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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 112 112 112 109 146 1 148 203 0
normalized size 1 1. 1. 0.97 1.3 0.01 1.32 1.81 0.
time (sec) N/A 0.414 0.09 0.008 1.363 0.186 0.153 0.21 0.
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 126 126 123 246 219 220 141 281 0
normalized size 1 1. 0.98 1.95 1.74 1.75 1.12 2.23 0.
time (sec) N/A 0.505 0.162 0.022 1.33 0.207 3.522 0.214 0.
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 85 196 140 158 507 0 0
normalized size 1 1. 1.01 2.33 1.67 1.88 6.04 0. 0.
time (sec) N/A 0.23 0.126 0.026 1.365 0.25 33.281 0. 0.
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 102 179 181 216 0 0 80
normalized size 1 1. 0.94 1.66 1.68 2. 0. 0. 0.74
time (sec) N/A 0.304 0.165 0.013 1.351 74.979 0. 0. 46.099
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A F(-1) F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 164 164 419 0 0 0 121
normalized size 1 1. 1.01 1.01 2.57 0. 0. 0. 0.74
time (sec) N/A 0.548 0.445 0.015 1.399 0. 0. 0. 88.332
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 23 23 23 20 26 26 20 30 20
normalized size 1 1. 1. 0.87 1.13 1.13 0.87 1.3 0.87
time (sec) N/A 0.044 0.011 0.01 1.359 0.26 0.285 0.215 5.417
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 43 43 33 34 46 72 32 42 34
normalized size 1 1. 0.77 0.79 1.07 1.67 0.74 0.98 0.79
time (sec) N/A 0.072 0.039 0.015 1.365 0.246 0.402 0.213 9.148
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 227 227 197 301 0 1 330 456 252
normalized size 1 1. 0.87 1.33 0. 0. 1.45 2.01 1.11
time (sec) N/A 0.782 0.606 0.033 0. 0.245 117.726 0.226 60.588
Problem 9 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 146 146 131 176 0 1 223 271 160
normalized size 1 1. 0.9 1.21 0. 0.01 1.53 1.86 1.1
time (sec) N/A 0.341 0.317 0.016 0. 0.246 57.523 0.218 26.263
Problem 10 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 77 77 81 89 0 1 148 142 80
normalized size 1 1. 1.05 1.16 0. 0.01 1.92 1.84 1.04
time (sec) N/A 0.114 0.214 0.017 0. 0.243 49.473 0.216 10.593
Problem 11 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 54 54 53 46 0 1 110 77 49
normalized size 1 1. 0.98 0.85 0. 0.02 2.04 1.43 0.91
time (sec) N/A 0.073 0.076 0.011 0. 0.225 6.313 0.216 7.956
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 101 196 0 1 270 151 88
normalized size 1 1. 1. 1.94 0. 0.01 2.67 1.5 0.87
time (sec) N/A 0.386 0.367 0.026 0. 0.301 42.442 0.218 35.831
Problem 13 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 127 127 124 192 0 1 1467 192 114
normalized size 1 1. 0.98 1.51 0. 0.01 11.55 1.51 0.9
time (sec) N/A 0.38 0.268 0.031 0. 0.337 81.722 0.218 40.712
Problem 14 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 208 208 184 424 0 1 0 405 189
normalized size 1 1. 0.88 2.04 0. 0. 0. 1.95 0.91
time (sec) N/A 0.833 0.572 0.028 0. 0.84 0. 0.228 86.964
Problem 15 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 226 226 236 301 0 1 330 456 252
normalized size 1 1. 1.04 1.33 0. 0. 1.46 2.02 1.12
time (sec) N/A 0.756 0.615 0.016 0. 0.231 94.618 0.227 60.542
Problem 16 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 145 145 157 176 0 1 223 271 160
normalized size 1 1. 1.08 1.21 0. 0.01 1.54 1.87 1.1
time (sec) N/A 0.319 0.352 0.014 0. 0.229 52. 0.236 26.244
Problem 17 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 77 77 92 89 0 1 148 142 80
normalized size 1 1. 1.19 1.16 0. 0.01 1.92 1.84 1.04
time (sec) N/A 0.113 0.254 0.013 0. 0.23 46.486 0.215 10.185
Problem 18 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 54 54 53 46 0 1 110 77 49
normalized size 1 1. 0.98 0.85 0. 0.02 2.04 1.43 0.91
time (sec) N/A 0.073 0.074 0.01 0. 0.226 6.015 0.209 7.576
Problem 19 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 101 101 101 103 0 1 287 151 88
normalized size 1 1. 1. 1.02 0. 0.01 2.84 1.5 0.87
time (sec) N/A 0.38 0.399 0.024 0. 0.285 37.913 0.218 34.504
Problem 20 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 128 128 123 137 0 1 1409 192 114
normalized size 1 1. 0.96 1.07 0. 0.01 11.01 1.5 0.89
time (sec) N/A 0.39 0.374 0.026 0. 0.342 76.5 0.222 40.923
Problem 21 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 205 205 180 221 0 1 0 406 189
normalized size 1 1. 0.88 1.08 0. 0. 0. 1.98 0.92
time (sec) N/A 0.815 0.563 0.024 0. 0.938 0. 0.223 84.989
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 89 132 0 88 484 85 100
normalized size 1 1. 0.8 1.19 0. 0.79 4.36 0.77 0.9
time (sec) N/A 0.158 0.093 0.056 0. 0.226 69.764 0.229 17.424
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 81 111 0 77 393 72 78
normalized size 1 1. 0.93 1.28 0. 0.89 4.52 0.83 0.9
time (sec) N/A 0.123 0.075 0.021 0. 0.229 48.113 0.224 14.119
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 73 90 0 66 269 54 56
normalized size 1 1. 1.16 1.43 0. 1.05 4.27 0.86 0.89
time (sec) N/A 0.093 0.07 0.017 0. 0.243 37.144 0.217 11.379
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 61 70 0 58 133 38 29
normalized size 1 1. 1.65 1.89 0. 1.57 3.59 1.03 0.78
time (sec) N/A 0.065 0.053 0.024 0. 0.239 18.963 0.242 7.75
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 53 69 0 63 71 59 24
normalized size 1 1. 1.83 2.38 0. 2.17 2.45 2.03 0.83
time (sec) N/A 0.065 0.047 0.026 0. 0.229 19.516 0.221 8.282
Problem 27 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 29 25 0 36 107 119 41
normalized size 1 1. 0.64 0.56 0. 0.8 2.38 2.64 0.91
time (sec) N/A 0.062 0.034 0.007 0. 0.221 26.098 0.217 7.654
Problem 28 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 73 73 37 33 0 47 189 176 66
normalized size 1 1. 0.51 0.45 0. 0.64 2.59 2.41 0.9
time (sec) N/A 0.088 0.038 0.008 0. 0.224 42.515 0.225 10.504
Problem 29 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 97 97 45 41 0 58 274 236 88
normalized size 1 1. 0.46 0.42 0. 0.6 2.82 2.43 0.91
time (sec) N/A 0.117 0.043 0.008 0. 0.226 74.305 0.226 13.297
Problem 30 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 121 121 53 49 0 69 359 293 110
normalized size 1 1. 0.44 0.4 0. 0.57 2.97 2.42 0.91
time (sec) N/A 0.147 0.045 0.009 0. 0.223 150.567 0.226 16.635
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 39 44 28 82 0 58 32
normalized size 1 1. 1. 1.13 0.72 2.1 0. 1.49 0.82
time (sec) N/A 0.07 0.046 0.028 1.497 0.232 0. 0.217 7.143
Problem 32 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 39 44 28 82 0 58 32
normalized size 1 1. 1. 1.13 0.72 2.1 0. 1.49 0.82
time (sec) N/A 0.116 0.027 0.006 1.489 0.232 0. 0.217 13.226
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 309 624 0 0 0 0 107
normalized size 1 1. 2.13 4.3 0. 0. 0. 0. 0.74
time (sec) N/A 0.681 2.308 0.245 0. 0. 0. 0. 84.363
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 221 221 312 940 0 0 0 0 194
normalized size 1 1. 1.41 4.25 0. 0. 0. 0. 0.88
time (sec) N/A 1.068 3.829 0.174 0. 0. 0. 0. 134.127
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 281 281 135 166 0 0 0 0 0
normalized size 1 1. 0.48 0.59 0. 0. 0. 0. 0.
time (sec) N/A 0.877 0.425 0.097 0. 0. 0. 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 243 243 130 161 0 0 0 0 286
normalized size 1 1. 0.53 0.66 0. 0. 0. 0. 1.18
time (sec) N/A 0.721 0.343 0.017 0. 0. 0. 0. 94.619
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 125 156 0 0 0 0 226
normalized size 1 1. 0.65 0.81 0. 0. 0. 0. 1.17
time (sec) N/A 0.463 0.33 0.017 0. 0. 0. 0. 46.376
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 120 151 0 0 0 0 197
normalized size 1 1. 0.74 0.93 0. 0. 0. 0. 1.22
time (sec) N/A 0.376 0.248 0.013 0. 0. 0. 0. 34.899
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 182 182 141 192 0 0 0 0 0
normalized size 1 1. 0.77 1.05 0. 0. 0. 0. 0.
time (sec) N/A 0.791 0.423 0.032 0. 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 132 338 0 0 0 0 0
normalized size 1 1. 0.7 1.79 0. 0. 0. 0. 0.
time (sec) N/A 0.797 0.751 0.038 0. 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 227 227 136 488 0 0 0 0 0
normalized size 1 1. 0.6 2.15 0. 0. 0. 0. 0.
time (sec) N/A 0.962 0.527 0.04 0. 0. 0. 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 263 263 141 638 0 0 0 0 0
normalized size 1 1. 0.54 2.43 0. 0. 0. 0. 0.
time (sec) N/A 1.131 0.629 0.04 0. 0. 0. 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 570 570 29892 3678 0 0 0 0 0
normalized size 1 1. 52.44 6.45 0. 0. 0. 0. 0.
time (sec) N/A 4.401 19.097 0.097 0. 0. 0. 0. 0.
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 243 243 130 161 0 0 0 0 286
normalized size 1 1. 0.53 0.66 0. 0. 0. 0. 1.18
time (sec) N/A 0.729 0.395 0.035 0. 0. 0. 0. 164.158
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 205 205 125 156 0 0 0 0 226
normalized size 1 1. 0.61 0.76 0. 0. 0. 0. 1.1
time (sec) N/A 0.59 0.358 0.018 0. 0. 0. 0. 75.934
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 120 151 0 0 0 0 196
normalized size 1 1. 0.74 0.93 0. 0. 0. 0. 1.21
time (sec) N/A 0.398 0.271 0.016 0. 0. 0. 0. 37.383
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 131 131 115 146 0 0 0 0 167
normalized size 1 1. 0.88 1.11 0. 0. 0. 0. 1.27
time (sec) N/A 0.303 0.258 0.011 0. 0. 0. 0. 26.75
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 97 85 0 0 0 0 214
normalized size 1 1. 0.64 0.56 0. 0. 0. 0. 1.42
time (sec) N/A 0.64 0.208 0.02 0. 0. 0. 0. 39.396
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 132 338 0 0 0 0 0
normalized size 1 1. 0.7 1.79 0. 0. 0. 0. 0.
time (sec) N/A 0.799 0.859 0.024 0. 0. 0. 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 225 225 137 488 0 0 0 0 0
normalized size 1 1. 0.61 2.17 0. 0. 0. 0. 0.
time (sec) N/A 0.962 0.664 0.025 0. 0. 0. 0. 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 205 205 125 156 0 0 0 0 257
normalized size 1 1. 0.61 0.76 0. 0. 0. 0. 1.25
time (sec) N/A 0.594 0.304 0.037 0. 0. 0. 0. 131.002
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 120 151 0 0 0 0 196
normalized size 1 1. 0.72 0.9 0. 0. 0. 0. 1.17
time (sec) N/A 0.496 0.303 0.022 0. 0. 0. 0. 60.279
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 131 131 115 146 0 0 0 0 170
normalized size 1 1. 0.88 1.11 0. 0. 0. 0. 1.3
time (sec) N/A 0.329 0.237 0.02 0. 0. 0. 0. 30.094
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B C F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 111 61 0 0 0 0 65
normalized size 1 1. 2.36 1.3 0. 0. 0. 0. 1.38
time (sec) N/A 0.101 0.732 0.018 0. 0. 0. 0. 8.733
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 70 62 0 0 0 0 138
normalized size 1 1. 0.68 0.6 0. 0. 0. 0. 1.34
time (sec) N/A 0.476 0.221 0.021 0. 0. 0. 0. 25.564
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 132 338 0 0 0 0 0
normalized size 1 1. 0.7 1.79 0. 0. 0. 0. 0.
time (sec) N/A 0.798 0.876 0.026 0. 0. 0. 0. 0.
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 225 225 144 488 0 0 0 0 0
normalized size 1 1. 0.64 2.17 0. 0. 0. 0. 0.
time (sec) N/A 0.974 0.409 0.027 0. 0. 0. 0. 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 293 293 202 382 0 0 0 0 240
normalized size 1 1. 0.69 1.3 0. 0. 0. 0. 0.82
time (sec) N/A 2.338 1.171 0.069 0. 0. 0. 0. 104.411
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 449 449 381 968 0 0 0 0 379
normalized size 1 1. 0.85 2.16 0. 0. 0. 0. 0.84
time (sec) N/A 2.939 10.635 0.039 0. 0. 0. 0. 171.238
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 203 125 156 0 0 0 0 0
normalized size 1 1. 0.62 0.77 0. 0. 0. 0. 0.
time (sec) N/A 0.6 0.358 0.04 0. 0. 0. 0. 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 165 165 120 151 0 0 0 0 197
normalized size 1 1. 0.73 0.92 0. 0. 0. 0. 1.19
time (sec) N/A 0.489 0.323 0.024 0. 0. 0. 0. 96.782
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 129 129 115 146 0 0 0 0 170
normalized size 1 1. 0.89 1.13 0. 0. 0. 0. 1.32
time (sec) N/A 0.356 0.275 0.023 0. 0. 0. 0. 44.621
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 187 63 0 0 0 0 141
normalized size 1 1. 1.91 0.64 0. 0. 0. 0. 1.44
time (sec) N/A 0.252 0.725 0.021 0. 0. 0. 0. 22.209
Problem 64 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 48 48 79 39 0 0 0 0 65
normalized size 1 1. 1.65 0.81 0. 0. 0. 0. 1.35
time (sec) N/A 0.094 0.182 0.02 0. 0. 0. 0. 8.99
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 99 40 0 0 0 0 73
normalized size 1 1. 1.94 0.78 0. 0. 0. 0. 1.43
time (sec) N/A 0.285 0.314 0.023 0. 0. 0. 0. 10.184
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 132 338 0 0 0 0 0
normalized size 1 1. 0.7 1.79 0. 0. 0. 0. 0.
time (sec) N/A 0.786 0.806 0.03 0. 0. 0. 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 225 225 147 488 0 0 0 0 0
normalized size 1 1. 0.65 2.17 0. 0. 0. 0. 0.
time (sec) N/A 0.969 0.428 0.038 0. 0. 0. 0. 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 180 552 0 0 0 0 114
normalized size 1 1. 1.31 4.03 0. 0. 0. 0. 0.83
time (sec) N/A 0.365 0.944 0.033 0. 0. 0. 0. 55.414
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 284 284 319 559 0 0 0 0 241
normalized size 1 1. 1.12 1.97 0. 0. 0. 0. 0.85
time (sec) N/A 1.034 3.031 0.058 0. 0. 0. 0. 116.765
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 165 165 225 223 0 0 0 0 129
normalized size 1 1. 1.36 1.35 0. 0. 0. 0. 0.78
time (sec) N/A 1.593 1.271 0.041 0. 0. 0. 0. 17.823
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 393 393 1698 2842 0 0 0 0 316
normalized size 1 1. 4.32 7.23 0. 0. 0. 0. 0.8
time (sec) N/A 2.537 14.338 0.136 0. 0. 0. 0. 140.58
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F(-1) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 875 875 12193 17330 0 0 0 0 0
normalized size 1 1. 13.93 19.81 0. 0. 0. 0. 0.
time (sec) N/A 5.195 21.638 0.372 0. 0. 0. 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 203 184 0 0 0 0 102
normalized size 1 1. 2.74 2.49 0. 0. 0. 0. 1.38
time (sec) N/A 0.649 0.855 0.132 0. 0. 0. 0. 17.292
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 203 181 0 0 0 0 107
normalized size 1 1. 2.74 2.45 0. 0. 0. 0. 1.45
time (sec) N/A 0.755 0.128 0.034 0. 0. 0. 0. 14.894
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 218 212 0 0 0 0 121
normalized size 1 1. 2.53 2.47 0. 0. 0. 0. 1.41
time (sec) N/A 0.657 0.817 0.134 0. 0. 0. 0. 19.17
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 218 205 0 0 0 0 128
normalized size 1 1. 2.53 2.38 0. 0. 0. 0. 1.49
time (sec) N/A 0.759 0.186 0.035 0. 0. 0. 0. 15.482
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 471 471 350 949 0 0 0 0 0
normalized size 1 1. 0.74 2.01 0. 0. 0. 0. 0.
time (sec) N/A 1.626 3.742 0.148 0. 0. 0. 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 429 429 345 944 0 0 0 0 0
normalized size 1 1. 0.8 2.2 0. 0. 0. 0. 0.
time (sec) N/A 1.445 3.711 0.028 0. 0. 0. 0. 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 391 391 340 939 0 0 0 0 0
normalized size 1 1. 0.87 2.4 0. 0. 0. 0. 0.
time (sec) N/A 1.258 3.631 0.026 0. 0. 0. 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 351 351 347 934 0 0 0 0 0
normalized size 1 1. 0.99 2.66 0. 0. 0. 0. 0.
time (sec) N/A 1.116 3.38 0.046 0. 0. 0. 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 349 349 330 929 0 0 0 0 0
normalized size 1 1. 0.95 2.66 0. 0. 0. 0. 0.
time (sec) N/A 1.131 3.328 0.057 0. 0. 0. 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 391 391 366 1221 0 0 0 0 0
normalized size 1 1. 0.94 3.12 0. 0. 0. 0. 0.
time (sec) N/A 1.312 3.499 0.058 0. 0. 0. 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 330 330 251 1033 0 0 0 0 0
normalized size 1 1. 0.76 3.13 0. 0. 0. 0. 0.
time (sec) N/A 1.032 2.055 0.059 0. 0. 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 370 370 259 1232 0 0 0 0 0
normalized size 1 1. 0.7 3.33 0. 0. 0. 0. 0.
time (sec) N/A 1.247 2.712 0.061 0. 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 429 429 345 944 0 0 0 0 0
normalized size 1 1. 0.8 2.2 0. 0. 0. 0. 0.
time (sec) N/A 1.494 3.755 0.057 0. 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 391 391 340 939 0 0 0 0 0
normalized size 1 1. 0.87 2.4 0. 0. 0. 0. 0.
time (sec) N/A 1.269 3.457 0.034 0. 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 351 351 347 934 0 0 0 0 0
normalized size 1 1. 0.99 2.66 0. 0. 0. 0. 0.
time (sec) N/A 1.126 4.345 0.029 0. 0. 0. 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 365 365 318 929 0 0 0 0 396
normalized size 1 1. 0.87 2.55 0. 0. 0. 0. 1.08
time (sec) N/A 0.834 1.906 0.033 0. 0. 0. 0. 67.115
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 279 279 326 924 0 0 0 0 0
normalized size 1 1. 1.17 3.31 0. 0. 0. 0. 0.
time (sec) N/A 0.626 3.205 0.036 0. 0. 0. 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 290 290 246 834 0 0 0 0 0
normalized size 1 1. 0.85 2.88 0. 0. 0. 0. 0.
time (sec) N/A 0.847 1.959 0.035 0. 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 330 330 251 1033 0 0 0 0 0
normalized size 1 1. 0.76 3.13 0. 0. 0. 0. 0.
time (sec) N/A 1.043 2.004 0.039 0. 0. 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 370 370 258 1232 0 0 0 0 0
normalized size 1 1. 0.7 3.33 0. 0. 0. 0. 0.
time (sec) N/A 1.245 2.624 0.039 0. 0. 0. 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 391 391 340 939 0 0 0 0 0
normalized size 1 1. 0.87 2.4 0. 0. 0. 0. 0.
time (sec) N/A 1.294 3.344 0.054 0. 0. 0. 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 351 351 349 934 0 0 0 0 0
normalized size 1 1. 0.99 2.66 0. 0. 0. 0. 0.
time (sec) N/A 1.138 5.131 0.033 0. 0. 0. 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 365 365 347 929 0 0 0 0 593
normalized size 1 1. 0.95 2.55 0. 0. 0. 0. 1.62
time (sec) N/A 0.816 2.195 0.031 0. 0. 0. 0. 85.869
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 101 101 170 184 0 0 0 0 294
normalized size 1 1. 1.68 1.82 0. 0. 0. 0. 2.91
time (sec) N/A 0.199 0.548 0.038 0. 0. 0. 0. 39.058
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A B B B F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 195 237 348 0 0 0 0 396
normalized size 1 3.25 3.95 5.8 0. 0. 0. 0. 6.6
time (sec) N/A 0.406 1.908 0.036 0. 0. 0. 0. 33.807
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 290 290 248 834 0 0 0 0 0
normalized size 1 1. 0.86 2.88 0. 0. 0. 0. 0.
time (sec) N/A 0.855 2.039 0.038 0. 0. 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F(-1) F F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 721 721 6667 18077 0 0 0 0 0
normalized size 1 1. 9.25 25.07 0. 0. 0. 0. 0.
time (sec) N/A 2.724 15.973 0.19 0. 0. 0. 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 208 206 4590 0 0 0 0 178
normalized size 1 1.29 1.28 28.51 0. 0. 0. 0. 1.11
time (sec) N/A 0.464 8.681 0.173 0. 0. 0. 0. 73.525
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 351 351 347 934 0 0 0 0 0
normalized size 1 1. 0.99 2.66 0. 0. 0. 0. 0.
time (sec) N/A 1.098 3.231 0.053 0. 0. 0. 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 469 469 347 929 0 0 0 0 806
normalized size 1 1. 0.74 1.98 0. 0. 0. 0. 1.72
time (sec) N/A 1.116 1.894 0.034 0. 0. 0. 0. 128.168
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 100 100 185 182 0 0 0 0 87
normalized size 1 1. 1.85 1.82 0. 0. 0. 0. 0.87
time (sec) N/A 0.196 0.617 0.031 0. 0. 0. 0. 22.319
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 118 140 0 0 0 0 148
normalized size 1 1. 1.66 1.97 0. 0. 0. 0. 2.08
time (sec) N/A 0.166 0.342 0.033 0. 0. 0. 0. 16.544
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 195 270 237 635 0 0 0 0 479
normalized size 1 1.38 1.22 3.26 0. 0. 0. 0. 2.46
time (sec) N/A 0.661 1.684 0.038 0. 0. 0. 0. 58.46
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 288 288 246 834 0 0 0 0 0
normalized size 1 1. 0.85 2.9 0. 0. 0. 0. 0.
time (sec) N/A 0.83 1.814 0.042 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 F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 968 968 6638 16526 0 0 0 0 0
normalized size 1 1. 6.86 17.07 0. 0. 0. 0. 0.
time (sec) N/A 3.838 15.33 0.119 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) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 228 228 584 2465 0 0 0 0 180
normalized size 1 1. 2.56 10.81 0. 0. 0. 0. 0.79
time (sec) N/A 0.846 9.51 0.076 0. 0. 0. 0. 78.027
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 198 227 270 0 0 0 0 172
normalized size 1 1.23 1.41 1.68 0. 0. 0. 0. 1.07
time (sec) N/A 0.426 2.01 0.082 0. 0. 0. 0. 99.293
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 429 429 3247 4660 0 0 0 0 0
normalized size 1 1. 7.57 10.86 0. 0. 0. 0. 0.
time (sec) N/A 1.171 16.114 0.138 0. 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A F B B F F F(-1) F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 786 0 7061 21094 0 0 0 0 0
normalized size 1 0. 8.98 26.84 0. 0. 0. 0. 0.
time (sec) N/A 0.147 22.022 0.293 0. 0. 0. 0. 0.
Problem 112 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 319 319 262 0 0 0 0 0 267
normalized size 1 1. 0.82 0. 0. 0. 0. 0. 0.84
time (sec) N/A 0.719 0.885 0.171 0. 0. 0. 0. 97.907
Problem 113 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 216 216 262 0 0 0 0 0 170
normalized size 1 1. 1.21 0. 0. 0. 0. 0. 0.79
time (sec) N/A 0.44 0.855 0.101 0. 0. 0. 0. 65.192
Problem 114 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 158 158 153 0 0 0 0 0 117
normalized size 1 1. 0.97 0. 0. 0. 0. 0. 0.74
time (sec) N/A 0.319 0.272 0.089 0. 0. 0. 0. 48.135
Problem 115 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 124 124 116 0 0 0 0 0 94
normalized size 1 1. 0.94 0. 0. 0. 0. 0. 0.76
time (sec) N/A 0.154 0.135 0.087 0. 0. 0. 0. 23.404
Problem 116 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 124 124 116 0 0 0 0 0 94
normalized size 1 1. 0.94 0. 0. 0. 0. 0. 0.76
time (sec) N/A 0.131 0.121 0.082 0. 0. 0. 0. 20.365
Problem 117 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 175 175 177 0 0 0 0 0 129
normalized size 1 1. 1.01 0. 0. 0. 0. 0. 0.74
time (sec) N/A 0.352 0.63 0.068 0. 0. 0. 0. 49.546
Problem 118 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 222 222 228 0 0 0 0 0 175
normalized size 1 1. 1.03 0. 0. 0. 0. 0. 0.79
time (sec) N/A 0.448 1.181 0.106 0. 0. 0. 0. 60.913
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 241 726 0 1184 8218 1 180
normalized size 1 1. 1.44 4.35 0. 7.09 49.21 0.01 1.08
time (sec) N/A 0.373 0.671 0.012 0. 0.249 25.948 0.218 123.205
Problem 120 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 134 134 317 0 0 0 0 0 119
normalized size 1 1. 2.37 0. 0. 0. 0. 0. 0.89
time (sec) N/A 0.246 1.54 0.075 0. 0. 0. 0. 19.181
Problem 121 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 140 140 390 0 0 0 0 0 100
normalized size 1 1. 2.79 0. 0. 0. 0. 0. 0.71
time (sec) N/A 0.247 3.04 0.087 0. 0. 0. 0. 28.508
Problem 122 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 224 224 229 0 0 0 0 0 162
normalized size 1 1. 1.02 0. 0. 0. 0. 0. 0.72
time (sec) N/A 0.58 0.74 0.131 0. 0. 0. 0. 81.298
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 140 140 309 0 0 0 0 0 104
normalized size 1 1. 2.21 0. 0. 0. 0. 0. 0.74
time (sec) N/A 0.383 1.218 0.097 0. 0. 0. 0. 39.07
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 266 266 335 0 0 0 0 0 257
normalized size 1 1. 1.26 0. 0. 0. 0. 0. 0.97
time (sec) N/A 0.496 1.831 0.093 0. 0. 0. 0. 152.063
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 245 245 1043 0 0 0 0 0 224
normalized size 1 1. 4.26 0. 0. 0. 0. 0. 0.91
time (sec) N/A 0.464 6.167 0.088 0. 0. 0. 0. 43.049
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 235 235 324 0 0 0 0 0 216
normalized size 1 1. 1.38 0. 0. 0. 0. 0. 0.92
time (sec) N/A 0.395 1.317 0.087 0. 0. 0. 0. 39.519
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 261 261 346 0 0 0 0 0 238
normalized size 1 1. 1.33 0. 0. 0. 0. 0. 0.91
time (sec) N/A 0.567 2.152 0.077 0. 0. 0. 0. 61.865
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 203 205 303 0 0 0 0 0 175
normalized size 1 1.01 1.49 0. 0. 0. 0. 0. 0.86
time (sec) N/A 0.378 2.5 0.075 0. 0. 0. 0. 33.058
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F(-1) F(-2) A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 246 246 633 0 0 0 0 0 240
normalized size 1 1. 2.57 0. 0. 0. 0. 0. 0.98
time (sec) N/A 0.629 2.98 0.071 0. 0. 0. 0. 40.52
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 362 362 315 894 0 2240 0 0 337
normalized size 1 1. 0.87 2.47 0. 6.19 0. 0. 0.93
time (sec) N/A 0.988 1.421 0.012 0. 0.261 0. 0. 127.151
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 507 507 495 2343 0 4645 0 0 0
normalized size 1 1. 0.98 4.62 0. 9.16 0. 0. 0.
time (sec) N/A 1.454 3.337 0.016 0. 0.275 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F(-1) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 815 803 10997 0 0 0 0 0 0
normalized size 1 0.99 13.49 0. 0. 0. 0. 0. 0.
time (sec) N/A 4.051 66.911 0.082 0. 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F(-1) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 572 566 10700 0 0 0 0 0 0
normalized size 1 0.99 18.71 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.129 8.021 0.076 0. 0. 0. 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 363 360 321 906 0 2171 0 0 337
normalized size 1 0.99 0.88 2.5 0. 5.98 0. 0. 0.93
time (sec) N/A 1.125 2.355 0.012 0. 0.258 0. 0. 125.324
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 188 186 201 509 0 1222 0 0 156
normalized size 1 0.99 1.07 2.71 0. 6.5 0. 0. 0.83
time (sec) N/A 0.305 0.655 0.011 0. 0.256 0. 0. 45.37
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F(-1) F A
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 177 190 692 0 0 0 0 0 144
normalized size 1 1.07 3.91 0. 0. 0. 0. 0. 0.81
time (sec) N/A 0.382 1.358 0.091 0. 0. 0. 0. 54.903
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 250 250 551 0 0 0 0 0 199
normalized size 1 1. 2.2 0. 0. 0. 0. 0. 0.8
time (sec) N/A 0.727 2.697 0.076 0. 0. 0. 0. 158.767
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F(-1) F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 530 530 0 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 3.251 12.885 0.37 0. 0. 0. 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 393 393 0 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.473 4.218 0.251 0. 0. 0. 0. 0.
Problem 140 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 N/A TBD TBD TBD TBD TBD TBD
size 256 256 0 0 0 0 0 0 201
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.79
time (sec) N/A 0.657 4.42 0.215 0. 0. 0. 0. 164.493
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 123 123 296 0 0 0 0 0 94
normalized size 1 1. 2.41 0. 0. 0. 0. 0. 0.76
time (sec) N/A 0.267 0.23 0.21 0. 0. 0. 0. 79.022
Problem 142 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 32 0 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.069 0.366 0.22 0. 0. 0. 0. 0.
Problem 143 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 N/A TBD TBD TBD TBD TBD TBD
size 268 268 0 0 0 0 0 0 211
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.79
time (sec) N/A 0.718 4.66 0.22 0. 0. 0. 0. 164.387
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 283 283 576 0 0 0 0 0 218
normalized size 1 1. 2.04 0. 0. 0. 0. 0. 0.77
time (sec) N/A 0.807 2.856 0.208 0. 0. 0. 0. 171.238
Problem 145 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 NO TBD TBD TBD TBD TBD TBD
size 277 277 487 0 0 0 0 0 214
normalized size 1 1. 1.76 0. 0. 0. 0. 0. 0.77
time (sec) N/A 0.604 1.094 0.206 0. 0. 0. 0. 106.458
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 263 261 10558 0 0 0 0 0 212
normalized size 1 0.99 40.14 0. 0. 0. 0. 0. 0.81
time (sec) N/A 0.675 8.867 0.221 0. 0. 0. 0. 60.389
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F(-1) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 558 558 31260 0 0 0 0 0 0
normalized size 1 1. 56.02 0. 0. 0. 0. 0. 0.
time (sec) N/A 3.137 12.62 0.222 0. 0. 0. 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 57 139 134 306 313 123 68
normalized size 1 1. 0.72 1.76 1.7 3.87 3.96 1.56 0.86
time (sec) N/A 0.275 0.094 0.051 1.515 0.225 108.341 0.234 26.734
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 45 117 105 244 282 97 41
normalized size 1 1. 0.71 1.86 1.67 3.87 4.48 1.54 0.65
time (sec) N/A 0.15 0.061 0.021 1.488 0.231 55.04 0.229 15.392
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 54 94 89 171 245 0 39
normalized size 1 1. 1.12 1.96 1.85 3.56 5.1 0. 0.81
time (sec) N/A 0.346 0.065 0.027 1.535 0.235 57.691 0. 30.214
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 54 97 89 212 221 0 37
normalized size 1 1. 1.12 2.02 1.85 4.42 4.6 0. 0.77
time (sec) N/A 0.345 0.088 0.03 1.509 0.241 65.748 0. 27.354
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 70 108 132 255 218 0 56
normalized size 1 1. 0.99 1.52 1.86 3.59 3.07 0. 0.79
time (sec) N/A 0.364 0.102 0.032 1.512 0.224 81.23 0. 27.079
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 151 80 137 147 370 308 130 119
normalized size 1 1.74 0.92 1.57 1.69 4.25 3.54 1.49 1.37
time (sec) N/A 0.288 0.133 0.031 1.347 0.233 107.586 0.246 28.533
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A B A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 135 68 120 142 259 277 104 87
normalized size 1 2.6 1.31 2.31 2.73 4.98 5.33 2. 1.67
time (sec) N/A 0.181 0.087 0.022 1.324 0.222 54.632 0.257 17.098
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A B A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 135 76 93 86 212 240 96 65
normalized size 1 2.45 1.38 1.69 1.56 3.85 4.36 1.75 1.18
time (sec) N/A 0.36 0.108 0.027 1.473 0.234 57.202 0.225 21.179
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A B A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 135 76 96 86 178 216 112 48
normalized size 1 2.45 1.38 1.75 1.56 3.24 3.93 2.04 0.87
time (sec) N/A 0.357 0.097 0.027 1.501 0.236 66.205 0.23 17.554
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 129 64 103 88 238 212 196 88
normalized size 1 1.55 0.77 1.24 1.06 2.87 2.55 2.36 1.06
time (sec) N/A 0.359 0.113 0.028 1.497 0.227 82.14 0.238 20.402
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 171 75 123 119 297 219 266 119
normalized size 1 1.47 0.65 1.06 1.03 2.56 1.89 2.29 1.03
time (sec) N/A 0.457 0.145 0.03 1.502 0.229 156.309 0.229 25.013

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 [72] had the largest ratio of [ 0.3429 ]

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 2 1 1. 21 0.048
2 A 2 1 1. 23 0.043
3 A 2 1 1. 25 0.04
4 A 2 1 1. 27 0.037
5 A 2 1 1. 29 0.034
6 A 2 1 1. 17 0.059
7 A 3 2 1. 22 0.091
8 A 6 5 1. 25 0.2
9 A 5 5 1. 25 0.2
10 A 4 4 1. 23 0.174
11 A 4 4 1. 18 0.222
12 A 6 5 1. 25 0.2
13 A 6 5 1. 25 0.2
14 A 7 6 1. 25 0.24
15 A 6 5 1. 25 0.2
16 A 5 5 1. 25 0.2
17 A 4 4 1. 23 0.174
18 A 4 4 1. 18 0.222
19 A 6 5 1. 25 0.2
20 A 6 5 1. 25 0.2
21 A 7 6 1. 25 0.24
22 A 8 6 1. 26 0.231
23 A 7 6 1. 26 0.231
24 A 6 6 1. 24 0.25
25 A 4 4 1. 23 0.174
26 A 5 5 1. 26 0.192
27 A 3 3 1. 26 0.115
28 A 4 4 1. 26 0.154
29 A 5 4 1. 26 0.154
30 A 6 4 1. 26 0.154
31 A 4 4 1. 24 0.167
32 A 5 5 1. 36 0.139
33 A 3 3 1. 45 0.067
34 A 5 5 1. 39 0.128
35 A 10 8 1. 35 0.229
36 A 9 8 1. 35 0.229
37 A 8 6 1. 33 0.182
38 A 7 7 1. 28 0.25
39 A 10 10 1. 35 0.286
40 A 10 10 1. 35 0.286
41 A 11 11 1. 35 0.314
42 A 12 11 1. 35 0.314
43 A 12 10 1. 35 0.286
44 A 9 8 1. 35 0.229
45 A 8 8 1. 35 0.229
46 A 7 6 1. 33 0.182
47 A 6 6 1. 28 0.214
48 A 9 9 1. 35 0.257
49 A 10 10 1. 35 0.286
50 A 11 11 1. 35 0.314
51 A 8 8 1. 35 0.229
52 A 7 7 1. 35 0.2
53 A 6 6 1. 33 0.182
54 A 2 2 1. 28 0.071
55 A 6 6 1. 35 0.171
56 A 10 10 1. 35 0.286
57 A 11 11 1. 35 0.314
58 A 8 6 1. 35 0.171
59 A 11 8 1. 35 0.229
60 A 8 8 1. 35 0.229
61 A 7 7 1. 35 0.2
62 A 7 7 1. 35 0.2
63 A 5 5 1. 33 0.152
64 A 2 2 1. 28 0.071
65 A 3 3 1. 35 0.086
66 A 10 10 1. 35 0.286
67 A 11 11 1. 35 0.314
68 A 3 3 1. 36 0.083
69 A 6 5 1. 33 0.152
70 A 4 3 1. 35 0.086
71 A 10 8 1. 35 0.229
72 A 18 12 1. 35 0.343
73 A 3 3 1. 36 0.083
74 A 4 4 1. 31 0.129
75 A 3 3 1. 40 0.075
76 A 4 4 1. 31 0.129
77 A 13 11 1. 37 0.297
78 A 12 11 1. 37 0.297
79 A 11 11 1. 37 0.297
80 A 10 10 1. 37 0.27
81 A 10 10 1. 37 0.27
82 A 11 11 1. 37 0.297
83 A 9 8 1. 37 0.216
84 A 10 8 1. 37 0.216
85 A 12 11 1. 37 0.297
86 A 11 11 1. 37 0.297
87 A 10 10 1. 37 0.27
88 A 9 8 1. 37 0.216
89 A 7 7 1. 37 0.189
90 A 8 8 1. 37 0.216
91 A 9 8 1. 37 0.216
92 A 10 8 1. 37 0.216
93 A 11 11 1. 37 0.297
94 A 10 10 1. 37 0.27
95 A 9 8 1. 37 0.216
96 A 2 2 1. 37 0.054
97 B 5 5 3.25 37 0.135
98 A 8 8 1. 37 0.216
99 A 7 7 1. 37 0.189
100 A 2 2 1.29 37 0.054
101 A 10 10 1. 37 0.27
102 A 12 10 1. 37 0.27
103 A 2 2 1. 37 0.054
104 A 2 2 1. 37 0.054
105 A 8 7 1.38 37 0.189
106 A 8 8 1. 37 0.216
107 A 10 8 1. 37 0.216
108 A 2 2 1. 37 0.054
109 A 2 2 1.23 37 0.054
110 A 5 5 1. 37 0.135
111 F 0 0 N/A 0 N/A
112 A 8 3 1. 25 0.12
113 A 6 3 1. 25 0.12
114 A 4 2 1. 25 0.08
115 A 3 2 1. 23 0.087
116 A 3 2 1. 22 0.091
117 A 5 3 1. 25 0.12
118 A 6 4 1. 25 0.16
119 A 2 1 1. 23 0.043
120 A 2 2 1. 25 0.08
121 A 3 2 1. 27 0.074
122 A 5 2 1. 29 0.069
123 A 6 3 1. 25 0.12
124 A 3 3 1. 25 0.12
125 A 3 3 1. 29 0.103
126 A 3 3 1. 27 0.111
127 A 3 3 1. 29 0.103
128 A 3 3 1.01 29 0.103
129 A 3 3 1. 29 0.103
130 A 3 3 1. 29 0.103
131 A 4 3 1. 29 0.103
132 A 10 9 0.99 31 0.29
133 A 9 8 0.99 31 0.258
134 A 3 3 0.99 29 0.103
135 A 3 3 0.99 24 0.125
136 A 5 5 1.07 27 0.185
137 A 7 4 1. 29 0.138
138 A 31 5 1. 29 0.172
139 A 15 5 1. 29 0.172
140 A 7 4 1. 27 0.148
141 A 3 3 1. 22 0.136
142 A 0 0 0. 0 0.
143 A 7 4 1. 33 0.121
144 A 7 4 1. 34 0.118
145 A 5 5 1. 34 0.147
146 A 3 3 0.99 34 0.088
147 A 4 3 1. 34 0.088
148 A 4 4 1. 31 0.129
149 A 4 4 1. 30 0.133
150 A 7 7 1. 33 0.212
151 A 7 7 1. 33 0.212
152 A 6 6 1. 33 0.182
153 A 5 5 1.74 30 0.167
154 B 5 5 2.6 29 0.172
155 B 8 8 2.45 32 0.25
156 B 8 8 2.45 32 0.25
157 A 6 6 1.55 32 0.188
158 A 7 7 1.47 32 0.219

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