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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 94 94 94 97 130 1 104 131 0
normalized size 1 1. 1. 1.03 1.38 0.01 1.11 1.39 0.
time (sec) N/A 0.149 0.035 0. 1.41 0.18 0.145 0.218 0.
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 70 73 95 1 80 100 0
normalized size 1 1. 1. 1.04 1.36 0.01 1.14 1.43 0.
time (sec) N/A 0.103 0.021 0.001 1.376 0.181 0.123 0.214 0.
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 50 49 65 1 51 68 0
normalized size 1 1. 1. 0.98 1.3 0.02 1.02 1.36 0.
time (sec) N/A 0.074 0.014 0.001 1.361 0.181 0.109 0.213 0.
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 28 25 32 1 26 35 0
normalized size 1 1. 1. 0.89 1.14 0.04 0.93 1.25 0.
time (sec) N/A 0.039 0.009 0.002 1.353 0.182 0.075 0.211 0.
Problem 5 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 144 144 128 195 0 176 71 217 134
normalized size 1 1. 0.89 1.35 0. 1.22 0.49 1.51 0.93
time (sec) N/A 0.211 0.14 0.007 0. 0.215 1.937 0.217 32.683
Problem 6 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 169 169 145 221 0 275 97 246 155
normalized size 1 1. 0.86 1.31 0. 1.63 0.57 1.46 0.92
time (sec) N/A 0.195 0.17 0.011 0. 0.215 2.62 0.218 34.232
Problem 7 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 197 197 175 249 0 414 133 273 180
normalized size 1 1. 0.89 1.26 0. 2.1 0.68 1.39 0.91
time (sec) N/A 0.229 0.225 0.014 0. 0.214 3.771 0.221 39.124
Problem 8 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 122 122 122 125 167 1 139 178 0
normalized size 1 1. 1. 1.02 1.37 0.01 1.14 1.46 0.
time (sec) N/A 0.175 0.034 0. 1.37 0.182 0.166 0.211 0.
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 82 87 111 1 90 123 0
normalized size 1 1. 1. 1.06 1.35 0.01 1.1 1.5 0.
time (sec) N/A 0.117 0.023 0.001 1.407 0.181 0.138 0.211 0.
Problem 10 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 50 50 50 49 65 1 51 68 0
normalized size 1 1. 1. 0.98 1.3 0.02 1.02 1.36 0.
time (sec) N/A 0.075 0.014 0. 1.383 0.18 0.102 0.21 0.
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 173 173 167 334 0 258 156 336 0
normalized size 1 1. 0.97 1.93 0. 1.49 0.9 1.94 0.
time (sec) N/A 0.276 0.171 0.004 0. 0.212 2.861 0.219 0.
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 203 210 367 0 435 189 358 0
normalized size 1 1. 1.03 1.81 0. 2.14 0.93 1.76 0.
time (sec) N/A 0.495 0.379 0.014 0. 0.218 4.832 0.22 0.
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 258 258 234 388 0 637 233 400 243
normalized size 1 1. 0.91 1.5 0. 2.47 0.9 1.55 0.94
time (sec) N/A 0.477 0.466 0.015 0. 0.219 7.431 0.222 53.106
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 252 252 253 661 0 494 369 622 0
normalized size 1 1. 1. 2.62 0. 1.96 1.46 2.47 0.
time (sec) N/A 0.415 0.199 0.006 0. 0.216 5.404 0.22 0.
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 208 208 203 486 0 379 255 473 0
normalized size 1 1. 0.98 2.34 0. 1.82 1.23 2.27 0.
time (sec) N/A 0.317 0.156 0.004 0. 0.216 4.164 0.22 0.
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 173 173 167 334 0 259 156 336 0
normalized size 1 1. 0.97 1.93 0. 1.5 0.9 1.94 0.
time (sec) N/A 0.266 0.185 0.005 0. 0.212 2.995 0.218 0.
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 145 145 129 195 0 184 71 217 134
normalized size 1 1. 0.89 1.34 0. 1.27 0.49 1.5 0.92
time (sec) N/A 0.182 0.109 0.005 0. 0.216 2.025 0.216 37.706
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 288 288 224 222 0 377 447 375 260
normalized size 1 1. 0.78 0.77 0. 1.31 1.55 1.3 0.9
time (sec) N/A 0.321 0.22 0.009 0. 0.279 104.613 0.228 68.209
Problem 19 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 346 346 336 406 0 625 0 598 321
normalized size 1 1. 0.97 1.17 0. 1.81 0. 1.73 0.93
time (sec) N/A 0.613 0.351 0.018 0. 7.366 0. 0.227 108.441
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 320 320 313 905 0 1000 536 822 0
normalized size 1 1. 0.98 2.83 0. 3.12 1.68 2.57 0.
time (sec) N/A 0.633 0.439 0.017 0. 0.223 25.775 0.222 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 267 267 260 708 0 794 403 643 0
normalized size 1 1. 0.97 2.65 0. 2.97 1.51 2.41 0.
time (sec) N/A 0.498 0.364 0.016 0. 0.223 14.071 0.221 0.
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 234 234 227 529 0 606 289 495 0
normalized size 1 1. 0.97 2.26 0. 2.59 1.24 2.12 0.
time (sec) N/A 0.482 0.261 0.013 0. 0.22 8.056 0.221 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 203 205 367 0 427 189 350 0
normalized size 1 1. 1.01 1.81 0. 2.1 0.93 1.72 0.
time (sec) N/A 0.498 0.412 0.013 0. 0.219 5.08 0.218 0.
Problem 24 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 169 169 145 221 0 277 97 246 155
normalized size 1 1. 0.86 1.31 0. 1.64 0.57 1.46 0.92
time (sec) N/A 0.193 0.173 0.012 0. 0.216 2.686 0.218 34.112
Problem 25 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 346 346 337 406 0 633 0 598 321
normalized size 1 1. 0.97 1.17 0. 1.83 0. 1.73 0.93
time (sec) N/A 0.589 0.36 0.017 0. 7.404 0. 0.229 109.102
Problem 26 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 419 419 381 606 0 1250 0 896 386
normalized size 1 1. 0.91 1.45 0. 2.98 0. 2.14 0.92
time (sec) N/A 1.078 1.638 0.023 0. 77.342 0. 0.23 177.573
Problem 27 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 109 109 120 134 246 224 0 0 102
normalized size 1 1. 1.1 1.23 2.26 2.06 0. 0. 0.94
time (sec) N/A 0.116 0.133 0.01 1.52 0.222 0. 0. 17.977
Problem 28 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 78 78 73 76 147 139 0 0 71
normalized size 1 1. 0.94 0.97 1.88 1.78 0. 0. 0.91
time (sec) N/A 0.07 0.084 0.01 1.384 0.219 0. 0. 11.286
Problem 29 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 47 47 37 34 69 73 0 0 41
normalized size 1 1. 0.79 0.72 1.47 1.55 0. 0. 0.87
time (sec) N/A 0.036 0.045 0.005 1.361 0.218 0. 0. 5.491
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A A F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 16 16 674 15 19 31 29 0 12
normalized size 1 1. 42.12 0.94 1.19 1.94 1.81 0. 0.75
time (sec) N/A 0.009 2.202 0.003 1.402 0.211 1.952 0. 1.257
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 208 208 168 0 0 0 0 0 185
normalized size 1 1. 0.81 0. 0. 0. 0. 0. 0.89
time (sec) N/A 0.458 0.344 0.061 0. 0. 0. 0. 34.618
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 241 241 198 0 0 0 0 0 216
normalized size 1 1. 0.82 0. 0. 0. 0. 0. 0.9
time (sec) N/A 0.385 0.582 0.058 0. 0. 0. 0. 44.998
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 276 276 219 0 0 0 0 0 252
normalized size 1 1. 0.79 0. 0. 0. 0. 0. 0.91
time (sec) N/A 0.457 0.728 0.059 0. 0. 0. 0. 58.583
Problem 34 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 79 79 172 0 0 0 0 0 61
normalized size 1 1. 2.18 0. 0. 0. 0. 0. 0.77
time (sec) N/A 0.107 0.355 0.114 0. 0. 0. 0. 21.148
Problem 35 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 167 176 106 0 0 0 0 0 153
normalized size 1 1.05 0.63 0. 0. 0. 0. 0. 0.92
time (sec) N/A 0.278 0.08 0.082 0. 0. 0. 0. 33.094
Problem 36 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 84 85 75 0 0 0 0 0 73
normalized size 1 1.01 0.89 0. 0. 0. 0. 0. 0.87
time (sec) N/A 0.098 0.031 0.048 0. 0. 0. 0. 11.049
Problem 37 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 57 57 162 0 0 0 0 0 42
normalized size 1 1. 2.84 0. 0. 0. 0. 0. 0.74
time (sec) N/A 0.075 0.284 0.069 0. 0. 0. 0. 21.65
Problem 38 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 57 57 162 0 0 0 0 0 44
normalized size 1 1. 2.84 0. 0. 0. 0. 0. 0.77
time (sec) N/A 0.073 0.296 0.097 0. 0. 0. 0. 20.499
Problem 39 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 Yes TBD TBD TBD TBD TBD TBD
size 298 298 137 0 0 0 0 0 0
normalized size 1 1. 0.46 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.69 0.104 0.07 0. 0. 0. 0. 0.
Problem 40 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 176 176 106 0 0 0 0 0 153
normalized size 1 1. 0.6 0. 0. 0. 0. 0. 0.87
time (sec) N/A 0.282 0.057 0.07 0. 0. 0. 0. 32.217
Problem 41 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 93 85 75 0 0 0 0 0 73
normalized size 1 0.91 0.81 0. 0. 0. 0. 0. 0.78
time (sec) N/A 0.1 0.03 0.055 0. 0. 0. 0. 10.716
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F A F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 44 44 196 0 0 0 34 0 34
normalized size 1 1. 4.45 0. 0. 0. 0.77 0. 0.77
time (sec) N/A 0.027 0.287 0.035 0. 0. 54.267 0. 3.922
Problem 43 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 57 57 162 0 0 0 0 0 42
normalized size 1 1. 2.84 0. 0. 0. 0. 0. 0.74
time (sec) N/A 0.071 0.327 0.076 0. 0. 0. 0. 21.223
Problem 44 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 57 57 162 0 0 0 0 0 44
normalized size 1 1. 2.84 0. 0. 0. 0. 0. 0.77
time (sec) N/A 0.072 0.298 0.095 0. 0. 0. 0. 19.708
Problem 45 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 57 57 162 0 0 0 0 0 44
normalized size 1 1. 2.84 0. 0. 0. 0. 0. 0.77
time (sec) N/A 0.071 0.392 0.078 0. 0. 0. 0. 19.867
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F A F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 53 53 594 71 0 123 0 0 44
normalized size 1 1. 11.21 1.34 0. 2.32 0. 0. 0.83
time (sec) N/A 0.061 2.436 0.006 0. 0.252 0. 0. 10.552
Problem 47 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 94 94 94 97 130 1 107 132 0
normalized size 1 1. 1. 1.03 1.38 0.01 1.14 1.4 0.
time (sec) N/A 0.145 0.035 0.001 1.362 0.192 0.149 0.213 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 70 73 95 1 76 100 0
normalized size 1 1. 1. 1.04 1.36 0.01 1.09 1.43 0.
time (sec) N/A 0.104 0.031 0.001 1.356 0.192 0.122 0.212 0.
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 50 50 50 49 65 1 53 68 0
normalized size 1 1. 1. 0.98 1.3 0.02 1.06 1.36 0.
time (sec) N/A 0.074 0.02 0.001 1.413 0.19 0.105 0.211 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 28 28 28 25 32 1 26 35 0
normalized size 1 1. 1. 0.89 1.14 0.04 0.93 1.25 0.
time (sec) N/A 0.038 0.009 0.001 1.364 0.189 0.071 0.211 0.
Problem 51 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 223 223 196 266 0 743 87 331 204
normalized size 1 1. 0.88 1.19 0. 3.33 0.39 1.48 0.91
time (sec) N/A 0.328 0.228 0.01 0. 0.24 2.235 0.22 57.162
Problem 52 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 245 245 212 295 0 838 112 359 226
normalized size 1 1. 0.87 1.2 0. 3.42 0.46 1.47 0.92
time (sec) N/A 0.312 0.29 0.013 0. 0.241 3.207 0.219 59.134
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 273 273 243 314 0 941 151 386 258
normalized size 1 1. 0.89 1.15 0. 3.45 0.55 1.41 0.95
time (sec) N/A 0.357 0.372 0.016 0. 0.239 6.697 0.222 65.639
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 154 163 213 1 185 234 0
normalized size 1 1. 1. 1.06 1.38 0.01 1.2 1.52 0.
time (sec) N/A 0.236 0.062 0.001 1.372 0.189 0.183 0.21 0.
Problem 55 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 122 122 122 125 167 1 139 178 0
normalized size 1 1. 1. 1.02 1.37 0.01 1.14 1.46 0.
time (sec) N/A 0.173 0.043 0.002 1.358 0.191 0.156 0.212 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 82 87 111 1 97 123 0
normalized size 1 1. 1. 1.06 1.35 0.01 1.18 1.5 0.
time (sec) N/A 0.119 0.032 0.001 1.378 0.19 0.138 0.209 0.
Problem 57 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 50 50 50 49 65 1 53 68 0
normalized size 1 1. 1. 0.98 1.3 0.02 1.06 1.36 0.
time (sec) N/A 0.073 0.014 0.002 1.395 0.192 0.108 0.215 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 253 253 231 436 0 1457 187 477 0
normalized size 1 1. 0.91 1.72 0. 5.76 0.74 1.89 0.
time (sec) N/A 0.415 0.193 0.002 0. 0.241 3.589 0.221 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 291 291 298 475 0 1592 219 508 0
normalized size 1 1. 1.02 1.63 0. 5.47 0.75 1.75 0.
time (sec) N/A 0.723 0.283 0.002 0. 0.256 6.902 0.222 0.
Problem 60 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 349 349 319 499 0 1692 264 549 337
normalized size 1 1. 0.91 1.43 0. 4.85 0.76 1.57 0.97
time (sec) N/A 0.55 0.321 0.002 0. 0.258 20.563 0.223 82.463
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 332 332 322 837 0 2939 430 833 0
normalized size 1 1. 0.97 2.52 0. 8.85 1.3 2.51 0.
time (sec) N/A 0.581 0.329 0.008 0. 0.259 9.621 0.22 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 288 288 271 627 0 2198 301 649 0
normalized size 1 1. 0.94 2.18 0. 7.63 1.05 2.25 0.
time (sec) N/A 0.45 0.235 0.002 0. 0.251 6.181 0.218 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 253 253 231 436 0 1458 187 477 0
normalized size 1 1. 0.91 1.72 0. 5.76 0.74 1.89 0.
time (sec) N/A 0.401 0.173 0.003 0. 0.243 3.885 0.218 0.
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 223 223 196 266 0 743 87 331 204
normalized size 1 1. 0.88 1.19 0. 3.33 0.39 1.48 0.91
time (sec) N/A 0.299 0.215 0.005 0. 0.238 2.379 0.218 61.206
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 449 449 340 320 0 1472 0 0 400
normalized size 1 1. 0.76 0.71 0. 3.28 0. 0. 0.89
time (sec) N/A 0.567 0.282 0.002 0. 0.395 0. 0. 119.517
Problem 66 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 513 513 498 550 0 3665 0 900 474
normalized size 1 1. 0.97 1.07 0. 7.14 0. 1.75 0.92
time (sec) N/A 0.884 0.562 0.003 0. 21.891 0. 0.228 174.262
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 407 407 391 1118 0 3853 0 1077 0
normalized size 1 1. 0.96 2.75 0. 9.47 0. 2.65 0.
time (sec) N/A 0.786 0.673 0.018 0. 0.268 0. 0.221 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 357 357 341 885 0 3083 466 867 0
normalized size 1 1. 0.96 2.48 0. 8.64 1.31 2.43 0.
time (sec) N/A 0.719 0.501 0.017 0. 0.257 89.201 0.221 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 317 317 301 669 0 2306 335 670 0
normalized size 1 1. 0.95 2.11 0. 7.27 1.06 2.11 0.
time (sec) N/A 0.611 0.4 0.001 0. 0.248 20.583 0.222 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 291 291 297 475 0 1592 219 508 0
normalized size 1 1. 1.02 1.63 0. 5.47 0.75 1.75 0.
time (sec) N/A 0.724 0.3 0.014 0. 0.245 7.239 0.222 0.
Problem 71 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 245 245 212 295 0 838 112 359 226
normalized size 1 1. 0.87 1.2 0. 3.42 0.46 1.47 0.92
time (sec) N/A 0.317 0.304 0.011 0. 0.23 3.409 0.22 62.06
Problem 72 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 513 513 499 550 0 3665 0 900 474
normalized size 1 1. 0.97 1.07 0. 7.14 0. 1.75 0.92
time (sec) N/A 0.903 0.545 0.018 0. 22.335 0. 0.228 168.513
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) F(-1) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 596 596 561 784 0 0 0 0 0
normalized size 1 1. 0.94 1.32 0. 0. 0. 0. 0.
time (sec) N/A 1.468 3.493 0.003 0. 0. 0. 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 321 321 385 408 0 0 0 0 292
normalized size 1 1. 1.2 1.27 0. 0. 0. 0. 0.91
time (sec) N/A 0.914 1.729 0.069 0. 0. 0. 0. 151.844
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 277 277 419 311 0 0 0 0 248
normalized size 1 1. 1.51 1.12 0. 0. 0. 0. 0.9
time (sec) N/A 0.679 0.743 0.027 0. 0. 0. 0. 110.42
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 240 240 155 259 0 0 0 0 211
normalized size 1 1. 0.65 1.08 0. 0. 0. 0. 0.88
time (sec) N/A 0.449 0.277 0.025 0. 0. 0. 0. 73.184
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 162 162 156 183 0 0 0 0 143
normalized size 1 1. 0.96 1.13 0. 0. 0. 0. 0.88
time (sec) N/A 0.326 0.235 0.023 0. 0. 0. 0. 52.459
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 281 281 329 301 0 0 0 0 241
normalized size 1 1. 1.17 1.07 0. 0. 0. 0. 0.86
time (sec) N/A 0.609 0.603 0.043 0. 0. 0. 0. 106.733
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 334 334 396 361 0 0 0 0 298
normalized size 1 1. 1.19 1.08 0. 0. 0. 0. 0.89
time (sec) N/A 0.962 1.568 0.047 0. 0. 0. 0. 165.584
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 973 973 435 322 0 0 0 0 0
normalized size 1 1. 0.45 0.33 0. 0. 0. 0. 0.
time (sec) N/A 3.707 1.147 0.036 0. 0. 0. 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F F A
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 932 932 161 273 0 0 0 0 814
normalized size 1 1. 0.17 0.29 0. 0. 0. 0. 0.87
time (sec) N/A 1.766 0.238 0.023 0. 0. 0. 0. 149.324
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F F A
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 775 775 161 191 0 0 0 0 690
normalized size 1 1. 0.21 0.25 0. 0. 0. 0. 0.89
time (sec) N/A 1.234 0.081 0.021 0. 0. 0. 0. 100.558
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 969 969 342 313 0 0 0 0 0
normalized size 1 1. 0.35 0.32 0. 0. 0. 0. 0.
time (sec) N/A 2.406 0.495 0.043 0. 0. 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 1029 1029 406 371 0 0 0 0 0
normalized size 1 1. 0.39 0.36 0. 0. 0. 0. 0.
time (sec) N/A 4.384 1.641 0.047 0. 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F(-1) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 426 426 580 540 0 0 0 0 0
normalized size 1 1. 1.36 1.27 0. 0. 0. 0. 0.
time (sec) N/A 1.391 1.826 0.041 0. 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 365 365 491 412 0 0 0 0 333
normalized size 1 1. 1.35 1.13 0. 0. 0. 0. 0.91
time (sec) N/A 1.049 1.362 0.04 0. 0. 0. 0. 168.627
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 309 309 423 329 0 0 0 0 279
normalized size 1 1. 1.37 1.06 0. 0. 0. 0. 0.9
time (sec) N/A 0.746 0.594 0.036 0. 0. 0. 0. 107.566
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 276 276 310 294 0 0 0 0 243
normalized size 1 1. 1.12 1.07 0. 0. 0. 0. 0.88
time (sec) N/A 0.621 0.269 0.033 0. 0. 0. 0. 97.147
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 310 310 349 322 0 0 0 0 270
normalized size 1 1. 1.13 1.04 0. 0. 0. 0. 0.87
time (sec) N/A 0.688 0.991 0.035 0. 0. 0. 0. 109.539
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 362 362 465 375 0 0 0 0 323
normalized size 1 1. 1.28 1.04 0. 0. 0. 0. 0.89
time (sec) N/A 1.074 1.186 0.058 0. 0. 0. 0. 175.193
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F(-1) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 439 439 617 484 0 0 0 0 0
normalized size 1 1. 1.41 1.1 0. 0. 0. 0. 0.
time (sec) N/A 1.439 2.184 0.057 0. 0. 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F A F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 103 103 155 103 0 450 0 0 94
normalized size 1 1. 1.5 1. 0. 4.37 0. 0. 0.91
time (sec) N/A 0.141 0.242 0.024 0. 0.592 0. 0. 22.737
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F A F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 116 116 155 158 0 500 0 0 100
normalized size 1 1. 1.34 1.36 0. 4.31 0. 0. 0.86
time (sec) N/A 0.079 0.272 0.025 0. 0.587 0. 0. 12.654
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F A F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 211 211 396 0 0 2776 0 0 192
normalized size 1 1. 1.88 0. 0. 13.16 0. 0. 0.91
time (sec) N/A 0.523 1.806 0.084 0. 2.723 0. 0. 62.95
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F A F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 173 173 161 0 0 1006 0 0 148
normalized size 1 1. 0.93 0. 0. 5.82 0. 0. 0.86
time (sec) N/A 0.24 0.255 0.055 0. 0.294 0. 0. 37.997
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 105 105 122 0 0 0 0 0 90
normalized size 1 1. 1.16 0. 0. 0. 0. 0. 0.86
time (sec) N/A 0.136 0.124 0.05 0. 0. 0. 0. 23.604
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 134 134 153 0 0 0 0 0 117
normalized size 1 1. 1.14 0. 0. 0. 0. 0. 0.87
time (sec) N/A 0.236 0.368 0.055 0. 0. 0. 0. 34.045
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 180 180 184 0 0 0 0 0 158
normalized size 1 1. 1.02 0. 0. 0. 0. 0. 0.88
time (sec) N/A 0.49 0.563 0.057 0. 0. 0. 0. 80.616
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 233 233 231 0 0 0 0 0 212
normalized size 1 1. 0.99 0. 0. 0. 0. 0. 0.91
time (sec) N/A 0.73 0.684 0.061 0. 0. 0. 0. 133.593
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 316 316 396 0 0 0 0 0 282
normalized size 1 1. 1.25 0. 0. 0. 0. 0. 0.89
time (sec) N/A 0.922 1.725 0.098 0. 0. 0. 0. 112.517
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F(-1) F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 274 274 435 0 0 0 0 0 235
normalized size 1 1. 1.59 0. 0. 0. 0. 0. 0.86
time (sec) N/A 0.493 0.714 0.094 0. 0. 0. 0. 62.65
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F(-1) F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 166 166 160 0 0 0 0 0 143
normalized size 1 1. 0.96 0. 0. 0. 0. 0. 0.86
time (sec) N/A 0.293 0.247 0.055 0. 0. 0. 0. 41.329
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F(-1) F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 259 259 161 0 0 0 0 0 221
normalized size 1 1. 0.62 0. 0. 0. 0. 0. 0.85
time (sec) N/A 0.471 0.087 0.052 0. 0. 0. 0. 62.698
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F(-1) F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 304 304 343 0 0 0 0 0 265
normalized size 1 1. 1.13 0. 0. 0. 0. 0. 0.87
time (sec) N/A 0.698 0.536 0.054 0. 0. 0. 0. 99.62
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 357 357 407 0 0 0 0 0 318
normalized size 1 1. 1.14 0. 0. 0. 0. 0. 0.89
time (sec) N/A 1.08 1.561 0.058 0. 0. 0. 0. 161.555
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F A F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 280 280 735 0 0 3868 0 0 255
normalized size 1 1. 2.62 0. 0. 13.81 0. 0. 0.91
time (sec) N/A 0.893 4.048 0.096 0. 19.954 0. 0. 101.332
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F A F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 230 230 462 0 0 1972 0 0 206
normalized size 1 1. 2.01 0. 0. 8.57 0. 0. 0.9
time (sec) N/A 0.439 0.819 0.059 0. 1.425 0. 0. 63.515
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 135 135 152 0 0 0 0 0 119
normalized size 1 1. 1.13 0. 0. 0. 0. 0. 0.88
time (sec) N/A 0.204 0.351 0.056 0. 0. 0. 0. 31.236
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 162 162 171 0 0 0 0 0 141
normalized size 1 1. 1.06 0. 0. 0. 0. 0. 0.87
time (sec) N/A 0.301 0.285 0.066 0. 0. 0. 0. 36.648
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 205 205 204 0 0 0 0 0 180
normalized size 1 1. 1. 0. 0. 0. 0. 0. 0.88
time (sec) N/A 0.495 0.449 0.059 0. 0. 0. 0. 77.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 266 266 242 0 0 0 0 0 240
normalized size 1 1. 0.91 0. 0. 0. 0. 0. 0.9
time (sec) N/A 0.885 0.822 0.064 0. 0. 0. 0. 144.937
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 353 353 506 0 0 0 0 0 316
normalized size 1 1. 1.43 0. 0. 0. 0. 0. 0.9
time (sec) N/A 0.987 1.294 0.094 0. 0. 0. 0. 112.913
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 298 298 440 0 0 0 0 0 260
normalized size 1 1. 1.48 0. 0. 0. 0. 0. 0.87
time (sec) N/A 0.704 0.646 0.059 0. 0. 0. 0. 83.37
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 308 308 322 0 0 0 0 0 267
normalized size 1 1. 1.05 0. 0. 0. 0. 0. 0.87
time (sec) N/A 0.637 0.288 0.058 0. 0. 0. 0. 85.741
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 330 330 341 0 0 0 0 0 292
normalized size 1 1. 1.03 0. 0. 0. 0. 0. 0.88
time (sec) N/A 0.753 0.891 0.059 0. 0. 0. 0. 96.992
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F(-1) F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 390 390 485 0 0 0 0 0 350
normalized size 1 1. 1.24 0. 0. 0. 0. 0. 0.9
time (sec) N/A 1.164 1.038 0.06 0. 0. 0. 0. 157.932
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 70 0 0 273 0 0 49
normalized size 1 1. 1.32 0. 0. 5.15 0. 0. 0.92
time (sec) N/A 0.057 0.085 0.038 0. 4.313 0. 0. 4.794
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 57 57 76 0 0 0 0 0 49
normalized size 1 1. 1.33 0. 0. 0. 0. 0. 0.86
time (sec) N/A 0.069 0.11 0.076 0. 0. 0. 0. 9.04
Problem 119 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 79 79 172 0 0 0 0 0 61
normalized size 1 1. 2.18 0. 0. 0. 0. 0. 0.77
time (sec) N/A 0.123 0.359 0.115 0. 0. 0. 0. 21.945
Problem 120 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 176 176 106 0 0 0 0 0 153
normalized size 1 1. 0.6 0. 0. 0. 0. 0. 0.87
time (sec) N/A 0.316 0.079 0.057 0. 0. 0. 0. 32.823
Problem 121 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 93 85 75 0 0 0 0 0 73
normalized size 1 0.91 0.81 0. 0. 0. 0. 0. 0.78
time (sec) N/A 0.111 0.035 0.049 0. 0. 0. 0. 11.371
Problem 122 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 57 57 162 0 0 0 0 0 42
normalized size 1 1. 2.84 0. 0. 0. 0. 0. 0.74
time (sec) N/A 0.084 0.281 0.072 0. 0. 0. 0. 21.903
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 57 57 162 0 0 0 0 0 44
normalized size 1 1. 2.84 0. 0. 0. 0. 0. 0.77
time (sec) N/A 0.083 0.308 0.064 0. 0. 0. 0. 20.222
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-2) F(-1) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 545 545 379 0 0 0 0 0 0
normalized size 1 1. 0.7 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.311 1.626 0.055 0. 0. 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 143 143 131 248 0 1 491 0 131
normalized size 1 1. 0.92 1.73 0. 0.01 3.43 0. 0.92
time (sec) N/A 0.417 0.205 0.02 0. 0.26 15.493 0. 50.01
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 85 191 0 1 156 0 82
normalized size 1 1. 0.86 1.93 0. 0.01 1.58 0. 0.83
time (sec) N/A 0.218 0.134 0.017 0. 0.257 12.042 0. 20.394
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 63 163 0 1 121 0 63
normalized size 1 1. 0.85 2.2 0. 0.01 1.64 0. 0.85
time (sec) N/A 0.146 0.122 0.016 0. 0.259 21.053 0. 12.818
Problem 128 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 39 39 50 74 0 1 42 86 31
normalized size 1 1. 1.28 1.9 0. 0.03 1.08 2.21 0.79
time (sec) N/A 0.057 0.035 0.006 0. 0.257 6.494 0.233 5.903
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 153 286 0 1 0 0 90
normalized size 1 1. 1.47 2.75 0. 0.01 0. 0. 0.87
time (sec) N/A 0.355 0.359 0.03 0. 0.288 0. 0. 41.254
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 147 147 197 939 0 1 0 0 122
normalized size 1 1. 1.34 6.39 0. 0.01 0. 0. 0.83
time (sec) N/A 0.607 0.599 0.028 0. 0.3 0. 0. 67.723
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 213 213 275 1963 0 1 0 4 182
normalized size 1 1. 1.29 9.22 0. 0. 0. 0.02 0.85
time (sec) N/A 0.968 0.789 0.028 0. 0.402 0. 0.561 111.143
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 164 164 169 332 0 1 1862 0 151
normalized size 1 1. 1.03 2.02 0. 0.01 11.35 0. 0.92
time (sec) N/A 0.448 0.259 0.02 0. 0.255 41.585 0. 48.464
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 126 126 115 244 0 1 576 0 107
normalized size 1 1. 0.91 1.94 0. 0.01 4.57 0. 0.85
time (sec) N/A 0.249 0.239 0.019 0. 0.259 26.834 0. 22.461
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 84 194 0 1 204 0 87
normalized size 1 1. 0.84 1.94 0. 0.01 2.04 0. 0.87
time (sec) N/A 0.182 0.163 0.016 0. 0.259 32.568 0. 14.757
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 56 94 0 1 92 0 44
normalized size 1 1. 1.04 1.74 0. 0.02 1.7 0. 0.81
time (sec) N/A 0.077 0.046 0.006 0. 0.264 9.18 0. 7.711
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 156 528 0 1 0 0 92
normalized size 1 1. 1.47 4.98 0. 0.01 0. 0. 0.87
time (sec) N/A 0.384 0.494 0.02 0. 0.296 0. 0. 37.956
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 156 156 231 1202 0 1 0 0 129
normalized size 1 1. 1.48 7.71 0. 0.01 0. 0. 0.83
time (sec) N/A 0.67 0.479 0.02 0. 0.293 0. 0. 68.384
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 209 209 256 2373 0 1 0 4 182
normalized size 1 1. 1.22 11.35 0. 0. 0. 0.02 0.87
time (sec) N/A 0.984 0.512 0.021 0. 0.328 0. 0.551 106.166
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 198 198 212 434 0 1 5557 0 184
normalized size 1 1. 1.07 2.19 0. 0.01 28.07 0. 0.93
time (sec) N/A 0.5 0.355 0.022 0. 0.261 82.497 0. 54.841
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 152 152 156 318 0 1 1884 0 131
normalized size 1 1. 1.03 2.09 0. 0.01 12.39 0. 0.86
time (sec) N/A 0.299 0.25 0.02 0. 0.252 48.817 0. 26.754
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 125 125 105 240 0 1 561 0 110
normalized size 1 1. 0.84 1.92 0. 0.01 4.49 0. 0.88
time (sec) N/A 0.209 0.252 0.016 0. 0.263 47.699 0. 17.605
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 71 112 0 1 99 0 60
normalized size 1 1. 1. 1.58 0. 0.01 1.39 0. 0.85
time (sec) N/A 0.101 0.102 0.005 0. 0.256 13.361 0. 9.588
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 172 859 0 1 0 0 114
normalized size 1 1. 1.28 6.41 0. 0.01 0. 0. 0.85
time (sec) N/A 0.639 0.228 0.023 0. 0.436 0. 0. 62.059
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 166 166 219 2014 0 1 0 0 138
normalized size 1 1. 1.32 12.13 0. 0.01 0. 0. 0.83
time (sec) N/A 0.669 0.604 0.024 0. 0.373 0. 0. 63.203
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 237 237 304 2807 0 1 0 4 204
normalized size 1 1. 1.28 11.84 0. 0. 0. 0.02 0.86
time (sec) N/A 1.022 0.651 0.022 0. 0.342 0. 0.549 106.304
Problem 146 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 126 126 99 540 0 1 377 207 114
normalized size 1 1. 0.79 4.29 0. 0.01 2.99 1.64 0.9
time (sec) N/A 0.284 0.289 0.021 0. 0.253 15.563 0.257 25.537
Problem 147 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 73 73 75 354 0 1 105 131 60
normalized size 1 1. 1.03 4.85 0. 0.01 1.44 1.79 0.82
time (sec) N/A 0.181 0.161 0.02 0. 0.248 12.382 0.256 16.515
Problem 148 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 51 51 62 179 0 1 73 99 42
normalized size 1 1. 1.22 3.51 0. 0.02 1.43 1.94 0.82
time (sec) N/A 0.11 0.075 0.017 0. 0.25 25.068 0.251 9.442
Problem 149 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 43 43 53 70 0 1 44 96 32
normalized size 1 1. 1.23 1.63 0. 0.02 1.02 2.23 0.74
time (sec) N/A 0.059 0.047 0.005 0. 0.247 7.839 0.237 5.357
Problem 150 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 108 108 157 389 0 1 0 174 92
normalized size 1 1. 1.45 3.6 0. 0.01 0. 1.61 0.85
time (sec) N/A 0.317 0.467 0.019 0. 0.277 0. 0.253 40.759
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 172 172 224 1137 0 1 0 393 141
normalized size 1 1. 1.3 6.61 0. 0.01 0. 2.28 0.82
time (sec) N/A 0.65 0.841 0.029 0. 0.36 0. 0.257 68.013
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 250 250 301 2269 0 1 0 459 218
normalized size 1 1. 1.2 9.08 0. 0. 0. 1.84 0.87
time (sec) N/A 1.083 0.95 0.025 0. 0.767 0. 0.261 117.385
Problem 153 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 132 132 123 976 0 1 0 297 122
normalized size 1 1. 0.93 7.39 0. 0.01 0. 2.25 0.92
time (sec) N/A 0.327 0.179 0.025 0. 0.257 0. 0.252 27.207
Problem 154 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 94 90 100 796 0 1 0 217 82
normalized size 1 0.96 1.06 8.47 0. 0.01 0. 2.31 0.87
time (sec) N/A 0.248 0.188 0.022 0. 0.243 0. 0.252 18.821
Problem 155 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 76 76 81 394 0 1 224 165 66
normalized size 1 1. 1.07 5.18 0. 0.01 2.95 2.17 0.87
time (sec) N/A 0.155 0.117 0.018 0. 0.247 21.432 0.254 12.511
Problem 156 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 61 61 67 203 0 1 71 116 51
normalized size 1 1. 1.1 3.33 0. 0.02 1.16 1.9 0.84
time (sec) N/A 0.083 0.1 0.005 0. 0.251 11.453 0.25 8.025
Problem 157 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 147 147 197 1480 0 1 0 261 122
normalized size 1 1. 1.34 10.07 0. 0.01 0. 1.78 0.83
time (sec) N/A 0.619 1.228 0.026 0. 0.386 0. 0.254 67.665
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 224 224 290 3121 0 1 0 560 194
normalized size 1 1. 1.29 13.93 0. 0. 0. 2.5 0.87
time (sec) N/A 0.962 1.108 0.026 0. 0.812 0. 0.256 110.149
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 320 320 385 5164 0 1 0 678 0
normalized size 1 1. 1.2 16.14 0. 0. 0. 2.12 0.
time (sec) N/A 1.524 1.824 0.027 0. 2.248 0. 0.261 0.
Problem 160 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 143 143 145 1157 0 1 0 267 138
normalized size 1 1. 1.01 8.09 0. 0.01 0. 1.87 0.97
time (sec) N/A 0.429 0.242 0.023 0. 0.255 0. 0.26 27.837
Problem 161 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 122 118 123 595 0 1 0 217 107
normalized size 1 0.97 1.01 4.88 0. 0.01 0. 1.78 0.88
time (sec) N/A 0.296 0.189 0.02 0. 0.254 0. 0.258 22.725
Problem 162 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 103 103 102 548 0 1 1479 185 90
normalized size 1 1. 0.99 5.32 0. 0.01 14.36 1.8 0.87
time (sec) N/A 0.199 0.141 0.019 0. 0.242 39.109 0.256 16.362
Problem 163 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 82 82 82 276 0 1 774 132 70
normalized size 1 1. 1. 3.37 0. 0.01 9.44 1.61 0.85
time (sec) N/A 0.113 0.134 0.006 0. 0.242 17.9 0.254 11.539
Problem 164 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 201 201 250 2490 0 1 0 332 173
normalized size 1 1. 1.24 12.39 0. 0. 0. 1.65 0.86
time (sec) N/A 0.946 0.963 0.024 0. 0.903 0. 0.258 106.153
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 287 287 364 4648 0 1 0 779 252
normalized size 1 1. 1.27 16.2 0. 0. 0. 2.71 0.88
time (sec) N/A 1.409 1.844 0.028 0. 2.542 0. 0.281 160.074
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 409 409 465 7306 0 1 0 703 0
normalized size 1 1. 1.14 17.86 0. 0. 0. 1.72 0.
time (sec) N/A 2.072 3.82 0.031 0. 6.637 0. 0.266 0.
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 168 253 0 1 0 0 104
normalized size 1 1. 1.37 2.06 0. 0.01 0. 0. 0.85
time (sec) N/A 0.354 0.355 0.033 0. 0.729 0. 0. 32.876
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 98 155 0 1 0 0 65
normalized size 1 1. 1.21 1.91 0. 0.01 0. 0. 0.8
time (sec) N/A 0.193 0.195 0.034 0. 0.327 0. 0. 14.874
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 122 122 112 280 0 1 0 0 114
normalized size 1 1. 0.92 2.3 0. 0.01 0. 0. 0.93
time (sec) N/A 0.301 0.214 0.049 0. 0.329 0. 0. 24.182
Problem 170 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 96 96 206 0 0 0 0 0 66
normalized size 1 1. 2.15 0. 0. 0. 0. 0. 0.69
time (sec) N/A 0.181 0.493 0.142 0. 0. 0. 0. 23.234
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 40 45 0 1 82 45 34
normalized size 1 1. 1.03 1.15 0. 0.03 2.1 1.15 0.87
time (sec) N/A 0.072 0.044 0.007 0. 0.235 1.665 0.214 11.336
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 233 233 205 277 0 0 0 0 202
normalized size 1 1. 0.88 1.19 0. 0. 0. 0. 0.87
time (sec) N/A 0.634 0.52 0.05 0. 0. 0. 0. 62.946
Problem 173 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 232 232 86 94 0 0 0 0 199
normalized size 1 1. 0.37 0.41 0. 0. 0. 0. 0.86
time (sec) N/A 0.588 0.102 0.029 0. 0. 0. 0. 56.681
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 262 262 191 185 0 0 0 0 230
normalized size 1 1. 0.73 0.71 0. 0. 0. 0. 0.88
time (sec) N/A 0.836 0.377 0.065 0. 0. 0. 0. 80.5
Problem 175 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 79 79 252 0 0 0 0 0 63
normalized size 1 1. 3.19 0. 0. 0. 0. 0. 0.8
time (sec) N/A 0.234 0.701 0.141 0. 0. 0. 0. 31.42
Problem 176 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 145 145 129 195 0 184 71 217 134
normalized size 1 1. 0.89 1.34 0. 1.27 0.49 1.5 0.92
time (sec) N/A 0.258 0.166 0.007 0. 0.239 2.223 0.22 37.577
Problem 177 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 49 49 51 59 63 65 82 66 0
normalized size 1 1. 1.04 1.2 1.29 1.33 1.67 1.35 0.
time (sec) N/A 0.122 0.044 0.007 1.706 0.24 0.818 0.216 0.
Problem 178 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 26 26 26 21 27 27 24 27 0
normalized size 1 1. 1. 0.81 1.04 1.04 0.92 1.04 0.
time (sec) N/A 0.046 0.01 0.004 1.4 0.23 0.472 0.215 0.
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 31 24 31 31 27 32 15
normalized size 1 1. 1.82 1.41 1.82 1.82 1.59 1.88 0.88
time (sec) N/A 0.05 0.01 0.005 1.391 0.227 0.649 0.217 10.383
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 102 66 90 123 102 0 99
normalized size 1 1. 0.98 0.63 0.87 1.18 0.98 0. 0.95
time (sec) N/A 0.203 0.05 0.009 1.648 0.242 20.267 0. 19.88
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 30 23 30 30 26 31 0
normalized size 1 1. 1. 0.77 1. 1. 0.87 1.03 0.
time (sec) N/A 0.055 0.011 0.004 1.376 0.237 0.405 0.216 0.
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-2) F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 151 0 0 0 0 0 66
normalized size 1 1. 1.91 0. 0. 0. 0. 0. 0.84
time (sec) N/A 0.083 0.262 0.118 0. 0. 0. 0. 19.689
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-2) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 116 0 0 0 0 0 63
normalized size 1 1. 1.53 0. 0. 0. 0. 0. 0.83
time (sec) N/A 0.076 0.147 0.068 0. 0. 0. 0. 19.437
Problem 184 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 72 72 72 0 0 0 0 0 56
normalized size 1 1. 1. 0. 0. 0. 0. 0. 0.78
time (sec) N/A 0.073 0.126 0.242 0. 0. 0. 0. 21.4
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 123 138 0 711 2744 1073 0
normalized size 1 1. 0.93 1.05 0. 5.39 20.79 8.13 0.
time (sec) N/A 0.251 0.19 0.018 0. 0.263 9.819 0.229 0.
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 92 104 0 431 1540 656 0
normalized size 1 1. 0.93 1.05 0. 4.35 15.56 6.63 0.
time (sec) N/A 0.167 0.145 0.016 0. 0.248 5.26 0.225 0.
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 65 74 0 236 726 342 0
normalized size 1 1. 0.93 1.06 0. 3.37 10.37 4.89 0.
time (sec) N/A 0.114 0.109 0.014 0. 0.257 2.792 0.221 0.
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 37 43 0 93 236 126 0
normalized size 1 1. 0.92 1.08 0. 2.32 5.9 3.15 0.
time (sec) N/A 0.059 0.083 0.012 0. 0.25 1.312 0.214 0.
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 40 0 0 0 0 0 31
normalized size 1 1. 0.93 0. 0. 0. 0. 0. 0.72
time (sec) N/A 0.055 0.037 0.083 0. 0. 0. 0. 7.203
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 68 0 0 0 0 0 53
normalized size 1 1. 0.93 0. 0. 0. 0. 0. 0.73
time (sec) N/A 0.091 0.079 0.064 0. 0. 0. 0. 9.663
Problem 191 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 78 78 96 0 0 0 0 0 60
normalized size 1 1. 1.23 0. 0. 0. 0. 0. 0.77
time (sec) N/A 0.092 0.108 0.076 0. 0. 0. 0. 10.156
Problem 192 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 78 78 136 0 0 0 0 0 60
normalized size 1 1. 1.74 0. 0. 0. 0. 0. 0.77
time (sec) N/A 0.09 0.165 0.093 0. 0. 0. 0. 10.142
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-2) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 158 158 149 164 0 900 0 1 0
normalized size 1 1. 0.94 1.04 0. 5.7 0. 0.01 0.
time (sec) N/A 0.291 0.251 0.019 0. 0.253 0. 0.227 0.
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-2) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 112 112 105 117 0 500 0 782 0
normalized size 1 1. 0.94 1.04 0. 4.46 0. 6.98 0.
time (sec) N/A 0.187 0.259 0.017 0. 0.256 0. 0.227 0.
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 65 74 0 236 726 342 0
normalized size 1 1. 0.93 1.06 0. 3.37 10.37 4.89 0.
time (sec) N/A 0.114 0.111 0.014 0. 0.255 2.771 0.22 0.
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 82 0 0 0 0 0 70
normalized size 1 1. 0.98 0. 0. 0. 0. 0. 0.83
time (sec) N/A 0.219 0.069 0.062 0. 0. 0. 0. 22.834
Problem 197 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 115 115 95 0 0 0 0 0 95
normalized size 1 1. 0.83 0. 0. 0. 0. 0. 0.83
time (sec) N/A 0.245 0.191 0.067 0. 0. 0. 0. 23.097
Problem 198 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 160 160 133 0 0 0 0 0 141
normalized size 1 1. 0.83 0. 0. 0. 0. 0. 0.88
time (sec) N/A 0.359 0.173 0.079 0. 0. 0. 0. 27.925
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-2) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 310 310 146 0 0 0 0 0 0
normalized size 1 1. 0.47 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.128 0.185 0.072 0. 0. 0. 0. 0.
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-2) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 173 173 104 0 0 0 0 0 0
normalized size 1 1. 0.6 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.614 0.507 0.068 0. 0. 0. 0. 0.
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 82 0 0 0 0 0 70
normalized size 1 1. 0.98 0. 0. 0. 0. 0. 0.83
time (sec) N/A 0.236 0.071 0.062 0. 0. 0. 0. 22.161
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 40 0 0 0 0 0 31
normalized size 1 1. 0.95 0. 0. 0. 0. 0. 0.74
time (sec) N/A 0.053 0.033 0.058 0. 0. 0. 0. 6.355
Problem 203 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 72 72 64 0 0 0 0 0 53
normalized size 1 1. 0.89 0. 0. 0. 0. 0. 0.74
time (sec) N/A 0.079 0.055 0.091 0. 0. 0. 0. 10.966
Problem 204 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 123 123 121 0 0 0 0 0 100
normalized size 1 1. 0.98 0. 0. 0. 0. 0. 0.81
time (sec) N/A 0.36 0.217 0.165 0. 0. 0. 0. 48.486
Problem 205 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 210 210 210 0 0 0 0 0 218
normalized size 1 1. 1. 0. 0. 0. 0. 0. 1.04
time (sec) N/A 0.819 0.334 0.175 0. 0. 0. 0. 112.827
Problem 206 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 Yes TBD TBD TBD TBD TBD TBD
size 341 341 217 0 0 0 0 0 0
normalized size 1 1. 0.64 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.287 0.337 0.078 0. 0. 0. 0. 0.
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 200 200 167 0 0 0 0 0 172
normalized size 1 1. 0.84 0. 0. 0. 0. 0. 0.86
time (sec) N/A 0.61 0.458 0.073 0. 0. 0. 0. 65.611
Problem 208 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 115 115 96 0 0 0 0 0 97
normalized size 1 1. 0.83 0. 0. 0. 0. 0. 0.84
time (sec) N/A 0.237 0.2 0.066 0. 0. 0. 0. 22.598
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 68 0 0 0 0 0 53
normalized size 1 1. 0.94 0. 0. 0. 0. 0. 0.74
time (sec) N/A 0.084 0.077 0.065 0. 0. 0. 0. 9.
Problem 210 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 122 122 108 0 0 0 0 0 100
normalized size 1 1. 0.89 0. 0. 0. 0. 0. 0.82
time (sec) N/A 0.344 0.255 0.154 0. 0. 0. 0. 48.624
Problem 211 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 193 193 147 0 0 0 0 0 162
normalized size 1 1. 0.76 0. 0. 0. 0. 0. 0.84
time (sec) N/A 0.695 0.344 0.153 0. 0. 0. 0. 105.36
Problem 212 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 Yes TBD TBD TBD TBD TBD TBD
size 299 299 233 0 0 0 0 0 0
normalized size 1 1. 0.78 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.305 0.536 0.187 0. 0. 0. 0. 0.
Problem 213 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 81 81 190 0 0 0 0 0 63
normalized size 1 1. 2.35 0. 0. 0. 0. 0. 0.78
time (sec) N/A 0.129 0.662 0.207 0. 0. 0. 0. 21.667
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-2) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 402 401 168 0 0 0 0 0 0
normalized size 1 1. 0.42 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.285 0.444 0.159 0. 0. 0. 0. 0.
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-2) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 202 197 140 0 0 0 0 0 173
normalized size 1 0.98 0.69 0. 0. 0. 0. 0. 0.86
time (sec) N/A 0.624 0.248 0.137 0. 0. 0. 0. 36.28
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-2) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 89 85 0 0 0 0 0 80
normalized size 1 0.91 0.87 0. 0. 0. 0. 0. 0.82
time (sec) N/A 0.12 0.103 0.135 0. 0. 0. 0. 11.037
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 46 0 0 0 0 0 36
normalized size 1 1. 1. 0. 0. 0. 0. 0. 0.78
time (sec) N/A 0.032 0.027 0.002 0. 0. 0. 0. 3.704
Problem 218 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 59 59 180 0 0 0 0 0 44
normalized size 1 1. 3.05 0. 0. 0. 0. 0. 0.75
time (sec) N/A 0.084 0.418 0.122 0. 0. 0. 0. 21.433
Problem 219 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 59 59 180 0 0 0 0 0 46
normalized size 1 1. 3.05 0. 0. 0. 0. 0. 0.78
time (sec) N/A 0.083 0.474 0.103 0. 0. 0. 0. 19.946
Problem 220 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 59 59 180 0 0 0 0 0 46
normalized size 1 1. 3.05 0. 0. 0. 0. 0. 0.78
time (sec) N/A 0.084 0.692 0.112 0. 0. 0. 0. 20.116
Problem 221 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 93 93 93 0 0 0 0 0 83
normalized size 1 1. 1. 0. 0. 0. 0. 0. 0.89
time (sec) N/A 0.073 0.558 0.249 0. 0. 0. 0. 8.191
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 178 178 198 0 0 645 0 0 156
normalized size 1 1. 1.11 0. 0. 3.62 0. 0. 0.88
time (sec) N/A 0.241 0.608 0.203 0. 0.255 0. 0. 35.596
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 139 0 0 312 0 0 100
normalized size 1 1. 1.2 0. 0. 2.69 0. 0. 0.86
time (sec) N/A 0.113 0.314 0.177 0. 0.257 0. 0. 18.101
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 82 0 0 115 0 0 48
normalized size 1 1. 1.41 0. 0. 1.98 0. 0. 0.83
time (sec) N/A 0.048 0.169 0.165 0. 0.267 0. 0. 6.749
Problem 225 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 53 0 42 0 0 12
normalized size 1 1. 1. 2.94 0. 2.33 0. 0. 0.67
time (sec) N/A 0.012 0.04 0.036 0. 0.249 0. 0. 1.391
Problem 226 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 53 53 79 0 0 0 0 0 39
normalized size 1 1. 1.49 0. 0. 0. 0. 0. 0.74
time (sec) N/A 0.048 0.301 0.12 0. 0. 0. 0. 6.259
Problem 227 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 54 54 53 0 0 0 0 0 42
normalized size 1 1. 0.98 0. 0. 0. 0. 0. 0.78
time (sec) N/A 0.05 0.135 0.112 0. 0. 0. 0. 6.155
Problem 228 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A F F F F F(-1) F A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 56 56 0 0 0 0 0 0 44
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.79
time (sec) N/A 0.052 179.999 0.115 0. 0. 0. 0. 6.47
Problem 229 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 193 179 1414 0 0 0 0 0 155
normalized size 1 0.93 7.33 0. 0. 0. 0. 0. 0.8
time (sec) N/A 0.206 53.257 0.264 0. 0. 0. 0. 25.243
Problem 230 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F A F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 57 57 461 0 0 146 0 0 41
normalized size 1 1. 8.09 0. 0. 2.56 0. 0. 0.72
time (sec) N/A 0.085 1.939 0.306 0. 0.265 0. 0. 13.522
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 327 327 153 0 0 540 0 0 286
normalized size 1 1. 0.47 0. 0. 1.65 0. 0. 0.87
time (sec) N/A 0.548 0.305 0.21 0. 0.26 0. 0. 81.854
Problem 232 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 96 0 0 234 0 0 105
normalized size 1 1. 0.76 0. 0. 1.84 0. 0. 0.83
time (sec) N/A 0.173 0.139 0.18 0. 0.261 0. 0. 17.83
Problem 233 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 55 0 0 92 0 0 39
normalized size 1 1. 1.1 0. 0. 1.84 0. 0. 0.78
time (sec) N/A 0.04 0.037 0.131 0. 0.256 0. 0. 3.682
Problem 234 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 Yes TBD TBD TBD TBD TBD TBD
size 95 95 153 0 0 0 0 0 70
normalized size 1 1. 1.61 0. 0. 0. 0. 0. 0.74
time (sec) N/A 0.106 2.236 0.126 0. 0. 0. 0. 13.62
Problem 235 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 127 127 1070 0 0 0 0 0 95
normalized size 1 1. 8.43 0. 0. 0. 0. 0. 0.75
time (sec) N/A 0.151 62.191 0.116 0. 0. 0. 0. 19.246
Problem 236 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 131 131 1241 0 0 0 0 0 105
normalized size 1 1. 9.47 0. 0. 0. 0. 0. 0.8
time (sec) N/A 0.162 43.768 0.113 0. 0. 0. 0. 19.697
Problem 237 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A F F F F F(-1) F A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 133 133 0 0 0 0 0 0 107
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.8
time (sec) N/A 0.171 179.999 0.137 0. 0. 0. 0. 20.657
Problem 238 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 152 164 109 92 240 741 0 309 150
normalized size 1 1.08 0.72 0.61 1.58 4.88 0. 2.03 0.99
time (sec) N/A 0.407 0.094 0.01 1.392 0.743 0. 0.257 25.853
Problem 239 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 109 118 88 68 167 582 0 227 105
normalized size 1 1.08 0.81 0.62 1.53 5.34 0. 2.08 0.96
time (sec) N/A 0.291 0.075 0.009 1.381 0.413 0. 0.231 17.54
Problem 240 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 72 62 44 95 421 0 126 61
normalized size 1 1.07 0.93 0.66 1.42 6.28 0. 1.88 0.91
time (sec) N/A 0.151 0.058 0.006 1.378 0.28 0. 0.217 9.894
Problem 241 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 80 80 75 174 0 383 0 109 65
normalized size 1 1. 0.94 2.17 0. 4.79 0. 1.36 0.81
time (sec) N/A 0.286 0.143 0.02 0. 0.25 0. 0.225 17.384
Problem 242 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 96 114 105 182 0 419 0 212 95
normalized size 1 1.19 1.09 1.9 0. 4.36 0. 2.21 0.99
time (sec) N/A 0.32 0.197 0.02 0. 0.251 0. 0.24 18.789
Problem 243 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 164 132 226 0 539 0 437 141
normalized size 1 1.36 1.09 1.87 0. 4.45 0. 3.61 1.17
time (sec) N/A 0.399 0.179 0.023 0. 0.263 0. 0.244 22.663
Problem 244 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 208 208 146 298 356 976 0 394 187
normalized size 1 1. 0.7 1.43 1.71 4.69 0. 1.89 0.9
time (sec) N/A 0.476 0.178 0.032 1.411 0.652 0. 0.306 34.333
Problem 245 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 159 159 120 240 284 741 0 311 139
normalized size 1 1. 0.75 1.51 1.79 4.66 0. 1.96 0.87
time (sec) N/A 0.377 0.122 0.018 1.389 0.346 0. 0.29 23.938
Problem 246 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 96 182 205 517 0 204 129
normalized size 1 1. 0.84 1.6 1.8 4.54 0. 1.79 1.13
time (sec) N/A 0.161 0.083 0.016 1.435 0.26 0. 0.279 19.364
Problem 247 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 81 153 0 379 0 149 90
normalized size 1 1. 0.78 1.47 0. 3.64 0. 1.43 0.87
time (sec) N/A 0.256 0.107 0.021 0. 0.242 0. 0.23 16.744
Problem 248 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 78 153 0 313 0 231 70
normalized size 1 1. 0.93 1.82 0. 3.73 0. 2.75 0.83
time (sec) N/A 0.26 0.162 0.022 0. 0.238 0. 0.234 15.525
Problem 249 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 125 125 102 191 231 581 216 205 116
normalized size 1 1. 0.82 1.53 1.85 4.65 1.73 1.64 0.93
time (sec) N/A 0.335 0.137 0.05 1.486 0.27 134.074 0.247 17.229
Problem 250 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 103 103 61 57 128 333 216 130 95
normalized size 1 1. 0.59 0.55 1.24 3.23 2.1 1.26 0.92
time (sec) N/A 0.266 0.063 0.009 1.394 0.254 89.855 0.218 13.39
Problem 251 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 87 83 147 177 406 212 151 80
normalized size 1 1. 0.95 1.69 2.03 4.67 2.44 1.74 0.92
time (sec) N/A 0.262 0.094 0.028 1.381 0.244 86.612 0.249 12.753
Problem 252 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 65 65 43 38 73 216 202 74 58
normalized size 1 1. 0.66 0.58 1.12 3.32 3.11 1.14 0.89
time (sec) N/A 0.142 0.049 0.006 1.417 0.243 57.389 0.22 8.283
Problem 253 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 47 47 63 103 120 220 182 96 44
normalized size 1 1. 1.34 2.19 2.55 4.68 3.87 2.04 0.94
time (sec) N/A 0.09 0.054 0.023 1.425 0.242 37.1 0.246 8.934
Problem 254 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 47 62 42 149 162 61 41
normalized size 1 1. 1.02 1.35 0.91 3.24 3.52 1.33 0.89
time (sec) N/A 0.211 0.065 0.026 1.707 0.242 36.489 0.218 9.713
Problem 255 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 33 33 53 77 68 109 148 78 27
normalized size 1 1. 1.61 2.33 2.06 3.3 4.48 2.36 0.82
time (sec) N/A 0.183 0.055 0.029 1.694 0.24 42.474 0.223 8.576
Problem 256 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 61 84 66 223 141 154 49
normalized size 1 1. 1.02 1.4 1.1 3.72 2.35 2.57 0.82
time (sec) N/A 0.216 0.089 0.028 1.544 0.242 56.108 0.229 9.672
Problem 257 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 42 37 73 140 146 157 51
normalized size 1 1. 0.68 0.6 1.18 2.26 2.35 2.53 0.82
time (sec) N/A 0.217 0.052 0.008 1.613 0.23 84.097 0.225 9.318
Problem 258 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 80 125 120 423 148 362 88
normalized size 1 1. 0.81 1.26 1.21 4.27 1.49 3.66 0.89
time (sec) N/A 0.286 0.133 0.029 1.587 0.245 124.583 0.229 13.774
Problem 259 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 164 164 123 240 289 734 0 246 146
normalized size 1 1. 0.75 1.46 1.76 4.48 0. 1.5 0.89
time (sec) N/A 0.422 0.171 0.04 1.398 0.361 0. 0.258 26.19
Problem 260 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 74 68 167 420 240 151 105
normalized size 1 1. 0.63 0.58 1.42 3.56 2.03 1.28 0.89
time (sec) N/A 0.306 0.08 0.009 1.375 0.275 136.219 0.222 17.574
Problem 261 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 118 118 96 182 216 508 236 176 104
normalized size 1 1. 0.81 1.54 1.83 4.31 2. 1.49 0.88
time (sec) N/A 0.318 0.106 0.03 1.386 0.253 117.765 0.255 17.997
Problem 262 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 48 43 93 262 223 82 61
normalized size 1 1. 0.67 0.6 1.29 3.64 3.1 1.14 0.85
time (sec) N/A 0.159 0.056 0.006 1.384 0.241 76.023 0.218 9.97
Problem 263 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 68 68 71 124 140 261 199 107 75
normalized size 1 1. 1.04 1.82 2.06 3.84 2.93 1.57 1.1
time (sec) N/A 0.116 0.067 0.025 1.396 0.238 43.666 0.256 13.259
Problem 264 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 56 56 55 108 0 176 178 74 44
normalized size 1 1. 0.98 1.93 0. 3.14 3.18 1.32 0.79
time (sec) N/A 0.242 0.1 0.026 0. 0.241 44.724 0.22 12.883
Problem 265 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 57 57 60 97 0 117 165 89 46
normalized size 1 1. 1.05 1.7 0. 2.05 2.89 1.56 0.81
time (sec) N/A 0.227 0.073 0.029 0. 0.237 51.506 0.225 11.526
Problem 266 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 103 158 0 279 162 190 63
normalized size 1 1. 1.36 2.08 0. 3.67 2.13 2.5 0.83
time (sec) N/A 0.261 0.139 0.029 0. 0.245 68.558 0.23 13.362
Problem 267 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 75 75 56 49 0 162 170 185 63
normalized size 1 1. 0.75 0.65 0. 2.16 2.27 2.47 0.84
time (sec) N/A 0.254 0.074 0.008 0. 0.238 108.996 0.234 11.989
Problem 268 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 135 227 0 544 172 439 107
normalized size 1 1. 1.1 1.85 0. 4.42 1.4 3.57 0.87
time (sec) N/A 0.343 0.196 0.03 0. 0.272 157.614 0.24 19.736
Problem 269 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 161 161 150 316 289 702 233 290 146
normalized size 1 1. 0.93 1.96 1.8 4.36 1.45 1.8 0.91
time (sec) N/A 0.418 0.196 0.047 1.435 0.245 102.515 0.243 26.809
Problem 270 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 72 68 166 354 226 194 102
normalized size 1 1. 0.63 0.59 1.44 3.08 1.97 1.69 0.89
time (sec) N/A 0.316 0.09 0.008 1.404 0.255 82.293 0.236 18.613
Problem 271 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 152 152 121 254 211 448 212 208 134
normalized size 1 1. 0.8 1.67 1.39 2.95 1.39 1.37 0.88
time (sec) N/A 0.381 0.161 0.033 1.414 0.246 80.972 0.241 24.675
Problem 272 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 76 76 45 43 93 196 201 127 65
normalized size 1 1. 0.59 0.57 1.22 2.58 2.64 1.67 0.86
time (sec) N/A 0.182 0.076 0.005 1.381 0.247 71.83 0.229 11.335
Problem 273 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 63 100 160 115 153 182 153 94
normalized size 1 1. 1.59 2.54 1.83 2.43 2.89 2.43 1.49
time (sec) N/A 0.115 0.093 0.027 1.418 0.237 70.116 0.232 21.082
Problem 274 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 65 65 96 188 0 223 172 155 53
normalized size 1 1. 1.48 2.89 0. 3.43 2.65 2.38 0.82
time (sec) N/A 0.266 0.159 0.034 0. 0.242 93.709 0.253 14.22
Problem 275 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 67 67 51 48 0 117 165 296 56
normalized size 1 1. 0.76 0.72 0. 1.75 2.46 4.42 0.84
time (sec) N/A 0.239 0.085 0.007 0. 0.237 152.285 0.278 11.399
Problem 276 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 126 315 0 474 0 285 100
normalized size 1 1. 1.08 2.69 0. 4.05 0. 2.44 0.85
time (sec) N/A 0.348 0.29 0.036 0. 0.255 0. 0.296 21.452
Problem 277 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 119 119 77 73 0 193 0 327 105
normalized size 1 1. 0.65 0.61 0. 1.62 0. 2.75 0.88
time (sec) N/A 0.324 0.108 0.008 0. 0.236 0. 0.314 17.908
Problem 278 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 166 166 157 387 0 707 0 543 150
normalized size 1 1. 0.95 2.33 0. 4.26 0. 3.27 0.9
time (sec) N/A 0.459 0.382 0.038 0. 0.305 0. 0.345 30.958
Problem 279 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 42 53 34 127 148 54 34
normalized size 1 1. 1.05 1.32 0.85 3.18 3.7 1.35 0.85
time (sec) N/A 0.199 0.054 0.024 1.529 0.241 31.06 0.22 9.29
Problem 280 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 53 53 1424 66 107 88 0 0 42
normalized size 1 1. 26.87 1.25 2.02 1.66 0. 0. 0.79
time (sec) N/A 0.298 4.263 0.014 1.859 0.262 0. 0. 10.087
Problem 281 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F A F F(-2) A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 36 36 0 0 0 93 0 0 31
normalized size 1 1. 0. 0. 0. 2.58 0. 0. 0.86
time (sec) N/A 0.071 0.948 0.062 0. 0.236 0. 0. 8.379
Problem 282 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F A F F A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 75 75 0 0 0 68 0 0 65
normalized size 1 1. 0. 0. 0. 0.91 0. 0. 0.87
time (sec) N/A 0.146 1.963 0.059 0. 0.242 0. 0. 18.21
Problem 283 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 113 113 0 0 0 0 0 0 88
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.78
time (sec) N/A 0.235 0.37 0.813 0. 0. 0. 0. 37.859
Problem 284 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 87 87 0 0 0 0 0 0 70
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.8
time (sec) N/A 0.15 0.278 0.806 0. 0. 0. 0. 32.525
Problem 285 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 76 76 258 0 0 0 0 0 58
normalized size 1 1. 3.39 0. 0. 0. 0. 0. 0.76
time (sec) N/A 0.168 0.493 0.139 0. 0. 0. 0. 35.352
Problem 286 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F A F(-1) F A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 96 104 0 0 0 243 0 0 102
normalized size 1 1.08 0. 0. 0. 2.53 0. 0. 1.06
time (sec) N/A 0.361 0.929 1.044 0. 0.289 0. 0. 51.438

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 [180] had the largest ratio of [ 0.5294 ]

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. 17 0.059
2 A 2 1 1. 17 0.059
3 A 2 1 1. 17 0.059
4 A 2 1 1. 15 0.067
5 A 7 7 1. 17 0.412
6 A 7 7 1. 17 0.412
7 A 8 8 1. 17 0.471
8 A 2 1 1. 19 0.053
9 A 2 1 1. 19 0.053
10 A 2 1 1. 17 0.059
11 A 8 7 1. 19 0.368
12 A 9 8 1. 19 0.421
13 A 8 8 1. 19 0.421
14 A 8 7 1. 19 0.368
15 A 8 7 1. 19 0.368
16 A 8 7 1. 19 0.368
17 A 7 7 1. 17 0.412
18 A 13 7 1. 19 0.368
19 A 14 8 1. 19 0.421
20 A 9 8 1. 19 0.421
21 A 9 8 1. 19 0.421
22 A 9 8 1. 19 0.421
23 A 9 8 1. 19 0.421
24 A 7 7 1. 17 0.412
25 A 14 8 1. 19 0.421
26 A 15 9 1. 19 0.474
27 A 4 2 1. 21 0.095
28 A 3 2 1. 21 0.095
29 A 2 2 1. 19 0.105
30 A 1 1 1. 11 0.091
31 A 7 7 1. 21 0.333
32 A 8 8 1. 21 0.381
33 A 9 8 1. 21 0.381
34 A 3 2 1. 19 0.105
35 A 4 4 1.05 19 0.21
36 A 3 3 1.01 17 0.176
37 A 2 2 1. 19 0.105
38 A 2 2 1. 19 0.105
39 A 5 5 1. 19 0.263
40 A 4 4 1. 19 0.21
41 A 3 3 0.91 17 0.176
42 A 2 2 1. 9 0.222
43 A 2 2 1. 19 0.105
44 A 2 2 1. 19 0.105
45 A 2 2 1. 19 0.105
46 A 1 1 1. 50 0.02
47 A 2 1 1. 17 0.059
48 A 2 1 1. 17 0.059
49 A 2 1 1. 17 0.059
50 A 2 1 1. 15 0.067
51 A 10 7 1. 17 0.412
52 A 10 7 1. 17 0.412
53 A 11 8 1. 17 0.471
54 A 2 1 1. 19 0.053
55 A 2 1 1. 19 0.053
56 A 2 1 1. 19 0.053
57 A 2 1 1. 17 0.059
58 A 11 7 1. 19 0.368
59 A 12 8 1. 19 0.421
60 A 11 8 1. 19 0.421
61 A 11 7 1. 19 0.368
62 A 11 7 1. 19 0.368
63 A 11 7 1. 19 0.368
64 A 10 7 1. 17 0.412
65 A 19 7 1. 19 0.368
66 A 20 8 1. 19 0.421
67 A 12 8 1. 19 0.421
68 A 12 8 1. 19 0.421
69 A 12 8 1. 19 0.421
70 A 12 8 1. 19 0.421
71 A 10 7 1. 17 0.412
72 A 20 8 1. 19 0.421
73 A 21 9 1. 19 0.474
74 A 10 8 1. 23 0.348
75 A 9 7 1. 23 0.304
76 A 8 6 1. 23 0.261
77 A 5 3 1. 23 0.13
78 A 9 7 1. 23 0.304
79 A 10 8 1. 23 0.348
80 A 8 5 1. 21 0.238
81 A 7 4 1. 21 0.19
82 A 5 3 1. 21 0.143
83 A 8 5 1. 21 0.238
84 A 9 6 1. 21 0.286
85 A 11 8 1. 23 0.348
86 A 10 8 1. 23 0.348
87 A 9 7 1. 23 0.304
88 A 9 7 1. 23 0.304
89 A 9 7 1. 23 0.304
90 A 10 8 1. 23 0.348
91 A 11 8 1. 23 0.348
92 A 4 4 1. 25 0.16
93 A 1 1 1. 25 0.04
94 A 10 9 1. 21 0.429
95 A 9 8 1. 21 0.381
96 A 4 4 1. 21 0.19
97 A 5 5 1. 21 0.238
98 A 7 7 1. 21 0.333
99 A 8 7 1. 21 0.333
100 A 11 10 1. 21 0.476
101 A 10 9 1. 21 0.429
102 A 4 3 1. 21 0.143
103 A 9 8 1. 21 0.381
104 A 10 9 1. 21 0.429
105 A 11 10 1. 21 0.476
106 A 11 10 1. 21 0.476
107 A 10 9 1. 21 0.429
108 A 5 5 1. 21 0.238
109 A 5 5 1. 21 0.238
110 A 7 7 1. 21 0.333
111 A 8 7 1. 21 0.333
112 A 11 10 1. 21 0.476
113 A 10 9 1. 21 0.429
114 A 10 9 1. 21 0.429
115 A 10 9 1. 21 0.429
116 A 11 10 1. 21 0.476
117 A 4 4 1. 17 0.235
118 A 4 4 1. 26 0.154
119 A 3 2 1. 19 0.105
120 A 4 4 1. 19 0.21
121 A 3 3 0.91 17 0.176
122 A 2 2 1. 19 0.105
123 A 2 2 1. 19 0.105
124 A 7 7 1. 21 0.333
125 A 6 6 1. 21 0.286
126 A 6 6 1. 21 0.286
127 A 5 5 1. 19 0.263
128 A 4 4 1. 11 0.364
129 A 7 6 1. 21 0.286
130 A 8 7 1. 21 0.333
131 A 9 7 1. 21 0.333
132 A 7 7 1. 21 0.333
133 A 7 6 1. 21 0.286
134 A 6 5 1. 19 0.263
135 A 5 5 1. 11 0.454
136 A 7 6 1. 21 0.286
137 A 8 7 1. 21 0.333
138 A 9 7 1. 21 0.333
139 A 8 7 1. 21 0.333
140 A 8 6 1. 21 0.286
141 A 7 5 1. 19 0.263
142 A 6 5 1. 11 0.454
143 A 8 7 1. 21 0.333
144 A 8 7 1. 21 0.333
145 A 9 8 1. 21 0.381
146 A 5 5 1. 21 0.238
147 A 5 5 1. 21 0.238
148 A 4 4 1. 19 0.21
149 A 4 4 1. 11 0.364
150 A 7 6 1. 21 0.286
151 A 8 7 1. 21 0.333
152 A 9 7 1. 21 0.333
153 A 5 5 1. 21 0.238
154 A 5 5 0.96 21 0.238
155 A 5 5 1. 19 0.263
156 A 5 4 1. 11 0.364
157 A 8 7 1. 21 0.333
158 A 9 8 1. 21 0.381
159 A 10 8 1. 21 0.381
160 A 5 5 1. 21 0.238
161 A 6 6 0.97 21 0.286
162 A 6 5 1. 19 0.263
163 A 6 4 1. 11 0.364
164 A 9 7 1. 21 0.333
165 A 10 8 1. 21 0.381
166 A 11 8 1. 21 0.381
167 A 7 6 1. 23 0.261
168 A 4 4 1. 23 0.174
169 A 5 5 1. 23 0.217
170 A 3 3 1. 19 0.158
171 A 3 3 1. 17 0.176
172 A 6 6 1. 23 0.261
173 A 7 7 1. 23 0.304
174 A 7 7 1. 23 0.304
175 A 4 3 1. 19 0.158
176 A 8 8 1. 17 0.471
177 A 3 2 1. 21 0.095
178 A 3 2 1. 17 0.118
179 A 4 4 1. 17 0.235
180 A 9 9 1. 17 0.529
181 A 4 3 1. 17 0.176
182 A 3 3 1. 24 0.125
183 A 3 3 1. 24 0.125
184 A 3 3 1. 20 0.15
185 A 2 1 1. 17 0.059
186 A 2 1 1. 17 0.059
187 A 2 1 1. 17 0.059
188 A 2 1 1. 15 0.067
189 A 2 2 1. 17 0.118
190 A 2 2 1. 17 0.118
191 A 2 2 1. 17 0.118
192 A 2 2 1. 17 0.118
193 A 2 1 1. 19 0.053
194 A 2 1 1. 19 0.053
195 A 2 1 1. 17 0.059
196 A 3 3 1. 19 0.158
197 A 3 3 1. 19 0.158
198 A 3 3 1. 19 0.158
199 A 5 4 1. 19 0.21
200 A 4 4 1. 19 0.21
201 A 3 3 1. 19 0.158
202 A 2 2 1. 17 0.118
203 A 3 2 1. 19 0.105
204 A 4 3 1. 19 0.158
205 A 5 4 1. 19 0.21
206 A 5 4 1. 19 0.21
207 A 4 4 1. 19 0.21
208 A 3 3 1. 19 0.158
209 A 2 2 1. 17 0.118
210 A 4 3 1. 19 0.158
211 A 5 4 1. 19 0.21
212 A 6 4 1. 19 0.21
213 A 3 2 1. 19 0.105
214 A 5 5 1. 19 0.263
215 A 4 4 0.98 19 0.21
216 A 3 3 0.91 17 0.176
217 A 2 2 1. 9 0.222
218 A 2 2 1. 19 0.105
219 A 2 2 1. 19 0.105
220 A 2 2 1. 19 0.105
221 A 1 1 1. 28 0.036
222 A 4 2 1. 25 0.08
223 A 3 2 1. 25 0.08
224 A 2 2 1. 23 0.087
225 A 1 1 1. 15 0.067
226 A 1 1 1. 23 0.043
227 A 1 1 1. 25 0.04
228 A 1 1 1. 25 0.04
229 A 2 2 0.93 28 0.071
230 A 1 1 1. 69 0.014
231 A 5 3 1. 25 0.12
232 A 3 3 1. 23 0.13
233 A 2 2 1. 15 0.133
234 A 2 2 1. 25 0.08
235 A 2 2 1. 23 0.087
236 A 2 2 1. 25 0.08
237 A 2 2 1. 25 0.08
238 A 6 4 1.08 31 0.129
239 A 4 4 1.08 31 0.129
240 A 2 2 1.07 29 0.069
241 A 5 5 1. 31 0.161
242 A 5 5 1.19 31 0.161
243 A 5 4 1.36 31 0.129
244 A 8 7 1. 31 0.226
245 A 6 6 1. 31 0.194
246 A 4 4 1. 28 0.143
247 A 4 4 1. 31 0.129
248 A 5 5 1. 31 0.161
249 A 5 5 1. 29 0.172
250 A 4 4 1. 29 0.138
251 A 3 3 1. 29 0.103
252 A 2 2 1. 27 0.074
253 A 2 2 1. 26 0.077
254 A 3 3 1. 29 0.103
255 A 2 2 1. 29 0.069
256 A 3 3 1. 29 0.103
257 A 2 2 1. 29 0.069
258 A 5 5 1. 29 0.172
259 A 7 6 1. 31 0.194
260 A 4 4 1. 31 0.129
261 A 5 5 1. 31 0.161
262 A 2 2 1. 29 0.069
263 A 3 3 1. 28 0.107
264 A 3 3 1. 31 0.097
265 A 3 3 1. 31 0.097
266 A 3 3 1. 31 0.097
267 A 2 2 1. 31 0.065
268 A 5 5 1. 31 0.161
269 A 7 7 1. 31 0.226
270 A 4 4 1. 31 0.129
271 A 6 6 1. 31 0.194
272 A 2 2 1. 29 0.069
273 A 3 3 1. 28 0.107
274 A 3 3 1. 31 0.097
275 A 2 2 1. 31 0.065
276 A 5 5 1. 31 0.161
277 A 4 4 1. 31 0.129
278 A 7 7 1. 31 0.226
279 A 3 3 1. 31 0.097
280 A 1 1 1. 57 0.018
281 A 3 3 1. 32 0.094
282 A 3 3 1. 41 0.073
283 A 4 3 1. 31 0.097
284 A 4 4 1. 35 0.114
285 A 3 3 1. 31 0.097
286 A 2 2 1.08 76 0.026

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