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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 147 147 158 173 0 1 0 178 139
normalized size 1 1. 1.07 1.18 0. 0.01 0. 1.21 0.95
time (sec) N/A 0.129 0.217 0.007 0. 0.243 0. 0.226 16.086
Problem 2 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 121 121 117 91 176 494 0 0 104
normalized size 1 1. 0.97 0.75 1.45 4.08 0. 0. 0.86
time (sec) N/A 0.072 0.116 0.029 0.79 0.226 0. 0. 4.326
Problem 3 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 95 95 86 71 139 386 0 0 80
normalized size 1 1. 0.91 0.75 1.46 4.06 0. 0. 0.84
time (sec) N/A 0.053 0.096 0.01 0.783 0.235 0. 0. 3.273
Problem 4 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 69 69 83 51 103 278 0 0 56
normalized size 1 1. 1.2 0.74 1.49 4.03 0. 0. 0.81
time (sec) N/A 0.037 0.073 0.01 0.793 0.219 0. 0. 2.431
Problem 5 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 43 43 62 31 66 170 0 0 32
normalized size 1 1. 1.44 0.72 1.53 3.95 0. 0. 0.74
time (sec) N/A 0.025 0.054 0.01 0.807 0.218 0. 0. 1.829
Problem 6 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 101 101 102 82 158 92 0 77 90
normalized size 1 1. 1.01 0.81 1.56 0.91 0. 0.76 0.89
time (sec) N/A 0.064 0.11 0.005 0.79 0.22 0. 0.215 3.579
Problem 7 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 79 79 92 64 122 78 0 63 70
normalized size 1 1. 1.16 0.81 1.54 0.99 0. 0.8 0.89
time (sec) N/A 0.047 0.061 0.006 0.798 0.216 0. 0.214 2.818
Problem 8 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 57 57 74 46 85 65 0 50 49
normalized size 1 1. 1.3 0.81 1.49 1.14 0. 0.88 0.86
time (sec) N/A 0.033 0.071 0.004 0.794 0.21 0. 0.216 2.184
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 72 28 49 51 0 36 29
normalized size 1 1. 2.06 0.8 1.4 1.46 0. 1.03 0.83
time (sec) N/A 0.023 0.033 0.004 0.804 0.212 0. 0.211 1.726
Problem 10 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 35 35 45 28 49 47 0 34 26
normalized size 1 1. 1.29 0.8 1.4 1.34 0. 0.97 0.74
time (sec) N/A 0.024 0.043 0.005 0.799 0.213 0. 0.209 1.689
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 72 28 49 51 0 36 29
normalized size 1 1. 2.06 0.8 1.4 1.46 0. 1.03 0.83
time (sec) N/A 0.024 0.039 0.005 0.852 0.211 0. 0.211 1.729
Problem 12 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 51 51 63 42 74 58 0 47 41
normalized size 1 1. 1.24 0.82 1.45 1.14 0. 0.92 0.8
time (sec) N/A 0.027 0.069 0.005 0.795 0.231 0. 0.213 1.894
Problem 13 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 35 35 40 33 55 144 0 45 31
normalized size 1 1. 1.14 0.94 1.57 4.11 0. 1.29 0.89
time (sec) N/A 0.02 0.043 0.005 0.75 0.232 0. 0.211 1.478
Problem 14 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 37 37 44 33 58 144 0 45 32
normalized size 1 1. 1.19 0.89 1.57 3.89 0. 1.22 0.86
time (sec) N/A 0.02 0.044 0.005 0.727 0.215 0. 0.211 1.488
Problem 15 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 39 39 46 33 58 163 0 50 29
normalized size 1 1. 1.18 0.85 1.49 4.18 0. 1.28 0.74
time (sec) N/A 0.02 0.045 0.005 0.716 0.216 0. 0.211 1.482
Problem 16 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 83 83 70 75 150 127 0 100 82
normalized size 1 1. 0.84 0.9 1.81 1.53 0. 1.2 0.99
time (sec) N/A 0.052 0.066 0.006 0.739 0.217 0. 0.222 4.947
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 50 10 28 26 0 0 8
normalized size 1 1. 3.12 0.62 1.75 1.62 0. 0. 0.5
time (sec) N/A 0.016 0.018 0.01 0.792 0.213 0. 0. 1.361
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 24 21 38 42 0 0 20
normalized size 1 1. 0.92 0.81 1.46 1.62 0. 0. 0.77
time (sec) N/A 0.01 0.015 0.01 0.711 0.212 0. 0. 1.279
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 36 42 74 127 0 0 42
normalized size 1 1. 0.68 0.79 1.4 2.4 0. 0. 0.79
time (sec) N/A 0.022 0.024 0.01 0.694 0.223 0. 0. 1.841
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 48 62 111 197 0 0 65
normalized size 1 1. 0.61 0.78 1.41 2.49 0. 0. 0.82
time (sec) N/A 0.035 0.032 0.012 0.695 0.225 0. 0. 2.58
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 45 9 11 26 0 11 8
normalized size 1 1. 3.75 0.75 0.92 2.17 0. 0.92 0.67
time (sec) N/A 0.014 0.016 0.005 0.778 0.216 0. 0.214 1.353
Problem 22 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 21 25 38 24 0 39 19
normalized size 1 1. 0.95 1.14 1.73 1.09 0. 1.77 0.86
time (sec) N/A 0.01 0.014 0.005 0.698 0.221 0. 0.217 1.182
Problem 23 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 31 35 74 53 0 53 37
normalized size 1 1. 0.69 0.78 1.64 1.18 0. 1.18 0.82
time (sec) N/A 0.02 0.023 0.004 0.69 0.216 0. 0.219 1.616
Problem 24 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 67 67 51 45 111 76 0 66 56
normalized size 1 1. 0.76 0.67 1.66 1.13 0. 0.99 0.84
time (sec) N/A 0.033 0.032 0.005 0.704 0.226 0. 0.221 2.153
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 58 35 0 36 0 20 8
normalized size 1 1. 4.83 2.92 0. 3. 0. 1.67 0.67
time (sec) N/A 0.019 0.032 0.009 0. 0.216 0. 0.221 3.317
Problem 26 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 24 24 45 37 0 36 0 49 20
normalized size 1 1. 1.88 1.54 0. 1.5 0. 2.04 0.83
time (sec) N/A 0.02 0.039 0.004 0. 0.212 0. 0.222 2.541
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 38 7 11 24 0 8 5
normalized size 1 1. 3.8 0.7 1.1 2.4 0. 0.8 0.5
time (sec) N/A 0.015 0.014 0.005 0.782 0.22 0. 0.213 1.342
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 33 14 23 23 0 24 14
normalized size 1 1. 2.06 0.88 1.44 1.44 0. 1.5 0.88
time (sec) N/A 0.011 0.013 0.004 0.728 0.212 0. 0.212 1.191
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 37 14 23 23 0 24 14
normalized size 1 1. 2.31 0.88 1.44 1.44 0. 1.5 0.88
time (sec) N/A 0.011 0.014 0.005 0.704 0.212 0. 0.213 1.186
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 448 448 94 0 0 0 0 0 398
normalized size 1 1. 0.21 0. 0. 0. 0. 0. 0.89
time (sec) N/A 1.338 0.084 0.057 0. 0. 0. 0. 41.363
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 387 387 70 0 0 0 0 0 332
normalized size 1 1. 0.18 0. 0. 0. 0. 0. 0.86
time (sec) N/A 0.932 0.057 0.044 0. 0. 0. 0. 32.401
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 322 322 44 0 0 0 0 0 264
normalized size 1 1. 0.14 0. 0. 0. 0. 0. 0.82
time (sec) N/A 0.788 0.023 0.055 0. 0. 0. 0. 23.123
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 384 384 57 0 0 0 0 0 328
normalized size 1 1. 0.15 0. 0. 0. 0. 0. 0.85
time (sec) N/A 0.922 0.049 0.084 0. 0. 0. 0. 32.462
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 448 448 90 0 0 0 0 0 400
normalized size 1 1. 0.2 0. 0. 0. 0. 0. 0.89
time (sec) N/A 1.063 0.097 0.142 0. 0. 0. 0. 41.483
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 842 842 94 0 0 0 0 0 731
normalized size 1 1. 0.11 0. 0. 0. 0. 0. 0.87
time (sec) N/A 2.02 0.07 0.058 0. 0. 0. 0. 82.292
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 781 781 70 0 0 0 0 0 663
normalized size 1 1. 0.09 0. 0. 0. 0. 0. 0.85
time (sec) N/A 1.829 0.053 0.054 0. 0. 0. 0. 68.578
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 715 715 46 0 0 0 0 0 595
normalized size 1 1. 0.06 0. 0. 0. 0. 0. 0.83
time (sec) N/A 1.665 0.026 0.047 0. 0. 0. 0. 55.449
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 773 773 57 0 0 0 0 0 660
normalized size 1 1. 0.07 0. 0. 0. 0. 0. 0.85
time (sec) N/A 1.835 0.046 0.087 0. 0. 0. 0. 68.937
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 838 838 90 0 0 0 0 0 728
normalized size 1 1. 0.11 0. 0. 0. 0. 0. 0.87
time (sec) N/A 1.994 0.099 0.144 0. 0. 0. 0. 82.681
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 94 0 0 0 0 0 109
normalized size 1 1. 0.79 0. 0. 0. 0. 0. 0.92
time (sec) N/A 0.111 0.07 0.063 0. 0. 0. 0. 17.234
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 70 0 0 0 0 0 80
normalized size 1 1. 0.78 0. 0. 0. 0. 0. 0.89
time (sec) N/A 0.078 0.064 0.056 0. 0. 0. 0. 14.028
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 70 0 0 0 0 0 78
normalized size 1 1. 0.78 0. 0. 0. 0. 0. 0.87
time (sec) N/A 0.075 0.052 0.049 0. 0. 0. 0. 13.896
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 46 0 0 0 0 0 51
normalized size 1 1. 0.79 0. 0. 0. 0. 0. 0.88
time (sec) N/A 0.051 0.029 0.047 0. 0. 0. 0. 11.858
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 44 0 0 0 0 0 53
normalized size 1 1. 0.75 0. 0. 0. 0. 0. 0.9
time (sec) N/A 0.05 0.022 0.058 0. 0. 0. 0. 11.931
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 59 0 0 0 0 0 75
normalized size 1 1. 0.71 0. 0. 0. 0. 0. 0.9
time (sec) N/A 0.073 0.053 0.09 0. 0. 0. 0. 13.592
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 90 0 0 0 0 0 109
normalized size 1 1. 0.78 0. 0. 0. 0. 0. 0.95
time (sec) N/A 0.101 0.105 0.153 0. 0. 0. 0. 16.242
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 146 146 114 0 0 0 0 0 139
normalized size 1 1. 0.78 0. 0. 0. 0. 0. 0.95
time (sec) N/A 0.13 0.144 0.1 0. 0. 0. 0. 19.614
Problem 48 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 55 55 45 0 0 0 0 0 42
normalized size 1 1. 0.82 0. 0. 0. 0. 0. 0.76
time (sec) N/A 0.032 0.041 0.044 0. 0. 0. 0. 2.753
Problem 49 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 51 51 51 44 58 1 49 58 0
normalized size 1 1. 1. 0.86 1.14 0.02 0.96 1.14 0.
time (sec) N/A 0.044 0.003 0.001 0.701 0.185 0.107 0.209 0.
Problem 50 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 35 35 35 32 42 1 32 42 0
normalized size 1 1. 1. 0.91 1.2 0.03 0.91 1.2 0.
time (sec) N/A 0.029 0.002 0.002 0.694 0.187 0.098 0.208 0.
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 25 25 25 22 28 1 22 28 0
normalized size 1 1. 1. 0.88 1.12 0.04 0.88 1.12 0.
time (sec) N/A 0.019 0.002 0.002 0.704 0.191 0.088 0.21 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 12 12 12 11 14 1 8 14 0
normalized size 1 1. 1. 0.92 1.17 0.08 0.67 1.17 0.
time (sec) N/A 0.008 0. 0.001 0.698 0.19 0.067 0.209 0.
Problem 53 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 24 24 24 16 0 1 53 20 22
normalized size 1 1. 1. 0.67 0. 0.04 2.21 0.83 0.92
time (sec) N/A 0.019 0.008 0.005 0. 0.221 0.29 0.209 2.447
Problem 54 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 45 45 45 36 0 1 78 47 36
normalized size 1 1. 1. 0.8 0. 0.02 1.73 1.04 0.8
time (sec) N/A 0.029 0.045 0.002 0. 0.229 1.41 0.21 3.773
Problem 55 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 62 62 55 51 0 1 105 61 54
normalized size 1 1. 0.89 0.82 0. 0.02 1.69 0.98 0.87
time (sec) N/A 0.041 0.088 0.002 0. 0.23 1.834 0.209 5.708
Problem 56 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 84 84 71 66 0 1 97 85 78
normalized size 1 1. 0.85 0.79 0. 0.01 1.15 1.01 0.93
time (sec) N/A 0.054 0.081 0.006 0. 0.249 14.343 0.215 5.836
Problem 57 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 65 65 62 51 0 1 70 66 60
normalized size 1 1. 0.95 0.78 0. 0.02 1.08 1.02 0.92
time (sec) N/A 0.037 0.058 0.004 0. 0.24 9.943 0.215 4.418
Problem 58 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 46 46 49 36 0 1 41 50 39
normalized size 1 1. 1.07 0.78 0. 0.02 0.89 1.09 0.85
time (sec) N/A 0.024 0.024 0.003 0. 0.236 6.226 0.211 3.174
Problem 59 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 25 25 25 21 0 1 17 31 22
normalized size 1 1. 1. 0.84 0. 0.04 0.68 1.24 0.88
time (sec) N/A 0.015 0.01 0.003 0. 0.227 3.573 0.215 2.432
Problem 60 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 31 17 19 12
normalized size 1 1. 1. 0.94 1.19 1.94 1.06 1.19 0.75
time (sec) N/A 0.008 0.012 0.004 0.706 0.215 1.803 0.215 1.274
Problem 61 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 29 26 42 63 95 36 32
normalized size 1 1. 0.74 0.67 1.08 1.62 2.44 0.92 0.82
time (sec) N/A 0.021 0.021 0.004 0.702 0.225 2.666 0.215 2.014
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 58 58 40 37 62 93 413 55 51
normalized size 1 1. 0.69 0.64 1.07 1.6 7.12 0.95 0.88
time (sec) N/A 0.03 0.027 0.004 0.708 0.235 5.259 0.217 3.327
Problem 63 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 77 77 51 48 82 123 1265 74 70
normalized size 1 1. 0.66 0.62 1.06 1.6 16.43 0.96 0.91
time (sec) N/A 0.043 0.032 0.006 0.699 0.252 9.963 0.217 5.014
Problem 64 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 23 23 20 35 41 26 0 69 19
normalized size 1 1. 0.87 1.52 1.78 1.13 0. 3. 0.83
time (sec) N/A 0.01 0.016 0.004 0.804 0.209 0. 0.209 1.22
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 23 23 25 25 41 12 0 35 19
normalized size 1 1. 1.09 1.09 1.78 0.52 0. 1.52 0.83
time (sec) N/A 0.01 0.009 0.004 0.769 0.219 0. 0.21 1.246
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 29 29 26 23 8 11 0 34 26
normalized size 1 1. 0.9 0.79 0.28 0.38 0. 1.17 0.9
time (sec) N/A 0.014 0.01 0.007 0.791 0.212 0. 0.212 1.546
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 25 25 20 17 12 19 0 4 20
normalized size 1 1. 0.8 0.68 0.48 0.76 0. 0.16 0.8
time (sec) N/A 0.01 0.01 0.005 0.787 0.221 0. 0.562 1.224
Problem 68 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 25 25 41 12 8 35 20
normalized size 1 1. 1.09 1.09 1.78 0.52 0.35 1.52 0.87
time (sec) N/A 0.01 0.02 0.005 0.799 0.216 0.105 0.211 1.401
Problem 69 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 26 23 8 11 7 20 27
normalized size 1 1. 0.9 0.79 0.28 0.38 0.24 0.69 0.93
time (sec) N/A 0.014 0.018 0.007 0.805 0.233 0.116 0.21 1.754
Problem 70 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 23 23 27 27 41 12 0 39 20
normalized size 1 1. 1.17 1.17 1.78 0.52 0. 1.7 0.87
time (sec) N/A 0.009 0.013 0.003 0.776 0.209 0. 0.21 1.458
Problem 71 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 29 29 28 25 8 8 0 35 27
normalized size 1 1. 0.97 0.86 0.28 0.28 0. 1.21 0.93
time (sec) N/A 0.014 0.012 0.005 0.806 0.221 0. 0.211 1.798
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 23 23 27 27 41 12 0 39 20
normalized size 1 1. 1.17 1.17 1.78 0.52 0. 1.7 0.87
time (sec) N/A 0.01 0.011 0.003 0.792 0.215 0. 0.209 1.395
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 29 29 28 25 8 8 0 35 27
normalized size 1 1. 0.97 0.86 0.28 0.28 0. 1.21 0.93
time (sec) N/A 0.017 0.007 0.003 0.796 0.216 0. 0.212 1.89
Problem 74 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 109 109 207 636 316 315 253 489 95
normalized size 1 1. 1.9 5.83 2.9 2.89 2.32 4.49 0.87
time (sec) N/A 0.302 0.055 0.007 0.721 0.22 0.433 0.209 48.389
Problem 75 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 109 109 207 636 316 317 250 489 95
normalized size 1 1. 1.9 5.83 2.9 2.91 2.29 4.49 0.87
time (sec) N/A 0.295 0.076 0.006 0.718 0.213 0.419 0.209 47.351
Problem 76 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 109 109 199 636 316 306 253 489 99
normalized size 1 1. 1.83 5.83 2.9 2.81 2.32 4.49 0.91
time (sec) N/A 0.289 0.052 0.006 0.732 0.212 0.431 0.209 47.709
Problem 77 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 109 109 207 636 316 317 248 489 97
normalized size 1 1. 1.9 5.83 2.9 2.91 2.28 4.49 0.89
time (sec) N/A 0.292 0.078 0.006 0.726 0.217 0.411 0.209 44.205
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 18 18 18 17 22 22 22 22 19
normalized size 1 1. 1. 0.94 1.22 1.22 1.22 1.22 1.06
time (sec) N/A 0.027 0.008 0.005 0.795 0.224 0.225 0.206 1.416
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 9 11 0 7 11 7
normalized size 1 1. 1. 0.75 0.92 0. 0.58 0.92 0.58
time (sec) N/A 0.017 0.023 0.018 0.792 0. 0.393 0.21 1.358
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 19 19 34 17 36 51 39 42 22
normalized size 1 1. 1.79 0.89 1.89 2.68 2.05 2.21 1.16
time (sec) N/A 0.036 0.035 0.002 0.82 0.22 0.22 0.211 1.437
Problem 81 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 14 18 18 10 20 10
normalized size 1 1. 1. 1.08 1.38 1.38 0.77 1.54 0.77
time (sec) N/A 0.012 0.005 0.007 0.739 0.214 0.19 0.208 1.513
Problem 82 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 20 14 23 14
normalized size 1 1. 1. 0.76 0.95 0.95 0.67 1.1 0.67
time (sec) N/A 0.014 0.005 0.008 0.728 0.213 0.212 0.21 1.655
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A B B B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 6 17 17 14 18 18 12 20 12
normalized size 1 2.83 2.83 2.33 3. 3. 2. 3.33 2.
time (sec) N/A 0.012 0.005 0.008 0.727 0.226 0.179 0.209 1.421
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 27 27 27 24 51 82 76 54 26
normalized size 1 1. 1. 0.89 1.89 3.04 2.81 2. 0.96
time (sec) N/A 0.04 0.014 0.005 0.742 0.244 0.526 0.21 3.156
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 27 27 29 26 53 81 76 61 26
normalized size 1 1. 1.07 0.96 1.96 3. 2.81 2.26 0.96
time (sec) N/A 0.041 0.014 0.004 0.734 0.219 0.566 0.211 3.085
Problem 86 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 31 31 31 28 36 46 87 36 24
normalized size 1 1. 1. 0.9 1.16 1.48 2.81 1.16 0.77
time (sec) N/A 0.046 0.014 0.004 0.728 0.23 0.442 0.208 2.863
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 27 27 29 26 53 81 76 61 26
normalized size 1 1. 1.07 0.96 1.96 3. 2.81 2.26 0.96
time (sec) N/A 0.039 0.014 0.006 0.716 0.224 0.584 0.209 2.923
Problem 88 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 38 38 38 35 0 1 124 46 34
normalized size 1 1. 1. 0.92 0. 0.03 3.26 1.21 0.89
time (sec) N/A 0.065 0.019 0.008 0. 0.217 0.553 0.209 4.595
Problem 89 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 34 35 0 1 100 41 27
normalized size 1 1. 0.97 1. 0. 0.03 2.86 1.17 0.77
time (sec) N/A 0.065 0.016 0.008 0. 0.218 0.578 0.208 7.517
Problem 90 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 32 32 41 31 0 115 102 74 27
normalized size 1 1. 1.28 0.97 0. 3.59 3.19 2.31 0.84
time (sec) N/A 0.051 0.018 0.005 0. 0.216 0.654 0.213 7.222
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 43 43 43 37 49 68 39 49 36
normalized size 1 1. 1. 0.86 1.14 1.58 0.91 1.14 0.84
time (sec) N/A 0.037 0.04 0.005 0.791 0.212 0.335 0.207 1.864
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 43 43 62 37 63 99 58 69 39
normalized size 1 1. 1.44 0.86 1.47 2.3 1.35 1.6 0.91
time (sec) N/A 0.04 0.054 0.003 0.785 0.215 0.325 0.208 1.865
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 34 34 33 32 46 72 29 49 29
normalized size 1 1. 0.97 0.94 1.35 2.12 0.85 1.44 0.85
time (sec) N/A 0.022 0.019 0.014 0.722 0.217 0.312 0.21 1.951
Problem 94 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 42 32 46 72 32 49 32
normalized size 1 1. 1. 0.76 1.1 1.71 0.76 1.17 0.76
time (sec) N/A 0.026 0.023 0.013 0.716 0.22 0.324 0.21 2.156
Problem 95 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 71 71 70 68 0 1 265 90 60
normalized size 1 1. 0.99 0.96 0. 0.01 3.73 1.27 0.85
time (sec) N/A 0.082 0.105 0.005 0. 0.232 2.781 0.208 7.53
Problem 96 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 72 72 72 86 0 1 228 101 58
normalized size 1 1. 1. 1.19 0. 0.01 3.17 1.4 0.81
time (sec) N/A 0.096 0.072 0.004 0. 0.225 2.589 0.209 11.565
Problem 97 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 69 69 78 84 0 216 218 122 60
normalized size 1 1. 1.13 1.22 0. 3.13 3.16 1.77 0.87
time (sec) N/A 0.07 0.11 0.004 0. 0.237 2.674 0.214 9.552
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 62 62 65 111 215 120 212 135 94
normalized size 1 1. 1.05 1.79 3.47 1.94 3.42 2.18 1.52
time (sec) N/A 0.268 0.154 0.044 0.828 0.244 2.99 0.222 80.535
Problem 99 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 58 34 31 88 85 56 76 49
normalized size 1 1.76 1.03 0.94 2.67 2.58 1.7 2.3 1.48
time (sec) N/A 0.074 0.056 0.013 0.703 0.235 0.806 0.218 4.474
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 31 58 32 31 82 80 56 73 49
normalized size 1 1.87 1.03 1. 2.65 2.58 1.81 2.35 1.58
time (sec) N/A 0.064 0.051 0.009 0.756 0.23 0.795 0.22 4.648
Problem 101 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 17 17 19 33 36 20 165 36 17
normalized size 1 1. 1.12 1.94 2.12 1.18 9.71 2.12 1.
time (sec) N/A 0.039 0.034 0.02 0.795 0.226 0.45 0.207 3.907
Problem 102 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 NO TBD TBD TBD TBD TBD TBD
size 23 23 56 39 45 28 70 45 17
normalized size 1 1. 2.43 1.7 1.96 1.22 3.04 1.96 0.74
time (sec) N/A 0.054 0.061 0.044 0.788 0.231 2.255 0.208 4.857
Problem 103 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 38 38 39 29 51 177 0 54 44
normalized size 1 1. 1.03 0.76 1.34 4.66 0. 1.42 1.16
time (sec) N/A 0.027 0.028 0.005 0.791 0.215 0. 0.21 2.024
Problem 104 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 30 30 30 25 51 53 0 32 44
normalized size 1 1. 1. 0.83 1.7 1.77 0. 1.07 1.47
time (sec) N/A 0.024 0.025 0.004 0.829 0.221 0. 0.209 1.936
Problem 105 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 49 50 70 177 0 55 44
normalized size 1 1. 1. 1.02 1.43 3.61 0. 1.12 0.9
time (sec) N/A 0.028 0.027 0.006 0.804 0.216 0. 0.209 1.983
Problem 106 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 46 35 62 85 0 72 53
normalized size 1 1. 1.02 0.78 1.38 1.89 0. 1.6 1.18
time (sec) N/A 0.036 0.03 0.003 0.816 0.23 0. 0.212 2.054
Problem 107 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 46 35 62 70 0 49 56
normalized size 1 1. 1.02 0.78 1.38 1.56 0. 1.09 1.24
time (sec) N/A 0.043 0.035 0.005 0.832 0.221 0. 0.21 2.027
Problem 108 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 62 62 55 50 78 85 0 73 53
normalized size 1 1. 0.89 0.81 1.26 1.37 0. 1.18 0.85
time (sec) N/A 0.034 0.046 0.004 0.847 0.223 0. 0.213 2.013
Problem 109 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 43 43 44 32 55 72 0 42 56
normalized size 1 1. 1.02 0.74 1.28 1.67 0. 0.98 1.3
time (sec) N/A 0.029 0.034 0.004 0.821 0.224 0. 0.21 2.079
Problem 110 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 53 50 78 86 0 73 54
normalized size 1 1. 0.9 0.85 1.32 1.46 0. 1.24 0.92
time (sec) N/A 0.032 0.038 0.005 0.826 0.227 0. 0.212 2.004
Problem 111 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 54 46 62 115 0 51 53
normalized size 1 1. 0.92 0.78 1.05 1.95 0. 0.86 0.9
time (sec) N/A 0.033 0.049 0.007 0.917 0.22 0. 0.211 2.008
Problem 112 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 62 62 55 50 78 88 0 73 54
normalized size 1 1. 0.89 0.81 1.26 1.42 0. 1.18 0.87
time (sec) N/A 0.033 0.047 0.005 0.833 0.224 0. 0.212 2.102
Problem 113 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 39 39 40 32 55 69 0 42 54
normalized size 1 1. 1.03 0.82 1.41 1.77 0. 1.08 1.38
time (sec) N/A 0.022 0.033 0.005 0.865 0.223 0. 0.21 2.061
Problem 114 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 14 14 14 9 11 27 0 27 22
normalized size 1 1. 1. 0.64 0.79 1.93 0. 1.93 1.57
time (sec) N/A 0.017 0.009 0.004 0.871 0.218 0. 0.212 1.508
Problem 115 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 10 10 14 7 11 28 0 8 26
normalized size 1 1. 1.4 0.7 1.1 2.8 0. 0.8 2.6
time (sec) N/A 0.015 0.01 0.003 0.805 0.229 0. 0.212 1.528
Problem 116 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 25 25 24 30 30 27 0 28 22
normalized size 1 1. 0.96 1.2 1.2 1.08 0. 1.12 0.88
time (sec) N/A 0.016 0.01 0.005 0.872 0.233 0. 0.212 1.486
Problem 117 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 18 18 18 15 22 55 0 45 32
normalized size 1 1. 1. 0.83 1.22 3.06 0. 2.5 1.78
time (sec) N/A 0.022 0.011 0.004 0.829 0.232 0. 0.214 1.481
Problem 118 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 19 19 19 15 22 38 0 22 34
normalized size 1 1. 1. 0.79 1.16 2. 0. 1.16 1.79
time (sec) N/A 0.026 0.016 0.004 0.884 0.233 0. 0.215 1.532
Problem 119 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 35 35 28 30 38 54 0 46 32
normalized size 1 1. 0.8 0.86 1.09 1.54 0. 1.31 0.91
time (sec) N/A 0.02 0.017 0.004 0.848 0.231 0. 0.216 1.49
Problem 120 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 17 17 17 12 15 38 0 15 34
normalized size 1 1. 1. 0.71 0.88 2.24 0. 0.88 2.
time (sec) N/A 0.017 0.01 0.005 0.848 0.22 0. 0.216 1.498
Problem 121 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 32 32 26 30 38 54 0 46 32
normalized size 1 1. 0.81 0.94 1.19 1.69 0. 1.44 1.
time (sec) N/A 0.02 0.01 0.004 0.834 0.223 0. 0.214 1.481
Problem 122 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 33 33 28 26 22 86 0 24 34
normalized size 1 1. 0.85 0.79 0.67 2.61 0. 0.73 1.03
time (sec) N/A 0.02 0.022 0.003 0.797 0.223 0. 0.215 1.486
Problem 123 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 35 35 28 30 38 54 0 46 32
normalized size 1 1. 0.8 0.86 1.09 1.54 0. 1.31 0.91
time (sec) N/A 0.02 0.016 0.003 0.813 0.223 0. 0.216 1.495
Problem 124 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 13 13 13 12 15 38 0 15 34
normalized size 1 1. 1. 0.92 1.15 2.92 0. 1.15 2.62
time (sec) N/A 0.011 0.01 0.004 0.789 0.223 0. 0.215 1.525
Problem 125 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 22 22 22 51 0 1 0 66 42
normalized size 1 1. 1. 2.32 0. 0.05 0. 3. 1.91
time (sec) N/A 0.029 0.045 0.015 0. 0.237 0. 0.233 6.632
Problem 126 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 23 23 23 44 0 1 0 72 44
normalized size 1 1. 1. 1.91 0. 0.04 0. 3.13 1.91
time (sec) N/A 0.028 0.045 0.018 0. 0.236 0. 0.229 6.409
Problem 127 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 20 20 20 44 0 1 0 72 44
normalized size 1 1. 1. 2.2 0. 0.05 0. 3.6 2.2
time (sec) N/A 0.025 0.042 0.016 0. 0.247 0. 0.23 6.575
Problem 128 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 19 19 19 24 35 42 0 23 17
normalized size 1 1. 1. 1.26 1.84 2.21 0. 1.21 0.89
time (sec) N/A 0.011 0.012 0.005 0.746 0.221 0. 0.213 1.191
Problem 129 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 23 23 23 28 41 42 0 23 19
normalized size 1 1. 1. 1.22 1.78 1.83 0. 1. 0.83
time (sec) N/A 0.01 0.015 0.004 0.763 0.21 0. 0.212 1.286
Problem 130 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 23 23 23 26 41 39 0 39 17
normalized size 1 1. 1. 1.13 1.78 1.7 0. 1.7 0.74
time (sec) N/A 0.019 0.022 0.005 0.78 0.22 0. 0.214 3.757
Problem 131 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 43 43 31 36 80 66 0 49 36
normalized size 1 1. 0.72 0.84 1.86 1.53 0. 1.14 0.84
time (sec) N/A 0.02 0.027 0.004 0.75 0.218 0. 0.216 1.683
Problem 132 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 122 122 126 0 0 0 0 0 105
normalized size 1 1. 1.03 0. 0. 0. 0. 0. 0.86
time (sec) N/A 0.087 0.155 0.157 0. 0. 0. 0. 4.819
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 37 37 93 0 0 0 0 0 27
normalized size 1 1. 2.51 0. 0. 0. 0. 0. 0.73
time (sec) N/A 0.037 0.11 0.26 0. 0. 0. 0. 2.114
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 32 32 94 0 0 0 0 0 26
normalized size 1 1. 2.94 0. 0. 0. 0. 0. 0.81
time (sec) N/A 0.033 0.146 0.231 0. 0. 0. 0. 1.917
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 37 37 93 0 0 0 0 0 27
normalized size 1 1. 2.51 0. 0. 0. 0. 0. 0.73
time (sec) N/A 0.036 0.109 0.184 0. 0. 0. 0. 1.984
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 21 21 92 0 0 0 0 0 17
normalized size 1 1. 4.38 0. 0. 0. 0. 0. 0.81
time (sec) N/A 0.023 0.101 0.228 0. 0. 0. 0. 1.73
Problem 137 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 54 54 48 0 0 0 0 0 44
normalized size 1 1. 0.89 0. 0. 0. 0. 0. 0.81
time (sec) N/A 0.028 0.029 0.068 0. 0. 0. 0. 1.935
Problem 138 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 17 0 26 20 22 12
normalized size 1 1. 0.94 0.94 0. 1.44 1.11 1.22 0.67
time (sec) N/A 0.008 0.008 0.003 0. 0.236 0.074 0.206 1.484
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 83 0 0 0 0 0 26
normalized size 1 1. 2.68 0. 0. 0. 0. 0. 0.84
time (sec) N/A 0.028 0.08 0.151 0. 0. 0. 0. 1.956
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 31 31 86 0 0 0 0 0 26
normalized size 1 1. 2.77 0. 0. 0. 0. 0. 0.84
time (sec) N/A 0.026 0.173 0.154 0. 0. 0. 0. 2.04
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 38 38 81 0 0 0 0 0 27
normalized size 1 1. 2.13 0. 0. 0. 0. 0. 0.71
time (sec) N/A 0.032 0.112 0.157 0. 0. 0. 0. 2.068
Problem 142 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 35 35 58 0 0 0 0 0 26
normalized size 1 1. 1.66 0. 0. 0. 0. 0. 0.74
time (sec) N/A 0.033 0.036 0.096 0. 0. 0. 0. 1.955
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 38 38 81 0 0 0 0 0 27
normalized size 1 1. 2.13 0. 0. 0. 0. 0. 0.71
time (sec) N/A 0.03 0.114 0.158 0. 0. 0. 0. 2.102

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 [35] had the largest ratio of [ 0.5385 ]

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 6 3 1. 13 0.231
2 A 6 3 1. 15 0.2
3 A 5 3 1. 15 0.2
4 A 4 3 1. 15 0.2
5 A 3 3 1. 15 0.2
6 A 6 3 1. 13 0.231
7 A 5 3 1. 13 0.231
8 A 4 3 1. 13 0.231
9 A 3 3 1. 13 0.231
10 A 3 3 1. 13 0.231
11 A 3 3 1. 13 0.231
12 A 4 3 1. 11 0.273
13 A 3 3 1. 11 0.273
14 A 3 3 1. 11 0.273
15 A 3 3 1. 11 0.273
16 A 3 2 1. 13 0.154
17 A 2 2 1. 15 0.133
18 A 1 1 1. 15 0.067
19 A 2 2 1. 15 0.133
20 A 3 2 1. 15 0.133
21 A 2 2 1. 13 0.154
22 A 1 1 1. 13 0.077
23 A 2 2 1. 13 0.154
24 A 3 2 1. 13 0.154
25 A 2 2 1. 16 0.125
26 A 2 2 1. 15 0.133
27 A 2 2 1. 13 0.154
28 A 2 2 1. 11 0.182
29 A 2 2 1. 11 0.182
30 A 6 5 1. 13 0.385
31 A 5 5 1. 13 0.385
32 A 4 4 1. 13 0.308
33 A 5 5 1. 13 0.385
34 A 6 5 1. 13 0.385
35 A 8 7 1. 13 0.538
36 A 7 7 1. 13 0.538
37 A 6 6 1. 13 0.462
38 A 7 7 1. 13 0.538
39 A 8 7 1. 13 0.538
40 A 5 4 1. 13 0.308
41 A 4 4 1. 13 0.308
42 A 4 4 1. 13 0.308
43 A 3 3 1. 13 0.231
44 A 3 3 1. 13 0.231
45 A 4 4 1. 13 0.308
46 A 5 4 1. 13 0.308
47 A 6 4 1. 13 0.308
48 A 1 1 1. 11 0.091
49 A 2 1 1. 9 0.111
50 A 2 1 1. 9 0.111
51 A 2 1 1. 9 0.111
52 A 1 0 1. 7 0.
53 A 1 1 1. 9 0.111
54 A 2 2 1. 9 0.222
55 A 3 2 1. 9 0.222
56 A 5 3 1. 11 0.273
57 A 4 3 1. 11 0.273
58 A 3 3 1. 11 0.273
59 A 2 2 1. 11 0.182
60 A 1 1 1. 11 0.091
61 A 2 2 1. 11 0.182
62 A 3 2 1. 11 0.182
63 A 4 2 1. 11 0.182
64 A 1 1 1. 14 0.071
65 A 1 1 1. 14 0.071
66 A 2 2 1. 14 0.143
67 A 1 1 1. 14 0.071
68 A 1 1 1. 14 0.071
69 A 2 2 1. 14 0.143
70 A 1 1 1. 14 0.071
71 A 2 2 1. 14 0.143
72 A 1 1 1. 14 0.071
73 A 2 2 1. 14 0.143
74 A 3 2 1. 23 0.087
75 A 3 2 1. 23 0.087
76 A 3 2 1. 23 0.087
77 A 3 2 1. 23 0.087
78 A 2 2 1. 12 0.167
79 A 2 2 1. 15 0.133
80 A 2 2 1. 12 0.167
81 A 3 2 1. 12 0.167
82 A 3 2 1. 12 0.167
83 B 3 2 2.83 10 0.2
84 A 2 2 1. 12 0.167
85 A 2 2 1. 12 0.167
86 A 2 2 1. 12 0.167
87 A 2 2 1. 12 0.167
88 A 2 2 1. 12 0.167
89 A 2 2 1. 13 0.154
90 A 2 2 1. 14 0.143
91 A 3 3 1. 12 0.25
92 A 3 3 1. 12 0.25
93 A 4 3 1. 12 0.25
94 A 4 3 1. 12 0.25
95 A 3 3 1. 12 0.25
96 A 3 3 1. 13 0.231
97 A 3 3 1. 14 0.214
98 A 2 2 1. 40 0.05
99 A 3 2 1.76 30 0.067
100 A 3 2 1.87 31 0.065
101 A 2 2 1. 14 0.143
102 A 2 2 1. 16 0.125
103 A 3 3 1. 14 0.214
104 A 3 3 1. 14 0.214
105 A 3 3 1. 14 0.214
106 A 3 3 1. 14 0.214
107 A 3 3 1. 14 0.214
108 A 3 3 1. 14 0.214
109 A 3 3 1. 14 0.214
110 A 3 3 1. 14 0.214
111 A 3 3 1. 14 0.214
112 A 3 3 1. 14 0.214
113 A 3 3 1. 14 0.214
114 A 2 2 1. 14 0.143
115 A 2 2 1. 14 0.143
116 A 2 2 1. 14 0.143
117 A 2 2 1. 14 0.143
118 A 2 2 1. 14 0.143
119 A 2 2 1. 14 0.143
120 A 2 2 1. 14 0.143
121 A 2 2 1. 14 0.143
122 A 2 2 1. 14 0.143
123 A 2 2 1. 14 0.143
124 A 2 2 1. 14 0.143
125 A 2 2 1. 27 0.074
126 A 2 2 1. 30 0.067
127 A 2 2 1. 28 0.071
128 A 1 1 1. 12 0.083
129 A 1 1 1. 14 0.071
130 A 1 1 1. 16 0.062
131 A 2 2 1. 14 0.143
132 A 1 1 1. 12 0.083
133 A 2 2 1. 12 0.167
134 A 2 2 1. 12 0.167
135 A 2 2 1. 12 0.167
136 A 2 2 1. 12 0.167
137 A 1 1 1. 10 0.1
138 A 1 1 1. 7 0.143
139 A 2 2 1. 12 0.167
140 A 2 2 1. 12 0.167
141 A 2 2 1. 12 0.167
142 A 2 2 1. 12 0.167
143 A 2 2 1. 12 0.167

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