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2.2.1 Integrals 1 to 63

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 B F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 133 106 125 243 286 0 0 0

N.S.

1 1.25 1.00 1.18 2.29 2.70 0.00 0.00 0.00

time (sec)

N/A 0.611 0.013 0.490 0.600 0.280 0.000 0.000 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 96 77 103 163 200 0 0 0

N.S.

1 1.25 1.00 1.34 2.12 2.60 0.00 0.00 0.00

time (sec)

N/A 0.465 0.009 0.429 0.682 0.259 0.000 0.000 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 61 54 78 92 122 0 0 129

N.S.

1 1.13 1.00 1.44 1.70 2.26 0.00 0.00 2.39

time (sec)

N/A 0.321 0.006 0.438 0.397 0.242 0.000 0.000 3.346

Problem 4

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

10 10 12 10 12 12 8 12 12

N.S.

1 1.00 1.20 1.00 1.20 1.20 0.80 1.20 1.20

time (sec)

N/A 0.180 1.555 0.240 0.446 0.253 0.315 0.340 3.237

Problem 5

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

10 10 12 10 12 12 10 12 12

N.S.

1 1.00 1.20 1.00 1.20 1.20 1.00 1.20 1.20

time (sec)

N/A 0.182 2.420 0.205 0.452 0.237 0.281 0.337 3.065

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 122 115 133 639 225 0 0 0

N.S.

1 1.24 1.17 1.36 6.52 2.30 0.00 0.00 0.00

time (sec)

N/A 0.587 0.686 0.632 0.397 0.256 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 87 160 108 257 144 0 0 0

N.S.

1 1.19 2.19 1.48 3.52 1.97 0.00 0.00 0.00

time (sec)

N/A 0.435 5.051 0.550 0.631 0.247 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 43 34 214 38 41 162 35

N.S.

1 1.00 1.43 1.13 7.13 1.27 1.37 5.40 1.17

time (sec)

N/A 0.245 0.146 0.459 0.524 0.251 0.216 0.604 0.163

Problem 9

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

12 12 14 12 243 14 10 14 14

N.S.

1 1.00 1.17 1.00 20.25 1.17 0.83 1.17 1.17

time (sec)

N/A 0.195 3.216 0.339 0.956 0.242 0.309 0.633 3.566

Problem 10

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

12 12 14 12 250 14 12 14 14

N.S.

1 1.00 1.17 1.00 20.83 1.17 1.00 1.17 1.17

time (sec)

N/A 0.197 2.442 0.311 0.447 0.237 0.287 0.671 2.928

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

205 245 370 251 1205 344 0 0 0

N.S.

1 1.20 1.80 1.22 5.88 1.68 0.00 0.00 0.00

time (sec)

N/A 1.300 6.536 0.355 0.471 0.274 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 149 172 180 736 240 0 0 0

N.S.

1 1.16 1.34 1.41 5.75 1.88 0.00 0.00 0.00

time (sec)

N/A 0.849 2.281 0.299 0.659 0.261 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 98 171 122 386 146 0 0 0

N.S.

1 1.09 1.90 1.36 4.29 1.62 0.00 0.00 0.00

time (sec)

N/A 0.480 4.577 0.271 0.783 0.257 0.000 0.000 0.000

Problem 14

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

12 12 14 12 534 14 10 14 14

N.S.

1 1.00 1.17 1.00 44.50 1.17 0.83 1.17 1.17

time (sec)

N/A 0.194 4.854 0.174 0.913 0.242 0.334 0.921 3.176

Problem 15

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

12 12 14 12 536 14 12 14 14

N.S.

1 1.00 1.17 1.00 44.67 1.17 1.00 1.17 1.17

time (sec)

N/A 0.194 2.584 0.188 0.713 0.242 0.284 0.962 2.826

Problem 16

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

18 18 18 0 0 16 0 0 50

N.S.

1 1.00 1.00 0.00 0.00 0.89 0.00 0.00 2.78

time (sec)

N/A 2.908 1.811 0.000 0.000 0.262 0.000 0.000 3.610

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A F F A F F B

verified

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

size

17 0 17 0 0 15 0 0 45

N.S.

1 0.00 1.00 0.00 0.00 0.88 0.00 0.00 2.65

time (sec)

N/A 0.000 0.916 0.000 0.000 0.250 0.000 0.000 5.453

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 206 278 170 0 164 258 188 423

N.S.

1 1.09 1.47 0.90 0.00 0.87 1.37 0.99 2.24

time (sec)

N/A 0.704 0.802 0.674 0.000 0.255 0.263 0.382 4.118

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 147 178 108 0 105 165 119 241

N.S.

1 1.07 1.30 0.79 0.00 0.77 1.20 0.87 1.76

time (sec)

N/A 0.481 0.493 0.520 0.000 0.251 0.190 0.359 3.706

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 90 96 50 0 55 92 62 105

N.S.

1 1.07 1.14 0.60 0.00 0.65 1.10 0.74 1.25

time (sec)

N/A 0.311 0.741 0.471 0.000 0.243 0.148 0.353 3.446

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 152 166 65 112 51 0 138 0

N.S.

1 0.94 1.03 0.40 0.70 0.32 0.00 0.86 0.00

time (sec)

N/A 0.731 0.610 0.601 0.282 0.252 0.000 0.371 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

168 167 224 96 119 83 0 1013 0

N.S.

1 0.99 1.33 0.57 0.71 0.49 0.00 6.03 0.00

time (sec)

N/A 0.745 0.767 0.508 0.585 0.259 0.000 2.299 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

227 225 285 216 158 130 0 532 0

N.S.

1 0.99 1.26 0.95 0.70 0.57 0.00 2.34 0.00

time (sec)

N/A 0.967 1.000 0.569 0.595 0.250 0.000 0.442 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

270 270 473 283 0 267 665 368 289

N.S.

1 1.00 1.75 1.05 0.00 0.99 2.46 1.36 1.07

time (sec)

N/A 0.532 2.541 0.746 0.000 0.251 0.415 0.434 4.301

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

202 202 282 173 0 163 418 217 183

N.S.

1 1.00 1.40 0.86 0.00 0.81 2.07 1.07 0.91

time (sec)

N/A 0.437 1.612 0.780 0.000 0.245 0.329 0.449 3.651

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 151 130 82 0 79 226 101 103

N.S.

1 1.00 0.86 0.54 0.00 0.52 1.50 0.67 0.68

time (sec)

N/A 0.388 1.070 0.801 0.000 0.248 0.258 0.416 3.130

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

305 305 211 114 194 84 0 404 0

N.S.

1 1.00 0.69 0.37 0.64 0.28 0.00 1.32 0.00

time (sec)

N/A 1.046 0.848 0.871 0.304 0.244 0.000 0.417 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

436 436 467 175 211 142 0 1967 0

N.S.

1 1.00 1.07 0.40 0.48 0.33 0.00 4.51 0.00

time (sec)

N/A 1.049 1.672 0.892 0.480 0.278 0.000 11.298 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

396 396 667 396 0 370 945 548 411

N.S.

1 1.00 1.68 1.00 0.00 0.93 2.39 1.38 1.04

time (sec)

N/A 0.670 3.764 1.209 0.000 0.245 0.538 0.580 4.249

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

294 294 405 238 0 221 588 315 263

N.S.

1 1.00 1.38 0.81 0.00 0.75 2.00 1.07 0.89

time (sec)

N/A 0.540 2.736 1.082 0.000 0.248 0.504 0.619 3.949

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

209 208 205 114 0 105 311 142 146

N.S.

1 1.00 0.98 0.55 0.00 0.50 1.49 0.68 0.70

time (sec)

N/A 0.493 1.516 0.884 0.000 0.246 0.343 0.559 3.940

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

449 449 336 163 276 117 0 810 0

N.S.

1 1.00 0.75 0.36 0.61 0.26 0.00 1.80 0.00

time (sec)

N/A 1.980 1.137 0.934 0.315 0.255 0.000 0.584 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

712 712 833 254 297 197 0 2915 0

N.S.

1 1.00 1.17 0.36 0.42 0.28 0.00 4.09 0.00

time (sec)

N/A 2.063 2.853 1.063 0.431 0.247 0.000 30.478 0.000

Problem 34

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

23 23 25 21 520 115 51 23 24

N.S.

1 1.00 1.09 0.91 22.61 5.00 2.22 1.00 1.04

time (sec)

N/A 0.225 42.842 0.192 1.833 0.250 5.317 0.641 3.372

Problem 35

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

21 21 23 19 79 34 29 21 22

N.S.

1 1.00 1.10 0.90 3.76 1.62 1.38 1.00 1.05

time (sec)

N/A 0.211 9.865 0.163 0.500 0.242 2.400 0.357 3.337

Problem 36

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

98 98 133 0 0 85 0 0 0

N.S.

1 1.00 1.36 0.00 0.00 0.87 0.00 0.00 0.00

time (sec)

N/A 0.335 1.771 0.000 0.000 0.085 0.000 0.000 0.000

Problem 37

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

171 171 192 0 0 144 0 0 0

N.S.

1 1.00 1.12 0.00 0.00 0.84 0.00 0.00 0.00

time (sec)

N/A 0.432 4.489 0.000 0.000 0.087 0.000 0.000 0.000

Problem 38

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

251 251 269 0 0 198 0 0 0

N.S.

1 1.00 1.07 0.00 0.00 0.79 0.00 0.00 0.00

time (sec)

N/A 0.507 13.029 0.000 0.000 0.087 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 152 342 500 672 500 0 0 0

N.S.

1 1.00 2.25 3.29 4.42 3.29 0.00 0.00 0.00

time (sec)

N/A 0.463 0.146 0.641 0.715 0.274 0.000 0.000 0.000

Problem 40

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

115 115 191 314 373 317 0 0 0

N.S.

1 1.00 1.66 2.73 3.24 2.76 0.00 0.00 0.00

time (sec)

N/A 0.413 0.080 0.583 0.520 0.261 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 84 87 143 130 160 0 0 161

N.S.

1 1.00 1.04 1.70 1.55 1.90 0.00 0.00 1.92

time (sec)

N/A 0.321 0.013 0.547 0.377 0.260 0.000 0.000 3.597

Problem 42

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 86 20 15 20 20

N.S.

1 1.00 1.11 1.00 4.78 1.11 0.83 1.11 1.11

time (sec)

N/A 0.208 1.914 0.217 0.440 0.243 0.663 0.389 3.534

Problem 43

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 18 142 31 17 20 20

N.S.

1 1.00 1.11 1.00 7.89 1.72 0.94 1.11 1.11

time (sec)

N/A 0.206 5.096 0.220 0.463 0.242 2.494 4.371 3.676

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

300 300 1337 952 2525 759 0 0 0

N.S.

1 1.00 4.46 3.17 8.42 2.53 0.00 0.00 0.00

time (sec)

N/A 0.764 7.326 1.603 1.726 0.276 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

229 229 649 575 1263 450 0 0 0

N.S.

1 1.00 2.83 2.51 5.52 1.97 0.00 0.00 0.00

time (sec)

N/A 0.601 6.833 1.389 0.912 0.264 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 135 200 238 527 219 0 0 0

N.S.

1 0.99 1.47 1.75 3.88 1.61 0.00 0.00 0.00

time (sec)

N/A 0.393 7.410 1.308 0.409 0.258 0.000 0.000 0.000

Problem 47

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

20 20 22 20 491 36 17 22 22

N.S.

1 1.00 1.10 1.00 24.55 1.80 0.85 1.10 1.10

time (sec)

N/A 0.224 19.689 0.366 0.827 0.252 1.091 0.565 4.172

Problem 48

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

20 20 22 20 609 47 19 22 22

N.S.

1 1.00 1.10 1.00 30.45 2.35 0.95 1.10 1.10

time (sec)

N/A 0.228 14.033 0.388 1.683 0.254 2.107 15.426 3.644

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

612 612 2594 1930 6861 1177 0 0 0

N.S.

1 1.00 4.24 3.15 11.21 1.92 0.00 0.00 0.00

time (sec)

N/A 1.285 7.568 1.210 10.883 0.268 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

436 427 1846 1138 3407 688 0 0 0

N.S.

1 0.98 4.23 2.61 7.81 1.58 0.00 0.00 0.00

time (sec)

N/A 0.912 7.164 1.058 1.972 0.290 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

277 275 277 493 1319 327 0 0 0

N.S.

1 0.99 1.00 1.78 4.76 1.18 0.00 0.00 0.00

time (sec)

N/A 0.594 8.323 0.915 0.670 0.266 0.000 0.000 0.000

Problem 52

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

20 20 22 20 1935 52 17 22 22

N.S.

1 1.00 1.10 1.00 96.75 2.60 0.85 1.10 1.10

time (sec)

N/A 0.222 14.685 0.621 3.085 0.251 1.330 1.075 3.911

Problem 53

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

20 20 22 20 2194 63 19 22 22

N.S.

1 1.00 1.10 1.00 109.70 3.15 0.95 1.10 1.10

time (sec)

N/A 0.225 17.927 0.760 9.084 0.253 2.439 18.056 4.929

Problem 54

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

243 246 297 1468 983 1183 0 0 0

N.S.

1 1.01 1.22 6.04 4.05 4.87 0.00 0.00 0.00

time (sec)

N/A 0.972 1.676 0.780 0.568 0.282 0.000 0.000 0.000

Problem 55

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

181 188 236 940 715 834 0 0 0

N.S.

1 1.04 1.30 5.19 3.95 4.61 0.00 0.00 0.00

time (sec)

N/A 0.746 1.426 0.693 0.553 0.272 0.000 0.000 0.000

Problem 56

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

125 132 177 462 399 527 0 0 0

N.S.

1 1.06 1.42 3.70 3.19 4.22 0.00 0.00 0.00

time (sec)

N/A 0.478 1.560 0.637 0.603 0.272 0.000 0.000 0.000

Problem 57

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

20 20 22 20 279 27 17 22 22

N.S.

1 1.00 1.10 1.00 13.95 1.35 0.85 1.10 1.10

time (sec)

N/A 0.232 2.414 0.424 0.890 0.239 1.022 0.417 3.963

Problem 58

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

20 20 22 20 424 51 19 22 22

N.S.

1 1.00 1.10 1.00 21.20 2.55 0.95 1.10 1.10

time (sec)

N/A 0.227 4.558 0.317 1.726 0.252 1.759 4.307 4.091

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

848 848 1724 5959 4631 2537 0 0 0

N.S.

1 1.00 2.03 7.03 5.46 2.99 0.00 0.00 0.00

time (sec)

N/A 2.248 9.637 0.967 2.409 0.327 0.000 0.000 0.000

Problem 60

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

654 654 761 3901 2530 1576 0 0 0

N.S.

1 1.00 1.16 5.96 3.87 2.41 0.00 0.00 0.00

time (sec)

N/A 1.809 7.529 0.969 1.023 0.286 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

214 228 745 2001 1156 843 0 0 0

N.S.

1 1.07 3.48 9.35 5.40 3.94 0.00 0.00 0.00

time (sec)

N/A 0.771 7.889 0.862 0.705 0.268 0.000 0.000 0.000

Problem 62

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

20 20 22 20 1498 55 19 22 22

N.S.

1 1.00 1.10 1.00 74.90 2.75 0.95 1.10 1.10

time (sec)

N/A 0.233 13.937 0.550 8.731 0.252 1.670 0.541 4.538

Problem 63

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

20 20 22 20 1977 96 20 22 22

N.S.

1 1.00 1.10 1.00 98.85 4.80 1.00 1.10 1.10

time (sec)

N/A 0.234 15.452 0.652 27.223 0.248 3.181 22.558 3.988

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