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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by the 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 as F.

In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 126 82 85 306 85 151 86 122

N.S.

1 1.00 0.65 0.67 2.43 0.67 1.20 0.68 0.97

time (sec)

N/A 0.464 0.151 0.164 0.227 0.287 0.309 0.288 0.343

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 96 65 67 201 67 117 68 92

N.S.

1 1.00 0.68 0.70 2.09 0.70 1.22 0.71 0.96

time (sec)

N/A 0.387 0.129 0.145 0.212 0.276 0.239 0.285 0.198

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 65 45 47 117 48 82 49 62

N.S.

1 1.00 0.69 0.72 1.80 0.74 1.26 0.75 0.95

time (sec)

N/A 0.288 0.109 0.136 0.192 0.274 0.187 0.291 6.084

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 27 29 53 30 46 31 35

N.S.

1 1.00 0.96 1.04 1.89 1.07 1.64 1.11 1.25

time (sec)

N/A 0.223 0.089 0.108 0.190 0.264 0.148 0.294 0.090

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 40 31 522 32 37 339 0

N.S.

1 1.00 1.38 1.07 18.00 1.10 1.28 11.69 0.00

time (sec)

N/A 0.304 0.069 0.141 0.263 0.270 2.611 0.294 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 60 56 108 54 0 569 0

N.S.

1 1.00 1.25 1.17 2.25 1.12 0.00 11.85 0.00

time (sec)

N/A 0.374 0.150 0.153 0.404 0.280 0.000 0.297 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 89 76 88 112 83 0 796 0

N.S.

1 1.00 0.85 0.99 1.26 0.93 0.00 8.94 0.00

time (sec)

N/A 0.431 0.245 0.163 0.439 0.269 0.000 0.302 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 132 110 117 111 108 0 961 0

N.S.

1 1.00 0.83 0.89 0.84 0.82 0.00 7.28 0.00

time (sec)

N/A 0.480 0.289 0.192 0.460 0.260 0.000 0.308 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

166 166 138 145 110 124 0 1108 0

N.S.

1 1.00 0.83 0.87 0.66 0.75 0.00 6.67 0.00

time (sec)

N/A 0.533 0.242 0.216 0.495 0.271 0.000 0.311 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

186 186 101 127 406 126 228 128 172

N.S.

1 1.00 0.54 0.68 2.18 0.68 1.23 0.69 0.92

time (sec)

N/A 0.526 0.161 0.253 0.208 0.277 0.342 0.290 0.325

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 135 87 94 259 95 172 95 128

N.S.

1 1.00 0.64 0.70 1.92 0.70 1.27 0.70 0.95

time (sec)

N/A 0.387 0.127 0.254 0.199 0.289 0.265 0.271 6.034

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 52 57 61 141 63 112 65 84

N.S.

1 1.04 1.14 1.22 2.82 1.26 2.24 1.30 1.68

time (sec)

N/A 0.323 0.126 0.221 0.194 0.261 0.201 0.279 5.929

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 62 51 79 80 61 92 551 0

N.S.

1 1.00 0.82 1.27 1.29 0.98 1.48 8.89 0.00

time (sec)

N/A 0.346 0.202 0.256 0.455 0.277 1.410 0.279 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 64 74 122 84 0 743 0

N.S.

1 1.00 0.89 1.03 1.69 1.17 0.00 10.32 0.00

time (sec)

N/A 0.406 0.163 0.247 0.684 0.283 0.000 0.286 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 121 95 114 189 110 0 1182 0

N.S.

1 1.00 0.79 0.94 1.56 0.91 0.00 9.77 0.00

time (sec)

N/A 0.507 0.273 0.265 1.106 0.263 0.000 0.300 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

175 175 154 158 187 145 0 1400 0

N.S.

1 1.00 0.88 0.90 1.07 0.83 0.00 8.00 0.00

time (sec)

N/A 0.580 0.345 0.298 1.238 0.260 0.000 0.299 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

248 248 204 201 186 180 0 1712 0

N.S.

1 1.00 0.82 0.81 0.75 0.73 0.00 6.90 0.00

time (sec)

N/A 0.656 0.274 0.336 1.356 0.269 0.000 0.318 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F C F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

218 218 158 328 0 188 0 3337 0

N.S.

1 1.00 0.72 1.50 0.00 0.86 0.00 15.31 0.00

time (sec)

N/A 0.665 0.414 0.424 0.000 0.269 0.000 0.355 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 152 117 237 0 141 0 2709 0

N.S.

1 1.00 0.77 1.56 0.00 0.93 0.00 17.82 0.00

time (sec)

N/A 0.504 0.354 0.316 0.000 0.287 0.000 0.343 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 99 87 180 0 108 0 2205 0

N.S.

1 1.00 0.88 1.82 0.00 1.09 0.00 22.27 0.00

time (sec)

N/A 0.432 0.192 0.274 0.000 0.280 0.000 0.350 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 69 63 150 776 78 0 1647 0

N.S.

1 1.00 0.91 2.17 11.25 1.13 0.00 23.87 0.00

time (sec)

N/A 0.359 0.106 0.254 0.283 0.270 0.000 0.316 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 49 73 141 63 0 597 0

N.S.

1 1.00 0.96 1.43 2.76 1.24 0.00 11.71 0.00

time (sec)

N/A 0.358 0.069 0.219 0.224 0.274 0.000 0.326 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 63 99 0 76 0 838 0

N.S.

1 1.00 0.86 1.36 0.00 1.04 0.00 11.48 0.00

time (sec)

N/A 0.422 0.105 0.236 0.000 0.324 0.000 0.309 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 114 101 144 0 118 0 2897 0

N.S.

1 1.00 0.89 1.26 0.00 1.04 0.00 25.41 0.00

time (sec)

N/A 0.531 0.265 0.305 0.000 0.274 0.000 0.360 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 189 176 202 0 186 0 4565 0

N.S.

1 1.00 0.93 1.07 0.00 0.98 0.00 24.15 0.00

time (sec)

N/A 0.671 0.427 0.361 0.000 0.280 0.000 0.355 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

233 233 177 734 0 287 0 1973 0

N.S.

1 1.00 0.76 3.15 0.00 1.23 0.00 8.47 0.00

time (sec)

N/A 0.726 0.667 0.475 0.000 0.300 0.000 0.372 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

181 181 153 607 0 246 0 1474 0

N.S.

1 1.00 0.85 3.35 0.00 1.36 0.00 8.14 0.00

time (sec)

N/A 0.616 0.578 0.408 0.000 0.289 0.000 0.376 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 149 117 402 0 202 0 1120 0

N.S.

1 1.00 0.79 2.70 0.00 1.36 0.00 7.52 0.00

time (sec)

N/A 0.574 0.530 0.309 0.000 0.293 0.000 0.331 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 124 96 313 0 155 0 951 0

N.S.

1 1.00 0.77 2.52 0.00 1.25 0.00 7.67 0.00

time (sec)

N/A 0.498 0.336 0.280 0.000 0.284 0.000 0.346 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 76 66 107 164 96 0 518 0

N.S.

1 1.06 0.92 1.49 2.28 1.33 0.00 7.19 0.00

time (sec)

N/A 0.490 0.169 0.251 0.238 0.277 0.000 0.299 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 149 138 210 0 189 0 1281 0

N.S.

1 1.00 0.93 1.41 0.00 1.27 0.00 8.60 0.00

time (sec)

N/A 0.572 0.702 0.283 0.000 0.293 0.000 0.335 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 188 184 256 0 262 0 3180 0

N.S.

1 1.00 0.98 1.36 0.00 1.39 0.00 16.91 0.00

time (sec)

N/A 0.699 1.254 0.336 0.000 0.315 0.000 0.379 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

265 265 235 705 0 388 0 16724 0

N.S.

1 1.00 0.89 2.66 0.00 1.46 0.00 63.11 0.00

time (sec)

N/A 0.810 0.642 0.484 0.000 0.326 0.000 0.640 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

241 241 154 621 0 325 0 15410 0

N.S.

1 1.00 0.64 2.58 0.00 1.35 0.00 63.94 0.00

time (sec)

N/A 0.745 0.852 0.388 0.000 0.295 0.000 0.619 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 179 157 419 0 263 0 10535 0

N.S.

1 1.00 0.88 2.34 0.00 1.47 0.00 58.85 0.00

time (sec)

N/A 0.560 0.388 0.353 0.000 0.307 0.000 0.541 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 105 87 145 199 164 0 5727 0

N.S.

1 1.01 0.84 1.39 1.91 1.58 0.00 55.07 0.00

time (sec)

N/A 0.590 0.485 0.319 0.289 0.287 0.000 0.409 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

261 261 449 359 0 391 0 17806 0

N.S.

1 1.00 1.72 1.38 0.00 1.50 0.00 68.22 0.00

time (sec)

N/A 0.767 0.648 0.369 0.000 0.319 0.000 0.671 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

299 299 540 405 0 500 0 20808 0

N.S.

1 1.00 1.81 1.35 0.00 1.67 0.00 69.59 0.00

time (sec)

N/A 0.874 1.190 0.438 0.000 0.311 0.000 0.710 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

377 377 630 466 0 585 0 24116 0

N.S.

1 1.00 1.67 1.24 0.00 1.55 0.00 63.97 0.00

time (sec)

N/A 1.020 1.238 0.544 0.000 0.332 0.000 0.756 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 141 92 96 372 95 168 97 121

N.S.

1 1.00 0.65 0.68 2.64 0.67 1.19 0.69 0.86

time (sec)

N/A 0.396 0.132 0.170 0.198 0.299 0.417 0.295 0.436

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 111 75 78 258 77 134 79 97

N.S.

1 1.00 0.68 0.70 2.32 0.69 1.21 0.71 0.87

time (sec)

N/A 0.331 0.080 0.146 0.191 0.272 0.324 0.280 6.074

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 80 57 59 165 60 99 60 73

N.S.

1 1.00 0.71 0.74 2.06 0.75 1.24 0.75 0.91

time (sec)

N/A 0.266 0.065 0.164 0.187 0.284 0.255 0.299 0.166

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 41 43 91 41 65 42 49

N.S.

1 1.00 0.77 0.81 1.72 0.77 1.23 0.79 0.92

time (sec)

N/A 0.216 0.043 0.134 0.182 0.266 0.188 0.294 5.946

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 54 60 66 46 65 432 0

N.S.

1 1.00 1.32 1.46 1.61 1.12 1.59 10.54 0.00

time (sec)

N/A 0.241 0.079 0.151 0.397 0.271 1.872 0.324 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 44 48 937 53 0 411 0

N.S.

1 1.00 1.00 1.09 21.30 1.20 0.00 9.34 0.00

time (sec)

N/A 0.246 0.057 0.157 0.375 0.276 0.000 0.290 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 82 73 123 62 0 766 0

N.S.

1 1.00 1.11 0.99 1.66 0.84 0.00 10.35 0.00

time (sec)

N/A 0.306 0.109 0.166 0.651 0.279 0.000 0.294 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 106 95 102 121 82 0 834 0

N.S.

1 1.00 0.90 0.96 1.14 0.77 0.00 7.87 0.00

time (sec)

N/A 0.359 0.097 0.197 0.723 0.272 0.000 0.308 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 149 125 131 121 101 0 1086 0

N.S.

1 1.00 0.84 0.88 0.81 0.68 0.00 7.29 0.00

time (sec)

N/A 0.409 0.120 0.226 0.804 0.324 0.000 0.300 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

236 236 139 160 612 154 286 162 186

N.S.

1 1.00 0.59 0.68 2.59 0.65 1.21 0.69 0.79

time (sec)

N/A 0.536 0.262 0.293 0.217 0.288 0.557 0.286 0.669

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 185 113 127 438 126 226 129 151

N.S.

1 1.00 0.61 0.69 2.37 0.68 1.22 0.70 0.82

time (sec)

N/A 0.428 0.156 0.273 0.206 0.280 0.433 0.278 6.328

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 138 86 94 292 97 172 99 118

N.S.

1 1.00 0.62 0.68 2.12 0.70 1.25 0.72 0.86

time (sec)

N/A 0.332 0.116 0.247 0.188 0.275 0.326 0.295 6.263

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C A A C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 111 82 128 116 97 160 725 0

N.S.

1 1.00 0.74 1.15 1.05 0.87 1.44 6.53 0.00

time (sec)

N/A 0.338 0.274 0.322 1.380 0.280 2.486 0.310 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 97 97 156 97 96 0 1638 0

N.S.

1 1.00 1.00 1.61 1.00 0.99 0.00 16.89 0.00

time (sec)

N/A 0.322 0.178 0.347 1.118 0.303 0.000 0.322 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 114 99 124 150 107 0 1058 0

N.S.

1 1.00 0.87 1.09 1.32 0.94 0.00 9.28 0.00

time (sec)

N/A 0.359 0.294 0.370 2.085 0.285 0.000 0.301 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 134 114 120 140 116 0 1032 0

N.S.

1 1.00 0.85 0.90 1.04 0.87 0.00 7.70 0.00

time (sec)

N/A 0.418 0.276 0.357 1.489 0.287 0.000 0.302 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

177 177 122 157 222 129 0 1497 0

N.S.

1 1.00 0.69 0.89 1.25 0.73 0.00 8.46 0.00

time (sec)

N/A 0.520 0.341 0.416 8.166 0.293 0.000 0.299 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

273 273 269 323 0 240 0 0 0

N.S.

1 1.00 0.99 1.18 0.00 0.88 0.00 0.00 0.00

time (sec)

N/A 0.826 1.461 0.515 0.000 0.312 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

209 209 214 266 0 185 0 0 0

N.S.

1 1.00 1.02 1.27 0.00 0.89 0.00 0.00 0.00

time (sec)

N/A 0.542 1.108 0.378 0.000 0.317 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

227 227 216 264 0 195 0 0 0

N.S.

1 1.00 0.95 1.16 0.00 0.86 0.00 0.00 0.00

time (sec)

N/A 0.512 0.653 0.309 0.000 0.314 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

177 177 155 234 0 146 0 0 0

N.S.

1 1.00 0.88 1.32 0.00 0.82 0.00 0.00 0.00

time (sec)

N/A 0.420 0.277 0.260 0.000 0.286 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

213 213 163 225 0 187 0 0 0

N.S.

1 1.00 0.77 1.06 0.00 0.88 0.00 0.00 0.00

time (sec)

N/A 0.440 0.401 0.256 0.000 0.297 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

197 197 174 200 0 162 0 0 0

N.S.

1 1.00 0.88 1.02 0.00 0.82 0.00 0.00 0.00

time (sec)

N/A 0.547 0.358 0.266 0.000 0.302 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

250 250 238 266 0 234 0 0 0

N.S.

1 1.00 0.95 1.06 0.00 0.94 0.00 0.00 0.00

time (sec)

N/A 0.623 0.573 0.332 0.000 0.339 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

270 270 240 259 0 225 0 0 0

N.S.

1 1.00 0.89 0.96 0.00 0.83 0.00 0.00 0.00

time (sec)

N/A 0.660 0.833 0.377 0.000 0.302 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

450 476 298 524 0 351 0 0 0

N.S.

1 1.06 0.66 1.16 0.00 0.78 0.00 0.00 0.00

time (sec)

N/A 1.165 3.153 0.779 0.000 0.321 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

431 441 286 852 0 291 0 0 0

N.S.

1 1.02 0.66 1.98 0.00 0.68 0.00 0.00 0.00

time (sec)

N/A 0.999 1.825 0.627 0.000 0.316 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

416 429 274 748 0 333 0 0 0

N.S.

1 1.03 0.66 1.80 0.00 0.80 0.00 0.00 0.00

time (sec)

N/A 0.960 2.013 0.517 0.000 0.298 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

239 244 236 412 0 244 0 0 0

N.S.

1 1.02 0.99 1.72 0.00 1.02 0.00 0.00 0.00

time (sec)

N/A 0.501 0.972 0.427 0.000 0.297 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

476 476 280 491 0 333 0 0 0

N.S.

1 1.00 0.59 1.03 0.00 0.70 0.00 0.00 0.00

time (sec)

N/A 1.010 1.952 0.349 0.000 0.323 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

435 435 419 478 0 320 0 0 0

N.S.

1 1.00 0.96 1.10 0.00 0.74 0.00 0.00 0.00

time (sec)

N/A 0.993 0.949 0.396 0.000 0.306 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

501 501 330 622 0 400 0 0 0

N.S.

1 1.00 0.66 1.24 0.00 0.80 0.00 0.00 0.00

time (sec)

N/A 1.364 2.305 0.477 0.000 0.338 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

476 714 330 640 0 492 0 0 0

N.S.

1 1.50 0.69 1.34 0.00 1.03 0.00 0.00 0.00

time (sec)

N/A 1.806 2.476 1.102 0.000 0.296 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

746 759 364 912 0 604 0 0 0

N.S.

1 1.02 0.49 1.22 0.00 0.81 0.00 0.00 0.00

time (sec)

N/A 1.795 3.364 0.862 0.000 0.316 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

512 507 317 628 0 483 0 0 0

N.S.

1 0.99 0.62 1.23 0.00 0.94 0.00 0.00 0.00

time (sec)

N/A 0.995 2.529 0.685 0.000 0.317 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

856 856 374 598 0 611 0 0 0

N.S.

1 1.00 0.44 0.70 0.00 0.71 0.00 0.00 0.00

time (sec)

N/A 1.589 2.987 0.525 0.000 0.297 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

730 730 672 580 0 637 0 0 0

N.S.

1 1.00 0.92 0.79 0.00 0.87 0.00 0.00 0.00

time (sec)

N/A 1.923 2.363 0.562 0.000 0.365 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

875 875 593 910 0 714 0 0 0

N.S.

1 1.00 0.68 1.04 0.00 0.82 0.00 0.00 0.00

time (sec)

N/A 2.747 4.043 0.801 0.000 0.297 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

791 791 432 697 0 758 0 0 0

N.S.

1 1.00 0.55 0.88 0.00 0.96 0.00 0.00 0.00

time (sec)

N/A 2.046 1.857 1.754 0.000 0.307 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 156 101 106 449 104 185 106 151

N.S.

1 1.00 0.65 0.68 2.88 0.67 1.19 0.68 0.97

time (sec)

N/A 0.444 0.145 0.174 0.216 0.284 0.546 0.325 0.724

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 126 84 88 326 87 151 88 121

N.S.

1 1.00 0.67 0.70 2.59 0.69 1.20 0.70 0.96

time (sec)

N/A 0.369 0.089 0.153 0.207 0.257 0.434 0.286 6.370

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 95 66 69 224 68 116 69 92

N.S.

1 1.00 0.69 0.73 2.36 0.72 1.22 0.73 0.97

time (sec)

N/A 0.309 0.069 0.136 0.194 0.264 0.316 0.307 6.111

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 50 52 141 52 82 54 65

N.S.

1 1.00 0.74 0.76 2.07 0.76 1.21 0.79 0.96

time (sec)

N/A 0.254 0.055 0.136 0.194 0.264 0.240 0.287 0.132

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C A A C F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

57 57 50 98 76 58 83 510 0

N.S.

1 1.00 0.88 1.72 1.33 1.02 1.46 8.95 0.00

time (sec)

N/A 0.284 0.118 0.180 0.584 0.280 2.753 0.319 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 56 79 69 64 0 489 0

N.S.

1 1.00 1.00 1.41 1.23 1.14 0.00 8.73 0.00

time (sec)

N/A 0.272 0.081 0.207 0.543 0.278 0.000 0.304 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 66 65 1146 66 0 564 0

N.S.

1 1.00 0.94 0.93 16.37 0.94 0.00 8.06 0.00

time (sec)

N/A 0.280 0.089 0.201 0.449 0.268 0.000 0.322 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 91 104 87 132 89 0 796 0

N.S.

1 1.00 1.14 0.96 1.45 0.98 0.00 8.75 0.00

time (sec)

N/A 0.351 0.118 0.220 0.904 0.278 0.000 0.301 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

235 235 139 161 662 161 284 161 225

N.S.

1 1.00 0.59 0.69 2.82 0.69 1.21 0.69 0.96

time (sec)

N/A 0.547 0.238 0.318 0.245 0.303 0.798 0.309 6.446

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 188 112 124 489 129 226 131 184

N.S.

1 1.00 0.60 0.66 2.60 0.69 1.20 0.70 0.98

time (sec)

N/A 0.461 0.199 0.277 0.226 0.286 0.569 0.316 0.771

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C A A C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 161 108 178 147 128 207 921 0

N.S.

1 1.00 0.67 1.11 0.91 0.80 1.29 5.72 0.00

time (sec)

N/A 0.433 0.350 0.426 5.679 0.270 3.693 0.340 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C A F C F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

145 145 145 214 129 127 0 2038 0

N.S.

1 1.00 1.00 1.48 0.89 0.88 0.00 14.06 0.00

time (sec)

N/A 0.410 0.250 0.494 6.468 0.263 0.000 0.341 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C A F C F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

142 142 138 210 110 123 0 2171 0

N.S.

1 1.00 0.97 1.48 0.77 0.87 0.00 15.29 0.00

time (sec)

N/A 0.397 0.245 0.496 2.189 0.277 0.000 0.317 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 151 135 196 173 145 0 1181 0

N.S.

1 1.00 0.89 1.30 1.15 0.96 0.00 7.82 0.00

time (sec)

N/A 0.430 0.452 0.491 7.106 0.270 0.000 0.341 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

167 167 148 167 164 153 0 1255 0

N.S.

1 1.00 0.89 1.00 0.98 0.92 0.00 7.51 0.00

time (sec)

N/A 0.469 0.372 0.559 5.946 0.304 0.000 0.307 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

371 371 231 558 0 397 0 0 0

N.S.

1 1.00 0.62 1.50 0.00 1.07 0.00 0.00 0.00

time (sec)

N/A 1.008 0.139 0.400 0.000 0.321 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

357 357 216 392 0 393 0 0 0

N.S.

1 1.00 0.61 1.10 0.00 1.10 0.00 0.00 0.00

time (sec)

N/A 0.816 0.109 0.370 0.000 0.298 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

281 281 186 266 0 292 0 0 0

N.S.

1 1.00 0.66 0.95 0.00 1.04 0.00 0.00 0.00

time (sec)

N/A 0.671 5.041 0.286 0.000 0.276 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

343 343 196 176 0 379 0 0 0

N.S.

1 1.00 0.57 0.51 0.00 1.10 0.00 0.00 0.00

time (sec)

N/A 0.649 5.052 0.279 0.000 0.302 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

343 343 196 85 0 385 0 0 0

N.S.

1 1.00 0.57 0.25 0.00 1.12 0.00 0.00 0.00

time (sec)

N/A 0.625 5.049 0.267 0.000 0.301 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

301 301 206 88 0 308 0 0 0

N.S.

1 1.00 0.68 0.29 0.00 1.02 0.00 0.00 0.00

time (sec)

N/A 0.726 0.133 0.291 0.000 0.345 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

380 380 233 116 0 448 0 0 0

N.S.

1 1.00 0.61 0.31 0.00 1.18 0.00 0.00 0.00

time (sec)

N/A 0.786 0.175 0.408 0.000 0.315 0.000 0.000 0.000

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