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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 172 172 172 176 236 1 236 284 0
normalized size 1 1. 1. 1.02 1.37 0.01 1.37 1.65 0.
time (sec) N/A 0.541 0.185 0.002 1.355 0.183 0.112 0.229 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 130 130 130 135 181 1 173 217 0
normalized size 1 1. 1. 1.04 1.39 0.01 1.33 1.67 0.
time (sec) N/A 0.381 0.12 0.002 1.347 0.184 0.087 0.229 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 94 94 96 94 126 1 121 154 0
normalized size 1 1. 1.02 1. 1.34 0.01 1.29 1.64 0.
time (sec) N/A 0.249 0.07 0.002 1.351 0.182 0.074 0.226 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 56 56 56 53 70 1 63 89 0
normalized size 1 1. 1. 0.95 1.25 0.02 1.12 1.59 0.
time (sec) N/A 0.116 0.025 0.001 1.349 0.184 0.056 0.227 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 81 81 72 119 0 1 206 108 76
normalized size 1 1. 0.89 1.47 0. 0.01 2.54 1.33 0.94
time (sec) N/A 0.207 0.107 0.009 0. 0.217 1.621 0.227 25.974
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 108 108 95 163 0 1 190 128 92
normalized size 1 1. 0.88 1.51 0. 0.01 1.76 1.19 0.85
time (sec) N/A 0.244 0.127 0.013 0. 0.218 3.173 0.229 27.511
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 130 130 130 175 0 1 246 182 117
normalized size 1 1. 1. 1.35 0. 0.01 1.89 1.4 0.9
time (sec) N/A 0.313 0.153 0.011 0. 0.218 7.201 0.228 29.802
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 171 171 171 210 0 1 313 248 156
normalized size 1 1. 1. 1.23 0. 0.01 1.83 1.45 0.91
time (sec) N/A 0.479 0.195 0.014 0. 0.222 14.924 0.232 34.675
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 226 226 226 237 319 1 304 382 0
normalized size 1 1. 1. 1.05 1.41 0. 1.35 1.69 0.
time (sec) N/A 0.626 0.165 0.001 1.355 0.184 0.119 0.227 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 158 158 158 169 227 1 216 273 0
normalized size 1 1. 1. 1.07 1.44 0.01 1.37 1.73 0.
time (sec) N/A 0.496 0.114 0.002 1.348 0.183 0.099 0.228 0.
Problem 11 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 96 101 135 1 121 162 0
normalized size 1 1. 1.02 1.07 1.44 0.01 1.29 1.72 0.
time (sec) N/A 0.251 0.058 0.001 1.357 0.182 0.075 0.227 0.
Problem 12 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 142 142 115 243 0 1 343 240 153
normalized size 1 1. 0.81 1.71 0. 0.01 2.42 1.69 1.08
time (sec) N/A 0.534 0.12 0.007 0. 0.216 2.512 0.228 60.738
Problem 13 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 164 164 134 299 0 1 479 263 168
normalized size 1 1. 0.82 1.82 0. 0.01 2.92 1.6 1.02
time (sec) N/A 0.61 0.172 0.014 0. 0.221 6.531 0.23 58.195
Problem 14 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 207 207 183 397 0 1 400 321 196
normalized size 1 1. 0.88 1.92 0. 0. 1.93 1.55 0.95
time (sec) N/A 0.644 0.238 0.016 0. 0.226 29.016 0.229 63.162
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 240 240 242 360 0 1 486 420 236
normalized size 1 1. 1.01 1.5 0. 0. 2.02 1.75 0.98
time (sec) N/A 0.754 0.313 0.015 0. 0.224 120.765 0.232 66.166
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 310 310 310 339 440 1 423 541 0
normalized size 1 1. 1. 1.09 1.42 0. 1.36 1.75 0.
time (sec) N/A 0.9 0.242 0.002 1.361 0.183 0.147 0.227 0.
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 226 226 226 244 323 1 304 390 0
normalized size 1 1. 1. 1.08 1.43 0. 1.35 1.73 0.
time (sec) N/A 0.617 0.169 0.002 1.346 0.184 0.117 0.223 0.
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 130 130 149 197 1 173 234 0
normalized size 1 1. 1. 1.15 1.52 0.01 1.33 1.8 0.
time (sec) N/A 0.38 0.097 0. 1.367 0.183 0.087 0.225 0.
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 227 227 179 401 0 1 508 414 279
normalized size 1 1. 0.79 1.77 0. 0. 2.24 1.82 1.23
time (sec) N/A 0.918 0.177 0.007 0. 0.218 3.7 0.229 120.378
Problem 20 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 242 242 176 475 0 1 654 433 275
normalized size 1 1. 0.73 1.96 0. 0. 2.7 1.79 1.14
time (sec) N/A 1.033 0.24 0.017 0. 0.228 11.501 0.23 128.165
Problem 21 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 291 291 219 589 0 1 862 501 332
normalized size 1 1. 0.75 2.02 0. 0. 2.96 1.72 1.14
time (sec) N/A 1.059 0.317 0.018 0. 0.227 74.199 0.228 129.74
Problem 22 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 348 348 295 735 0 1 0 603 359
normalized size 1 1. 0.85 2.11 0. 0. 0. 1.73 1.03
time (sec) N/A 1.178 0.427 0.021 0. 0.229 0. 0.224 148.443
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 544 544 373 1332 0 0 0 0 0
normalized size 1 1. 0.69 2.45 0. 0. 0. 0. 0.
time (sec) N/A 1.896 2.065 0.06 0. 0. 0. 0. 0.
Problem 24 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 381 381 267 865 0 0 0 0 374
normalized size 1 1. 0.7 2.27 0. 0. 0. 0. 0.98
time (sec) N/A 1.102 1.322 0.023 0. 0. 0. 0. 115.453
Problem 25 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 283 283 212 394 0 0 0 0 252
normalized size 1 1. 0.75 1.39 0. 0. 0. 0. 0.89
time (sec) N/A 0.611 0.638 0.029 0. 0. 0. 0. 69.583
Problem 26 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 271 271 192 328 0 0 0 0 224
normalized size 1 1. 0.71 1.21 0. 0. 0. 0. 0.83
time (sec) N/A 0.589 0.562 0.058 0. 0. 0. 0. 70.4
Problem 27 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 274 274 297 1236 0 0 0 0 231
normalized size 1 1. 1.08 4.51 0. 0. 0. 0. 0.84
time (sec) N/A 0.619 1.739 0.067 0. 0. 0. 0. 66.203
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 385 385 379 2856 0 0 0 0 0
normalized size 1 1. 0.98 7.42 0. 0. 0. 0. 0.
time (sec) N/A 1.121 2.306 0.08 0. 0. 0. 0. 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 543 543 372 1332 0 0 0 0 0
normalized size 1 1. 0.69 2.45 0. 0. 0. 0. 0.
time (sec) N/A 1.714 2.121 0.028 0. 0. 0. 0. 0.
Problem 30 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 400 400 275 870 0 0 0 0 389
normalized size 1 1. 0.69 2.17 0. 0. 0. 0. 0.97
time (sec) N/A 1.216 1.518 0.027 0. 0. 0. 0. 114.798
Problem 31 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 369 369 248 671 0 0 0 0 345
normalized size 1 1. 0.67 1.82 0. 0. 0. 0. 0.93
time (sec) N/A 1.124 1.197 0.038 0. 0. 0. 0. 114.324
Problem 32 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 373 373 296 1225 0 0 0 0 342
normalized size 1 1. 0.79 3.28 0. 0. 0. 0. 0.92
time (sec) N/A 1.144 1.811 0.043 0. 0. 0. 0. 118.492
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 376 376 382 2860 0 0 0 0 333
normalized size 1 1. 1.02 7.61 0. 0. 0. 0. 0.89
time (sec) N/A 1.137 2.353 0.055 0. 0. 0. 0. 108.873
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 531 531 545 5113 0 0 0 0 0
normalized size 1 1. 1.03 9.63 0. 0. 0. 0. 0.
time (sec) N/A 1.725 3.278 0.1 0. 0. 0. 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 551 551 386 1386 0 0 0 0 0
normalized size 1 1. 0.7 2.52 0. 0. 0. 0. 0.
time (sec) N/A 1.796 2.193 0.037 0. 0. 0. 0. 0.
Problem 36 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 396 396 279 924 0 0 0 0 389
normalized size 1 1. 0.7 2.33 0. 0. 0. 0. 0.98
time (sec) N/A 1.287 1.484 0.028 0. 0. 0. 0. 114.943
Problem 37 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 282 282 215 501 0 0 0 0 250
normalized size 1 1. 0.76 1.78 0. 0. 0. 0. 0.89
time (sec) N/A 0.601 0.7 0.024 0. 0. 0. 0. 68.772
Problem 38 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 206 206 131 158 0 0 0 0 177
normalized size 1 1. 0.64 0.77 0. 0. 0. 0. 0.86
time (sec) N/A 0.371 0.193 0.03 0. 0. 0. 0. 44.518
Problem 39 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 209 209 206 334 0 0 0 0 173
normalized size 1 1. 0.99 1.6 0. 0. 0. 0. 0.83
time (sec) N/A 0.314 1.049 0.04 0. 0. 0. 0. 35.322
Problem 40 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 284 284 302 1352 0 0 0 0 257
normalized size 1 1. 1.06 4.76 0. 0. 0. 0. 0.9
time (sec) N/A 0.63 2.138 0.049 0. 0. 0. 0. 90.132
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 401 401 393 3039 0 0 0 0 0
normalized size 1 1. 0.98 7.58 0. 0. 0. 0. 0.
time (sec) N/A 1.182 2.286 0.059 0. 0. 0. 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 501 501 369 1169 0 0 0 0 0
normalized size 1 1. 0.74 2.33 0. 0. 0. 0. 0.
time (sec) N/A 1.696 2.058 0.069 0. 0. 0. 0. 0.
Problem 43 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 358 358 260 750 0 0 0 0 345
normalized size 1 1. 0.73 2.09 0. 0. 0. 0. 0.96
time (sec) N/A 1.096 1.302 0.038 0. 0. 0. 0. 113.906
Problem 44 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 258 258 208 393 0 0 0 0 230
normalized size 1 1. 0.81 1.52 0. 0. 0. 0. 0.89
time (sec) N/A 0.56 0.594 0.035 0. 0. 0. 0. 73.774
Problem 45 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 209 209 212 349 0 0 0 0 173
normalized size 1 1. 1.01 1.67 0. 0. 0. 0. 0.83
time (sec) N/A 0.312 0.608 0.044 0. 0. 0. 0. 37.087
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 272 272 262 581 0 0 0 0 236
normalized size 1 1. 0.96 2.14 0. 0. 0. 0. 0.87
time (sec) N/A 0.641 1.251 0.043 0. 0. 0. 0. 71.83
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 375 375 428 1742 0 0 0 0 0
normalized size 1 1. 1.14 4.65 0. 0. 0. 0. 0.
time (sec) N/A 1.12 3.827 0.056 0. 0. 0. 0. 0.
Problem 48 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 209 209 212 349 0 0 0 0 173
normalized size 1 1. 1.01 1.67 0. 0. 0. 0. 0.83
time (sec) N/A 0.306 0.648 0.042 0. 0. 0. 0. 35.635
Problem 49 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 247 247 220 359 0 0 0 0 209
normalized size 1 1. 0.89 1.45 0. 0. 0. 0. 0.85
time (sec) N/A 0.747 1.234 0.073 0. 0. 0. 0. 113.146
Problem 50 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 237 237 213 345 0 0 0 0 204
normalized size 1 1. 0.9 1.46 0. 0. 0. 0. 0.86
time (sec) N/A 0.712 0.687 0.06 0. 0. 0. 0. 112.439
Problem 51 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 242 242 221 354 0 0 0 0 202
normalized size 1 1. 0.91 1.46 0. 0. 0. 0. 0.83
time (sec) N/A 0.756 0.731 0.063 0. 0. 0. 0. 147.743
Problem 52 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 191 191 81 105 0 0 0 0 180
normalized size 1 1. 0.42 0.55 0. 0. 0. 0. 0.94
time (sec) N/A 0.343 0.139 0.051 0. 0. 0. 0. 37.869
Problem 53 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 262 262 142 367 0 0 0 0 245
normalized size 1 1. 0.54 1.4 0. 0. 0. 0. 0.94
time (sec) N/A 0.548 0.283 0.028 0. 0. 0. 0. 59.893
Problem 54 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 356 356 186 775 0 0 0 0 350
normalized size 1 1. 0.52 2.18 0. 0. 0. 0. 0.98
time (sec) N/A 0.926 0.533 0.033 0. 0. 0. 0. 101.835
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 104 0 0 0 0 0 100
normalized size 1 1. 0.92 0. 0. 0. 0. 0. 0.88
time (sec) N/A 0.488 0.661 0.29 0. 0. 0. 0. 47.707
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 526 526 203 0 0 0 0 0 0
normalized size 1 1. 0.39 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.863 0.699 0.2 0. 0. 0. 0. 0.
Problem 57 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 128 128 124 1942 0 1 0 227 117
normalized size 1 1. 0.97 15.17 0. 0.01 0. 1.77 0.91
time (sec) N/A 0.406 0.419 0.056 0. 1.326 0. 0.283 47.283
Problem 58 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 304 304 194 1541 0 1 0 392 280
normalized size 1 1. 0.64 5.07 0. 0. 0. 1.29 0.92
time (sec) N/A 0.909 0.423 0.062 0. 5.953 0. 0.273 100.828
Problem 59 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 166 166 133 1052 0 1 0 248 148
normalized size 1 1. 0.8 6.34 0. 0.01 0. 1.49 0.89
time (sec) N/A 0.419 0.249 0.023 0. 1.669 0. 0.272 54.89
Problem 60 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 91 91 93 646 0 1 0 159 78
normalized size 1 1. 1.02 7.1 0. 0.01 0. 1.75 0.86
time (sec) N/A 0.198 0.148 0.017 0. 1.074 0. 0.27 26.641
Problem 61 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 49 49 49 306 0 1 0 100 42
normalized size 1 1. 1. 6.24 0. 0.02 0. 2.04 0.86
time (sec) N/A 0.08 0.039 0.015 0. 0.264 0. 0.251 11.519
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 122 122 113 782 0 1 0 234 104
normalized size 1 1. 0.93 6.41 0. 0.01 0. 1.92 0.85
time (sec) N/A 0.345 0.277 0.056 0. 92.534 0. 0.267 41.852
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 203 203 1865 0 0 0 647 182
normalized size 1 1. 1. 9.19 0. 0. 0. 3.19 0.9
time (sec) N/A 0.752 0.987 0.082 0. 0. 0. 8.455 97.726
Problem 64 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 Yes TBD TBD TBD TBD TBD TBD
size 608 776 456 1891 0 0 0 0 0
normalized size 1 1.28 0.75 3.11 0. 0. 0. 0. 0.
time (sec) N/A 2.23 4.74 0.056 0. 0. 0. 0. 0.
Problem 65 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 400 400 346 1059 0 0 0 0 355
normalized size 1 1. 0.86 2.65 0. 0. 0. 0. 0.89
time (sec) N/A 0.968 2.58 0.028 0. 0. 0. 0. 130.427
Problem 66 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 321 321 184 340 0 0 0 0 269
normalized size 1 1. 0.57 1.06 0. 0. 0. 0. 0.84
time (sec) N/A 0.644 0.443 0.021 0. 0. 0. 0. 78.947
Problem 67 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 102 102 143 191 0 0 0 0 82
normalized size 1 1. 1.4 1.87 0. 0. 0. 0. 0.8
time (sec) N/A 0.141 0.193 0.028 0. 0. 0. 0. 19.443
Problem 68 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 209 209 347 390 0 0 0 0 170
normalized size 1 1. 1.66 1.87 0. 0. 0. 0. 0.81
time (sec) N/A 0.396 1.218 0.039 0. 0. 0. 0. 47.088
Problem 69 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 401 401 427 2068 0 0 0 0 333
normalized size 1 1. 1.06 5.16 0. 0. 0. 0. 0.83
time (sec) N/A 1.083 6.416 0.055 0. 0. 0. 0. 127.482
Problem 70 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 Yes TBD TBD TBD TBD TBD TBD
size 630 630 584 6245 0 0 0 0 0
normalized size 1 1. 0.93 9.91 0. 0. 0. 0. 0.
time (sec) N/A 2.048 5.488 0.087 0. 0. 0. 0. 0.
Problem 71 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 Yes TBD TBD TBD TBD TBD TBD
size 659 784 445 1939 0 0 0 0 0
normalized size 1 1.19 0.68 2.94 0. 0. 0. 0. 0.
time (sec) N/A 2.188 4.51 0.032 0. 0. 0. 0. 0.
Problem 72 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 403 403 739 1028 0 0 0 0 360
normalized size 1 1. 1.83 2.55 0. 0. 0. 0. 0.89
time (sec) N/A 0.945 2.926 0.027 0. 0. 0. 0. 131.911
Problem 73 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 328 328 184 300 0 0 0 0 269
normalized size 1 1. 0.56 0.91 0. 0. 0. 0. 0.82
time (sec) N/A 0.655 0.344 0.031 0. 0. 0. 0. 79.32
Problem 74 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 224 224 492 630 0 0 0 0 182
normalized size 1 1. 2.2 2.81 0. 0. 0. 0. 0.81
time (sec) N/A 0.408 2.207 0.043 0. 0. 0. 0. 50.467
Problem 75 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 391 391 999 1879 0 0 0 0 338
normalized size 1 1. 2.55 4.81 0. 0. 0. 0. 0.86
time (sec) N/A 1.147 3.249 0.055 0. 0. 0. 0. 148.299
Problem 76 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 Yes TBD TBD TBD TBD TBD TBD
size 639 639 570 6211 0 0 0 0 0
normalized size 1 1. 0.89 9.72 0. 0. 0. 0. 0.
time (sec) N/A 2.156 5.033 0.11 0. 0. 0. 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F F(-1) F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 621 621 350 988 0 0 0 0 552
normalized size 1 1. 0.56 1.59 0. 0. 0. 0. 0.89
time (sec) N/A 1.438 2.231 0.036 0. 0. 0. 0. 153.277
Problem 78 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 319 319 197 341 0 0 0 0 272
normalized size 1 1. 0.62 1.07 0. 0. 0. 0. 0.85
time (sec) N/A 0.616 0.364 0.031 0. 0. 0. 0. 80.453
Problem 79 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 102 102 143 191 0 0 0 0 82
normalized size 1 1. 1.4 1.87 0. 0. 0. 0. 0.8
time (sec) N/A 0.137 0.182 0.029 0. 0. 0. 0. 19.48
Problem 80 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 100 100 101 118 0 0 0 0 173
normalized size 1 1. 1.01 1.18 0. 0. 0. 0. 1.73
time (sec) N/A 0.479 0.15 0.03 0. 0. 0. 0. 50.401
Problem 81 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 344 344 365 413 0 0 0 0 289
normalized size 1 1. 1.06 1.2 0. 0. 0. 0. 0.84
time (sec) N/A 0.708 1.215 0.046 0. 0. 0. 0. 94.851
Problem 82 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 Yes TBD TBD TBD TBD TBD TBD
size 435 435 433 2062 0 0 0 0 0
normalized size 1 1. 1. 4.74 0. 0. 0. 0. 0.
time (sec) N/A 1.698 6.345 0.068 0. 0. 0. 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F F(-1) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 980 980 352 1063 0 0 0 0 0
normalized size 1 1. 0.36 1.08 0. 0. 0. 0. 0.
time (sec) N/A 3.204 2.515 0.047 0. 0. 0. 0. 0.
Problem 84 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 223 223 304 594 0 0 0 0 182
normalized size 1 1. 1.36 2.66 0. 0. 0. 0. 0.82
time (sec) N/A 0.416 1.589 0.043 0. 0. 0. 0. 49.031
Problem 85 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 209 209 207 285 0 0 0 0 170
normalized size 1 1. 0.99 1.36 0. 0. 0. 0. 0.81
time (sec) N/A 0.362 0.621 0.038 0. 0. 0. 0. 47.403
Problem 86 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 344 344 221 303 0 0 0 0 289
normalized size 1 1. 0.64 0.88 0. 0. 0. 0. 0.84
time (sec) N/A 0.711 0.919 0.044 0. 0. 0. 0. 94.239
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F F(-1) F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 539 539 1284 956 0 0 0 0 0
normalized size 1 1. 2.38 1.77 0. 0. 0. 0. 0.
time (sec) N/A 1.41 7.186 0.056 0. 0. 0. 0. 0.
Problem 88 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 Yes TBD TBD TBD TBD TBD TBD
size 814 814 2744 4115 0 0 0 0 0
normalized size 1 1. 3.37 5.06 0. 0. 0. 0. 0.
time (sec) N/A 2.698 9.028 0.088 0. 0. 0. 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 242 239 204 370 0 0 0 0 221
normalized size 1 0.99 0.84 1.53 0. 0. 0. 0. 0.91
time (sec) N/A 0.45 0.383 0.052 0. 0. 0. 0. 63.095
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 192 192 71 121 0 0 0 0 165
normalized size 1 1. 0.37 0.63 0. 0. 0. 0. 0.86
time (sec) N/A 0.293 0.184 0.015 0. 0. 0. 0. 42.308
Problem 91 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 58 58 50 64 0 0 0 0 58
normalized size 1 1. 0.86 1.1 0. 0. 0. 0. 1.
time (sec) N/A 0.076 0.101 0.021 0. 0. 0. 0. 13.364
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 122 147 0 0 0 0 109
normalized size 1 1. 1.01 1.21 0. 0. 0. 0. 0.9
time (sec) N/A 0.195 0.434 0.05 0. 0. 0. 0. 28.465
Problem 93 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 215 215 357 477 0 0 0 0 190
normalized size 1 1. 1.66 2.22 0. 0. 0. 0. 0.88
time (sec) N/A 0.425 0.478 0.051 0. 0. 0. 0. 55.113
Problem 94 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 298 298 134 293 0 0 0 0 277
normalized size 1 1. 0.45 0.98 0. 0. 0. 0. 0.93
time (sec) N/A 0.587 0.284 0.043 0. 0. 0. 0. 66.337
Problem 95 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 93 93 94 133 0 0 0 0 85
normalized size 1 1. 1.01 1.43 0. 0. 0. 0. 0.91
time (sec) N/A 0.135 0.11 0.032 0. 0. 0. 0. 17.251
Problem 96 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 49 49 52 53 0 0 0 0 177
normalized size 1 1. 1.06 1.08 0. 0. 0. 0. 3.61
time (sec) N/A 0.147 0.099 0.032 0. 0. 0. 0. 41.629
Problem 97 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 36 36 37 35 0 0 0 0 31
normalized size 1 1. 1.03 0.97 0. 0. 0. 0. 0.86
time (sec) N/A 0.089 0.07 0.042 0. 0. 0. 0. 19.654
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 114 1622 0 1 0 4 97
normalized size 1 1. 1.01 14.35 0. 0.01 0. 0.04 0.86
time (sec) N/A 0.337 0.237 0.049 0. 1.613 0. 1.637 34.095
Problem 99 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 359 359 422 793 0 0 0 0 308
normalized size 1 1. 1.18 2.21 0. 0. 0. 0. 0.86
time (sec) N/A 1.171 4.557 0.069 0. 0. 0. 0. 170.75
Problem 100 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 381 381 401 765 0 0 0 0 432
normalized size 1 1. 1.05 2.01 0. 0. 0. 0. 1.13
time (sec) N/A 1.076 5.213 0.059 0. 0. 0. 0. 119.931
Problem 101 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 Yes TBD TBD TBD TBD TBD TBD
size 426 426 773 1105 0 0 0 0 0
normalized size 1 1. 1.81 2.59 0. 0. 0. 0. 0.
time (sec) N/A 1.332 6.649 0.073 0. 0. 0. 0. 0.
Problem 102 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 485 485 587 1078 0 0 0 0 527
normalized size 1 1. 1.21 2.22 0. 0. 0. 0. 1.09
time (sec) N/A 1.226 6.161 0.043 0. 0. 0. 0. 160.607
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade N/A A A A A A A A F(-1)
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 37 0 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.165 1.234 0.104 0. 0. 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F F F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 545 545 0 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.641 0.121 0.082 0. 0. 0. 0. 0.
Problem 105 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 N/A TBD TBD TBD TBD TBD TBD
size 163 163 0 0 0 0 0 0 131
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.8
time (sec) N/A 0.55 0.134 0.087 0. 0. 0. 0. 90.671
Problem 106 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 N/A TBD TBD TBD TBD TBD TBD
size 148 148 0 0 0 0 0 0 580
normalized size 1 1. 0. 0. 0. 0. 0. 0. 3.92
time (sec) N/A 0.314 1.193 0.099 0. 0. 0. 0. 165.39
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade N/A A A A A A F(-1) A F(-1)
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 37 0 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.158 1.334 0.09 0. 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F F F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 484 484 0 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.224 0.856 0.082 0. 0. 0. 0. 0.
Problem 109 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 N/A TBD TBD TBD TBD TBD TBD
size 319 319 0 0 0 0 0 0 122
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.38
time (sec) N/A 1.357 1.206 0.104 0. 0. 0. 0. 51.607
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade N/A A A A A A F(-1) A F(-1)
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 37 0 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.163 1.687 0.104 0. 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F F F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 541 541 0 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.583 0.126 0.075 0. 0. 0. 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade N/A A A A A F(-1) A A F(-1)
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 37 0 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.168 0.203 0.09 0. 0. 0. 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F F F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 159 159 0 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.571 0.122 0.098 0. 0. 0. 0. 0.
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 148 148 152 0 0 0 0 0 214
normalized size 1 1. 1.03 0. 0. 0. 0. 0. 1.45
time (sec) N/A 0.315 0.506 0.093 0. 0. 0. 0. 67.087
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade N/A A A A A A A A F(-1)
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 37 0 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.172 1.111 0.101 0. 0. 0. 0. 0.

2.2 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [64] had the largest ratio of [ 0.2812 ]

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. 24 0.042
2 A 2 1 1. 24 0.042
3 A 2 1 1. 24 0.042
4 A 2 1 1. 22 0.045
5 A 3 3 1. 24 0.125
6 A 3 3 1. 24 0.125
7 A 3 3 1. 24 0.125
8 A 4 4 1. 24 0.167
9 A 2 1 1. 26 0.038
10 A 2 1 1. 26 0.038
11 A 2 1 1. 24 0.042
12 A 4 3 1. 26 0.115
13 A 4 4 1. 26 0.154
14 A 4 3 1. 26 0.115
15 A 4 3 1. 26 0.115
16 A 2 1 1. 26 0.038
17 A 2 1 1. 26 0.038
18 A 2 1 1. 24 0.042
19 A 5 3 1. 26 0.115
20 A 5 4 1. 26 0.154
21 A 5 4 1. 26 0.154
22 A 5 3 1. 26 0.115
23 A 7 5 1. 30 0.167
24 A 6 5 1. 30 0.167
25 A 5 5 1. 30 0.167
26 A 5 5 1. 30 0.167
27 A 4 4 1. 30 0.133
28 A 5 5 1. 30 0.167
29 A 7 5 1. 30 0.167
30 A 6 5 1. 30 0.167
31 A 6 6 1. 30 0.2
32 A 6 5 1. 30 0.167
33 A 5 4 1. 30 0.133
34 A 6 5 1. 30 0.167
35 A 7 5 1. 30 0.167
36 A 6 5 1. 30 0.167
37 A 5 5 1. 30 0.167
38 A 4 4 1. 30 0.133
39 A 3 3 1. 30 0.1
40 A 4 4 1. 30 0.133
41 A 5 4 1. 30 0.133
42 A 7 6 1. 30 0.2
43 A 6 6 1. 30 0.2
44 A 5 5 1. 30 0.167
45 A 3 3 1. 30 0.1
46 A 4 4 1. 30 0.133
47 A 5 4 1. 30 0.133
48 A 3 3 1. 30 0.1
49 A 8 7 1. 31 0.226
50 A 8 7 1. 31 0.226
51 A 8 7 1. 32 0.219
52 A 4 4 1. 30 0.133
53 A 5 5 1. 30 0.167
54 A 6 5 1. 30 0.167
55 A 2 2 1. 87 0.023
56 A 5 5 1. 81 0.062
57 A 6 6 1. 28 0.214
58 A 14 8 1. 30 0.267
59 A 9 7 1. 30 0.233
60 A 5 5 1. 28 0.179
61 A 2 2 1. 21 0.095
62 A 5 3 1. 30 0.1
63 A 7 5 1. 30 0.167
64 A 14 9 1.28 32 0.281
65 A 7 7 1. 32 0.219
66 A 6 6 1. 32 0.188
67 A 1 1 1. 32 0.031
68 A 3 3 1. 32 0.094
69 A 6 6 1. 32 0.188
70 A 9 8 1. 32 0.25
71 A 14 9 1.19 32 0.281
72 A 7 7 1. 32 0.219
73 A 6 6 1. 32 0.188
74 A 3 3 1. 32 0.094
75 A 6 6 1. 32 0.188
76 A 9 8 1. 32 0.25
77 A 12 8 1. 32 0.25
78 A 6 6 1. 32 0.188
79 A 1 1 1. 32 0.031
80 A 3 2 1. 32 0.062
81 A 5 5 1. 32 0.156
82 A 8 7 1. 32 0.219
83 A 14 9 1. 32 0.281
84 A 3 3 1. 32 0.094
85 A 3 3 1. 32 0.094
86 A 5 5 1. 32 0.156
87 A 8 7 1. 32 0.219
88 A 11 6 1. 32 0.188
89 A 7 7 0.99 28 0.25
90 A 6 6 1. 28 0.214
91 A 1 1 1. 28 0.036
92 A 3 3 1. 28 0.107
93 A 6 6 1. 28 0.214
94 A 6 6 1. 32 0.188
95 A 1 1 1. 32 0.031
96 A 1 1 1. 32 0.031
97 A 3 3 1. 30 0.1
98 A 4 4 1. 28 0.143
99 A 11 9 1. 33 0.273
100 A 8 7 1. 32 0.219
101 A 11 9 1. 33 0.273
102 A 8 7 1. 32 0.219
103 A 0 0 0. 0 0.
104 A 7 7 1. 34 0.206
105 A 2 2 1. 34 0.059
106 A 2 2 1. 34 0.059
107 A 0 0 0. 0 0.
108 A 8 8 1. 34 0.235
109 A 5 5 1. 34 0.147
110 A 0 0 0. 0 0.
111 A 7 7 1. 34 0.206
112 A 0 0 0. 0 0.
113 A 2 2 1. 34 0.059
114 A 2 2 1. 34 0.059
115 A 0 0 0. 0 0.

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