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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 B A A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 436 436 495 841 838 842 0 1 0
normalized size 1 1. 1.14 1.93 1.92 1.93 0. 0. 0.
time (sec) N/A 0.859 1.42 0.018 1.366 0.217 0. 0.234 0.
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 324 324 323 505 522 522 1510 903 0
normalized size 1 1. 1. 1.56 1.61 1.61 4.66 2.79 0.
time (sec) N/A 0.546 1.317 0.013 1.361 0.218 109.417 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 A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 212 212 184 241 267 266 848 494 226
normalized size 1 1. 0.87 1.14 1.26 1.25 4. 2.33 1.07
time (sec) N/A 0.346 0.331 0.008 1.358 0.212 57.283 0.225 81.08
Problem 4 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 82 91 173 122 354 201 110
normalized size 1 1. 0.71 0.79 1.5 1.06 3.08 1.75 0.96
time (sec) N/A 0.145 0.087 0.007 1.346 0.216 12.763 0.221 27.375
Problem 5 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 188 188 161 338 0 1 337 335 187
normalized size 1 1. 0.86 1.8 0. 0.01 1.79 1.78 0.99
time (sec) N/A 0.401 0.295 0.019 0. 0.228 75.297 0.213 122.665
Problem 6 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 201 201 186 566 0 1 0 366 228
normalized size 1 1. 0.93 2.82 0. 0. 0. 1.82 1.13
time (sec) N/A 1.076 0.924 0.026 0. 0.25 0. 0.214 124.728
Problem 7 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 279 279 253 1207 0 1 0 714 347
normalized size 1 1. 0.91 4.33 0. 0. 0. 2.56 1.24
time (sec) N/A 1.434 1.613 0.033 0. 0.243 0. 0.223 148.874
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 375 375 344 1186 0 1 0 1 0
normalized size 1 1. 0.92 3.16 0. 0. 0. 0. 0.
time (sec) N/A 1.867 2.631 0.036 0. 0.251 0. 0.228 0.
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 495 495 449 3252 0 1 0 1 0
normalized size 1 1. 0.91 6.57 0. 0. 0. 0. 0.
time (sec) N/A 2.157 2.267 0.039 0. 0.261 0. 0.236 0.
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 434 434 500 841 849 841 0 1 0
normalized size 1 1. 1.15 1.94 1.96 1.94 0. 0. 0.
time (sec) N/A 0.847 1.551 0.013 1.368 0.22 0. 0.227 0.
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 322 322 326 505 533 521 0 879 0
normalized size 1 1. 1.01 1.57 1.66 1.62 0. 2.73 0.
time (sec) N/A 0.541 0.973 0.012 1.37 0.223 0. 0.222 0.
Problem 12 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 210 210 188 241 278 265 7874 436 224
normalized size 1 1. 0.9 1.15 1.32 1.26 37.5 2.08 1.07
time (sec) N/A 0.343 0.374 0.008 1.355 0.213 48.601 0.216 81.177
Problem 13 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 113 113 82 91 138 122 2132 171 114
normalized size 1 1. 0.73 0.81 1.22 1.08 18.87 1.51 1.01
time (sec) N/A 0.143 0.089 0.009 1.352 0.218 19.388 0.211 27.843
Problem 14 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 193 193 159 366 0 1 0 270 243
normalized size 1 1. 0.82 1.9 0. 0.01 0. 1.4 1.26
time (sec) N/A 0.461 0.738 0.019 0. 0.229 0. 0.217 142.635
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 253 253 208 604 0 1 0 524 316
normalized size 1 1. 0.82 2.39 0. 0. 0. 2.07 1.25
time (sec) N/A 1.37 1.029 0.037 0. 0.249 0. 0.227 151.194
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 350 350 297 1225 0 1 0 833 0
normalized size 1 1. 0.85 3.5 0. 0. 0. 2.38 0.
time (sec) N/A 1.946 1.803 0.04 0. 0.248 0. 0.23 0.
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 463 463 382 2108 0 1 0 1 0
normalized size 1 1. 0.83 4.55 0. 0. 0. 0. 0.
time (sec) N/A 2.822 2.911 0.053 0. 0.272 0. 0.241 0.
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 434 434 485 841 846 856 0 1 0
normalized size 1 1. 1.12 1.94 1.95 1.97 0. 0. 0.
time (sec) N/A 0.862 2.384 0.013 1.373 0.231 0. 0.223 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 322 322 317 505 531 536 0 840 0
normalized size 1 1. 0.98 1.57 1.65 1.66 0. 2.61 0.
time (sec) N/A 0.546 0.962 0.012 1.365 0.223 0. 0.219 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 210 210 177 241 275 279 4235 408 226
normalized size 1 1. 0.84 1.15 1.31 1.33 20.17 1.94 1.08
time (sec) N/A 0.345 0.291 0.007 1.361 0.217 44.42 0.209 80.657
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 75 90 132 134 425 155 114
normalized size 1 1. 0.66 0.8 1.17 1.19 3.76 1.37 1.01
time (sec) N/A 0.144 0.093 0.007 1.364 0.211 4.315 0.211 27.536
Problem 22 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 210 210 201 464 0 1 0 379 298
normalized size 1 1. 0.96 2.21 0. 0. 0. 1.8 1.42
time (sec) N/A 0.634 1.085 0.026 0. 0.24 0. 0.219 156.355
Problem 23 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 336 336 268 730 0 1 0 593 410
normalized size 1 1. 0.8 2.17 0. 0. 0. 1.76 1.22
time (sec) N/A 1.726 1.453 0.038 0. 0.254 0. 0.23 173.146
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 438 438 360 1376 0 1 0 1035 0
normalized size 1 1. 0.82 3.14 0. 0. 0. 2.36 0.
time (sec) N/A 3.072 2.356 0.046 0. 0.269 0. 0.234 0.
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 455 455 977 5003 0 5250 0 1 0
normalized size 1 1. 2.15 11. 0. 11.54 0. 0. 0.
time (sec) N/A 0.943 3.903 0.03 0. 0.26 0. 0.234 0.
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 338 338 619 2588 0 2911 0 1 0
normalized size 1 1. 1.83 7.66 0. 8.61 0. 0. 0.
time (sec) N/A 0.581 2.201 0.02 0. 0.247 0. 0.222 0.
Problem 27 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 226 226 341 1039 0 1301 13311 1 228
normalized size 1 1. 1.51 4.6 0. 5.76 58.9 0. 1.01
time (sec) N/A 0.367 0.861 0.015 0. 0.238 107.572 0.209 142.042
Problem 28 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 126 126 148 308 0 532 3822 1091 112
normalized size 1 1. 1.17 2.44 0. 4.22 30.33 8.66 0.89
time (sec) N/A 0.159 0.211 0.01 0. 0.23 15.664 0.215 36.238
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F(-1) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 203 203 414 0 0 0 0 0 0
normalized size 1 1. 2.04 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.373 4.424 0.082 0. 0. 0. 0. 0.
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 220 220 0 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.182 0.285 0.065 0. 0. 0. 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 329 329 0 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.415 0.453 0.08 0. 0. 0. 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 141 141 202 0 0 0 0 0 117
normalized size 1 1. 1.43 0. 0. 0. 0. 0. 0.83
time (sec) N/A 0.23 0.51 0.082 0. 0. 0. 0. 32.186
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 268 266 327 0 0 0 0 0 230
normalized size 1 0.99 1.22 0. 0. 0. 0. 0. 0.86
time (sec) N/A 0.72 0.971 0.092 0. 0. 0. 0. 92.315
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F(-1) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 610 605 446 0 0 0 0 0 0
normalized size 1 0.99 0.73 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.337 3.404 0.051 0. 0. 0. 0. 0.
Problem 35 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 415 415 355 959 644 2512 0 1 415
normalized size 1 1. 0.86 2.31 1.55 6.05 0. 0. 1.
time (sec) N/A 1.473 0.77 0.042 1.501 0.261 0. 0.318 160.039
Problem 36 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 286 286 243 652 459 1705 0 1 282
normalized size 1 1. 0.85 2.28 1.6 5.96 0. 0. 0.99
time (sec) N/A 1.186 0.457 0.022 1.502 0.248 0. 0.274 94.085
Problem 37 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 168 170 138 377 263 921 0 429 155
normalized size 1 1.01 0.82 2.24 1.57 5.48 0. 2.55 0.92
time (sec) N/A 0.498 0.241 0.018 1.516 0.234 0. 0.25 45.975
Problem 38 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 95 95 71 185 154 487 0 198 70
normalized size 1 1. 0.75 1.95 1.62 5.13 0. 2.08 0.74
time (sec) N/A 0.155 0.087 0.015 1.519 0.229 0. 0.227 16.627
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 122 122 155 373 0 1 0 0 109
normalized size 1 1. 1.27 3.06 0. 0.01 0. 0. 0.89
time (sec) N/A 0.577 0.327 0.059 0. 7.896 0. 0. 69.155
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F(-2) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 211 899 0 1 0 0 146
normalized size 1 1. 1.29 5.52 0. 0.01 0. 0. 0.9
time (sec) N/A 0.649 0.528 0.065 0. 30.368 0. 0. 90.717
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F(-2) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 248 248 284 1449 0 1 0 0 230
normalized size 1 1. 1.15 5.84 0. 0. 0. 0. 0.93
time (sec) N/A 0.739 0.57 0.065 0. 0.275 0. 0. 170.366
Problem 42 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 340 340 241 643 524 1621 0 551 337
normalized size 1 1. 0.71 1.89 1.54 4.77 0. 1.62 0.99
time (sec) N/A 1.379 0.468 0.038 1.506 0.245 0. 0.245 144.536
Problem 43 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 228 228 160 423 356 1035 0 352 218
normalized size 1 1. 0.7 1.86 1.56 4.54 0. 1.54 0.96
time (sec) N/A 1.039 0.326 0.034 1.517 0.246 0. 0.225 86.49
Problem 44 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 130 133 88 235 205 479 0 186 116
normalized size 1 1.02 0.68 1.81 1.58 3.68 0. 1.43 0.89
time (sec) N/A 0.449 0.167 0.028 1.498 0.232 0. 0.225 43.239
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 45 117 105 244 282 97 41
normalized size 1 1. 0.71 1.86 1.67 3.87 4.48 1.54 0.65
time (sec) N/A 0.137 0.064 0.023 1.499 0.232 54.28 0.223 15.268
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 122 122 155 373 0 1 0 0 109
normalized size 1 1. 1.27 3.06 0. 0.01 0. 0. 0.89
time (sec) N/A 0.544 0.322 0. 0. 7.876 0. 0. 69.128
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F(-2) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 211 899 0 1 0 0 146
normalized size 1 1. 1.29 5.52 0. 0.01 0. 0. 0.9
time (sec) N/A 0.585 0.526 0. 0. 30.304 0. 0. 90.97
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F(-2) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 248 248 284 1449 0 1 0 0 230
normalized size 1 1. 1.15 5.84 0. 0. 0. 0. 0.93
time (sec) N/A 0.718 0.568 0. 0. 0.274 0. 0. 170.195
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 57 139 134 306 313 123 68
normalized size 1 1. 0.72 1.76 1.7 3.87 3.96 1.56 0.86
time (sec) N/A 0.253 0.092 0. 1.511 0.234 108.768 0.216 26.453
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 45 117 105 244 282 97 41
normalized size 1 1. 0.71 1.86 1.67 3.87 4.48 1.54 0.65
time (sec) N/A 0.136 0.062 0. 1.501 0.226 54.838 0.232 15.281
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 54 94 89 171 245 0 39
normalized size 1 1. 1.12 1.96 1.85 3.56 5.1 0. 0.81
time (sec) N/A 0.33 0.068 0. 1.489 0.237 58.607 0. 30.036
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 54 97 89 212 221 0 37
normalized size 1 1. 1.12 2.02 1.85 4.42 4.6 0. 0.77
time (sec) N/A 0.322 0.085 0. 1.498 0.236 65.661 0. 27.279
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 70 108 132 255 218 0 56
normalized size 1 1. 0.99 1.52 1.86 3.59 3.07 0. 0.79
time (sec) N/A 0.345 0.104 0. 1.504 0.228 81.954 0. 26.871
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 591 584 397 1446 0 1 0 0 0
normalized size 1 0.99 0.67 2.45 0. 0. 0. 0. 0.
time (sec) N/A 3.135 1.114 0.064 0. 0.307 0. 0. 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 451 450 281 987 0 1 0 0 0
normalized size 1 1. 0.62 2.19 0. 0. 0. 0. 0.
time (sec) N/A 2.039 0.688 0.024 0. 0.283 0. 0. 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 300 297 178 588 0 1 0 0 286
normalized size 1 0.99 0.59 1.96 0. 0. 0. 0. 0.95
time (sec) N/A 0.865 0.429 0.018 0. 0.256 0. 0. 93.536
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 221 221 125 287 0 1 0 0 172
normalized size 1 1. 0.57 1.3 0. 0. 0. 0. 0.78
time (sec) N/A 0.313 0.286 0.016 0. 0.242 0. 0. 35.242
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 278 278 238 503 0 0 0 358 219
normalized size 1 1. 0.86 1.81 0. 0. 0. 1.29 0.79
time (sec) N/A 0.939 0.722 0.069 0. 0. 0. 0.264 108.046
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 322 322 340 1200 0 0 0 4 282
normalized size 1 1. 1.06 3.73 0. 0. 0. 0.01 0.88
time (sec) N/A 1.138 1.131 0.066 0. 0. 0. 0.601 126.292
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-2) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 363 361 380 1848 0 1 0 4 0
normalized size 1 0.99 1.05 5.09 0. 0. 0. 0.01 0.
time (sec) N/A 1.381 1.315 0.075 0. 8.954 0. 1.309 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 501 496 289 965 0 1 0 0 0
normalized size 1 0.99 0.58 1.93 0. 0. 0. 0. 0.
time (sec) N/A 2.67 0.902 0.04 0. 0.288 0. 0. 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 368 369 202 635 0 1 0 0 337
normalized size 1 1. 0.55 1.73 0. 0. 0. 0. 0.92
time (sec) N/A 1.823 0.685 0.036 0. 0.271 0. 0. 170.581
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 246 249 130 365 0 1 0 0 211
normalized size 1 1.01 0.53 1.48 0. 0. 0. 0. 0.86
time (sec) N/A 0.818 0.373 0.03 0. 0.258 0. 0. 85.448
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 177 177 91 180 0 1 338 0 119
normalized size 1 1. 0.51 1.02 0. 0.01 1.91 0. 0.67
time (sec) N/A 0.266 0.165 0.024 0. 0.251 90.813 0. 30.016
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 278 278 238 503 0 0 0 358 219
normalized size 1 1. 0.86 1.81 0. 0. 0. 1.29 0.79
time (sec) N/A 0.916 0.706 0. 0. 0. 0. 0.279 108.663
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 322 322 340 1200 0 0 0 4 282
normalized size 1 1. 1.06 3.73 0. 0. 0. 0.01 0.88
time (sec) N/A 1.054 1.126 0. 0. 0. 0. 0.623 126.464
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-2) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 363 361 380 1848 0 1 0 4 0
normalized size 1 0.99 1.05 5.09 0. 0. 0. 0.01 0.
time (sec) N/A 1.28 1.303 0. 0. 8.991 0. 1.462 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 151 80 137 147 370 308 130 119
normalized size 1 1.74 0.92 1.57 1.69 4.25 3.54 1.49 1.37
time (sec) N/A 0.278 0.129 0. 1.355 0.237 107.638 0.281 28.674
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A B A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 135 68 120 142 259 277 104 87
normalized size 1 2.6 1.31 2.31 2.73 4.98 5.33 2. 1.67
time (sec) N/A 0.164 0.085 0. 1.361 0.236 54.7 0.26 17.168
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A B A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 135 76 93 86 212 240 96 65
normalized size 1 2.45 1.38 1.69 1.56 3.85 4.36 1.75 1.18
time (sec) N/A 0.354 0.107 0. 1.498 0.247 57.375 0.23 21.23
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A B A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 135 76 96 86 178 216 112 48
normalized size 1 2.45 1.38 1.75 1.56 3.24 3.93 2.04 0.87
time (sec) N/A 0.345 0.098 0. 1.554 0.248 66.447 0.234 17.716
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 129 64 103 88 238 212 196 88
normalized size 1 1.55 0.77 1.24 1.06 2.87 2.55 2.36 1.06
time (sec) N/A 0.348 0.112 0. 1.498 0.237 82.126 0.235 20.531
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 171 75 123 119 297 219 266 119
normalized size 1 1.47 0.65 1.06 1.03 2.56 1.89 2.29 1.03
time (sec) N/A 0.433 0.142 0. 1.484 0.237 156.866 0.232 24.916
Problem 74 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 NO TBD TBD TBD TBD TBD TBD
size 199 242 178 1095 0 1 0 817 306
normalized size 1 1.22 0.89 5.5 0. 0.01 0. 4.11 1.54
time (sec) N/A 0.652 0.709 0.075 0. 0.271 0. 0.41 84.841
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 1348 1345 1801 6728 0 1 0 1 0
normalized size 1 1. 1.34 4.99 0. 0. 0. 0. 0.
time (sec) N/A 6.35 6.532 0.062 0. 2.45 0. 0.48 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 721 719 675 3571 0 1 0 1 0
normalized size 1 1. 0.94 4.95 0. 0. 0. 0. 0.
time (sec) N/A 2.368 3.177 0.037 0. 0.889 0. 0.379 0.
Problem 77 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 330 330 300 1431 0 1 0 856 405
normalized size 1 1. 0.91 4.34 0. 0. 0. 2.59 1.23
time (sec) N/A 0.762 0.633 0.023 0. 0.325 0. 0.297 68.626
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 450 453 498 4227 0 0 0 1 0
normalized size 1 1.01 1.11 9.39 0. 0. 0. 0. 0.
time (sec) N/A 3.589 1.721 0.062 0. 0. 0. 0.429 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 521 521 489 5051 0 0 0 4 0
normalized size 1 1. 0.94 9.69 0. 0. 0. 0.01 0.
time (sec) N/A 4.624 1.683 0.06 0. 0. 0. 0.743 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 658 657 1165 12065 0 0 0 4 0
normalized size 1 1. 1.77 18.34 0. 0. 0. 0.01 0.
time (sec) N/A 6.507 6.856 0.089 0. 0. 0. 0.752 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 1032 1032 901 3958 0 1 0 1 0
normalized size 1 1. 0.87 3.84 0. 0. 0. 0. 0.
time (sec) N/A 5.057 4.378 0.059 0. 31.044 0. 0.309 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 540 540 470 2002 0 1 0 994 0
normalized size 1 1. 0.87 3.71 0. 0. 0. 1.84 0.
time (sec) N/A 1.798 1.552 0.043 0. 22.99 0. 0.281 0.
Problem 83 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 246 246 212 763 0 1 0 425 318
normalized size 1 1. 0.86 3.1 0. 0. 0. 1.73 1.29
time (sec) N/A 0.58 0.307 0.031 0. 1.295 0. 0.261 48.632
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 290 290 367 1822 0 0 0 797 354
normalized size 1 1. 1.27 6.28 0. 0. 0. 2.75 1.22
time (sec) N/A 1.641 0.764 0.046 0. 0. 0. 0.363 106.287
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 364 364 421 3670 0 0 0 4 332
normalized size 1 1. 1.16 10.08 0. 0. 0. 0.01 0.91
time (sec) N/A 2.624 1.789 0.063 0. 0. 0. 0.667 96.461
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F(-2) F(-1) F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 484 484 979 9100 0 0 0 0 468
normalized size 1 1. 2.02 18.8 0. 0. 0. 0. 0.97
time (sec) N/A 3.666 6.756 0.123 0. 0. 0. 0. 155.302
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 685 685 847 15990 0 1 0 0 0
normalized size 1 1. 1.24 23.34 0. 0. 0. 0. 0.
time (sec) N/A 4.902 6.054 0.223 0. 80.887 0. 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 718 715 645 2528 0 1 0 1 0
normalized size 1 1. 0.9 3.52 0. 0. 0. 0. 0.
time (sec) N/A 3.397 2.616 0.059 0. 35.095 0. 0.336 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 371 369 328 1199 0 1 0 603 0
normalized size 1 0.99 0.88 3.23 0. 0. 0. 1.63 0.
time (sec) N/A 1.205 0.775 0.043 0. 26.686 0. 0.321 0.
Problem 90 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 164 164 154 425 0 1 0 262 199
normalized size 1 1. 0.94 2.59 0. 0.01 0. 1.6 1.21
time (sec) N/A 0.386 0.193 0.032 0. 1.431 0. 0.302 35.956
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 188 188 280 746 0 0 0 467 211
normalized size 1 1. 1.49 3.97 0. 0. 0. 2.48 1.12
time (sec) N/A 0.787 0.528 0.049 0. 0. 0. 0.449 74.35
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 254 254 397 2973 0 0 0 4 265
normalized size 1 1. 1.56 11.7 0. 0. 0. 0.02 1.04
time (sec) N/A 1.468 2.044 0.074 0. 0. 0. 0.727 95.062
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-2) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 424 424 604 7119 0 1 0 0 0
normalized size 1 1. 1.42 16.79 0. 0. 0. 0. 0.
time (sec) N/A 2.355 2.704 0.165 0. 32.688 0. 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 826 826 1586 18802 0 1 0 0 0
normalized size 1 1. 1.92 22.76 0. 0. 0. 0. 0.
time (sec) N/A 8.031 7.762 0.441 0. 148.303 0. 0. 0.
Problem 95 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 1182 1154 11933 14778 0 0 0 0 0
normalized size 1 0.98 10.1 12.5 0. 0. 0. 0. 0.
time (sec) N/A 14.309 22.367 0.129 0. 0. 0. 0. 0.
Problem 96 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 774 769 7297 10268 0 0 0 0 0
normalized size 1 0.99 9.43 13.27 0. 0. 0. 0. 0.
time (sec) N/A 6.898 18.749 0.076 0. 0. 0. 0. 0.
Problem 97 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 706 706 9487 6257 0 0 0 0 0
normalized size 1 1. 13.44 8.86 0. 0. 0. 0. 0.
time (sec) N/A 5.129 15.628 0.095 0. 0. 0. 0. 0.
Problem 98 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 687 687 5831 16177 0 0 0 0 0
normalized size 1 1. 8.49 23.55 0. 0. 0. 0. 0.
time (sec) N/A 5.171 17.512 0.138 0. 0. 0. 0. 0.
Problem 99 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 NO TBD TBD TBD TBD TBD TBD
size 964 964 13960 34389 0 0 0 0 0
normalized size 1 1. 14.48 35.67 0. 0. 0. 0. 0.
time (sec) N/A 8.759 21.119 0.254 0. 0. 0. 0. 0.
Problem 100 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 NO TBD TBD TBD TBD TBD TBD
size 1716 1716 22671 68351 0 0 0 0 0
normalized size 1 1. 13.21 39.83 0. 0. 0. 0. 0.
time (sec) N/A 22.162 25.787 0.432 0. 0. 0. 0. 0.
Problem 101 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 NO TBD TBD TBD TBD TBD TBD
size 1235 1235 18421 15857 0 0 0 0 0
normalized size 1 1. 14.92 12.84 0. 0. 0. 0. 0.
time (sec) N/A 14.826 23.916 0.088 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 F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 766 766 10708 9543 0 0 0 0 0
normalized size 1 1. 13.98 12.46 0. 0. 0. 0. 0.
time (sec) N/A 6.736 19.563 0.05 0. 0. 0. 0. 0.
Problem 103 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 527 527 5393 6049 0 0 0 0 0
normalized size 1 1. 10.23 11.48 0. 0. 0. 0. 0.
time (sec) N/A 2.727 15.694 0.043 0. 0. 0. 0. 0.
Problem 104 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 540 540 551 4732 0 0 0 0 0
normalized size 1 1. 1.02 8.76 0. 0. 0. 0. 0.
time (sec) N/A 3.085 12.287 0.059 0. 0. 0. 0. 0.
Problem 105 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 597 596 5074 13614 0 0 0 0 0
normalized size 1 1. 8.5 22.8 0. 0. 0. 0. 0.
time (sec) N/A 3.827 16.817 0.115 0. 0. 0. 0. 0.
Problem 106 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 NO TBD TBD TBD TBD TBD TBD
size 1034 1034 13302 33007 0 0 0 0 0
normalized size 1 1. 12.86 31.92 0. 0. 0. 0. 0.
time (sec) N/A 9.585 20.966 0.261 0. 0. 0. 0. 0.
Problem 107 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 838 831 7300 10546 0 0 0 0 0
normalized size 1 0.99 8.71 12.58 0. 0. 0. 0. 0.
time (sec) N/A 7.857 19.903 0.082 0. 0. 0. 0. 0.
Problem 108 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 528 524 3657 6174 0 0 0 0 0
normalized size 1 0.99 6.93 11.69 0. 0. 0. 0. 0.
time (sec) N/A 2.938 15.704 0.045 0. 0. 0. 0. 0.
Problem 109 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 384 383 418 2497 0 0 0 0 0
normalized size 1 1. 1.09 6.5 0. 0. 0. 0. 0.
time (sec) N/A 1.576 10.263 0.042 0. 0. 0. 0. 0.
Problem 110 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 422 422 477 3979 0 0 0 0 0
normalized size 1 1. 1.13 9.43 0. 0. 0. 0. 0.
time (sec) N/A 2.049 9.643 0.059 0. 0. 0. 0. 0.
Problem 111 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 642 642 4349 12988 0 0 0 0 0
normalized size 1 1. 6.77 20.23 0. 0. 0. 0. 0.
time (sec) N/A 4.281 16.552 0.157 0. 0. 0. 0. 0.
Problem 112 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 1116 1116 8844 34100 0 0 0 0 0
normalized size 1 1. 7.92 30.56 0. 0. 0. 0. 0.
time (sec) N/A 9.807 20.192 0.406 0. 0. 0. 0. 0.
Problem 113 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 704 702 12665 8421 0 0 0 0 0
normalized size 1 1. 17.99 11.96 0. 0. 0. 0. 0.
time (sec) N/A 5.154 18.949 0.091 0. 0. 0. 0. 0.
Problem 114 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 410 410 442 2825 0 0 0 0 0
normalized size 1 1. 1.08 6.89 0. 0. 0. 0. 0.
time (sec) N/A 1.717 11.806 0.045 0. 0. 0. 0. 0.
Problem 115 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 291 291 326 673 0 0 0 0 248
normalized size 1 1. 1.12 2.31 0. 0. 0. 0. 0.85
time (sec) N/A 1.144 3.693 0.039 0. 0. 0. 0. 150.009
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F(-2) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 309 309 248 663 0 0 0 0 0
normalized size 1 1. 0.8 2.15 0. 0. 0. 0. 0.
time (sec) N/A 2.659 2.706 0.052 0. 0. 0. 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F(-1) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 680 680 16821 13405 0 0 0 0 0
normalized size 1 1. 24.74 19.71 0. 0. 0. 0. 0.
time (sec) N/A 4.869 20.322 0.143 0. 0. 0. 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F(-1) F(-1) F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 990 987 21555 55327 0 0 0 0 0
normalized size 1 1. 21.77 55.89 0. 0. 0. 0. 0.
time (sec) N/A 8.653 23.993 0.165 0. 0. 0. 0. 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F(-1) F(-1) F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 734 732 6667 20235 0 0 0 0 0
normalized size 1 1. 9.08 27.57 0. 0. 0. 0. 0.
time (sec) N/A 3.398 17.735 0.092 0. 0. 0. 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 436 436 583 3003 0 0 0 0 0
normalized size 1 1. 1.34 6.89 0. 0. 0. 0. 0.
time (sec) N/A 2.025 10.343 0.116 0. 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F F(-1) F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 616 616 1753 9443 0 0 0 0 0
normalized size 1 1. 2.85 15.33 0. 0. 0. 0. 0.
time (sec) N/A 2.744 18.171 0.21 0. 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F F(-1) F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 1128 1119 10645 75992 0 0 0 0 0
normalized size 1 0.99 9.44 67.37 0. 0. 0. 0. 0.
time (sec) N/A 9.953 37.51 1.96 0. 0. 0. 0. 0.
Problem 123 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 681 679 12443 8125 0 0 0 0 0
normalized size 1 1. 18.27 11.93 0. 0. 0. 0. 0.
time (sec) N/A 5.756 18.259 0.061 0. 0. 0. 0. 0.
Problem 124 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 402 402 450 3224 0 0 0 0 0
normalized size 1 1. 1.12 8.02 0. 0. 0. 0. 0.
time (sec) N/A 2.278 9.622 0.045 0. 0. 0. 0. 0.
Problem 125 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 284 284 319 559 0 0 0 0 241
normalized size 1 1. 1.12 1.97 0. 0. 0. 0. 0.85
time (sec) N/A 1.025 3.113 0.033 0. 0. 0. 0. 117.404
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 313 313 244 665 0 0 0 0 0
normalized size 1 1. 0.78 2.12 0. 0. 0. 0. 0.
time (sec) N/A 2.659 2.261 0.046 0. 0. 0. 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F(-2) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 678 678 14516 13380 0 0 0 0 0
normalized size 1 1. 21.41 19.73 0. 0. 0. 0. 0.
time (sec) N/A 4.591 19.354 0.107 0. 0. 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F(-1) F(-1) F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 995 992 21555 54623 0 0 0 0 0
normalized size 1 1. 21.66 54.9 0. 0. 0. 0. 0.
time (sec) N/A 9.674 23.957 0.156 0. 0. 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F(-1) F F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 736 735 6648 20733 0 0 0 0 0
normalized size 1 1. 9.03 28.17 0. 0. 0. 0. 0.
time (sec) N/A 4.425 17.566 0.089 0. 0. 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 440 440 586 2453 0 0 0 0 0
normalized size 1 1. 1.33 5.58 0. 0. 0. 0. 0.
time (sec) N/A 2.041 10.196 0.107 0. 0. 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F F(-1) F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 606 606 1749 9328 0 0 0 0 0
normalized size 1 1. 2.89 15.39 0. 0. 0. 0. 0.
time (sec) N/A 2.447 17.501 0.2 0. 0. 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F F(-1) F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 1081 1080 10637 71656 0 0 0 0 0
normalized size 1 1. 9.84 66.29 0. 0. 0. 0. 0.
time (sec) N/A 8.317 35.716 1.606 0. 0. 0. 0. 0.
Problem 133 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 1096 1080 18383 12279 0 0 0 0 0
normalized size 1 0.99 16.77 11.2 0. 0. 0. 0. 0.
time (sec) N/A 13.687 23.922 0.1 0. 0. 0. 0. 0.
Problem 134 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 608 605 8828 5679 0 0 0 0 0
normalized size 1 1. 14.52 9.34 0. 0. 0. 0. 0.
time (sec) N/A 3.718 17.009 0.052 0. 0. 0. 0. 0.
Problem 135 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 368 367 390 1804 0 0 0 0 0
normalized size 1 1. 1.06 4.9 0. 0. 0. 0. 0.
time (sec) N/A 1.562 7.776 0.036 0. 0. 0. 0. 0.
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 465 465 13075 1368 0 0 0 0 0
normalized size 1 1. 28.12 2.94 0. 0. 0. 0. 0.
time (sec) N/A 3.022 16.367 0.049 0. 0. 0. 0. 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F(-2) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 738 738 17743 17460 0 0 0 0 0
normalized size 1 1. 24.04 23.66 0. 0. 0. 0. 0.
time (sec) N/A 5.534 21.155 0.131 0. 0. 0. 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F(-1) F(-1) F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 1405 1388 38310 89498 0 0 0 0 0
normalized size 1 0.99 27.27 63.7 0. 0. 0. 0. 0.
time (sec) N/A 24.538 35.812 0.276 0. 0. 0. 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F(-1) F(-1) F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 951 950 16659 42545 0 0 0 0 0
normalized size 1 1. 17.52 44.74 0. 0. 0. 0. 0.
time (sec) N/A 6.868 21.51 0.128 0. 0. 0. 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F(-1) F(-1) F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 757 757 6207 15875 0 0 0 0 0
normalized size 1 1. 8.2 20.97 0. 0. 0. 0. 0.
time (sec) N/A 4.048 16.527 0.12 0. 0. 0. 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F(-1) F(-1) F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 867 867 2103 20597 0 0 0 0 0
normalized size 1 1. 2.43 23.76 0. 0. 0. 0. 0.
time (sec) N/A 7.156 18.54 0.222 0. 0. 0. 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F F(-1) F F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 1070 1070 19544 72702 0 0 0 0 0
normalized size 1 1. 18.27 67.95 0. 0. 0. 0. 0.
time (sec) N/A 8.22 35.436 1.787 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 [70] had the largest ratio of [ 0.25 ]

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. 32 0.031
2 A 2 1 1. 32 0.031
3 A 2 1 1. 30 0.033
4 A 2 1 1. 25 0.04
5 A 4 3 1. 32 0.094
6 A 5 4 1. 32 0.125
7 A 5 5 1. 32 0.156
8 A 5 5 1. 32 0.156
9 A 6 6 1. 32 0.188
10 A 2 1 1. 32 0.031
11 A 2 1 1. 32 0.031
12 A 2 1 1. 30 0.033
13 A 2 1 1. 25 0.04
14 A 6 4 1. 32 0.125
15 A 5 4 1. 32 0.125
16 A 5 5 1. 32 0.156
17 A 6 6 1. 32 0.188
18 A 2 1 1. 32 0.031
19 A 2 1 1. 32 0.031
20 A 2 1 1. 30 0.033
21 A 2 1 1. 25 0.04
22 A 4 3 1. 32 0.094
23 A 5 4 1. 32 0.125
24 A 6 5 1. 32 0.156
25 A 2 1 1. 30 0.033
26 A 2 1 1. 30 0.033
27 A 2 1 1. 28 0.036
28 A 2 1 1. 23 0.043
29 A 3 2 1. 30 0.067
30 A 4 4 1. 30 0.133
31 A 4 4 1. 30 0.133
32 A 3 3 1. 20 0.15
33 A 4 4 0.99 25 0.16
34 A 5 5 0.99 30 0.167
35 A 7 6 1. 37 0.162
36 A 6 6 1. 37 0.162
37 A 5 5 1.01 35 0.143
38 A 5 5 1. 30 0.167
39 A 6 6 1. 37 0.162
40 A 6 6 1. 37 0.162
41 A 5 5 1. 37 0.135
42 A 6 5 1. 37 0.135
43 A 5 5 1. 37 0.135
44 A 4 4 1.02 35 0.114
45 A 4 4 1. 30 0.133
46 A 6 6 1. 37 0.162
47 A 6 6 1. 37 0.162
48 A 5 5 1. 37 0.135
49 A 4 4 1. 31 0.129
50 A 4 4 1. 30 0.133
51 A 7 7 1. 33 0.212
52 A 7 7 1. 33 0.212
53 A 6 6 1. 33 0.182
54 A 8 7 0.99 40 0.175
55 A 7 7 1. 40 0.175
56 A 6 6 0.99 38 0.158
57 A 6 6 1. 33 0.182
58 A 7 7 1. 40 0.175
59 A 7 7 1. 40 0.175
60 A 5 5 0.99 40 0.125
61 A 7 6 0.99 40 0.15
62 A 6 6 1. 40 0.15
63 A 5 5 1.01 38 0.132
64 A 5 5 1. 33 0.152
65 A 7 7 1. 40 0.175
66 A 7 7 1. 40 0.175
67 A 5 5 0.99 40 0.125
68 A 5 5 1.74 30 0.167
69 B 5 5 2.6 29 0.172
70 B 8 8 2.45 32 0.25
71 B 8 8 2.45 32 0.25
72 A 6 6 1.55 32 0.188
73 A 7 7 1.47 32 0.219
74 A 5 5 1.22 32 0.156
75 A 7 6 1. 36 0.167
76 A 6 5 1. 34 0.147
77 A 6 5 1. 29 0.172
78 A 8 6 1.01 36 0.167
79 A 8 6 1. 36 0.167
80 A 8 7 1. 36 0.194
81 A 6 6 1. 36 0.167
82 A 5 5 1. 34 0.147
83 A 5 5 1. 29 0.172
84 A 7 6 1. 36 0.167
85 A 7 6 1. 36 0.167
86 A 7 6 1. 36 0.167
87 A 6 6 1. 36 0.167
88 A 5 5 1. 36 0.139
89 A 4 4 0.99 34 0.118
90 A 4 4 1. 29 0.138
91 A 6 5 1. 36 0.139
92 A 6 5 1. 36 0.139
93 A 5 5 1. 36 0.139
94 A 6 5 1. 36 0.139
95 A 10 7 0.98 38 0.184
96 A 9 7 0.99 38 0.184
97 A 9 7 1. 38 0.184
98 A 9 8 1. 38 0.21
99 A 9 7 1. 38 0.184
100 A 10 8 1. 38 0.21
101 A 10 7 1. 38 0.184
102 A 9 7 1. 38 0.184
103 A 8 7 1. 38 0.184
104 A 8 7 1. 38 0.184
105 A 8 7 1. 38 0.184
106 A 9 8 1. 38 0.21
107 A 9 7 0.99 38 0.184
108 A 8 7 0.99 38 0.184
109 A 7 6 1. 38 0.158
110 A 7 6 1. 38 0.158
111 A 8 7 1. 38 0.184
112 A 9 7 1. 38 0.184
113 A 8 7 1. 58 0.121
114 A 7 6 1. 53 0.113
115 A 7 6 1. 60 0.1
116 A 10 8 1. 60 0.133
117 A 13 11 1. 60 0.183
118 A 10 10 1. 62 0.161
119 A 9 9 1. 62 0.145
120 A 7 7 1. 62 0.113
121 A 8 8 1. 62 0.129
122 A 9 8 0.99 62 0.129
123 A 9 7 1. 40 0.175
124 A 8 7 1. 38 0.184
125 A 6 5 1. 33 0.152
126 A 9 7 1. 40 0.175
127 A 12 10 1. 40 0.25
128 A 11 10 1. 42 0.238
129 A 10 10 1. 42 0.238
130 A 6 6 1. 42 0.143
131 A 7 7 1. 42 0.167
132 A 8 7 1. 42 0.167
133 A 9 7 0.99 42 0.167
134 A 8 7 1. 40 0.175
135 A 7 6 1. 35 0.171
136 A 11 9 1. 42 0.214
137 A 12 10 1. 42 0.238
138 A 11 10 0.99 44 0.227
139 A 10 10 1. 44 0.227
140 A 9 9 1. 44 0.204
141 A 10 10 1. 44 0.227
142 A 8 7 1. 44 0.159

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