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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 F(-1) B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 104 136 121 95 159 0 0 235

N.S.

1 0.90 1.18 1.05 0.83 1.38 0.00 0.00 2.04

time (sec)

N/A 0.247 0.293 1.529 0.185 0.298 0.000 0.000 5.738

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

71 66 82 81 51 87 0 22388 154

N.S.

1 0.93 1.15 1.14 0.72 1.23 0.00 315.32 2.17

time (sec)

N/A 0.227 0.082 0.848 0.204 0.301 0.000 105.659 6.058

Problem 3

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

30 29 38 23 25 27 0 1200 43

N.S.

1 0.97 1.27 0.77 0.83 0.90 0.00 40.00 1.43

time (sec)

N/A 0.201 0.016 0.807 0.191 0.293 0.000 0.503 5.856

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 24 47 23 22 24 0 23 38

N.S.

1 1.00 1.96 0.96 0.92 1.00 0.00 0.96 1.58

time (sec)

N/A 0.193 0.017 0.526 0.192 0.285 0.000 0.352 5.773

Problem 5

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

54 48 60 67 45 69 0 60 146

N.S.

1 0.89 1.11 1.24 0.83 1.28 0.00 1.11 2.70

time (sec)

N/A 0.218 0.086 1.014 0.193 0.295 0.000 0.377 5.970

Problem 6

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

81 69 96 101 69 110 0 82 207

N.S.

1 0.85 1.19 1.25 0.85 1.36 0.00 1.01 2.56

time (sec)

N/A 0.232 0.038 1.499 0.199 0.316 0.000 0.423 5.969

Problem 7

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

115 97 111 143 91 158 0 104 267

N.S.

1 0.84 0.97 1.24 0.79 1.37 0.00 0.90 2.32

time (sec)

N/A 0.257 0.283 2.523 0.206 0.318 0.000 0.483 6.784

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 101 110 135 87 116 0 0 351

N.S.

1 1.00 1.09 1.34 0.86 1.15 0.00 0.00 3.48

time (sec)

N/A 0.294 0.198 2.329 0.318 0.287 0.000 0.000 11.215

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 81 98 65 88 0 0 231

N.S.

1 1.00 1.12 1.36 0.90 1.22 0.00 0.00 3.21

time (sec)

N/A 0.265 0.128 1.510 0.288 0.285 0.000 0.000 8.949

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 48 47 56 39 80 0 1008 111

N.S.

1 1.23 1.21 1.44 1.00 2.05 0.00 25.85 2.85

time (sec)

N/A 0.406 0.103 1.092 0.277 0.288 0.000 1.092 5.812

Problem 11

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

41 41 75 49 54 84 0 108 108

N.S.

1 1.00 1.83 1.20 1.32 2.05 0.00 2.63 2.63

time (sec)

N/A 0.231 0.084 0.519 0.282 0.288 0.000 0.540 6.107

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 82 125 86 92 160 0 141 228

N.S.

1 1.00 1.52 1.05 1.12 1.95 0.00 1.72 2.78

time (sec)

N/A 0.290 0.145 0.806 0.280 0.303 0.000 0.554 5.746

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 122 164 129 125 222 0 199 291

N.S.

1 1.00 1.34 1.06 1.02 1.82 0.00 1.63 2.39

time (sec)

N/A 0.306 0.160 1.415 0.285 0.302 0.000 0.643 5.737

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 108 75 195 96 168 0 0 283

N.S.

1 0.91 0.63 1.64 0.81 1.41 0.00 0.00 2.38

time (sec)

N/A 0.272 0.179 3.947 0.198 0.309 0.000 0.000 6.159

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 65 54 125 58 90 0 0 204

N.S.

1 0.90 0.75 1.74 0.81 1.25 0.00 0.00 2.83

time (sec)

N/A 0.242 0.074 1.981 0.194 0.312 0.000 0.000 6.338

Problem 16

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

52 48 40 70 43 45 0 5671 178

N.S.

1 0.92 0.77 1.35 0.83 0.87 0.00 109.06 3.42

time (sec)

N/A 0.219 0.027 1.117 0.186 0.300 0.000 1.481 6.032

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 28 94 53 76 0 47 56

N.S.

1 1.00 0.93 3.13 1.77 2.53 0.00 1.57 1.87

time (sec)

N/A 0.203 0.032 1.204 0.195 0.278 0.000 0.502 5.780

Problem 18

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

132 114 86 228 107 206 0 121 392

N.S.

1 0.86 0.65 1.73 0.81 1.56 0.00 0.92 2.97

time (sec)

N/A 0.263 0.151 4.641 0.204 0.321 0.000 0.749 10.758

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 149 174 188 152 152 0 0 392

N.S.

1 1.00 1.17 1.26 1.02 1.02 0.00 0.00 2.63

time (sec)

N/A 0.373 1.129 6.026 0.281 0.317 0.000 0.000 10.142

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 128 159 132 120 196 0 0 287

N.S.

1 1.07 1.32 1.10 1.00 1.63 0.00 0.00 2.39

time (sec)

N/A 0.574 1.307 2.965 0.277 0.280 0.000 0.000 9.422

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 63 120 79 84 125 0 5370 213

N.S.

1 0.89 1.69 1.11 1.18 1.76 0.00 75.63 3.00

time (sec)

N/A 0.274 0.489 2.125 0.273 0.295 0.000 9.590 8.092

Problem 22

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

45 45 34 32 47 41 78 38 123

N.S.

1 1.00 0.76 0.71 1.04 0.91 1.73 0.84 2.73

time (sec)

N/A 0.185 0.250 0.460 0.190 0.319 0.093 0.523 5.695

Problem 23

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

74 78 94 80 79 105 0 143 201

N.S.

1 1.05 1.27 1.08 1.07 1.42 0.00 1.93 2.72

time (sec)

N/A 0.295 5.624 0.744 0.272 0.312 0.000 0.653 5.912

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 102 191 146 139 192 0 209 293

N.S.

1 1.04 1.95 1.49 1.42 1.96 0.00 2.13 2.99

time (sec)

N/A 0.345 9.390 1.784 0.272 0.309 0.000 0.735 5.885

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

160 143 99 260 133 240 0 0 398

N.S.

1 0.89 0.62 1.62 0.83 1.50 0.00 0.00 2.49

time (sec)

N/A 0.301 0.299 19.811 0.192 0.344 0.000 0.000 6.296

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 81 66 142 72 104 0 0 262

N.S.

1 0.89 0.73 1.56 0.79 1.14 0.00 0.00 2.88

time (sec)

N/A 0.256 0.137 5.375 0.188 0.311 0.000 0.000 6.946

Problem 27

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

70 63 52 49 57 61 0 24693 281

N.S.

1 0.90 0.74 0.70 0.81 0.87 0.00 352.76 4.01

time (sec)

N/A 0.228 0.038 2.673 0.195 0.295 0.000 15.223 6.281

Problem 28

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

98 86 66 116 80 118 0 94 253

N.S.

1 0.88 0.67 1.18 0.82 1.20 0.00 0.96 2.58

time (sec)

N/A 0.248 0.103 2.401 0.190 0.327 0.000 0.983 5.906

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

180 188 243 195 209 289 0 0 438

N.S.

1 1.04 1.35 1.08 1.16 1.61 0.00 0.00 2.43

time (sec)

N/A 1.026 8.811 15.578 0.286 0.291 0.000 0.000 10.388

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 123 177 149 165 220 0 0 371

N.S.

1 1.03 1.49 1.25 1.39 1.85 0.00 0.00 3.12

time (sec)

N/A 0.381 6.744 8.319 0.274 0.298 0.000 0.000 10.158

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 83 115 98 117 154 0 0 288

N.S.

1 0.93 1.29 1.10 1.31 1.73 0.00 0.00 3.24

time (sec)

N/A 0.301 5.639 4.996 0.280 0.314 0.000 0.000 9.791

Problem 32

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

63 63 44 43 72 54 121 55 156

N.S.

1 1.00 0.70 0.68 1.14 0.86 1.92 0.87 2.48

time (sec)

N/A 0.238 2.670 1.035 0.195 0.363 0.125 0.532 8.440

Problem 33

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

92 96 106 94 93 121 0 162 264

N.S.

1 1.04 1.15 1.02 1.01 1.32 0.00 1.76 2.87

time (sec)

N/A 0.317 6.002 1.894 0.276 0.281 0.000 0.557 6.079

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 113 83 227 109 154 0 0 379

N.S.

1 0.88 0.64 1.76 0.84 1.19 0.00 0.00 2.94

time (sec)

N/A 0.276 0.290 26.934 0.195 0.338 0.000 0.000 7.453

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 94 76 159 85 116 0 0 320

N.S.

1 0.88 0.71 1.49 0.79 1.08 0.00 0.00 2.99

time (sec)

N/A 0.262 0.114 14.787 0.188 0.334 0.000 0.000 7.066

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 78 62 127 70 74 0 57842 131

N.S.

1 0.89 0.70 1.44 0.80 0.84 0.00 657.30 1.49

time (sec)

N/A 0.240 0.054 7.563 0.182 0.285 0.000 12.719 5.903

Problem 37

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

102 90 68 129 82 131 0 96 298

N.S.

1 0.88 0.67 1.26 0.80 1.28 0.00 0.94 2.92

time (sec)

N/A 0.249 0.113 6.430 0.189 0.314 0.000 0.568 6.484

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 126 252 166 238 247 0 0 437

N.S.

1 0.88 1.76 1.16 1.66 1.73 0.00 0.00 3.06

time (sec)

N/A 0.381 6.723 21.033 0.281 0.315 0.000 0.000 10.717

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 117 125 115 181 179 0 0 363

N.S.

1 1.04 1.11 1.02 1.60 1.58 0.00 0.00 3.21

time (sec)

N/A 0.349 6.258 12.040 0.275 0.363 0.000 0.000 9.712

Problem 40

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

87 87 57 56 108 70 224 72 237

N.S.

1 1.00 0.66 0.64 1.24 0.80 2.57 0.83 2.72

time (sec)

N/A 0.265 3.290 1.352 0.206 0.283 0.199 0.392 8.151

Problem 41

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

116 120 136 136 117 135 0 194 295

N.S.

1 1.03 1.17 1.17 1.01 1.16 0.00 1.67 2.54

time (sec)

N/A 0.341 11.247 5.782 0.277 0.319 0.000 0.457 6.342

Problem 42

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

140 144 209 222 218 219 0 274 384

N.S.

1 1.03 1.49 1.59 1.56 1.56 0.00 1.96 2.74

time (sec)

N/A 0.409 10.453 6.569 0.280 0.325 0.000 0.470 6.307

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

198 202 283 304 313 291 0 339 454

N.S.

1 1.02 1.43 1.54 1.58 1.47 0.00 1.71 2.29

time (sec)

N/A 0.569 7.214 13.016 0.278 0.357 0.000 0.582 6.077

Problem 44

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

130 136 101 115 175 167 0 136 388

N.S.

1 1.05 0.78 0.88 1.35 1.28 0.00 1.05 2.98

time (sec)

N/A 0.725 0.698 1.613 0.186 0.305 0.000 3.520 10.349

Problem 45

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

106 110 84 91 130 147 0 116 281

N.S.

1 1.04 0.79 0.86 1.23 1.39 0.00 1.09 2.65

time (sec)

N/A 0.601 0.223 0.947 0.191 0.292 0.000 1.547 9.999

Problem 46

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

82 84 54 67 89 125 0 96 172

N.S.

1 1.02 0.66 0.82 1.09 1.52 0.00 1.17 2.10

time (sec)

N/A 0.490 0.111 0.770 0.203 0.285 0.000 0.630 9.062

Problem 47

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

37 58 28 43 47 58 0 58 61

N.S.

1 1.57 0.76 1.16 1.27 1.57 0.00 1.57 1.65

time (sec)

N/A 0.378 0.026 0.666 0.191 0.289 0.000 0.351 6.152

Problem 48

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

32 34 32 27 31 28 0 33 32

N.S.

1 1.06 1.00 0.84 0.97 0.88 0.00 1.03 1.00

time (sec)

N/A 0.208 0.015 0.529 0.189 0.309 0.000 0.366 6.260

Problem 49

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

32 32 24 27 26 30 0 26 23

N.S.

1 1.00 0.75 0.84 0.81 0.94 0.00 0.81 0.72

time (sec)

N/A 0.300 0.025 0.731 0.192 0.278 0.000 0.448 5.843

Problem 50

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

51 47 30 49 46 63 0 46 45

N.S.

1 0.92 0.59 0.96 0.90 1.24 0.00 0.90 0.88

time (sec)

N/A 0.379 0.042 1.475 0.194 0.284 0.000 0.568 5.692

Problem 51

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

68 57 61 67 66 96 0 66 63

N.S.

1 0.84 0.90 0.99 0.97 1.41 0.00 0.97 0.93

time (sec)

N/A 0.405 0.098 2.720 0.188 0.294 0.000 0.602 6.268

Problem 52

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

84 67 77 87 86 127 0 86 83

N.S.

1 0.80 0.92 1.04 1.02 1.51 0.00 1.02 0.99

time (sec)

N/A 0.405 0.140 5.101 0.193 0.291 0.000 0.491 6.089

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 68 146 166 338 95 0 172 99

N.S.

1 0.81 1.74 1.98 4.02 1.13 0.00 2.05 1.18

time (sec)

N/A 0.366 0.677 1.314 0.197 0.272 0.000 2.214 7.924

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 58 106 120 214 75 0 120 73

N.S.

1 0.84 1.54 1.74 3.10 1.09 0.00 1.74 1.06

time (sec)

N/A 0.362 0.557 0.780 0.199 0.346 0.000 0.901 6.263

Problem 55

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 48 106 70 90 47 0 68 47

N.S.

1 0.96 2.12 1.40 1.80 0.94 0.00 1.36 0.94

time (sec)

N/A 0.354 0.417 0.800 0.192 0.284 0.000 0.464 5.887

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 48 22 27 42 27 21 21

N.S.

1 1.00 2.09 0.96 1.17 1.83 1.17 0.91 0.91

time (sec)

N/A 0.176 0.125 0.404 0.197 0.270 0.424 0.292 6.195

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 69 44 70 62 0 65 25

N.S.

1 1.00 2.38 1.52 2.41 2.14 0.00 2.24 0.86

time (sec)

N/A 0.293 0.472 0.699 0.196 0.288 0.000 0.369 6.065

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 58 124 94 155 111 0 127 115

N.S.

1 1.00 2.14 1.62 2.67 1.91 0.00 2.19 1.98

time (sec)

N/A 0.407 0.728 1.123 0.185 0.287 0.000 0.382 5.868

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 84 189 134 234 155 0 187 183

N.S.

1 1.02 2.30 1.63 2.85 1.89 0.00 2.28 2.23

time (sec)

N/A 0.514 0.963 1.928 0.190 0.301 0.000 0.438 6.204

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 110 284 168 315 198 0 244 387

N.S.

1 1.04 2.68 1.58 2.97 1.87 0.00 2.30 3.65

time (sec)

N/A 0.622 1.600 3.674 0.207 0.300 0.000 0.442 7.849

Problem 61

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

189 164 112 127 202 218 0 146 444

N.S.

1 0.87 0.59 0.67 1.07 1.15 0.00 0.77 2.35

time (sec)

N/A 0.334 1.092 4.067 0.193 0.297 0.000 3.348 10.306

Problem 62

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

146 127 91 103 167 198 0 126 361

N.S.

1 0.87 0.62 0.71 1.14 1.36 0.00 0.86 2.47

time (sec)

N/A 0.300 0.310 2.001 0.194 0.310 0.000 1.535 9.928

Problem 63

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

104 91 70 79 110 178 0 102 240

N.S.

1 0.88 0.67 0.76 1.06 1.71 0.00 0.98 2.31

time (sec)

N/A 0.268 0.211 1.161 0.211 0.297 0.000 0.646 9.573

Problem 64

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

60 54 36 55 70 104 0 90 116

N.S.

1 0.90 0.60 0.92 1.17 1.73 0.00 1.50 1.93

time (sec)

N/A 0.234 0.060 0.917 0.219 0.315 0.000 0.391 7.120

Problem 65

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

52 50 36 37 46 59 0 45 87

N.S.

1 0.96 0.69 0.71 0.88 1.13 0.00 0.87 1.67

time (sec)

N/A 0.232 0.042 0.907 0.196 0.320 0.000 0.299 6.004

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 61 49 49 0 76 0 115 103

N.S.

1 0.94 0.75 0.75 0.00 1.17 0.00 1.77 1.58

time (sec)

N/A 0.246 0.052 2.123 0.000 0.283 0.000 0.344 6.169

Problem 67

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

55 50 38 39 36 57 0 36 36

N.S.

1 0.91 0.69 0.71 0.65 1.04 0.00 0.65 0.65

time (sec)

N/A 0.226 0.055 4.703 0.193 0.288 0.000 0.408 6.052

Problem 68

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 65 48 49 46 94 0 46 46

N.S.

1 0.89 0.66 0.67 0.63 1.29 0.00 0.63 0.63

time (sec)

N/A 0.240 0.071 9.280 0.193 0.303 0.000 0.431 6.121

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

127 110 78 79 76 127 0 76 76

N.S.

1 0.87 0.61 0.62 0.60 1.00 0.00 0.60 0.60

time (sec)

N/A 0.264 0.100 17.326 0.213 0.296 0.000 0.446 6.043

Problem 70

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

145 125 88 89 86 162 0 86 85

N.S.

1 0.86 0.61 0.61 0.59 1.12 0.00 0.59 0.59

time (sec)

N/A 0.275 0.141 31.773 0.208 0.288 0.000 0.485 6.179

Problem 71

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

199 170 118 119 116 195 0 116 116

N.S.

1 0.85 0.59 0.60 0.58 0.98 0.00 0.58 0.58

time (sec)

N/A 0.300 0.217 53.983 0.198 0.327 0.000 0.533 6.378

Problem 72

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

171 149 102 115 188 248 0 136 418

N.S.

1 0.87 0.60 0.67 1.10 1.45 0.00 0.80 2.44

time (sec)

N/A 0.315 0.544 3.859 0.199 0.308 0.000 1.664 9.982

Problem 73

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

126 110 82 91 146 226 0 114 302

N.S.

1 0.87 0.65 0.72 1.16 1.79 0.00 0.90 2.40

time (sec)

N/A 0.278 0.239 2.135 0.197 0.306 0.000 0.998 9.692

Problem 74

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

82 73 52 67 98 154 0 81 186

N.S.

1 0.89 0.63 0.82 1.20 1.88 0.00 0.99 2.27

time (sec)

N/A 0.244 0.106 1.875 0.191 0.294 0.000 0.540 8.499

Problem 75

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

74 69 52 49 72 104 0 59 148

N.S.

1 0.93 0.70 0.66 0.97 1.41 0.00 0.80 2.00

time (sec)

N/A 0.238 0.124 2.026 0.192 0.301 0.000 0.473 6.435

Problem 76

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

86 78 61 61 80 147 0 154 169

N.S.

1 0.91 0.71 0.71 0.93 1.71 0.00 1.79 1.97

time (sec)

N/A 0.258 0.136 5.838 0.198 0.318 0.000 0.806 5.835

Problem 77

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

96 86 69 67 75 131 0 174 171

N.S.

1 0.90 0.72 0.70 0.78 1.36 0.00 1.81 1.78

time (sec)

N/A 0.263 0.210 12.749 0.187 0.298 0.000 0.418 6.093

Problem 78

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 65 48 49 46 84 0 46 46

N.S.

1 0.89 0.66 0.67 0.63 1.15 0.00 0.63 0.63

time (sec)

N/A 0.239 0.067 23.637 0.186 0.323 0.000 0.453 5.784

Problem 79

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

109 95 68 69 66 117 0 66 66

N.S.

1 0.87 0.62 0.63 0.61 1.07 0.00 0.61 0.61

time (sec)

N/A 0.243 0.051 41.732 0.193 0.289 0.000 0.510 6.089

Problem 80

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

145 125 88 89 86 152 0 86 86

N.S.

1 0.86 0.61 0.61 0.59 1.05 0.00 0.59 0.59

time (sec)

N/A 0.288 0.087 69.787 0.198 0.286 0.000 0.530 6.797

Problem 81

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

145 125 88 89 86 185 0 86 85

N.S.

1 0.86 0.61 0.61 0.59 1.28 0.00 0.59 0.59

time (sec)

N/A 0.270 0.084 117.450 0.194 0.321 0.000 0.555 6.144

Problem 82

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

195 168 112 127 213 290 0 146 476

N.S.

1 0.86 0.57 0.65 1.09 1.49 0.00 0.75 2.44

time (sec)

N/A 0.334 0.965 8.043 0.194 0.313 0.000 1.624 12.140

Problem 83

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

132 115 50 81 95 102 0 76 172

N.S.

1 0.87 0.38 0.61 0.72 0.77 0.00 0.58 1.30

time (sec)

N/A 0.281 0.077 5.244 0.195 0.280 0.000 0.740 6.887

Problem 84

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

105 92 62 79 121 198 0 91 240

N.S.

1 0.88 0.59 0.75 1.15 1.89 0.00 0.87 2.29

time (sec)

N/A 0.257 0.192 5.977 0.202 0.311 0.000 0.481 10.512

Problem 85

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

106 94 73 71 103 196 0 185 228

N.S.

1 0.89 0.69 0.67 0.97 1.85 0.00 1.75 2.15

time (sec)

N/A 0.272 0.527 15.887 0.191 0.301 0.000 0.404 6.435

Problem 86

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

135 119 89 89 95 186 0 232 235

N.S.

1 0.88 0.66 0.66 0.70 1.38 0.00 1.72 1.74

time (sec)

N/A 0.274 0.120 54.184 0.202 0.307 0.000 0.482 6.532

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 131 124 109 356 129 0 146 231

N.S.

1 1.03 0.98 0.86 2.80 1.02 0.00 1.15 1.82

time (sec)

N/A 0.501 0.824 5.724 0.203 0.284 0.000 0.556 7.763

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 112 315 119 288 369 0 135 203

N.S.

1 1.04 2.92 1.10 2.67 3.42 0.00 1.25 1.88

time (sec)

N/A 0.487 0.741 11.110 0.196 0.290 0.000 0.366 11.468

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 106 359 143 285 445 0 179 171

N.S.

1 0.88 2.99 1.19 2.38 3.71 0.00 1.49 1.42

time (sec)

N/A 0.418 5.056 23.636 0.203 0.308 0.000 0.416 7.750

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 137 733 165 279 439 0 204 209

N.S.

1 1.03 5.51 1.24 2.10 3.30 0.00 1.53 1.57

time (sec)

N/A 0.433 6.643 40.609 0.194 0.314 0.000 0.455 6.877

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

162 195 394 176 0 200 0 0 0

N.S.

1 1.20 2.43 1.09 0.00 1.23 0.00 0.00 0.00

time (sec)

N/A 1.232 5.592 0.826 0.000 0.342 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 107 114 89 0 169 0 428 0

N.S.

1 1.06 1.13 0.88 0.00 1.67 0.00 4.24 0.00

time (sec)

N/A 0.494 0.505 0.627 0.000 0.309 0.000 0.752 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 99 206 129 0 279 0 149 0

N.S.

1 1.11 2.31 1.45 0.00 3.13 0.00 1.67 0.00

time (sec)

N/A 0.512 0.932 0.804 0.000 0.310 0.000 0.457 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 175 309 170 0 380 0 211 0

N.S.

1 1.07 1.90 1.04 0.00 2.33 0.00 1.29 0.00

time (sec)

N/A 0.968 1.429 1.090 0.000 0.310 0.000 0.477 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

167 195 141 139 0 239 0 917 0

N.S.

1 1.17 0.84 0.83 0.00 1.43 0.00 5.49 0.00

time (sec)

N/A 1.381 5.772 0.658 0.000 0.352 0.000 1.300 0.000

Problem 96

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

88 93 46 55 145 48 0 209 0

N.S.

1 1.06 0.52 0.62 1.65 0.55 0.00 2.38 0.00

time (sec)

N/A 0.479 3.981 0.652 0.320 0.292 0.000 0.571 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 134 233 154 0 315 0 183 0

N.S.

1 1.11 1.93 1.27 0.00 2.60 0.00 1.51 0.00

time (sec)

N/A 0.714 5.858 0.902 0.000 0.320 0.000 0.336 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

197 208 334 196 0 424 0 246 0

N.S.

1 1.06 1.70 0.99 0.00 2.15 0.00 1.25 0.00

time (sec)

N/A 1.283 1.325 0.944 0.000 0.307 0.000 0.377 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 212 112 87 277 98 0 1485 0

N.S.

1 1.40 0.74 0.58 1.83 0.65 0.00 9.83 0.00

time (sec)

N/A 1.567 5.718 12.799 0.291 0.323 0.000 7.650 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 131 60 67 191 70 0 1411 0

N.S.

1 1.11 0.51 0.57 1.62 0.59 0.00 11.96 0.00

time (sec)

N/A 0.589 5.670 2.418 0.307 0.285 0.000 1.853 0.000

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