 1. 0.59 1.71 0.94 0.94 3.66 0.01 1.06
time (sec) N/A 0.077 0.054 0.015 1.408 0.253 5.653 0.216 5.921
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 94 225 144 155 665 1 0
normalized size 1 1. 0.58 1.39 0.89 0.96 4.1 0.01 0.
time (sec) N/A 0.282 0.11 0.024 1.409 0.243 16.629 0.229 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 161 93 231 142 150 668 1 0
normalized size 1 1. 0.58 1.43 0.88 0.93 4.15 0.01 0.
time (sec) N/A 0.271 0.093 0.023 1.39 0.224 16.633 0.226 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 261 261 169 437 251 274 1355 1 0
normalized size 1 1. 0.65 1.67 0.96 1.05 5.19 0. 0.
time (sec) N/A 0.679 0.211 0.031 1.489 0.25 45.431 0.255 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 260 260 168 441 248 273 1352 1 0
normalized size 1 1. 0.65 1.7 0.95 1.05 5.2 0. 0.
time (sec) N/A 0.663 0.175 0.03 1.45 0.244 45.556 0.256 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 20 26 23 114 18 0
normalized size 1 1. 1. 0.8 1.04 0.92 4.56 0.72 0.
time (sec) N/A 0.047 0.014 0.037 1.393 0.246 21.373 0.2 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 30 23 30 34 114 30 27
normalized size 1 1. 1. 0.77 1. 1.13 3.8 1. 0.9
time (sec) N/A 0.047 0.014 0.032 1.404 0.252 21.234 0.204 2.363
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 55 64 74 80 100 81 85
normalized size 1 1. 0.65 0.75 0.87 0.94 1.18 0.95 1.
time (sec) N/A 0.104 0.085 0.019 1.427 0.237 3.497 0.199 4.894
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 14 0 0 0 324 0 0 0 0
normalized size 1 0. 0. 0. 23.14 0. 0. 0. 0.
time (sec) N/A 0.686 1.077 0.344 0.132 0. 0. 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 11 55 22 0 24 0
normalized size 1 1. 1. 0.92 4.58 1.83 0. 2. 0.
time (sec) N/A 0.057 0.011 0.034 1.382 0.241 0. 0.212 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 76 143 0 1 0 132 61
normalized size 1 1. 0.99 1.86 0. 0.01 0. 1.71 0.79
time (sec) N/A 0.162 0.325 0.032 0. 0.238 0. 0.236 7.738
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 14 16 18 15 18 15
normalized size 1 1. 1. 0.82 0.94 1.06 0.88 1.06 0.88
time (sec) N/A 0.008 0.004 0. 1.43 0.228 0.538 0.219 0.503
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 14 14 18 15 18 15
normalized size 1 1. 1. 0.82 0.82 1.06 0.88 1.06 0.88
time (sec) N/A 0.007 0.004 0. 1.401 0.24 0.522 0.216 0.474
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 3 3 3 3 3 3 2 3 2
normalized size 1 1. 1. 1. 1. 1. 0.67 1. 0.67
time (sec) N/A 0.002 0. 0.001 1.393 0.206 0.045 0.215 0.458
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 9 11 11 8 11 5
normalized size 1 1. 1. 1.12 1.38 1.38 1. 1.38 0.62
time (sec) N/A 0.005 0.001 0.001 1.404 0.214 0.066 0.198 0.565
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 9 11 11 7 11 5
normalized size 1 1. 1. 1. 1.22 1.22 0.78 1.22 0.56
time (sec) N/A 0.005 0.001 0.001 1.388 0.214 0.061 0.198 0.606
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 4 4 4 9 5 5 3 5 3
normalized size 1 1. 1. 2.25 1.25 1.25 0.75 1.25 0.75
time (sec) N/A 0.017 0.002 0.002 1.486 0.202 1.296 0.198 1.34
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 31 31 30 15 32 22
normalized size 1 1. 1. 1.29 1.29 1.25 0.62 1.33 0.92
time (sec) N/A 0.031 0.007 0.003 1.432 0.209 0.125 0.199 3.019
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 11 14 14 8 14 8
normalized size 1 1. 1. 0.92 1.17 1.17 0.67 1.17 0.67
time (sec) N/A 0.035 0.006 0.002 1.418 0.22 0.082 0.198 3.309
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 15 19 16 14 19 0
normalized size 1 1. 1. 1.15 1.46 1.23 1.08 1.46 0.
time (sec) N/A 0.015 0.003 0.001 1.408 0.212 0.071 0.2 0.
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 31 22 0 1 26 28 29
normalized size 1 1. 1. 0.71 0. 0.03 0.84 0.9 0.94
time (sec) N/A 0.051 0.014 0.006 0. 0.222 0.19 0.2 5.51
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 14 14 18 18 19 18 15
normalized size 1 1. 0.67 0.67 0.86 0.86 0.9 0.86 0.71
time (sec) N/A 0.017 0.004 0.001 1.386 0.213 0.091 0.199 1.58
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 102 102 136 136 102 136 0
normalized size 1 1. 0.63 0.63 0.83 0.83 0.63 0.83 0.
time (sec) N/A 0.378 0.011 0.002 1.425 0.214 0.12 0.2 0.
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 19 0 24 17 292 15
normalized size 1 1. 1. 1.06 0. 1.33 0.94 16.22 0.83
time (sec) N/A 0.033 0.006 0.002 0. 0.212 0.963 0.222 1.864
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 15 0 19 24 320 15
normalized size 1 1. 1. 1.07 0. 1.36 1.71 22.86 1.07
time (sec) N/A 0.024 0.004 0.002 0. 0.221 0.9 0.215 1.706
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 21 14 26 0 0 14
normalized size 1 1. 1. 1.24 0.82 1.53 0. 0. 0.82
time (sec) N/A 0.03 0.007 0.011 1.48 0.226 0. 0. 2.243
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 43 79 0 73 0 0 54
normalized size 1 1. 0.67 1.23 0. 1.14 0. 0. 0.84
time (sec) N/A 0.153 0.051 0.02 0. 0.251 0. 0. 7.419
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 16 22 22 12 0 12
normalized size 1 1. 1. 1. 1.38 1.38 0.75 0. 0.75
time (sec) N/A 0.051 0.01 0.003 1.367 0.199 0.124 0. 2.816
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 15 15 17 15 8
normalized size 1 1. 1. 0.92 1.15 1.15 1.31 1.15 0.62
time (sec) N/A 0.013 0.003 0.002 1.414 0.211 0.082 0.198 1.11
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 8 12 9 8 12 8
normalized size 1 1. 1. 0.73 1.09 0.82 0.73 1.09 0.73
time (sec) N/A 0.007 0.002 0.002 1.459 0.238 0.288 0.201 0.487
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 7 8 8 5 8 5
normalized size 1 1. 1. 0.78 0.89 0.89 0.56 0.89 0.56
time (sec) N/A 0.011 0.002 0.001 1.394 0.197 0.067 0.207 1.013
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 16 18 23 23 14 0 0
normalized size 1 1. 0.59 0.67 0.85 0.85 0.52 0. 0.
time (sec) N/A 0.158 0.008 0.001 1.423 0.207 0.081 0. 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A F A A A A A F F(-1)
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 25 0 25 23 30 49 31 0 0
normalized size 1 0. 1. 0.92 1.2 1.96 1.24 0. 0.
time (sec) N/A 1.534 0.041 0.041 1.94 0.227 0.64 0. 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.071 0.012 0.015 0. 0. 0. 0. 0.
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 12 14 14 8 14 8
normalized size 1 1. 1. 1.09 1.27 1.27 0.73 1.27 0.73
time (sec) N/A 0.026 0.004 0.008 1.599 0.218 2.878 0.198 2.111
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 17 21 20 20 0 20 20
normalized size 1 1. 0.77 0.95 0.91 0.91 0. 0.91 0.91
time (sec) N/A 0.076 0.011 0.009 1.413 0.221 0. 0.198 4.459
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 17 28 15 15 10 15 17
normalized size 1 1. 0.74 1.22 0.65 0.65 0.43 0.65 0.74
time (sec) N/A 0.019 0.005 0.003 1.476 0.21 0.078 0.198 2.281
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A F(-2) A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 13 16 0 12 16 0
normalized size 1 1. 1. 0.81 1. 0. 0.75 1. 0.
time (sec) N/A 0.008 0. 0.001 1.548 0. 0.028 0.199 0.
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 43 48 0 1 920 65 49
normalized size 1 1. 0.75 0.84 0. 0.02 16.14 1.14 0.86
time (sec) N/A 0.062 0.042 0.008 0. 0.229 6.461 0.2 3.845
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 110 305 0 1 0 189 97
normalized size 1 1. 0.95 2.63 0. 0.01 0. 1.63 0.84
time (sec) N/A 0.138 0.082 0.011 0. 0.25 0. 0.218 7.757
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 13 16 16 12 16 12
normalized size 1 1. 1. 0.81 1. 1. 0.75 1. 0.75
time (sec) N/A 0.006 0.005 0.002 1.347 0.202 0.032 0.199 0.636
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 34 21 35 41 202 34 31
normalized size 1 1. 1. 0.62 1.03 1.21 5.94 1. 0.91
time (sec) N/A 0.024 0.012 0.002 1.342 0.202 1.695 0.198 2.432
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 46 32 55 57 666 62 49
normalized size 1 1. 0.87 0.6 1.04 1.08 12.57 1.17 0.92
time (sec) N/A 0.038 0.015 0.004 1.36 0.2 2.709 0.199 4.031
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 35 28 0 1 68 43 31
normalized size 1 1. 1. 0.8 0. 0.03 1.94 1.23 0.89
time (sec) N/A 0.034 0.016 0.005 0. 0.23 2.242 0.2 2.256
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 39 37 0 1 44 55 32
normalized size 1 1. 1. 0.95 0. 0.03 1.13 1.41 0.82
time (sec) N/A 0.035 0.033 0.007 0. 0.23 2.921 0.205 2.395
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 13 16 16 10 16 10
normalized size 1 1. 1. 0.93 1.14 1.14 0.71 1.14 0.71
time (sec) N/A 0.008 0.003 0.001 1.334 0.212 0.033 0.199 0.656
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 23 21 35 26 162 31 29
normalized size 1 1. 0.72 0.66 1.09 0.81 5.06 0.97 0.91
time (sec) N/A 0.031 0.012 0.002 1.319 0.202 1.729 0.198 2.398
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 35 32 55 42 600 62 48
normalized size 1 1. 0.69 0.63 1.08 0.82 11.76 1.22 0.94
time (sec) N/A 0.042 0.016 0.003 1.351 0.198 2.565 0.198 3.915
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 23 18 0 1 24 28 22
normalized size 1 1. 1. 0.78 0. 0.04 1.04 1.22 0.96
time (sec) N/A 0.02 0.01 0.004 0. 0.207 1.676 0.2 1.545
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 41 40 0 1 44 63 32
normalized size 1 1. 1. 0.98 0. 0.02 1.07 1.54 0.78
time (sec) N/A 0.037 0.023 0.005 0. 0.219 3.456 0.201 2.274
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 24 25 0 34 26 28 15
normalized size 1 1. 1.04 1.09 0. 1.48 1.13 1.22 0.65
time (sec) N/A 0.013 0.015 0.001 0. 0.225 0.041 0.199 0.895
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 38 43 61 78 216 122 37
normalized size 1 1. 0.79 0.9 1.27 1.62 4.5 2.54 0.77
time (sec) N/A 0.036 0.021 0.003 1.369 0.235 0.919 0.204 3.754
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 48 42 70 50 230 70 56
normalized size 1 1. 0.87 0.76 1.27 0.91 4.18 1.27 1.02
time (sec) N/A 0.067 0.064 0.006 1.552 0.237 2.109 0.202 3.586
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 38 11 19 19 2 20 10
normalized size 1 1. 3.17 0.92 1.58 1.58 0.17 1.67 0.83
time (sec) N/A 0.006 0.004 0.002 1.419 0.204 0.148 0.202 0.149
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 31 50 96 158 119 42 34
normalized size 1 1. 0.72 1.16 2.23 3.67 2.77 0.98 0.79
time (sec) N/A 0.02 0.025 0.005 1.364 0.211 3.969 0.227 1.733
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 17 22 22 20 22 46
normalized size 1 1. 1. 0.77 1. 1. 0.91 1. 2.09
time (sec) N/A 0.017 0.009 0.002 1.43 0.234 0.39 0.199 2.866
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 18 15 15 8 15 8
normalized size 1 1. 1. 1.38 1.15 1.15 0.62 1.15 0.62
time (sec) N/A 0.006 0.004 0.002 1.386 0.211 1.78 0.201 0.911
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 7 22 24 19 8 5
normalized size 1 1. 1. 0.88 2.75 3. 2.38 1. 0.62
time (sec) N/A 0.01 0.008 0.011 1.502 0.22 1.499 0.211 1.213
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 11 34 34 8 34 12
normalized size 1 1. 1. 0.79 2.43 2.43 0.57 2.43 0.86
time (sec) N/A 0.019 0.03 0.008 1.37 0.324 1.503 0.203 1.564
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 14 0 30 0 30 22
normalized size 1 1. 1. 0.78 0. 1.67 0. 1.67 1.22
time (sec) N/A 0.036 0.009 0.008 0. 0.212 0. 0.206 2.04
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 37 23 23 74 0 20 20
normalized size 1 1. 1.23 0.77 0.77 2.47 0. 0.67 0.67
time (sec) N/A 0.049 0.044 0.01 1.536 0.223 0. 0.219 3.84
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 15 19 46 0 0 10
normalized size 1 1. 1. 0.88 1.12 2.71 0. 0. 0.59
time (sec) N/A 0.037 0.024 0.004 1.508 0.215 0. 0. 2.079
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 2 2 2 3 3 19 2 19 2
normalized size 1 1. 1. 1.5 1.5 9.5 1. 9.5 1.
time (sec) N/A 0.003 0.004 0.002 1.552 0.238 0.135 0.235 0.077
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 30 15 19 19 17 0 0
normalized size 1 1. 1.5 0.75 0.95 0.95 0.85 0. 0.
time (sec) N/A 1.704 0.025 0.002 1.533 0.202 1.608 0. 0.
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 21 41 27 19 0 0
normalized size 1 1. 1. 0.88 1.71 1.12 0.79 0. 0.
time (sec) N/A 0.512 0.075 0.004 1.725 0.202 2.02 0. 0.
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 71 24 42 39 8 42 24
normalized size 1 1. 2.63 0.89 1.56 1.44 0.3 1.56 0.89
time (sec) N/A 0.016 0.012 0.002 1.366 0.21 0.195 0.206 0.906
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 161 25 0 1 51 0 73
normalized size 1 1. 1.96 0.3 0. 0.01 0.62 0. 0.89
time (sec) N/A 0.138 0.274 0.049 0. 0.24 2.274 0. 8.188
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 39 54 39 0 14 10
normalized size 1 1. 1. 3.25 4.5 3.25 0. 1.17 0.83
time (sec) N/A 0.082 0.009 0.058 1.486 0.219 0. 0.199 3.217
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 40 33 0 1 66 46 37
normalized size 1 1. 1. 0.82 0. 0.02 1.65 1.15 0.92
time (sec) N/A 0.026 0.015 0.002 0. 0.221 1.8 0.206 1.813
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 58 66 0 55 42 51 37
normalized size 1 1. 1.26 1.43 0. 1.2 0.91 1.11 0.8
time (sec) N/A 0.073 0.05 0.006 0. 0.212 1.953 0.203 5.012
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 48 52 0 47 0 54 39
normalized size 1 1. 1.3 1.41 0. 1.27 0. 1.46 1.05
time (sec) N/A 0.045 0.086 0.005 0. 0.217 0. 0.217 3.873
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 72 74 0 74 0 69 65
normalized size 1 1. 1.18 1.21 0. 1.21 0. 1.13 1.07
time (sec) N/A 0.056 0.144 0.004 0. 0.228 0. 0.234 5.634
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 23 20 26 26 29 26 15
normalized size 1 1. 1. 0.87 1.13 1.13 1.26 1.13 0.65
time (sec) N/A 0.01 0.006 0.002 1.316 0.208 0.765 0.2 1.397
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 28 25 32 32 36 22 19
normalized size 1 1. 1. 0.89 1.14 1.14 1.29 0.79 0.68
time (sec) N/A 0.01 0.008 0.003 1.359 0.214 0.99 0.202 1.792
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 66 47 0 1 0 81 56
normalized size 1 1. 1.18 0.84 0. 0.02 0. 1.45 1.
time (sec) N/A 0.078 0.089 0.01 0. 0.231 0. 0.264 4.303
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 84 70 0 1 0 97 75
normalized size 1 1. 1.04 0.86 0. 0.01 0. 1.2 0.93
time (sec) N/A 0.067 0.113 0.004 0. 0.233 0. 0.258 4.027
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 59 56 0 55 0 42 39
normalized size 1 1. 1.34 1.27 0. 1.25 0. 0.95 0.89
time (sec) N/A 0.094 0.13 0.011 0. 0.221 0. 0.263 7.004
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 80 78 0 85 0 42 65
normalized size 1 1. 1.18 1.15 0. 1.25 0. 0.62 0.96
time (sec) N/A 0.114 0.304 0.011 0. 0.228 0. 0.26 9.442
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 15 30 10 15 10
normalized size 1 1. 1. 0.92 1.15 2.31 0.77 1.15 0.77
time (sec) N/A 0.027 0.009 0.003 1.417 0.218 0.37 0.201 1.418
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 16 20 15 17 20 17
normalized size 1 1. 1. 0.84 1.05 0.79 0.89 1.05 0.89
time (sec) N/A 0.012 0.003 0.003 1.469 0.208 0.083 0.203 1.079
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 21 27 16 10 16 10
normalized size 1 1. 1. 1.75 2.25 1.33 0.83 1.33 0.83
time (sec) N/A 0.016 0.018 0.005 1.381 0.228 0.187 0.198 0.875
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 11 14 14 7 14 7
normalized size 1 1. 1. 1. 1.27 1.27 0.64 1.27 0.64
time (sec) N/A 0.039 0.011 0.008 1.478 0.217 0.52 0.203 2.556
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 24 31 30 20 32 0
normalized size 1 1. 1. 0.89 1.15 1.11 0.74 1.19 0.
time (sec) N/A 0.041 0.006 0.002 1.353 0.203 0.528 0.202 0.
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 21 16 27 127 165 89 29
normalized size 1 1. 0.64 0.48 0.82 3.85 5. 2.7 0.88
time (sec) N/A 0.014 0.015 0.002 1.329 0.203 72.813 0.204 1.221
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 10 12 12 7 15 7
normalized size 1 1. 1. 1.11 1.33 1.33 0.78 1.67 0.78
time (sec) N/A 0.006 0.003 0.003 1.357 0.196 0.075 0.202 0.89
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 14 38 38 39 43 17
normalized size 1 1. 1. 0.74 2. 2. 2.05 2.26 0.89
time (sec) N/A 0.014 0.007 0.003 1.505 0.208 0.759 0.201 1.116
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 16 13 15 19 15 15 15
normalized size 1 1. 0.84 0.68 0.79 1. 0.79 0.79 0.79
time (sec) N/A 0.007 0.004 0.002 1.369 0.221 0.663 0.201 0.976
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 112 85 0 138 155 139 78
normalized size 1 1. 1.27 0.97 0. 1.57 1.76 1.58 0.89
time (sec) N/A 0.087 0.058 0.005 0. 0.219 2.428 0.495 3.195
Problem 225 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 10 46 12 7 23 0
normalized size 1 1. 1. 1.11 5.11 1.33 0.78 2.56 0.
time (sec) N/A 0.019 0.005 0.006 1.388 0.217 0.176 0.199 0.
Problem 226 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 10 46 12 7 23 0
normalized size 1 1. 1. 1.11 5.11 1.33 0.78 2.56 0.
time (sec) N/A 0.018 0.005 0.004 1.365 0.217 0.169 0.229 0.
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 8 9 35 7 18 7
normalized size 1 1. 1. 0.89 1. 3.89 0.78 2. 0.78
time (sec) N/A 0.008 0.006 0.004 1.349 0.215 0.127 0.225 1.412
Problem 228 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 16 18 35 22 31 12
normalized size 1 1. 1. 1.33 1.5 2.92 1.83 2.58 1.
time (sec) N/A 0.052 0.018 0.009 1.334 0.23 2.108 0.226 6.597
Problem 229 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 28 23 30 43 76 30 0
normalized size 1 1. 1. 0.82 1.07 1.54 2.71 1.07 0.
time (sec) N/A 0.038 0.014 0.008 1.334 0.227 3.052 0.212 0.
Problem 230 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 21 16 20 18 15 20 15
normalized size 1 1. 1. 0.76 0.95 0.86 0.71 0.95 0.71
time (sec) N/A 0.018 0.003 0.002 1.608 0.212 0.316 0.198 1.971
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 21 16 20 18 15 23 15
normalized size 1 1. 1. 0.76 0.95 0.86 0.71 1.1 0.71
time (sec) N/A 0.018 0.003 0.002 1.625 0.209 0.326 0.199 1.944
Problem 232 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 32 23 30 26 26 30 26
normalized size 1 1. 1.39 1. 1.3 1.13 1.13 1.3 1.13
time (sec) N/A 0.033 0.003 0.002 1.431 0.214 0.543 0.217 1.031
Problem 233 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 15 19 38 32 19 0
normalized size 1 1. 1. 0.83 1.06 2.11 1.78 1.06 0.
time (sec) N/A 0.028 0.024 0.006 1.37 0.239 0.741 0.199 0.
Problem 234 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 15 19 38 32 19 0
normalized size 1 1. 1. 0.83 1.06 2.11 1.78 1.06 0.
time (sec) N/A 0.023 0.015 0.006 1.396 0.232 0.741 0.199 0.
Problem 235 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 40 17 58 32 0 0 14
normalized size 1 1. 3.33 1.42 4.83 2.67 0. 0. 1.17
time (sec) N/A 0.011 0.02 0.034 1.544 0.214 0. 0. 0.491
Problem 236 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 42 23 58 35 0 0 12
normalized size 1 1. 3. 1.64 4.14 2.5 0. 0. 0.86
time (sec) N/A 0.015 0.019 0.028 1.593 0.219 0. 0. 0.524
Problem 237 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 16 22 38 14 0 0 12
normalized size 1 1. 1.33 1.83 3.17 1.17 0. 0. 1.
time (sec) N/A 0.012 0.006 0.021 1.596 0.211 0. 0. 0.496
Problem 238 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 18 22 27 24 0 0 14
normalized size 1 1. 1.29 1.57 1.93 1.71 0. 0. 1.
time (sec) N/A 0.015 0.008 0.026 1.557 0.218 0. 0. 0.517
Problem 239 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 17 14 0 18 63 18 17
normalized size 1 1. 0.81 0.67 0. 0.86 3. 0.86 0.81
time (sec) N/A 0.015 0.024 0.002 0. 0.209 0.697 0.2 0.687
Problem 240 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 22 31 24 24 20 26 20
normalized size 1 1. 0.92 1.29 1. 1. 0.83 1.08 0.83
time (sec) N/A 0.024 0.008 0.003 1.383 0.21 0.131 0.23 1.496
Problem 241 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 9 45 22 7 22 7
normalized size 1 1. 1. 0.75 3.75 1.83 0.58 1.83 0.58
time (sec) N/A 0.012 0.007 0.005 1.363 0.23 1.502 0.212 1.102
Problem 242 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 32 92 32 32 0 32 0
normalized size 1 1. 1. 2.88 1. 1. 0. 1. 0.
time (sec) N/A 0.027 0.013 0.018 1.372 0.204 0. 0.2 0.
Problem 243 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 33 27 35 54 31 35 31
normalized size 1 1. 1. 0.82 1.06 1.64 0.94 1.06 0.94
time (sec) N/A 0.025 0.02 0.003 1.501 0.206 0.134 0.2 1.977
Problem 244 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 3 3 3 4 4 15 3 15 3
normalized size 1 1. 1. 1.33 1.33 5. 1. 5. 1.
time (sec) N/A 0.005 0.003 0.001 1.404 0.219 0.041 0.2 0.035
Problem 245 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 18 14 22 65 19 46 14
normalized size 1 1. 1.5 1.17 1.83 5.42 1.58 3.83 1.17
time (sec) N/A 0.015 0.005 0.004 1.553 0.247 0.052 0.208 0.52
Problem 246 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 3 3 3 4 4 24 7 15 10
normalized size 1 1. 1. 1.33 1.33 8. 2.33 5. 3.33
time (sec) N/A 0.006 0.003 0. 1.4 0.224 0.115 0.198 21.24
Problem 247 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 3 3 3 4 4 24 12 16 17
normalized size 1 1. 1. 1.33 1.33 8. 4. 5.33 5.67
time (sec) N/A 0.006 0.005 0.001 1.462 0.222 0.401 0.228 35.117
Problem 248 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 9 11 11 8 11 5
normalized size 1 1. 1. 1.12 1.38 1.38 1. 1.38 0.62
time (sec) N/A 0.005 0.001 0.002 1.365 0.214 0.067 0.207 0.56
Problem 249 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 29 32 14 14 0 15 39
normalized size 1 1. 0.59 0.65 0.29 0.29 0. 0.31 0.8
time (sec) N/A 0.038 0.014 0.003 1.48 0.207 0. 0.197 2.403
Problem 250 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 17 13 16 16 12 18 0
normalized size 1 1. 1.06 0.81 1. 1. 0.75 1.12 0.
time (sec) N/A 0.017 0.004 0.002 1.386 0.204 0.056 0.198 0.
Problem 251 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 36 0 0 41 0 54 32
normalized size 1 1. 0.9 0. 0. 1.02 0. 1.35 0.8
time (sec) N/A 0.043 0.028 0.003 0. 0.216 0. 0.202 2.506
Problem 252 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 128 128 67 63 78 74 109 77 0
normalized size 1 1. 0.52 0.49 0.61 0.58 0.85 0.6 0.
time (sec) N/A 0.292 0.189 0.009 1.371 0.234 8.013 0.202 0.
Problem 253 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 18 20 23 23 27 20 27
normalized size 1 1. 0.6 0.67 0.77 0.77 0.9 0.67 0.9
time (sec) N/A 0.055 0.027 0.004 1.355 0.219 1.023 0.2 3.061
Problem 254 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 9 8 9 23 17 9 7
normalized size 1 1. 0.82 0.73 0.82 2.09 1.55 0.82 0.64
time (sec) N/A 0.003 0.002 0.001 1.33 0.188 0.094 0.199 0.531
Problem 255 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 40 33 43 53 41 45 37
normalized size 1 1. 1. 0.82 1.08 1.32 1.02 1.12 0.92
time (sec) N/A 0.042 0.013 0.001 1.525 0.233 0.163 0.199 2.984
Problem 256 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 23 22 23 23 15 24 7
normalized size 1 1. 2.88 2.75 2.88 2.88 1.88 3. 0.88
time (sec) N/A 0.009 0.004 0.001 1.319 0.197 0.086 0.202 1.109
Problem 257 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 227 227 277 1210 0 0 0 0 321
normalized size 1 1. 1.22 5.33 0. 0. 0. 0. 1.41
time (sec) N/A 0.321 0.294 0.014 0. 0. 0. 0. 24.514
Problem 258 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 30 26 34 32 32 34 32
normalized size 1 1. 1.25 1.08 1.42 1.33 1.33 1.42 1.33
time (sec) N/A 0.018 0.005 0.002 1.321 0.222 2.813 0.201 0.667
Problem 259 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 71 54 77 81 73 0 70
normalized size 1 1. 0.91 0.69 0.99 1.04 0.94 0. 0.9
time (sec) N/A 0.09 0.035 0.003 1.509 0.213 0.606 0. 4.805
Problem 260 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 2 2 2 3 3 19 2 19 2
normalized size 1 1. 1. 1.5 1.5 9.5 1. 9.5 1.
time (sec) N/A 0.003 0.005 0. 1.544 0.205 0.137 0.2 0.076
Problem 261 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 21 27 109 24 34 24
normalized size 1 1. 1. 0.78 1. 4.04 0.89 1.26 0.89
time (sec) N/A 0.009 0.01 0.003 1.48 0.216 0.235 0.207 0.593
Problem 262 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 11 14 22 8 15 8
normalized size 1 1. 1. 1.1 1.4 2.2 0.8 1.5 0.8
time (sec) N/A 0.011 0.004 0.004 1.354 0.19 0.063 0.211 1.063
Problem 263 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 15 19 19 12 19 12
normalized size 1 1. 1. 0.94 1.19 1.19 0.75 1.19 0.75
time (sec) N/A 0.009 0.005 0.003 1.524 0.221 0.126 0.201 1.015
Problem 264 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 29 34 45 32 32 51 27
normalized size 1 1. 0.72 0.85 1.12 0.8 0.8 1.27 0.68
time (sec) N/A 0.049 0.02 0.003 1.496 0.232 0.447 0.202 3.041
Problem 265 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 29 14 18 39 0 20 0
normalized size 1 1. 1.38 0.67 0.86 1.86 0. 0.95 0.
time (sec) N/A 0.178 0.022 0.041 1.329 0.233 0. 0.211 0.
Problem 266 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 11 14 14 10 22 10
normalized size 1 1. 1. 0.79 1. 1. 0.71 1.57 0.71
time (sec) N/A 0.011 0.003 0.006 1.403 0.228 0.056 0.204 0.494
Problem 267 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 17 22 24 14 24 14
normalized size 1 1. 1. 0.94 1.22 1.33 0.78 1.33 0.78
time (sec) N/A 0.037 0.006 0.006 1.41 0.205 0.114 0.205 2.816
Problem 268 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 7 8 22 7 22 7
normalized size 1 1. 1. 0.7 0.8 2.2 0.7 2.2 0.7
time (sec) N/A 0.005 0.006 0.001 1.498 0.207 0.15 0.201 0.522
Problem 269 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 6 6 6 5 5 19 3 19 3
normalized size 1 1. 1. 0.83 0.83 3.17 0.5 3.17 0.5
time (sec) N/A 0.004 0.005 0.002 1.5 0.201 0.141 0.204 0.512
Problem 270 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 21 17 22 22 22 22 19
normalized size 1 1. 1. 0.81 1.05 1.05 1.05 1.05 0.9
time (sec) N/A 0.03 0.014 0.002 1.643 0.194 0.11 0.199 0.684
Problem 271 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 51 42 63 99 46 62 0
normalized size 1 1. 0.96 0.79 1.19 1.87 0.87 1.17 0.
time (sec) N/A 0.053 0.031 0.007 1.503 0.197 0.222 0.2 0.
Problem 272 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 49 66 55 55 762 59 0
normalized size 1 1. 1. 1.35 1.12 1.12 15.55 1.2 0.
time (sec) N/A 0.129 0.04 0.006 1.372 0.23 35.828 0.203 0.
Problem 273 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 0 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.007 4.25 0.023 0. 0. 0. 0. 0.
Problem 274 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A F A A A A A F F
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 28 0 28 28 36 59 26 0 0
normalized size 1 0. 1. 1. 1.29 2.11 0.93 0. 0.
time (sec) N/A 0.442 9.876 0.03 1.542 0.225 0.788 0. 0.
Problem 275 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 199 199 136 133 216 196 0 154 180
normalized size 1 1. 0.68 0.67 1.09 0.98 0. 0.77 0.9
time (sec) N/A 0.182 0.254 0.016 1.445 0.258 0. 0.21 13.122
Problem 276 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 16 20 24 15 20 15
normalized size 1 1. 1. 0.89 1.11 1.33 0.83 1.11 0.83
time (sec) N/A 0.09 0.011 0.004 1.393 0.204 0.541 0.211 0.49
Problem 277 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 22 28 43 36 50 20
normalized size 1 1. 1. 0.92 1.17 1.79 1.5 2.08 0.83
time (sec) N/A 0.025 0.045 0.002 1.399 0.206 0.804 0.22 0.615
Problem 278 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A F C B F A F F F(-1)
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 94 0 5137 1197351 0 242 0 0 0
normalized size 1 0. 54.65 12737.8 0. 2.57 0. 0. 0.
time (sec) N/A 2.88 6.138 0.703 0. 0.295 0. 0. 0.
Problem 279 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A F C C F A F F F(-1)
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 142 0 630 352 0 301 0 0 0
normalized size 1 0. 4.44 2.48 0. 2.12 0. 0. 0.
time (sec) N/A 5.567 2.385 0.177 0. 0.282 0. 0. 0.
Problem 280 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 97 1088 231 219 0 105 19
normalized size 1 1. 4.62 51.81 11. 10.43 0. 5. 0.9
time (sec) N/A 0.437 0.082 0.095 1.655 0.214 0. 0.35 18.515
Problem 281 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade N/A A A A A A A A A
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 48 0 3168 4640 0 0 0 0 0
normalized size 1 0. 66. 96.67 0. 0. 0. 0. 0.
time (sec) N/A 0.049 6.073 0.504 0. 0. 0. 0. 0.
Problem 282 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 330 330 181 1356 435 363 0 637 0
normalized size 1 1. 0.55 4.11 1.32 1.1 0. 1.93 0.
time (sec) N/A 1.419 0.219 0.086 1.594 0.226 0. 0.216 0.
Problem 283 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 4 4 4 5 5 5 5 5 5
normalized size 1 1. 1. 1.25 1.25 1.25 1.25 1.25 1.25
time (sec) N/A 0.017 0.002 0.007 1.371 0.226 0.623 0.202 1.363
Problem 284 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A F A A F A A F F(-1)
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 71 0 71 102 0 185 76 0 0
normalized size 1 0. 1. 1.44 0. 2.61 1.07 0. 0.
time (sec) N/A 1.213 0.061 0.017 0. 0.203 0.31 0. 0.

2.2 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 [50] had the largest ratio of [ 1.429 ]

Table 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 1 0 1. 6 0.
2 A 3 2 1. 13 0.154
3 A 2 1 1. 10 0.1
4 A 1 1 1. 3 0.333
5 A 2 1 1. 11 0.091
6 A 2 1 1. 14 0.071
7 A 2 1 1. 20 0.05
8 A 2 2 1. 12 0.167
9 A 3 3 1. 13 0.231
10 A 2 2 1. 10 0.2
11 A 6 5 1. 13 0.385
12 A 2 1 1. 23 0.043
13 A 4 3 1. 20 0.15
14 A 3 2 1. 22 0.091
15 A 5 4 1. 14 0.286
16 A 6 6 1. 9 0.667
17 A 3 2 1. 16 0.125
18 A 9 6 1. 7 0.857
19 A 9 6 1. 11 0.546
20 A 9 5 1. 10 0.5
21 A 1 1 1. 7 0.143
22 A 2 1 1. 9 0.111
23 A 2 1 1. 11 0.091
24 A 1 1 1. 7 0.143
25 A 1 1 1. 7 0.143
26 A 2 1 1. 9 0.111
27 A 2 1 1. 11 0.091
28 A 3 3 1. 11 0.273
29 A 2 1 1. 11 0.091
30 A 2 1 1. 11 0.091
31 A 1 1 1. 9 0.111
32 A 1 1 1. 11 0.091
33 A 6 6 1. 9 0.667
34 A 6 6 1. 7 0.857
35 A 6 6 1. 11 0.546
36 A 3 3 1. 7 0.429
37 A 3 3 1. 9 0.333
38 A 9 6 1.01 9 0.667
39 A 3 3 1. 12 0.25
40 A 3 3 1. 12 0.25
41 A 3 2 1. 12 0.167
42 A 3 2 1. 12 0.167
43 A 3 2 1. 12 0.167
44 A 9 5 1. 10 0.5
45 A 9 5 1. 12 0.417
46 A 10 6 1. 7 0.857
47 A 10 6 1. 7 0.857
48 A 10 6 1. 7 0.857
49 A 19 6 1. 7 0.857
50 A 13 10 1. 7 1.429
51 A 19 6 1. 12 0.5
52 A 7 7 1. 11 0.636
53 A 1 1 1. 2 0.5
54 A 1 1 1. 4 0.25
55 A 1 1 1. 6 0.167
56 A 1 1 1. 6 0.167
57 A 2 2 1. 4 0.5
58 A 11 2 1. 8 0.25
59 A 2 2 1. 8 0.25
60 A 1 1 1. 4 0.25
61 A 2 2 1. 6 0.333
62 A 2 2 1. 8 0.25
63 A 3 3 1. 8 0.375
64 A 2 2 1. 8 0.25
65 A 2 1 1. 8 0.125
66 A 4 4 1. 10 0.4
67 A 2 2 1. 10 0.2
68 A 3 2 1. 8 0.25
69 A 3 2 1. 10 0.2
70 A 3 3 1. 8 0.375
71 A 3 3 1. 10 0.3
72 A 4 3 1. 12 0.25
73 A 4 3 1. 12 0.25
74 A 3 3 1. 10 0.3
75 A 0 0 0. 0 0.
76 A 1 1 1. 2 0.5
77 A 1 1 1. 2 0.5
78 A 1 1 1. 2 0.5
79 A 1 1 1. 2 0.5
80 A 2 2 1. 6 0.333
81 A 1 1 1. 2 0.5
82 A 1 1 1. 2 0.5
83 A 2 2 1. 4 0.5
84 A 3 3 1. 8 0.375
85 A 2 1 1. 4 0.25
86 A 1 1 1. 4 0.25
87 A 3 2 1. 11 0.182
88 A 2 2 1. 4 0.5
89 A 2 1 1. 4 0.25
90 A 2 2 1. 4 0.5
91 A 1 1 1. 7 0.143
92 A 2 2 1. 4 0.5
93 A 3 2 1. 6 0.333
94 A 2 2 1. 6 0.333
95 A 4 4 1. 8 0.5
96 A 3 3 1. 6 0.5
97 A 2 2 1. 4 0.5
98 A 3 2 1. 6 0.333
99 A 2 2 1. 6 0.333
100 A 4 4 1. 8 0.5
101 A 3 3 1. 6 0.5
102 A 1 1 1. 6 0.167
103 A 1 1 1. 6 0.167
104 A 2 2 1. 6 0.333
105 A 3 2 1. 8 0.25
106 A 2 2 1. 4 0.5
107 A 1 1 1. 6 0.167
108 A 1 1 1. 6 0.167
109 A 1 1 1. 6 0.167
110 A 1 1 1. 6 0.167
111 A 1 1 1. 6 0.167
112 A 1 1 1. 6 0.167
113 A 2 2 1. 8 0.25
114 A 2 1 1. 8 0.125
115 A 2 2 1. 8 0.25
116 A 2 1 1. 8 0.125
117 A 2 2 1. 8 0.25
118 A 1 1 1. 6 0.167
119 A 1 1 1. 8 0.125
120 A 1 1 1. 6 0.167
121 A 1 1 1. 8 0.125
122 A 3 3 1. 8 0.375
123 A 3 3 1. 10 0.3
124 A 4 4 1. 12 0.333
125 A 1 1 1. 7 0.143
126 A 4 4 1. 12 0.333
127 A 2 2 1. 4 0.5
128 A 17 8 1. 8 1.
129 A 34 9 1. 8 1.125
130 A 3 3 1. 6 0.5
131 A 1 1 1. 9 0.111
132 A 3 3 1. 9 0.333
133 A 3 2 1. 9 0.222
134 A 1 1 1. 6 0.167
135 A 1 1 1. 6 0.167
136 A 4 3 1. 7 0.429
137 A 4 3 1. 7 0.429
138 A 11 5 1. 9 0.556
139 A 11 5 1. 9 0.556
140 A 25 5 1. 9 0.556
141 A 25 5 1. 9 0.556
142 A 5 2 1. 11 0.182
143 A 5 2 1. 11 0.182
144 A 6 4 1. 10 0.4
145 A 0 0 0. 0 0.
146 A 4 3 1. 9 0.333
147 A 5 5 1. 15 0.333
148 A 1 1 1. 3 0.333
149 A 1 1 1. 3 0.333
150 A 1 1 1. 3 0.333
151 A 1 1 1. 3 0.333
152 A 1 1 1. 5 0.2
153 A 1 1 1. 9 0.111
154 A 4 4 1. 11 0.364
155 A 3 2 1. 13 0.154
156 A 2 2 1. 9 0.222
157 A 2 2 1. 18 0.111
158 A 2 2 1. 7 0.286
159 A 21 2 1. 7 0.286
160 A 2 2 1. 9 0.222
161 A 2 2 1. 7 0.286
162 A 2 2 1. 7 0.286
163 A 5 3 1. 12 0.25
164 A 1 1 1. 14 0.071
165 A 1 1 1. 7 0.143
166 A 1 1 1. 5 0.2
167 A 1 1 1. 7 0.143
168 A 7 3 1. 12 0.25
169 F 0 0 N/A 0 N/A
170 A 0 0 0. 0 0.
171 A 2 3 1. 6 0.5
172 A 5 5 1. 7 0.714
173 A 2 2 1. 10 0.2
174 A 1 0 1. 13 0.
175 A 4 4 1. 12 0.333
176 A 4 3 1. 19 0.158
177 A 1 1 1. 9 0.111
178 A 2 1 1. 11 0.091
179 A 2 1 1. 13 0.077
180 A 3 3 1. 13 0.231
181 A 3 3 1. 13 0.231
182 A 1 1 1. 9 0.111
183 A 2 1 1. 11 0.091
184 A 2 1 1. 13 0.077
185 A 2 2 1. 13 0.154
186 A 3 3 1. 13 0.231
187 A 1 1 1. 11 0.091
188 A 2 1 1. 13 0.077
189 A 6 6 1. 18 0.333
190 A 2 2 1. 9 0.222
191 A 4 3 1. 13 0.231
192 A 3 3 1. 6 0.5
193 A 1 1 1. 13 0.077
194 A 2 2 1. 13 0.154
195 A 3 3 1. 13 0.231
196 A 3 3 1. 14 0.214
197 A 3 3 1. 18 0.167
198 A 1 1 1. 20 0.05
199 A 1 1 1. 9 0.111
200 A 3 2 1. 65 0.031
201 A 5 4 1. 68 0.059
202 A 5 2 1. 21 0.095
203 A 6 6 1. 21 0.286
204 A 4 3 1. 23 0.13
205 A 2 2 1. 16 0.125
206 A 3 3 1. 25 0.12
207 A 2 2 1. 24 0.083
208 A 2 2 1. 29 0.069
209 A 1 1 1. 18 0.056
210 A 1 1 1. 23 0.043
211 A 3 3 1. 24 0.125
212 A 3 3 1. 22 0.136
213 A 3 3 1. 26 0.115
214 A 3 3 1. 31 0.097
215 A 3 3 1. 16 0.188
216 A 1 1 1. 8 0.125
217 A 2 2 1. 6 0.333
218 A 1 1 1. 20 0.05
219 A 3 2 1. 13 0.154
220 A 2 2 1. 13 0.154
221 A 3 3 1. 9 0.333
222 A 2 2 1. 13 0.154
223 A 2 1 1. 11 0.091
224 A 5 5 1. 13 0.385
225 A 2 2 1. 4 0.5
226 A 2 2 1. 4 0.5
227 A 1 1 1. 4 0.25
228 A 1 1 1. 28 0.036
229 A 4 2 1. 11 0.182
230 A 3 3 1. 4 0.75
231 A 3 3 1. 4 0.75
232 A 3 3 1. 8 0.375
233 A 3 2 1. 7 0.286
234 A 3 2 1. 7 0.286
235 A 1 1 1. 8 0.125
236 A 1 1 1. 10 0.1
237 A 1 1 1. 8 0.125
238 A 1 1 1. 10 0.1
239 A 3 3 1. 17 0.176
240 A 4 3 1. 13 0.231
241 A 2 2 1. 11 0.182
242 A 4 3 1. 13 0.231
243 A 3 3 1. 8 0.375
244 A 1 1 1. 2 0.5
245 A 3 2 1. 4 0.5
246 A 1 1 1. 2 0.5
247 A 1 1 1. 2 0.5
248 A 1 1 1. 3 0.333
249 A 4 3 1. 12 0.25
250 A 2 1 1. 13 0.077
251 A 3 3 1. 14 0.214
252 A 14 8 1. 12 0.667
253 A 4 3 1. 7 0.429
254 A 1 1 1. 5 0.2
255 A 6 6 1. 9 0.667
256 A 2 2 1. 9 0.222
257 A 10 3 1. 15 0.2
258 A 6 2 1. 11 0.182
259 A 6 6 1. 7 0.857
260 A 1 1 1. 9 0.111
261 A 2 2 1. 9 0.222
262 A 2 1 1. 7 0.143
263 A 2 2 1. 2 1.
264 A 4 3 1. 6 0.5
265 A 4 2 1. 17 0.118
266 A 2 2 1. 4 0.5
267 A 2 1 1. 19 0.053
268 A 1 1 1. 11 0.091
269 A 1 1 1. 9 0.111
270 A 2 2 1. 12 0.167
271 A 3 2 1. 24 0.083
272 A 2 1 1. 29 0.034
273 A 0 0 0. 0 0.
274 F 0 0 N/A 0 N/A
275 A 4 3 1. 21 0.143
276 A 1 1 1. 2 0.5
277 A 1 1 1. 4 0.25
278 F 0 0 N/A 0 N/A
279 F 0 0 N/A 0 N/A
280 A 1 1 1. 85 0.012
281 A 0 0 0. 0 0.
282 A 20 8 1. 107 0.075
283 A 2 2 1. 7 0.286
284 F 0 0 N/A 0 N/A

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