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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 B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 101 76 143 481 169 311 170 219

N.S.

1 1.11 0.84 1.57 5.29 1.86 3.42 1.87 2.41

time (sec)

N/A 0.551 0.314 1.046 0.291 0.298 0.353 0.293 14.378

Problem 2

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

70 76 61 107 278 109 202 110 147

N.S.

1 1.09 0.87 1.53 3.97 1.56 2.89 1.57 2.10

time (sec)

N/A 0.435 0.210 0.905 0.232 0.274 0.273 0.295 14.064

Problem 3

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

49 52 44 60 136 62 112 64 84

N.S.

1 1.06 0.90 1.22 2.78 1.27 2.29 1.31 1.71

time (sec)

N/A 0.330 0.172 0.905 0.330 0.273 0.198 0.313 0.122

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

27 27 26 28 50 28 46 30 34

N.S.

1 1.00 0.96 1.04 1.85 1.04 1.70 1.11 1.26

time (sec)

N/A 0.229 0.113 0.684 0.264 0.279 0.158 0.324 0.093

Problem 5

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

52 52 50 77 142 62 0 577 0

N.S.

1 1.00 0.96 1.48 2.73 1.19 0.00 11.10 0.00

time (sec)

N/A 0.385 0.113 0.743 0.309 0.268 0.000 0.342 0.000

Problem 6

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

73 76 65 114 164 96 0 523 0

N.S.

1 1.04 0.89 1.56 2.25 1.32 0.00 7.16 0.00

time (sec)

N/A 0.479 0.417 0.769 0.327 0.283 0.000 0.314 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

104 105 89 148 199 165 0 5518 0

N.S.

1 1.01 0.86 1.42 1.91 1.59 0.00 53.06 0.00

time (sec)

N/A 0.593 0.668 0.908 0.435 0.294 0.000 0.484 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 134 144 184 249 235 0 8378 0

N.S.

1 1.06 1.13 1.45 1.96 1.85 0.00 65.97 0.00

time (sec)

N/A 0.731 0.611 1.113 0.469 0.293 0.000 0.558 0.000

Problem 9

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

161 166 132 145 717 287 660 222 349

N.S.

1 1.03 0.82 0.90 4.45 1.78 4.10 1.38 2.17

time (sec)

N/A 0.475 0.585 1.585 0.282 0.305 0.517 0.332 0.656

Problem 10

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

134 129 106 121 428 190 456 153 229

N.S.

1 0.96 0.79 0.90 3.19 1.42 3.40 1.14 1.71

time (sec)

N/A 0.346 0.447 1.142 0.325 0.271 0.399 0.301 14.343

Problem 11

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

95 97 77 81 222 113 264 94 179

N.S.

1 1.02 0.81 0.85 2.34 1.19 2.78 0.99 1.88

time (sec)

N/A 0.306 0.326 1.304 0.235 0.286 0.290 0.307 0.229

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 55 50 46 90 53 126 48 57

N.S.

1 1.00 0.91 0.84 1.64 0.96 2.29 0.87 1.04

time (sec)

N/A 0.210 0.269 0.613 0.244 0.281 0.217 0.292 0.103

Problem 13

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

78 78 65 107 163 71 0 610 0

N.S.

1 1.00 0.83 1.37 2.09 0.91 0.00 7.82 0.00

time (sec)

N/A 0.347 0.264 0.738 0.357 0.281 0.000 0.352 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 86 75 155 171 100 0 534 0

N.S.

1 1.04 0.90 1.87 2.06 1.20 0.00 6.43 0.00

time (sec)

N/A 0.512 0.654 0.822 0.350 0.270 0.000 0.356 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

112 146 102 193 204 176 0 5136 0

N.S.

1 1.30 0.91 1.72 1.82 1.57 0.00 45.86 0.00

time (sec)

N/A 0.489 1.037 1.037 0.443 0.297 0.000 0.499 0.000

Problem 16

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

225 304 385 173 925 350 772 351 532

N.S.

1 1.35 1.71 0.77 4.11 1.56 3.43 1.56 2.36

time (sec)

N/A 1.837 1.032 1.961 0.330 0.287 0.733 0.324 15.574

Problem 17

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

175 216 121 224 535 227 495 231 364

N.S.

1 1.23 0.69 1.28 3.06 1.30 2.83 1.32 2.08

time (sec)

N/A 1.104 0.996 1.674 0.282 0.298 0.494 0.311 14.923

Problem 18

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

123 137 93 128 267 128 284 137 173

N.S.

1 1.11 0.76 1.04 2.17 1.04 2.31 1.11 1.41

time (sec)

N/A 0.607 0.634 1.637 0.255 0.282 0.382 0.309 14.472

Problem 19

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

75 74 52 61 103 60 126 69 77

N.S.

1 0.99 0.69 0.81 1.37 0.80 1.68 0.92 1.03

time (sec)

N/A 0.344 0.227 1.259 0.279 0.268 0.265 0.299 14.235

Problem 20

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

121 121 103 171 278 123 0 6075 0

N.S.

1 1.00 0.85 1.41 2.30 1.02 0.00 50.21 0.00

time (sec)

N/A 0.450 0.409 0.820 0.374 0.309 0.000 0.554 0.000

Problem 21

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

145 148 200 247 304 177 0 1000 0

N.S.

1 1.02 1.38 1.70 2.10 1.22 0.00 6.90 0.00

time (sec)

N/A 0.438 0.744 0.982 0.471 0.318 0.000 0.440 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

184 243 221 316 339 289 0 115446 0

N.S.

1 1.32 1.20 1.72 1.84 1.57 0.00 627.42 0.00

time (sec)

N/A 0.962 0.913 1.442 0.637 0.293 0.000 3.420 0.000

Problem 23

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

172 237 100 102 303 115 253 108 138

N.S.

1 1.38 0.58 0.59 1.76 0.67 1.47 0.63 0.80

time (sec)

N/A 0.750 0.457 1.689 0.289 0.288 0.601 0.354 0.908

Problem 24

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

134 181 92 81 188 88 209 84 104

N.S.

1 1.35 0.69 0.60 1.40 0.66 1.56 0.63 0.78

time (sec)

N/A 0.615 0.197 1.300 0.248 0.290 0.414 0.398 14.456

Problem 25

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

80 85 53 62 98 63 138 64 63

N.S.

1 1.06 0.66 0.78 1.22 0.79 1.72 0.80 0.79

time (sec)

N/A 0.287 0.135 1.182 0.252 0.282 0.321 0.412 14.527

Problem 26

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

59 59 52 52 91 49 60 428 0

N.S.

1 1.00 0.88 0.88 1.54 0.83 1.02 7.25 0.00

time (sec)

N/A 0.316 0.158 0.673 0.331 0.288 1.098 0.433 0.000

Problem 27

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

66 70 79 90 717 66 0 3220 0

N.S.

1 1.06 1.20 1.36 10.86 1.00 0.00 48.79 0.00

time (sec)

N/A 0.311 0.230 0.744 0.316 0.303 0.000 0.377 0.000

Problem 28

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

90 138 119 124 790 100 0 3920 0

N.S.

1 1.53 1.32 1.38 8.78 1.11 0.00 43.56 0.00

time (sec)

N/A 0.493 0.342 0.721 0.359 0.290 0.000 0.489 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

205 223 196 685 722 970 0 0 0

N.S.

1 1.09 0.96 3.34 3.52 4.73 0.00 0.00 0.00

time (sec)

N/A 0.724 0.198 1.732 0.483 0.331 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 145 130 392 402 598 0 0 0

N.S.

1 1.06 0.95 2.86 2.93 4.36 0.00 0.00 0.00

time (sec)

N/A 0.483 0.101 1.468 0.420 0.322 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 75 87 128 0 306 0 0 0

N.S.

1 1.00 1.16 1.71 0.00 4.08 0.00 0.00 0.00

time (sec)

N/A 0.287 0.010 0.981 0.000 0.294 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD

size

14 14 16 14 16 16 12 16 18

N.S.

1 1.00 1.14 1.00 1.14 1.14 0.86 1.14 1.29

time (sec)

N/A 0.194 4.359 0.528 0.577 0.289 0.379 0.499 13.675

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 137 109 316 1059 790 0 0 0

N.S.

1 1.20 0.96 2.77 9.29 6.93 0.00 0.00 0.00

time (sec)

N/A 0.656 0.529 2.141 0.427 0.322 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 97 75 170 324 450 0 0 0

N.S.

1 1.18 0.91 2.07 3.95 5.49 0.00 0.00 0.00

time (sec)

N/A 0.476 0.264 1.878 0.487 0.292 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 36 52 159 45 0 1404 55

N.S.

1 1.00 1.29 1.86 5.68 1.61 0.00 50.14 1.96

time (sec)

N/A 0.250 0.017 1.204 0.352 0.305 0.000 0.642 14.505

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD

size

16 16 18 16 290 18 14 18 18

N.S.

1 1.00 1.12 1.00 18.12 1.12 0.88 1.12 1.12

time (sec)

N/A 0.209 6.061 0.534 0.547 0.293 0.409 0.381 13.698

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

337 358 311 1127 3831 1315 0 0 0

N.S.

1 1.06 0.92 3.34 11.37 3.90 0.00 0.00 0.00

time (sec)

N/A 1.222 3.050 1.946 1.558 0.365 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 207 184 584 1891 795 0 0 0

N.S.

1 1.07 0.95 3.03 9.80 4.12 0.00 0.00 0.00

time (sec)

N/A 0.754 1.011 1.780 0.658 0.336 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 118 389 267 0 435 0 0 0

N.S.

1 1.01 3.32 2.28 0.00 3.72 0.00 0.00 0.00

time (sec)

N/A 0.405 4.174 1.382 0.000 0.347 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD

size

16 16 18 16 290 18 14 18 18

N.S.

1 1.00 1.12 1.00 18.12 1.12 0.88 1.12 1.12

time (sec)

N/A 0.205 1.726 0.023 0.579 0.322 0.403 0.309 0.003

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

194 202 124 232 263 190 0 1246 0

N.S.

1 1.04 0.64 1.20 1.36 0.98 0.00 6.42 0.00

time (sec)

N/A 0.987 0.063 0.797 0.293 0.297 0.000 0.390 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 175 122 189 242 156 0 779 0

N.S.

1 1.04 0.72 1.12 1.43 0.92 0.00 4.61 0.00

time (sec)

N/A 0.812 0.094 0.931 0.264 0.298 0.000 0.357 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 145 122 144 196 126 0 426 0

N.S.

1 1.02 0.86 1.01 1.38 0.89 0.00 3.00 0.00

time (sec)

N/A 0.663 0.044 0.701 0.240 0.273 0.000 0.340 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 118 124 100 159 108 0 168 0

N.S.

1 1.00 1.05 0.85 1.35 0.92 0.00 1.42 0.00

time (sec)

N/A 0.513 0.061 0.688 0.294 0.259 0.000 0.322 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 144 147 140 129 144 0 0 0

N.S.

1 1.04 1.06 1.01 0.93 1.04 0.00 0.00 0.00

time (sec)

N/A 0.642 0.344 0.744 0.506 0.279 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

168 176 190 180 129 208 0 0 0

N.S.

1 1.05 1.13 1.07 0.77 1.24 0.00 0.00 0.00

time (sec)

N/A 0.793 0.355 0.829 0.515 0.272 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 206 228 220 129 296 0 0 0

N.S.

1 1.07 1.18 1.14 0.67 1.53 0.00 0.00 0.00

time (sec)

N/A 0.955 0.386 0.798 0.455 0.291 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

231 238 150 242 295 258 0 1331 0

N.S.

1 1.03 0.65 1.05 1.28 1.12 0.00 5.76 0.00

time (sec)

N/A 0.687 0.851 1.112 0.369 0.294 0.000 0.567 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

203 210 150 197 274 195 0 821 0

N.S.

1 1.03 0.74 0.97 1.35 0.96 0.00 4.04 0.00

time (sec)

N/A 0.600 0.643 0.961 0.386 0.301 0.000 0.472 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

158 158 150 150 229 148 0 436 0

N.S.

1 1.00 0.95 0.95 1.45 0.94 0.00 2.76 0.00

time (sec)

N/A 0.471 0.248 1.041 0.444 0.310 0.000 0.395 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 130 145 108 187 114 0 167 0

N.S.

1 1.00 1.12 0.83 1.44 0.88 0.00 1.28 0.00

time (sec)

N/A 0.399 0.250 0.913 0.371 0.286 0.000 0.328 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 140 175 146 135 136 0 0 0

N.S.

1 1.04 1.30 1.08 1.00 1.01 0.00 0.00 0.00

time (sec)

N/A 0.692 0.729 1.133 0.537 0.325 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

170 213 181 189 136 206 0 0 0

N.S.

1 1.25 1.06 1.11 0.80 1.21 0.00 0.00 0.00

time (sec)

N/A 0.566 1.458 1.073 0.481 0.335 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

216 223 237 230 136 323 0 0 0

N.S.

1 1.03 1.10 1.06 0.63 1.50 0.00 0.00 0.00

time (sec)

N/A 0.950 1.150 1.096 0.506 0.319 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

247 296 237 273 136 417 0 0 0

N.S.

1 1.20 0.96 1.11 0.55 1.69 0.00 0.00 0.00

time (sec)

N/A 0.795 0.904 1.107 0.504 0.332 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

410 576 236 474 547 368 0 2480 0

N.S.

1 1.40 0.58 1.16 1.33 0.90 0.00 6.05 0.00

time (sec)

N/A 2.632 1.499 1.994 0.454 0.317 0.000 0.827 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

354 502 251 386 497 299 0 1549 0

N.S.

1 1.42 0.71 1.09 1.40 0.84 0.00 4.38 0.00

time (sec)

N/A 2.174 1.100 0.938 0.399 0.295 0.000 0.612 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

304 304 234 294 424 245 0 848 0

N.S.

1 1.00 0.77 0.97 1.39 0.81 0.00 2.79 0.00

time (sec)

N/A 0.827 0.298 0.940 0.366 0.342 0.000 0.467 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

257 257 236 212 377 213 0 332 0

N.S.

1 1.00 0.92 0.82 1.47 0.83 0.00 1.29 0.00

time (sec)

N/A 0.653 0.356 1.040 0.344 0.317 0.000 0.330 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

271 286 293 286 253 265 0 0 0

N.S.

1 1.06 1.08 1.06 0.93 0.98 0.00 0.00 0.00

time (sec)

N/A 0.676 1.488 0.987 0.591 0.313 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

292 445 268 368 253 367 0 0 0

N.S.

1 1.52 0.92 1.26 0.87 1.26 0.00 0.00 0.00

time (sec)

N/A 1.550 2.080 0.825 0.585 0.332 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

356 506 448 450 254 528 0 0 0

N.S.

1 1.42 1.26 1.26 0.71 1.48 0.00 0.00 0.00

time (sec)

N/A 1.774 2.082 0.921 0.601 0.348 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 55 34 74 35 83 69 0

N.S.

1 1.00 1.12 0.69 1.51 0.71 1.69 1.41 0.00

time (sec)

N/A 0.331 0.016 0.365 0.337 0.268 3.008 0.295 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A C A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 48 27 67 26 61 53 26

N.S.

1 1.00 1.33 0.75 1.86 0.72 1.69 1.47 0.72

time (sec)

N/A 0.256 0.009 0.302 0.316 0.310 0.555 0.286 0.031

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A C A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 51 19 60 18 37 35 18

N.S.

1 1.00 2.12 0.79 2.50 0.75 1.54 1.46 0.75

time (sec)

N/A 0.202 0.009 0.304 0.333 0.265 0.479 0.300 0.037

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 63 28 21 31 61 0 0

N.S.

1 1.00 1.80 0.80 0.60 0.89 1.74 0.00 0.00

time (sec)

N/A 0.259 0.051 0.292 0.428 0.268 1.059 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

183 192 122 0 235 174 0 0 0

N.S.

1 1.05 0.67 0.00 1.28 0.95 0.00 0.00 0.00

time (sec)

N/A 0.571 0.114 0.000 0.248 0.100 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

152 159 122 0 186 140 0 0 0

N.S.

1 1.05 0.80 0.00 1.22 0.92 0.00 0.00 0.00

time (sec)

N/A 0.430 0.049 0.000 0.262 0.101 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

152 159 122 0 186 140 0 0 0

N.S.

1 1.05 0.80 0.00 1.22 0.92 0.00 0.00 0.00

time (sec)

N/A 0.421 0.053 0.000 0.253 0.094 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

135 135 124 0 137 118 0 0 0

N.S.

1 1.00 0.92 0.00 1.01 0.87 0.00 0.00 0.00

time (sec)

N/A 0.311 0.063 0.000 0.253 0.127 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

135 135 124 0 138 118 0 0 0

N.S.

1 1.00 0.92 0.00 1.02 0.87 0.00 0.00 0.00

time (sec)

N/A 0.326 0.066 0.000 0.242 0.094 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

151 158 121 0 138 169 0 0 0

N.S.

1 1.05 0.80 0.00 0.91 1.12 0.00 0.00 0.00

time (sec)

N/A 0.416 0.055 0.000 0.273 0.100 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

153 162 121 0 138 169 0 0 0

N.S.

1 1.06 0.79 0.00 0.90 1.10 0.00 0.00 0.00

time (sec)

N/A 0.429 0.056 0.000 0.285 0.100 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

182 193 125 0 137 259 0 0 0

N.S.

1 1.06 0.69 0.00 0.75 1.42 0.00 0.00 0.00

time (sec)

N/A 0.534 0.053 0.000 0.240 0.135 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A F(-2) N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD

size

12 12 14 10 12 0 12 12 12

N.S.

1 1.00 1.17 0.83 1.00 0.00 1.00 1.00 1.00

time (sec)

N/A 0.174 26.255 0.119 0.701 0.000 6.357 0.329 13.311

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 133 0 57 0 0 15

N.S.

1 1.00 1.00 8.31 0.00 3.56 0.00 0.00 0.94

time (sec)

N/A 0.165 0.009 1.268 0.000 0.096 0.000 0.000 0.042

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A F(-2) N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD

size

14 14 16 12 14 0 12 14 14

N.S.

1 1.00 1.14 0.86 1.00 0.00 0.86 1.00 1.00

time (sec)

N/A 0.182 0.808 0.151 0.574 0.000 2.994 0.344 13.504

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A F(-2) N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD

size

12 12 14 10 12 0 12 12 12

N.S.

1 1.00 1.17 0.83 1.00 0.00 1.00 1.00 1.00

time (sec)

N/A 0.264 2.291 0.131 0.696 0.000 87.663 0.368 13.726

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 36 179 0 68 0 0 35

N.S.

1 1.00 0.86 4.26 0.00 1.62 0.00 0.00 0.83

time (sec)

N/A 0.223 0.029 2.096 0.000 0.099 0.000 0.000 0.047

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A F(-2) N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD

size

14 14 16 12 14 0 12 14 14

N.S.

1 1.00 1.14 0.86 1.00 0.00 0.86 1.00 1.00

time (sec)

N/A 0.190 7.418 0.146 0.599 0.000 37.920 0.328 13.556

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F(-2) F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

42 42 40 0 0 0 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.201 1.020 0.000 0.000 0.000 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A F(-2) N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD

size

10 10 12 8 10 0 10 10 10

N.S.

1 1.00 1.20 0.80 1.00 0.00 1.00 1.00 1.00

time (sec)

N/A 0.293 6.110 0.195 0.414 0.000 92.969 0.323 13.057

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A F(-2) N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD

size

12 12 14 10 12 0 12 12 12

N.S.

1 1.00 1.17 0.83 1.00 0.00 1.00 1.00 1.00

time (sec)

N/A 0.181 0.278 0.178 0.644 0.000 3.071 0.345 13.326

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 18 0 51 0 0 15

N.S.

1 1.00 1.00 1.12 0.00 3.19 0.00 0.00 0.94

time (sec)

N/A 0.164 0.009 0.249 0.000 0.085 0.000 0.000 13.172

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A F(-2) N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD

size

14 14 16 12 14 0 14 14 14

N.S.

1 1.00 1.14 0.86 1.00 0.00 1.00 1.00 1.00

time (sec)

N/A 0.186 0.453 0.118 0.577 0.000 10.382 0.326 13.056

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A F(-2) N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD

size

12 12 14 10 12 0 12 12 12

N.S.

1 1.00 1.17 0.83 1.00 0.00 1.00 1.00 1.00

time (sec)

N/A 0.267 2.672 0.130 0.662 0.000 14.099 0.357 13.610

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 38 182 0 93 0 0 42

N.S.

1 1.00 1.00 4.79 0.00 2.45 0.00 0.00 1.11

time (sec)

N/A 0.224 0.051 1.507 0.000 0.091 0.000 0.000 13.781

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A F(-2) N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD

size

14 14 16 12 14 0 14 14 14

N.S.

1 1.00 1.14 0.86 1.00 0.00 1.00 1.00 1.00

time (sec)

N/A 0.182 10.729 0.130 0.630 0.000 36.925 0.352 13.676

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F(-2) F F B

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

38 38 33 0 0 0 0 0 51

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 1.34

time (sec)

N/A 0.190 1.141 0.000 0.000 0.000 0.000 0.000 13.825

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F(-2) F F B

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

20 20 17 0 0 0 0 0 15

N.S.

1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 0.75

time (sec)

N/A 0.179 0.132 0.000 0.000 0.000 0.000 0.000 13.152

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F A F F B

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

24 24 17 0 0 15 0 0 16

N.S.

1 1.00 0.71 0.00 0.00 0.62 0.00 0.00 0.67

time (sec)

N/A 0.177 0.111 0.000 0.000 0.277 0.000 0.000 0.147

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F(-2) F(-1) F B

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

47 47 33 0 0 0 0 0 31

N.S.

1 1.00 0.70 0.00 0.00 0.00 0.00 0.00 0.66

time (sec)

N/A 0.205 0.184 0.000 0.000 0.000 0.000 0.000 13.756

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F(-2) F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

32 32 29 0 0 0 0 0 0

N.S.

1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.223 0.196 0.000 0.000 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F(-2) F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

24 24 17 0 0 0 0 0 0

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.208 0.091 0.000 0.000 0.000 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F(-2) F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

24 24 17 0 0 0 0 0 0

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.209 0.270 0.000 0.000 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F(-2) F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

47 47 45 0 0 0 0 0 0

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.238 0.134 0.000 0.000 0.000 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F(-2) F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

62 62 51 0 0 0 0 0 0

N.S.

1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.289 0.101 0.000 0.000 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

N/A N/A N/A N/A TBD TBD TBD TBD TBD

size

18 18 20 18 20 20 17 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.11 0.94 1.11 1.11

time (sec)

N/A 0.214 1.111 0.345 0.672 0.260 8.741 1.195 14.057

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

275 275 253 0 0 188 0 0 0

N.S.

1 1.00 0.92 0.00 0.00 0.68 0.00 0.00 0.00

time (sec)

N/A 0.540 0.188 0.000 0.000 0.124 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

162 162 150 0 0 136 0 0 0

N.S.

1 1.00 0.93 0.00 0.00 0.84 0.00 0.00 0.00

time (sec)

N/A 0.417 0.215 0.000 0.000 0.094 0.000 0.000 0.000

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