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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 F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 85 136 0 1 0 113 82
normalized size 1 1. 0.83 1.33 0. 0.01 0. 1.11 0.8
time (sec) N/A 0.222 0.243 0.013 0. 0.37 0. 0.285 21.507
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 304 491 0 1 0 0 76
normalized size 1 1. 3.71 5.99 0. 0.01 0. 0. 0.93
time (sec) N/A 0.244 0.678 0.062 0. 0.456 0. 0. 25.074
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 249 307 0 1 0 0 61
normalized size 1 1. 3.77 4.65 0. 0.02 0. 0. 0.92
time (sec) N/A 0.168 0.473 0.038 0. 0.358 0. 0. 20.152
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 129 129 339 829 0 1 0 0 114
normalized size 1 1. 2.63 6.43 0. 0.01 0. 0. 0.88
time (sec) N/A 0.398 0.553 0.039 0. 0.591 0. 0. 73.181
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F A F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 224 224 486 1884 0 1 0 0 0
normalized size 1 1. 2.17 8.41 0. 0. 0. 0. 0.
time (sec) N/A 0.971 1.119 0.037 0. 1.792 0. 0. 0.
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F A F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 328 328 901 3695 0 1 0 0 0
normalized size 1 1. 2.75 11.27 0. 0. 0. 0. 0.
time (sec) N/A 2.111 6.348 0.047 0. 11.338 0. 0. 0.
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 463 1377 0 1 0 0 150
normalized size 1 1. 2.86 8.5 0. 0.01 0. 0. 0.93
time (sec) N/A 0.685 1.143 0.049 0. 1.005 0. 0. 134.701
Problem 8 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 28 28 28 27 0 51 0 70 31
normalized size 1 1. 1. 0.96 0. 1.82 0. 2.5 1.11
time (sec) N/A 0.045 0.063 0.019 0. 0.274 0. 0.266 15.435
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 142 0 0 0 0 0 126
normalized size 1 1. 1.04 0. 0. 0. 0. 0. 0.93
time (sec) N/A 0.222 0.243 0.353 0. 0. 0. 0. 28.281
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 200 200 172 0 0 0 0 0 194
normalized size 1 1. 0.86 0. 0. 0. 0. 0. 0.97
time (sec) N/A 0.297 0.453 0.409 0. 0. 0. 0. 43.474
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 27 16 14 73 0 66 41
normalized size 1 1. 0.56 0.33 0.29 1.52 0. 1.38 0.85
time (sec) N/A 0.052 0.027 0.103 0.783 0.26 0. 0.267 11.459
Problem 12 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 70 70 72 84 0 348 0 193 60
normalized size 1 1. 1.03 1.2 0. 4.97 0. 2.76 0.86
time (sec) N/A 0.125 0.072 0.026 0. 0.273 0. 0.271 22.108
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F F F F F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 1077 1077 600 666 0 0 0 0 0
normalized size 1 1. 0.56 0.62 0. 0. 0. 0. 0.
time (sec) N/A 6.638 3.421 0.268 0. 0. 0. 0. 0.
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 1087 341 0 213 0 231 116
normalized size 1 1. 11.09 3.48 0. 2.17 0. 2.36 1.18
time (sec) N/A 0.489 6.275 0.04 0. 0.29 0. 0.273 72.318
Problem 15 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 68 68 68 55 73 1 65 73 0
normalized size 1 1. 1. 0.81 1.07 0.01 0.96 1.07 0.
time (sec) N/A 0.08 0.005 0.002 0.698 0.231 0.068 0.263 0.
Problem 16 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 56 56 56 45 59 1 53 59 0
normalized size 1 1. 1. 0.8 1.05 0.02 0.95 1.05 0.
time (sec) N/A 0.065 0.003 0.002 0.691 0.231 0.063 0.263 0.
Problem 17 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 35 46 1 41 46 0
normalized size 1 1. 1. 0.8 1.05 0.02 0.93 1.05 0.
time (sec) N/A 0.048 0.002 0.001 0.689 0.231 0.056 0.262 0.
Problem 18 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 30 30 30 25 32 1 26 32 0
normalized size 1 1. 1. 0.83 1.07 0.03 0.87 1.07 0.
time (sec) N/A 0.031 0.002 0.001 0.688 0.238 0.041 0.262 0.
Problem 19 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 42 42 42 34 45 55 49 45 0
normalized size 1 1. 1. 0.81 1.07 1.31 1.17 1.07 0.
time (sec) N/A 0.08 0.028 0.006 0.782 0.262 0.135 0.266 0.
Problem 20 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 43 34 49 69 42 49 37
normalized size 1 1. 1. 0.79 1.14 1.6 0.98 1.14 0.86
time (sec) N/A 0.051 0.031 0.009 0.788 0.258 0.174 0.265 9.294
Problem 21 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 64 64 53 47 76 108 63 62 56
normalized size 1 1. 0.83 0.73 1.19 1.69 0.98 0.97 0.88
time (sec) N/A 0.066 0.052 0.009 0.787 0.268 0.225 0.265 9.851
Problem 22 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 80 80 80 65 86 1 76 86 0
normalized size 1 1. 1. 0.81 1.08 0.01 0.95 1.08 0.
time (sec) N/A 0.098 0.005 0.002 0.697 0.251 0.08 0.263 0.
Problem 23 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 66 66 66 55 73 1 63 73 0
normalized size 1 1. 1. 0.83 1.11 0.02 0.95 1.11 0.
time (sec) N/A 0.081 0.005 0.002 0.694 0.231 0.073 0.262 0.
Problem 24 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 1 51 59 0
normalized size 1 1. 1. 0.83 1.09 0.02 0.94 1.09 0.
time (sec) N/A 0.072 0.004 0.001 0.694 0.235 0.063 0.264 0.
Problem 25 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 35 46 1 41 46 0
normalized size 1 1. 1. 0.76 1. 0.02 0.89 1. 0.
time (sec) N/A 0.047 0.003 0.001 0.699 0.234 0.054 0.263 0.
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 56 56 53 44 58 73 63 58 0
normalized size 1 1. 0.95 0.79 1.04 1.3 1.12 1.04 0.
time (sec) N/A 0.094 0.043 0.005 0.771 0.258 0.149 0.265 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 63 63 59 51 70 117 65 70 0
normalized size 1 1. 0.94 0.81 1.11 1.86 1.03 1.11 0.
time (sec) N/A 0.111 0.055 0.009 0.776 0.26 0.21 0.265 0.
Problem 28 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 64 64 53 47 76 109 63 62 0
normalized size 1 1. 0.83 0.73 1.19 1.7 0.98 0.97 0.
time (sec) N/A 0.094 0.051 0.008 0.772 0.258 0.243 0.266 0.
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 85 85 63 57 103 149 83 76 100
normalized size 1 1. 0.74 0.67 1.21 1.75 0.98 0.89 1.18
time (sec) N/A 0.112 0.086 0.011 0.768 0.266 0.291 0.263 49.803
Problem 30 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 96 96 96 75 100 1 92 100 0
normalized size 1 1. 1. 0.78 1.04 0.01 0.96 1.04 0.
time (sec) N/A 0.128 0.005 0.002 0.69 0.235 0.089 0.264 0.
Problem 31 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 82 82 82 65 86 1 78 86 0
normalized size 1 1. 1. 0.79 1.05 0.01 0.95 1.05 0.
time (sec) N/A 0.107 0.003 0.002 0.7 0.234 0.075 0.262 0.
Problem 32 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 68 68 68 55 73 1 65 73 0
normalized size 1 1. 1. 0.81 1.07 0.01 0.96 1.07 0.
time (sec) N/A 0.088 0.004 0.002 0.688 0.234 0.068 0.261 0.
Problem 33 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 56 56 56 45 59 1 53 59 0
normalized size 1 1. 1. 0.8 1.05 0.02 0.95 1.05 0.
time (sec) N/A 0.06 0.002 0.002 0.687 0.233 0.062 0.264 0.
Problem 34 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 70 70 63 54 72 86 76 72 0
normalized size 1 1. 0.9 0.77 1.03 1.23 1.09 1.03 0.
time (sec) N/A 0.103 0.04 0.005 0.769 0.263 0.158 0.266 0.
Problem 35 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 77 77 77 61 84 131 78 84 0
normalized size 1 1. 1. 0.79 1.09 1.7 1.01 1.09 0.
time (sec) N/A 0.125 0.054 0.009 0.771 0.266 0.22 0.265 0.
Problem 36 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 84 84 78 63 97 171 85 84 0
normalized size 1 1. 0.93 0.75 1.15 2.04 1.01 1. 0.
time (sec) N/A 0.149 0.073 0.01 0.778 0.266 0.283 0.267 0.
Problem 37 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 84 84 72 64 85 100 87 85 0
normalized size 1 1. 0.86 0.76 1.01 1.19 1.04 1.01 0.
time (sec) N/A 0.112 0.052 0.007 0.774 0.262 0.169 0.266 0.
Problem 38 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 70 70 63 54 72 86 73 72 0
normalized size 1 1. 0.9 0.77 1.03 1.23 1.04 1.03 0.
time (sec) N/A 0.097 0.044 0.005 0.773 0.261 0.157 0.265 0.
Problem 39 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 56 56 52 44 58 73 60 58 58
normalized size 1 1. 0.93 0.79 1.04 1.3 1.07 1.04 1.04
time (sec) N/A 0.088 0.032 0.005 0.766 0.271 0.154 0.265 27.191
Problem 40 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 42 42 42 34 45 55 46 45 0
normalized size 1 1. 1. 0.81 1.07 1.31 1.1 1.07 0.
time (sec) N/A 0.067 0.02 0.004 0.77 0.268 0.136 0.265 0.
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 73 73 73 60 80 105 83 80 71
normalized size 1 1. 1. 0.82 1.1 1.44 1.14 1.1 0.97
time (sec) N/A 0.115 0.066 0.005 0.772 0.27 0.32 0.265 27.302
Problem 42 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 94 94 94 77 105 194 102 105 90
normalized size 1 1. 1. 0.82 1.12 2.06 1.09 1.12 0.96
time (sec) N/A 0.186 0.16 0.008 0.77 0.273 0.427 0.266 50.34
Problem 43 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 115 115 104 89 132 275 119 119 105
normalized size 1 1. 0.9 0.77 1.15 2.39 1.03 1.03 0.91
time (sec) N/A 0.271 0.286 0.01 0.77 0.275 0.507 0.267 74.262
Problem 44 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 91 91 91 71 97 144 88 97 0
normalized size 1 1. 1. 0.78 1.07 1.58 0.97 1.07 0.
time (sec) N/A 0.142 0.108 0.011 0.779 0.266 0.228 0.265 0.
Problem 45 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 77 77 77 61 84 131 75 84 0
normalized size 1 1. 1. 0.79 1.09 1.7 0.97 1.09 0.
time (sec) N/A 0.125 0.052 0.009 0.771 0.265 0.22 0.266 0.
Problem 46 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 63 63 63 51 70 116 61 70 0
normalized size 1 1. 1. 0.81 1.11 1.84 0.97 1.11 0.
time (sec) N/A 0.11 0.059 0.009 0.77 0.261 0.209 0.265 0.
Problem 47 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 43 34 49 69 41 49 37
normalized size 1 1. 1. 0.79 1.14 1.6 0.95 1.14 0.86
time (sec) N/A 0.049 0.03 0.007 0.765 0.258 0.17 0.265 9.561
Problem 48 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 94 94 94 77 105 194 102 105 90
normalized size 1 1. 1. 0.82 1.12 2.06 1.09 1.12 0.96
time (sec) N/A 0.193 0.11 0.008 0.773 0.278 0.413 0.264 50.449
Problem 49 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 127 127 106 94 130 262 122 130 116
normalized size 1 1. 0.83 0.74 1.02 2.06 0.96 1.02 0.91
time (sec) N/A 0.279 0.101 0.013 0.771 0.272 0.493 0.266 75.791
Problem 50 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 148 148 136 106 159 356 143 149 143
normalized size 1 1. 0.92 0.72 1.07 2.41 0.97 1.01 0.97
time (sec) N/A 0.365 0.128 0.013 0.767 0.275 0.579 0.266 106.206
Problem 51 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 98 98 98 73 111 185 95 97 0
normalized size 1 1. 1. 0.74 1.13 1.89 0.97 0.99 0.
time (sec) N/A 0.173 0.071 0.012 0.774 0.264 0.285 0.266 0.
Problem 52 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 84 84 84 63 97 170 82 84 0
normalized size 1 1. 1. 0.75 1.15 2.02 0.98 1. 0.
time (sec) N/A 0.15 0.07 0.01 0.769 0.266 0.282 0.266 0.
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 64 64 51 47 76 109 61 62 71
normalized size 1 1. 0.8 0.73 1.19 1.7 0.95 0.97 1.11
time (sec) N/A 0.096 0.061 0.008 0.769 0.266 0.244 0.264 45.731
Problem 54 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 64 64 51 47 76 108 61 62 54
normalized size 1 1. 0.8 0.73 1.19 1.69 0.95 0.97 0.84
time (sec) N/A 0.065 0.053 0.008 0.763 0.263 0.233 0.262 10.737
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 115 115 99 89 132 275 122 119 107
normalized size 1 1. 0.86 0.77 1.15 2.39 1.06 1.03 0.93
time (sec) N/A 0.281 0.338 0.01 0.767 0.272 0.486 0.265 77.854
Problem 56 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 160 160 136 106 157 343 143 149 134
normalized size 1 1. 0.85 0.66 0.98 2.14 0.89 0.93 0.84
time (sec) N/A 0.366 0.204 0.013 0.765 0.272 0.596 0.267 101.504
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 181 181 151 118 186 437 163 157 172
normalized size 1 1. 0.83 0.65 1.03 2.41 0.9 0.87 0.95
time (sec) N/A 0.454 0.164 0.014 0.768 0.28 0.699 0.268 126.545
Problem 58 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 208 208 85 166 239 143 0 126 192
normalized size 1 1. 0.41 0.8 1.15 0.69 0. 0.61 0.92
time (sec) N/A 0.484 0.113 0.039 0.795 0.284 0. 0.27 102.482
Problem 59 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 166 166 75 132 193 130 0 112 153
normalized size 1 1. 0.45 0.8 1.16 0.78 0. 0.67 0.92
time (sec) N/A 0.311 0.09 0.01 0.778 0.282 0. 0.27 68.403
Problem 60 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 124 124 65 98 147 116 0 99 105
normalized size 1 1. 0.52 0.79 1.19 0.94 0. 0.8 0.85
time (sec) N/A 0.175 0.079 0.009 0.77 0.278 0. 0.271 23.165
Problem 61 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 82 82 55 64 101 103 0 85 73
normalized size 1 1. 0.67 0.78 1.23 1.26 0. 1.04 0.89
time (sec) N/A 0.085 0.051 0.008 0.772 0.278 0. 0.27 10.173
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 174 174 1133 2065 0 1397 0 0 204
normalized size 1 1. 6.51 11.87 0. 8.03 0. 0. 1.17
time (sec) N/A 0.862 6.412 0.187 0. 0.337 0. 0. 75.479
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 188 188 1148 16357 0 1465 0 0 219
normalized size 1 1. 6.11 87.01 0. 7.79 0. 0. 1.16
time (sec) N/A 0.808 6.547 0.248 0. 0.354 0. 0. 80.306
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 223 223 1170 43932 0 1646 0 0 252
normalized size 1 1. 5.25 197. 0. 7.38 0. 0. 1.13
time (sec) N/A 0.971 6.474 0.401 0. 0.374 0. 0. 104.314
Problem 65 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 231 231 95 185 278 157 0 139 226
normalized size 1 1. 0.41 0.8 1.2 0.68 0. 0.6 0.98
time (sec) N/A 0.539 0.132 0.046 0.779 0.286 0. 0.271 127.504
Problem 66 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 189 189 85 151 232 143 0 126 201
normalized size 1 1. 0.45 0.8 1.23 0.76 0. 0.67 1.06
time (sec) N/A 0.314 0.11 0.01 0.77 0.287 0. 0.269 96.967
Problem 67 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 147 147 75 117 186 130 0 112 126
normalized size 1 1. 0.51 0.8 1.27 0.88 0. 0.76 0.86
time (sec) N/A 0.198 0.092 0.009 0.775 0.282 0. 0.27 24.137
Problem 68 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 105 105 65 83 140 116 0 99 94
normalized size 1 1. 0.62 0.79 1.33 1.1 0. 0.94 0.9
time (sec) N/A 0.104 0.072 0.007 0.768 0.279 0. 0.269 11.09
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 197 197 1175 3460 0 1486 0 0 226
normalized size 1 1. 5.96 17.56 0. 7.54 0. 0. 1.15
time (sec) N/A 1.008 6.454 0.058 0. 0.347 0. 0. 101.444
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 232 232 1180 28185 0 1548 0 0 255
normalized size 1 1. 5.09 121.49 0. 6.67 0. 0. 1.1
time (sec) N/A 1.164 6.469 0.182 0. 0.372 0. 0. 127.233
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 223 223 1171 81415 0 1601 0 0 284
normalized size 1 1. 5.25 365.09 0. 7.18 0. 0. 1.27
time (sec) N/A 0.911 6.575 0.373 0. 0.367 0. 0. 92.946
Problem 72 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 254 254 105 204 317 170 0 153 246
normalized size 1 1. 0.41 0.8 1.25 0.67 0. 0.6 0.97
time (sec) N/A 0.604 0.153 0.054 0.8 0.293 0. 0.274 128.005
Problem 73 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 212 212 95 170 271 157 0 139 221
normalized size 1 1. 0.45 0.8 1.28 0.74 0. 0.66 1.04
time (sec) N/A 0.369 0.126 0.01 0.79 0.286 0. 0.273 96.831
Problem 74 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 170 170 85 136 225 143 0 126 146
normalized size 1 1. 0.5 0.8 1.32 0.84 0. 0.74 0.86
time (sec) N/A 0.233 0.111 0.01 0.783 0.278 0. 0.27 25.215
Problem 75 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 128 128 75 102 180 130 0 112 114
normalized size 1 1. 0.59 0.8 1.41 1.02 0. 0.88 0.89
time (sec) N/A 0.124 0.087 0.008 0.794 0.283 0. 0.273 11.886
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 222 222 1189 4860 0 1519 0 0 250
normalized size 1 1. 5.36 21.89 0. 6.84 0. 0. 1.13
time (sec) N/A 1.113 6.459 0.064 0. 0.417 0. 0. 129.99
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 255 255 1196 40028 0 1621 0 0 270
normalized size 1 1. 4.69 156.97 0. 6.36 0. 0. 1.06
time (sec) N/A 1.385 6.481 0.185 0. 0.384 0. 0. 152.489
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 281 281 1203 119321 0 1773 0 0 284
normalized size 1 1. 4.28 424.63 0. 6.31 0. 0. 1.01
time (sec) N/A 1.385 6.509 0.42 0. 0.48 0. 0. 155.682
Problem 79 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 185 185 75 147 200 130 0 112 153
normalized size 1 1. 0.41 0.79 1.08 0.7 0. 0.61 0.83
time (sec) N/A 0.513 0.113 0.025 0.784 0.285 0. 0.277 71.679
Problem 80 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 143 143 65 113 154 116 0 99 124
normalized size 1 1. 0.45 0.79 1.08 0.81 0. 0.69 0.87
time (sec) N/A 0.287 0.086 0.009 0.791 0.281 0. 0.275 45.547
Problem 81 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 101 101 55 79 108 103 0 85 85
normalized size 1 1. 0.54 0.78 1.07 1.02 0. 0.84 0.84
time (sec) N/A 0.16 0.063 0.01 0.778 0.275 0. 0.274 22.385
Problem 82 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 59 59 46 45 62 89 0 72 53
normalized size 1 1. 0.78 0.76 1.05 1.51 0. 1.22 0.9
time (sec) N/A 0.073 0.05 0.007 0.784 0.282 0. 0.272 9.67
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 148 148 959 684 0 1299 0 0 172
normalized size 1 1. 6.48 4.62 0. 8.78 0. 0. 1.16
time (sec) N/A 0.627 6.413 0.006 0. 0.33 0. 0. 55.024
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 188 188 1147 5225 0 1505 0 0 216
normalized size 1 1. 6.1 27.79 0. 8.01 0. 0. 1.15
time (sec) N/A 0.885 6.449 0.009 0. 0.362 0. 0. 77.524
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 223 223 1170 13040 0 1601 0 0 258
normalized size 1 1. 5.25 58.48 0. 7.18 0. 0. 1.16
time (sec) N/A 0.969 6.467 0.037 0. 0.372 0. 0. 104.21
Problem 86 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 166 166 95 166 200 159 0 111 175
normalized size 1 1. 0.57 1. 1.2 0.96 0. 0.67 1.05
time (sec) N/A 0.335 0.095 0.036 0.782 0.29 0. 0.273 97.021
Problem 87 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 124 124 65 132 154 146 0 97 144
normalized size 1 1. 0.52 1.06 1.24 1.18 0. 0.78 1.16
time (sec) N/A 0.218 0.097 0.01 0.78 0.285 0. 0.273 72.126
Problem 88 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 82 82 55 98 108 132 0 84 112
normalized size 1 1. 0.67 1.2 1.32 1.61 0. 1.02 1.37
time (sec) N/A 0.127 0.079 0.009 0.782 0.28 0. 0.272 46.323
Problem 89 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 45 45 45 64 62 119 0 72 51
normalized size 1 1. 1. 1.42 1.38 2.64 0. 1.6 1.13
time (sec) N/A 0.054 0.052 0.007 0.781 0.278 0. 0.272 9.599
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 176 176 1129 718 0 1463 0 0 207
normalized size 1 1. 6.41 4.08 0. 8.31 0. 0. 1.18
time (sec) N/A 0.833 6.394 0.037 0. 0.333 0. 0. 79.311
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 211 211 1170 5942 0 1588 0 0 248
normalized size 1 1. 5.55 28.16 0. 7.53 0. 0. 1.18
time (sec) N/A 0.975 6.453 0.096 0. 0.373 0. 0. 99.989
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 246 246 1191 18844 0 1777 0 0 286
normalized size 1 1. 4.84 76.6 0. 7.22 0. 0. 1.16
time (sec) N/A 1.083 6.501 0.195 0. 0.384 0. 0. 130.217
Problem 93 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 147 147 75 214 342 186 0 109 180
normalized size 1 1. 0.51 1.46 2.33 1.27 0. 0.74 1.22
time (sec) N/A 0.278 0.155 0.043 0.792 0.291 0. 0.274 98.319
Problem 94 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 105 105 65 180 296 173 0 97 144
normalized size 1 1. 0.62 1.71 2.82 1.65 0. 0.92 1.37
time (sec) N/A 0.176 0.12 0.01 0.78 0.288 0. 0.274 72.99
Problem 95 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 68 68 55 146 250 159 0 82 114
normalized size 1 1. 0.81 2.15 3.68 2.34 0. 1.21 1.68
time (sec) N/A 0.101 0.104 0.009 0.779 0.281 0. 0.274 44.887
Problem 96 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 47 47 33 30 80 69 0 39 37
normalized size 1 1. 0.7 0.64 1.7 1.47 0. 0.83 0.79
time (sec) N/A 0.041 0.029 0.005 0.7 0.275 0. 0.27 9.367
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 199 199 1176 751 0 1601 0 0 238
normalized size 1 1. 5.91 3.77 0. 8.05 0. 0. 1.2
time (sec) N/A 0.942 6.43 0.04 0. 0.359 0. 0. 105.101
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 234 234 1191 5975 0 1763 0 0 274
normalized size 1 1. 5.09 25.53 0. 7.53 0. 0. 1.17
time (sec) N/A 1.097 6.454 0.097 0. 0.365 0. 0. 130.288
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 269 269 1218 18877 0 1871 0 0 308
normalized size 1 1. 4.53 70.17 0. 6.96 0. 0. 1.14
time (sec) N/A 1.232 6.484 0.203 0. 0.396 0. 0. 152.126
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 436 436 456 1429 0 1 0 861 0
normalized size 1 1. 1.05 3.28 0. 0. 0. 1.97 0.
time (sec) N/A 1.497 1.194 0.027 0. 0.564 0. 0.28 0.
Problem 101 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 175 175 171 453 0 1 0 286 160
normalized size 1 1. 0.98 2.59 0. 0.01 0. 1.63 0.91
time (sec) N/A 0.338 0.296 0.009 0. 0.307 0. 0.278 20.416
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 431 431 699 6019 0 0 0 0 420
normalized size 1 1. 1.62 13.97 0. 0. 0. 0. 0.97
time (sec) N/A 2.379 5.283 0.091 0. 0. 0. 0. 157.729
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) A F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 488 488 798 22287 0 0 0 4 0
normalized size 1 1. 1.64 45.67 0. 0. 0. 0.01 0.
time (sec) N/A 7.222 3.044 0.059 0. 0. 0. 0.799 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 564 564 766 2458 0 1 0 1 0
normalized size 1 1. 1.36 4.36 0. 0. 0. 0. 0.
time (sec) N/A 2.015 3.713 0.031 0. 1.156 0. 0.284 0.
Problem 105 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 236 236 290 862 0 1 0 563 223
normalized size 1 1. 1.23 3.65 0. 0. 0. 2.39 0.94
time (sec) N/A 0.497 0.658 0.011 0. 0.374 0. 0.28 30.602
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F(-2) F(-1) F(-1) F(-2) F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 679 678 1934 22523 0 0 0 0 0
normalized size 1 1. 2.85 33.17 0. 0. 0. 0. 0.
time (sec) N/A 18.25 6.264 0.045 0. 0. 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F(-1) F(-1) F(-2) F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 704 704 1844 72576 0 0 0 0 0
normalized size 1 1. 2.62 103.09 0. 0. 0. 0. 0.
time (sec) N/A 22.408 6.465 0.069 0. 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F(-1) F(-1) A F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 671 669 1621 178044 0 0 0 4 0
normalized size 1 1. 2.42 265.34 0. 0. 0. 0.01 0.
time (sec) N/A 17.629 6.666 0.121 0. 0. 0. 0.743 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 717 717 615 1930 0 1 0 1112 0
normalized size 1 1. 0.86 2.69 0. 0. 0. 1.55 0.
time (sec) N/A 6.354 1.261 0.033 0. 1.453 0. 0.293 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 316 316 251 706 0 1 0 410 0
normalized size 1 1. 0.79 2.23 0. 0. 0. 1.3 0.
time (sec) N/A 1.19 0.443 0.019 0. 0.845 0. 0.285 0.
Problem 111 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 116 116 95 185 0 1 0 132 97
normalized size 1 1. 0.82 1.59 0. 0.01 0. 1.14 0.84
time (sec) N/A 0.215 0.147 0.009 0. 0.571 0. 0.282 15.755
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 374 374 633 761 0 15237 0 0 357
normalized size 1 1. 1.69 2.03 0. 40.74 0. 0. 0.95
time (sec) N/A 1.369 5.146 0.037 0. 6.721 0. 0. 103.052
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F(-1) F(-1) A F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 789 787 1836 3858 0 0 0 4 0
normalized size 1 1. 2.33 4.89 0. 0. 0. 0.01 0.
time (sec) N/A 16.704 6.671 0.044 0. 0. 0. 0.738 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 649 649 745 2827 0 1 0 1 0
normalized size 1 1. 1.15 4.36 0. 0. 0. 0. 0.
time (sec) N/A 4.14 4.233 0.037 0. 1.437 0. 0.287 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 309 309 288 1011 0 1 0 549 0
normalized size 1 1. 0.93 3.27 0. 0. 0. 1.78 0.
time (sec) N/A 0.87 0.645 0.019 0. 0.954 0. 0.288 0.
Problem 116 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 111 111 113 249 0 1 0 165 105
normalized size 1 1. 1.02 2.24 0. 0.01 0. 1.49 0.95
time (sec) N/A 0.165 0.324 0.008 0. 0.576 0. 0.285 15.482
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 666 666 906 3889 0 0 0 0 0
normalized size 1 1. 1.36 5.84 0. 0. 0. 0. 0.
time (sec) N/A 4.631 4.557 0.039 0. 0. 0. 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 891 891 872 4635 0 1 0 1 0
normalized size 1 1. 0.98 5.2 0. 0. 0. 0. 0.
time (sec) N/A 5.044 4.886 0.045 0. 1.432 0. 0.288 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 444 444 387 1786 0 1 0 792 282
normalized size 1 1. 0.87 4.02 0. 0. 0. 1.78 0.64
time (sec) N/A 0.988 1.912 0.02 0. 0.835 0. 0.29 151.808
Problem 120 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 131 131 147 185 0 386 0 356 131
normalized size 1 1. 1.12 1.41 0. 2.95 0. 2.72 1.
time (sec) N/A 0.184 0.254 0.009 0. 0.663 0. 0.277 20.914
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 193 144 0 207 0 277 48
normalized size 1 1. 3.78 2.82 0. 4.06 0. 5.43 0.94
time (sec) N/A 0.165 0.051 0.028 0. 0.283 0. 0.281 50.391
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 1432 1432 670 928 0 0 0 0 0
normalized size 1 1. 0.47 0.65 0. 0. 0. 0. 0.
time (sec) N/A 13.044 5.027 0.331 0. 0. 0. 0. 0.
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F F A
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 710 652 390 420 0 0 0 0 462
normalized size 1 0.92 0.55 0.59 0. 0. 0. 0. 0.65
time (sec) N/A 1.626 1.129 0.776 0. 0. 0. 0. 85.439

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 [14] had the largest ratio of [ 0.4444 ]

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 4 4 1. 29 0.138
2 A 2 2 1. 31 0.065
3 A 2 2 1. 27 0.074
4 A 4 4 1. 27 0.148
5 A 5 5 1. 27 0.185
6 A 6 5 1. 27 0.185
7 A 4 4 1. 31 0.129
8 A 2 2 1. 23 0.087
9 A 2 2 1. 31 0.065
10 A 2 2 1. 34 0.059
11 A 3 3 1. 22 0.136
12 A 6 5 1. 18 0.278
13 A 3 3 1. 26 0.115
14 A 16 12 1. 27 0.444
15 A 2 1 1. 23 0.043
16 A 2 1 1. 23 0.043
17 A 2 1 1. 23 0.043
18 A 2 1 1. 21 0.048
19 A 6 5 1. 23 0.217
20 A 4 4 1. 23 0.174
21 A 5 5 1. 23 0.217
22 A 2 1 1. 25 0.04
23 A 2 1 1. 25 0.04
24 A 2 1 1. 25 0.04
25 A 2 1 1. 23 0.043
26 A 6 5 1. 25 0.2
27 A 7 6 1. 25 0.24
28 A 5 4 1. 25 0.16
29 A 6 5 1. 25 0.2
30 A 2 1 1. 25 0.04
31 A 2 1 1. 25 0.04
32 A 2 1 1. 25 0.04
33 A 2 1 1. 23 0.043
34 A 6 5 1. 25 0.2
35 A 7 6 1. 25 0.24
36 A 8 6 1. 25 0.24
37 A 6 5 1. 25 0.2
38 A 6 5 1. 25 0.2
39 A 6 5 1. 25 0.2
40 A 6 5 1. 23 0.217
41 A 9 5 1. 25 0.2
42 A 10 6 1. 25 0.24
43 A 11 7 1. 25 0.28
44 A 7 6 1. 25 0.24
45 A 7 6 1. 25 0.24
46 A 7 6 1. 25 0.24
47 A 4 4 1. 23 0.174
48 A 10 6 1. 25 0.24
49 A 11 7 1. 25 0.28
50 A 12 7 1. 25 0.28
51 A 8 6 1. 25 0.24
52 A 8 6 1. 25 0.24
53 A 5 4 1. 25 0.16
54 A 5 5 1. 23 0.217
55 A 11 7 1. 25 0.28
56 A 12 7 1. 25 0.28
57 A 13 7 1. 25 0.28
58 A 11 5 1. 27 0.185
59 A 9 5 1. 27 0.185
60 A 7 5 1. 27 0.185
61 A 5 5 1. 25 0.2
62 A 8 7 1. 27 0.259
63 A 6 5 1. 27 0.185
64 A 7 6 1. 27 0.222
65 A 12 5 1. 27 0.185
66 A 10 5 1. 27 0.185
67 A 8 5 1. 27 0.185
68 A 6 5 1. 25 0.2
69 A 9 8 1. 27 0.296
70 A 10 9 1. 27 0.333
71 A 7 6 1. 27 0.222
72 A 13 5 1. 27 0.185
73 A 11 5 1. 27 0.185
74 A 9 5 1. 27 0.185
75 A 7 5 1. 25 0.2
76 A 10 9 1. 27 0.333
77 A 11 9 1. 27 0.333
78 A 11 10 1. 27 0.37
79 A 10 4 1. 27 0.148
80 A 8 4 1. 27 0.148
81 A 6 4 1. 27 0.148
82 A 4 4 1. 25 0.16
83 A 5 4 1. 27 0.148
84 A 6 5 1. 27 0.185
85 A 7 6 1. 27 0.222
86 A 9 5 1. 27 0.185
87 A 7 5 1. 27 0.185
88 A 5 5 1. 27 0.185
89 A 4 4 1. 25 0.16
90 A 6 5 1. 27 0.185
91 A 7 6 1. 27 0.222
92 A 8 6 1. 27 0.222
93 A 8 5 1. 27 0.185
94 A 6 5 1. 27 0.185
95 A 5 4 1. 27 0.148
96 A 3 3 1. 25 0.12
97 A 7 6 1. 27 0.222
98 A 8 6 1. 27 0.222
99 A 9 6 1. 27 0.222
100 A 7 5 1. 27 0.185
101 A 5 5 1. 25 0.2
102 A 8 5 1. 27 0.185
103 A 6 4 1. 27 0.148
104 A 8 5 1. 27 0.185
105 A 6 5 1. 25 0.2
106 A 9 6 1. 27 0.222
107 A 10 7 1. 27 0.259
108 A 7 5 1. 27 0.185
109 A 8 4 1. 27 0.148
110 A 6 4 1. 27 0.148
111 A 4 4 1. 25 0.16
112 A 5 3 1. 27 0.111
113 A 6 4 1. 27 0.148
114 A 7 5 1. 27 0.185
115 A 5 5 1. 27 0.185
116 A 4 4 1. 25 0.16
117 A 6 4 1. 27 0.148
118 A 6 5 1. 27 0.185
119 A 5 4 1. 27 0.148
120 A 3 3 1. 25 0.12
121 A 5 4 1. 27 0.148
122 A 3 3 1. 29 0.103
123 A 3 3 0.92 29 0.103

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