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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 A A F(-1) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 74 120 98 73 75 0 266 70

N.S.

1 0.89 1.45 1.18 0.88 0.90 0.00 3.20 0.84

time (sec)

N/A 0.243 0.404 4.138 0.195 0.251 0.000 0.325 0.090

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 59 88 81 58 60 0 197 55

N.S.

1 0.89 1.33 1.23 0.88 0.91 0.00 2.98 0.83

time (sec)

N/A 0.241 0.034 0.256 0.188 0.268 0.000 0.323 17.328

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 40 53 62 40 42 0 57 39

N.S.

1 0.91 1.20 1.41 0.91 0.95 0.00 1.30 0.89

time (sec)

N/A 0.224 0.028 0.175 0.195 0.257 0.000 0.291 0.071

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 23 35 25 25 27 0 26 25

N.S.

1 0.96 1.46 1.04 1.04 1.12 0.00 1.08 1.04

time (sec)

N/A 0.202 0.042 0.079 0.193 0.239 0.000 0.274 0.052

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 26 84 40 44 60 0 60 29

N.S.

1 0.96 3.11 1.48 1.63 2.22 0.00 2.22 1.07

time (sec)

N/A 0.202 0.073 0.119 0.194 0.248 0.000 0.276 0.101

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 60 236 90 76 124 0 193 62

N.S.

1 1.13 4.45 1.70 1.43 2.34 0.00 3.64 1.17

time (sec)

N/A 0.235 0.874 0.216 0.190 0.251 0.000 0.298 17.323

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 97 198 120 101 178 0 262 86

N.S.

1 1.20 2.44 1.48 1.25 2.20 0.00 3.23 1.06

time (sec)

N/A 0.264 6.264 0.300 0.178 0.257 0.000 0.310 17.538

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 124 78 89 111 86 0 104 105

N.S.

1 1.27 0.80 0.91 1.13 0.88 0.00 1.06 1.07

time (sec)

N/A 0.337 0.424 0.445 0.281 0.250 0.000 0.306 18.465

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 90 54 71 82 68 0 82 79

N.S.

1 1.29 0.77 1.01 1.17 0.97 0.00 1.17 1.13

time (sec)

N/A 0.254 0.371 0.273 0.269 0.253 0.000 0.294 17.106

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 55 54 46 47 50 0 47 35

N.S.

1 1.31 1.29 1.10 1.12 1.19 0.00 1.12 0.83

time (sec)

N/A 0.218 0.164 0.141 0.278 0.257 0.000 0.282 17.630

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 16 15 31 0 15 17

N.S.

1 1.00 1.00 1.07 1.00 2.07 0.00 1.00 1.13

time (sec)

N/A 0.142 0.010 0.147 0.185 0.242 0.000 0.260 17.710

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 24 36 43 26 39 0 26 28

N.S.

1 0.92 1.38 1.65 1.00 1.50 0.00 1.00 1.08

time (sec)

N/A 0.214 0.069 0.227 0.179 0.234 0.000 0.280 19.045

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 41 84 73 43 66 0 50 46

N.S.

1 0.89 1.83 1.59 0.93 1.43 0.00 1.09 1.00

time (sec)

N/A 0.226 0.054 0.487 0.179 0.254 0.000 0.288 19.230

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 60 128 89 64 91 0 76 60

N.S.

1 0.88 1.88 1.31 0.94 1.34 0.00 1.12 0.88

time (sec)

N/A 0.239 0.726 0.664 0.179 0.251 0.000 0.315 18.929

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 86 118 155 89 90 0 414 87

N.S.

1 0.89 1.22 1.60 0.92 0.93 0.00 4.27 0.90

time (sec)

N/A 0.273 2.333 0.460 0.177 0.258 0.000 0.412 18.291

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 65 83 69 67 67 0 91 66

N.S.

1 0.90 1.15 0.96 0.93 0.93 0.00 1.26 0.92

time (sec)

N/A 0.259 1.882 0.265 0.179 0.257 0.000 0.368 18.215

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 41 75 42 42 44 0 44 45

N.S.

1 0.89 1.63 0.91 0.91 0.96 0.00 0.96 0.98

time (sec)

N/A 0.221 0.103 0.175 0.175 0.253 0.000 0.311 0.093

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 48 108 94 82 101 0 172 53

N.S.

1 0.92 2.08 1.81 1.58 1.94 0.00 3.31 1.02

time (sec)

N/A 0.246 0.911 0.218 0.181 0.260 0.000 0.318 0.159

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 117 1021 163 126 193 0 341 96

N.S.

1 1.12 9.82 1.57 1.21 1.86 0.00 3.28 0.92

time (sec)

N/A 0.307 8.090 0.379 0.176 0.262 0.000 0.352 18.508

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 162 218 211 165 286 0 493 135

N.S.

1 1.15 1.55 1.50 1.17 2.03 0.00 3.50 0.96

time (sec)

N/A 0.341 9.790 0.558 0.177 0.257 0.000 0.376 18.296

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 168 499 178 164 131 0 183 163

N.S.

1 1.14 3.37 1.20 1.11 0.89 0.00 1.24 1.10

time (sec)

N/A 0.458 3.433 0.608 0.260 0.263 0.000 0.406 19.110

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 129 153 123 120 107 0 123 116

N.S.

1 1.13 1.34 1.08 1.05 0.94 0.00 1.08 1.02

time (sec)

N/A 0.331 2.230 0.407 0.270 0.250 0.000 0.372 18.780

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 76 126 71 67 81 0 67 94

N.S.

1 1.04 1.73 0.97 0.92 1.11 0.00 0.92 1.29

time (sec)

N/A 0.261 2.189 0.253 0.257 0.261 0.000 0.334 19.134

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 44 41 46 44 58 0 49 42

N.S.

1 1.10 1.02 1.15 1.10 1.45 0.00 1.22 1.05

time (sec)

N/A 0.211 0.373 0.126 0.170 0.240 0.000 0.281 18.820

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 45 109 96 54 71 0 60 56

N.S.

1 0.90 2.18 1.92 1.08 1.42 0.00 1.20 1.12

time (sec)

N/A 0.243 2.618 0.214 0.176 0.252 0.000 0.327 18.617

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 68 151 130 80 101 0 98 85

N.S.

1 0.89 1.99 1.71 1.05 1.33 0.00 1.29 1.12

time (sec)

N/A 0.262 5.183 0.293 0.183 0.238 0.000 0.345 18.494

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 92 353 154 107 139 0 141 108

N.S.

1 0.89 3.43 1.50 1.04 1.35 0.00 1.37 1.05

time (sec)

N/A 0.289 2.667 0.453 0.198 0.249 0.000 0.388 18.749

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

98 91 425 115 102 229 0 349 123

N.S.

1 0.93 4.34 1.17 1.04 2.34 0.00 3.56 1.26

time (sec)

N/A 0.288 4.852 1.006 0.261 0.284 0.000 0.309 18.106

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

71 69 376 67 63 154 0 85 76

N.S.

1 0.97 5.30 0.94 0.89 2.17 0.00 1.20 1.07

time (sec)

N/A 0.244 2.207 0.486 0.276 0.268 0.000 0.292 0.117

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

47 46 329 44 40 118 0 42 39

N.S.

1 0.98 7.00 0.94 0.85 2.51 0.00 0.89 0.83

time (sec)

N/A 0.215 1.712 0.180 0.260 0.269 0.000 0.288 17.885

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 54 239 71 64 156 0 85 123

N.S.

1 0.98 4.35 1.29 1.16 2.84 0.00 1.55 2.24

time (sec)

N/A 0.236 1.239 0.144 0.264 0.281 0.000 0.292 0.247

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 99 371 115 128 327 0 209 392

N.S.

1 1.15 4.31 1.34 1.49 3.80 0.00 2.43 4.56

time (sec)

N/A 0.273 1.915 0.244 0.261 0.299 0.000 0.318 18.893

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 155 549 181 231 693 0 389 870

N.S.

1 1.20 4.26 1.40 1.79 5.37 0.00 3.02 6.74

time (sec)

N/A 0.325 5.212 0.720 0.261 0.325 0.000 0.332 22.212

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

166 199 357 170 209 428 0 237 1448

N.S.

1 1.20 2.15 1.02 1.26 2.58 0.00 1.43 8.72

time (sec)

N/A 0.422 3.575 2.537 0.261 0.298 0.000 0.306 19.652

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

117 141 303 119 137 332 0 152 494

N.S.

1 1.21 2.59 1.02 1.17 2.84 0.00 1.30 4.22

time (sec)

N/A 0.328 1.385 1.262 0.262 0.284 0.000 0.302 18.783

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

76 91 245 78 77 257 0 92 111

N.S.

1 1.20 3.22 1.03 1.01 3.38 0.00 1.21 1.46

time (sec)

N/A 0.272 0.607 0.574 0.261 0.285 0.000 0.298 18.391

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 182 46 44 231 0 65 460

N.S.

1 1.00 4.04 1.02 0.98 5.13 0.00 1.44 10.22

time (sec)

N/A 0.252 1.413 0.167 0.262 0.282 0.000 0.276 18.479

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 52 189 52 50 271 0 71 46

N.S.

1 0.96 3.50 0.96 0.93 5.02 0.00 1.31 0.85

time (sec)

N/A 0.232 0.886 0.293 0.263 0.295 0.000 0.295 18.116

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

76 77 226 69 82 397 0 103 80

N.S.

1 1.01 2.97 0.91 1.08 5.22 0.00 1.36 1.05

time (sec)

N/A 0.255 1.863 0.507 0.265 0.295 0.000 0.315 18.335

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

105 97 318 93 137 587 0 173 112

N.S.

1 0.92 3.03 0.89 1.30 5.59 0.00 1.65 1.07

time (sec)

N/A 0.321 1.777 0.785 0.263 0.294 0.000 0.339 19.026

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

161 136 454 159 148 405 0 509 195

N.S.

1 0.84 2.82 0.99 0.92 2.52 0.00 3.16 1.21

time (sec)

N/A 0.326 5.661 4.609 0.261 0.303 0.000 0.364 0.164

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

114 107 403 102 104 297 0 136 130

N.S.

1 0.94 3.54 0.89 0.91 2.61 0.00 1.19 1.14

time (sec)

N/A 0.305 2.914 2.459 0.263 0.284 0.000 0.337 0.138

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

84 83 393 69 70 201 0 72 72

N.S.

1 0.99 4.68 0.82 0.83 2.39 0.00 0.86 0.86

time (sec)

N/A 0.231 2.584 1.030 0.259 0.285 0.000 0.309 18.816

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 106 384 103 138 390 0 272 2188

N.S.

1 1.07 3.88 1.04 1.39 3.94 0.00 2.75 22.10

time (sec)

N/A 0.274 1.633 0.578 0.262 0.321 0.000 0.331 20.176

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 157 468 148 231 698 0 550 1845

N.S.

1 1.07 3.18 1.01 1.57 4.75 0.00 3.74 12.55

time (sec)

N/A 0.334 2.259 0.805 0.258 0.327 0.000 0.371 18.841

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

197 221 450 213 369 1202 0 669 4338

N.S.

1 1.12 2.28 1.08 1.87 6.10 0.00 3.40 22.02

time (sec)

N/A 0.398 2.637 1.221 0.273 0.365 0.000 0.412 23.158

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

267 298 2468 204 302 674 0 294 1461

N.S.

1 1.12 9.24 0.76 1.13 2.52 0.00 1.10 5.47

time (sec)

N/A 0.530 19.912 5.733 0.267 0.326 0.000 0.362 20.400

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

191 213 1105 147 205 522 0 193 435

N.S.

1 1.12 5.79 0.77 1.07 2.73 0.00 1.01 2.28

time (sec)

N/A 0.400 11.557 3.168 0.260 0.306 0.000 0.343 19.422

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

130 145 699 109 126 441 0 149 816

N.S.

1 1.12 5.38 0.84 0.97 3.39 0.00 1.15 6.28

time (sec)

N/A 0.317 8.734 1.685 0.265 0.300 0.000 0.329 18.499

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

92 111 240 90 106 435 0 114 2056

N.S.

1 1.21 2.61 0.98 1.15 4.73 0.00 1.24 22.35

time (sec)

N/A 0.249 2.679 0.409 0.260 0.312 0.000 0.275 20.406

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

91 92 242 78 117 407 0 127 91

N.S.

1 1.01 2.66 0.86 1.29 4.47 0.00 1.40 1.00

time (sec)

N/A 0.256 2.543 0.576 0.262 0.309 0.000 0.352 18.054

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

123 125 303 106 193 663 0 185 141

N.S.

1 1.02 2.46 0.86 1.57 5.39 0.00 1.50 1.15

time (sec)

N/A 0.374 5.803 0.907 0.267 0.307 0.000 0.387 19.580

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

188 195 777 124 268 987 0 254 198

N.S.

1 1.04 4.13 0.66 1.43 5.25 0.00 1.35 1.05

time (sec)

N/A 0.461 3.241 1.326 0.262 0.322 0.000 0.429 20.341

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

214 214 1641 190 204 579 0 781 255

N.S.

1 1.00 7.67 0.89 0.95 2.71 0.00 3.65 1.19

time (sec)

N/A 0.514 9.356 10.368 0.271 0.324 0.000 0.467 17.898

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

154 152 1153 125 149 439 0 174 172

N.S.

1 0.99 7.49 0.81 0.97 2.85 0.00 1.13 1.12

time (sec)

N/A 0.438 8.741 5.737 0.260 0.300 0.000 0.417 0.177

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

116 120 656 83 103 299 0 92 105

N.S.

1 1.03 5.66 0.72 0.89 2.58 0.00 0.79 0.91

time (sec)

N/A 0.251 5.522 2.949 0.260 0.289 0.000 0.380 0.154

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 173 447 156 261 779 0 592 3557

N.S.

1 1.12 2.90 1.01 1.69 5.06 0.00 3.84 23.10

time (sec)

N/A 0.362 4.217 1.471 0.260 0.396 0.000 0.407 21.902

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

213 237 532 198 399 1332 0 750 2728

N.S.

1 1.11 2.50 0.93 1.87 6.25 0.00 3.52 12.81

time (sec)

N/A 0.454 5.356 1.760 0.269 0.430 0.000 0.522 19.873

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

257 284 549 259 528 1833 0 1316 5613

N.S.

1 1.11 2.14 1.01 2.05 7.13 0.00 5.12 21.84

time (sec)

N/A 0.501 5.318 2.312 0.283 0.468 0.000 0.462 23.778

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

314 346 1639 247 418 930 0 351 2117

N.S.

1 1.10 5.22 0.79 1.33 2.96 0.00 1.12 6.74

time (sec)

N/A 0.601 17.416 11.695 0.272 0.359 0.000 0.492 22.332

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

238 261 2469 193 299 803 0 306 1317

N.S.

1 1.10 10.37 0.81 1.26 3.37 0.00 1.29 5.53

time (sec)

N/A 0.462 21.952 6.369 0.267 0.342 0.000 0.438 21.111

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

184 216 1915 155 272 815 0 208 2628

N.S.

1 1.17 10.41 0.84 1.48 4.43 0.00 1.13 14.28

time (sec)

N/A 0.394 15.357 4.212 0.273 0.334 0.000 0.406 22.316

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

144 175 332 147 231 819 0 196 3271

N.S.

1 1.22 2.31 1.02 1.60 5.69 0.00 1.36 22.72

time (sec)

N/A 0.320 6.393 1.535 0.266 0.327 0.000 0.288 22.736

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

124 132 749 97 219 615 0 177 146

N.S.

1 1.06 6.04 0.78 1.77 4.96 0.00 1.43 1.18

time (sec)

N/A 0.281 6.880 1.373 0.266 0.308 0.000 0.452 19.490

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

164 166 994 140 323 1009 0 264 207

N.S.

1 1.01 6.06 0.85 1.97 6.15 0.00 1.61 1.26

time (sec)

N/A 0.452 5.026 1.681 0.271 0.331 0.000 0.423 20.644

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

242 249 479 180 434 1423 0 367 267

N.S.

1 1.03 1.98 0.74 1.79 5.88 0.00 1.52 1.10

time (sec)

N/A 0.564 5.566 2.549 0.280 0.359 0.000 0.463 21.389

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 143 152 572 171 295 0 1281 0

N.S.

1 1.03 1.09 4.12 1.23 2.12 0.00 9.22 0.00

time (sec)

N/A 0.316 1.071 3.313 0.267 0.414 0.000 0.647 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 95 120 340 116 232 0 805 0

N.S.

1 0.95 1.20 3.40 1.16 2.32 0.00 8.05 0.00

time (sec)

N/A 0.272 0.364 0.381 0.264 0.386 0.000 0.467 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 64 99 93 88 182 0 55 87

N.S.

1 0.97 1.50 1.41 1.33 2.76 0.00 0.83 1.32

time (sec)

N/A 0.236 0.143 0.067 0.266 0.394 0.000 0.278 18.363

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 80 119 542 0 496 0 405 0

N.S.

1 0.98 1.45 6.61 0.00 6.05 0.00 4.94 0.00

time (sec)

N/A 0.282 0.298 0.560 0.000 0.337 0.000 0.699 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 131 163 2129 0 867 0 578 0

N.S.

1 1.06 1.31 17.17 0.00 6.99 0.00 4.66 0.00

time (sec)

N/A 0.321 0.662 0.444 0.000 0.396 0.000 0.824 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

183 207 209 4318 0 1476 0 867 0

N.S.

1 1.13 1.14 23.60 0.00 8.07 0.00 4.74 0.00

time (sec)

N/A 0.412 1.717 0.507 0.000 0.658 0.000 1.211 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes N/A No TBD TBD TBD TBD TBD

size

240 270 0 1180 0 1715 0 0 0

N.S.

1 1.12 0.00 4.92 0.00 7.15 0.00 0.00 0.00

time (sec)

N/A 0.505 0.000 12.638 0.000 2.887 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes N/A No TBD TBD TBD TBD TBD

size

181 197 0 791 0 1565 0 0 0

N.S.

1 1.09 0.00 4.37 0.00 8.65 0.00 0.00 0.00

time (sec)

N/A 0.393 0.000 9.838 0.000 1.085 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 127 432 516 0 1417 0 0 0

N.S.

1 1.03 3.51 4.20 0.00 11.52 0.00 0.00 0.00

time (sec)

N/A 0.309 4.291 7.378 0.000 0.606 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 77 284 353 3227 1227 0 0 0

N.S.

1 0.97 3.59 4.47 40.85 15.53 0.00 0.00 0.00

time (sec)

N/A 0.234 2.888 6.387 0.763 0.478 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 66 61 326 50 306 0 0 0

N.S.

1 0.97 0.90 4.79 0.74 4.50 0.00 0.00 0.00

time (sec)

N/A 0.246 0.198 5.342 0.180 0.310 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

105 100 285 1037 82 436 0 0 0

N.S.

1 0.95 2.71 9.88 0.78 4.15 0.00 0.00 0.00

time (sec)

N/A 0.273 2.761 7.325 0.184 0.473 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

149 157 941 1680 143 656 0 0 0

N.S.

1 1.05 6.32 11.28 0.96 4.40 0.00 0.00 0.00

time (sec)

N/A 0.325 8.732 7.177 0.187 1.387 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

196 175 188 802 277 351 0 1952 0

N.S.

1 0.89 0.96 4.09 1.41 1.79 0.00 9.96 0.00

time (sec)

N/A 0.321 1.155 7.029 0.265 0.527 0.000 1.951 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

162 144 164 552 250 278 0 1388 0

N.S.

1 0.89 1.01 3.41 1.54 1.72 0.00 8.57 0.00

time (sec)

N/A 0.308 0.557 6.934 0.270 0.497 0.000 1.242 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 98 73 121 142 231 0 87 61

N.S.

1 0.98 0.73 1.21 1.42 2.31 0.00 0.87 0.61

time (sec)

N/A 0.248 0.483 0.089 0.259 0.413 0.000 0.311 20.409

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 119 171 1437 0 715 0 0 0

N.S.

1 0.98 1.40 11.78 0.00 5.86 0.00 0.00 0.00

time (sec)

N/A 0.324 0.451 6.762 0.000 0.413 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 162 202 3470 0 984 0 0 0

N.S.

1 1.01 1.25 21.55 0.00 6.11 0.00 0.00 0.00

time (sec)

N/A 0.375 1.115 6.921 0.000 0.427 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

218 226 262 5131 0 1511 0 0 0

N.S.

1 1.04 1.20 23.54 0.00 6.93 0.00 0.00 0.00

time (sec)

N/A 0.473 2.604 6.610 0.000 0.468 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes N/A No TBD TBD TBD TBD TBD

size

298 311 0 1602 0 1855 0 0 0

N.S.

1 1.04 0.00 5.38 0.00 6.22 0.00 0.00 0.00

time (sec)

N/A 0.582 0.000 16.254 0.000 10.531 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

217 221 225 1186 0 1667 0 0 0

N.S.

1 1.02 1.04 5.47 0.00 7.68 0.00 0.00 0.00

time (sec)

N/A 0.471 3.567 16.911 0.000 3.352 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

161 159 493 900 0 1535 0 0 0

N.S.

1 0.99 3.06 5.59 0.00 9.53 0.00 0.00 0.00

time (sec)

N/A 0.360 3.784 11.543 0.000 1.180 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

118 116 527 709 0 1457 0 0 0

N.S.

1 0.98 4.47 6.01 0.00 12.35 0.00 0.00 0.00

time (sec)

N/A 0.275 3.456 9.876 0.000 0.615 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 103 64 741 98 370 0 0 0

N.S.

1 0.98 0.61 7.06 0.93 3.52 0.00 0.00 0.00

time (sec)

N/A 0.269 0.202 10.167 0.195 0.468 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

172 154 369 1141 243 472 0 0 0

N.S.

1 0.90 2.15 6.63 1.41 2.74 0.00 0.00 0.00

time (sec)

N/A 0.314 7.692 10.654 0.192 1.502 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

209 188 512 1851 273 682 0 0 0

N.S.

1 0.90 2.45 8.86 1.31 3.26 0.00 0.00 0.00

time (sec)

N/A 0.339 9.263 11.454 0.205 6.336 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 126 93 94 162 87 0 0 0

N.S.

1 1.02 0.76 0.76 1.32 0.71 0.00 0.00 0.00

time (sec)

N/A 0.302 0.972 1.170 0.199 0.269 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 72 64 58 83 57 0 0 0

N.S.

1 0.97 0.86 0.78 1.12 0.77 0.00 0.00 0.00

time (sec)

N/A 0.257 0.176 1.056 0.193 0.248 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 48 31 28 37 0 31 46

N.S.

1 1.00 1.60 1.03 0.93 1.23 0.00 1.03 1.53

time (sec)

N/A 0.211 0.101 0.271 0.188 0.248 0.000 0.299 17.825

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 86 247 0 140 0 305 0

N.S.

1 1.00 2.00 5.74 0.00 3.26 0.00 7.09 0.00

time (sec)

N/A 0.239 0.108 1.217 0.000 0.308 0.000 0.628 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

87 93 140 1215 0 305 0 0 0

N.S.

1 1.07 1.61 13.97 0.00 3.51 0.00 0.00 0.00

time (sec)

N/A 0.280 0.734 1.283 0.000 0.335 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 157 78 1760 0 491 0 0 0

N.S.

1 1.14 0.57 12.75 0.00 3.56 0.00 0.00 0.00

time (sec)

N/A 0.329 0.150 1.141 0.000 0.364 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 215 163 1136 0 639 0 0 0

N.S.

1 1.11 0.84 5.89 0.00 3.31 0.00 0.00 0.00

time (sec)

N/A 0.422 1.114 6.756 0.000 1.280 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 148 145 809 0 565 0 0 0

N.S.

1 1.10 1.07 5.99 0.00 4.19 0.00 0.00 0.00

time (sec)

N/A 0.317 0.335 5.557 0.000 0.565 0.000 0.000 0.000

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