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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 B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 120 77 87 124 88 333 112 236

N.S.

1 0.96 0.62 0.70 0.99 0.70 2.66 0.90 1.89

time (sec)

N/A 0.692 0.248 3.455 0.207 0.327 0.270 0.323 0.975

Problem 2

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

97 93 75 67 101 74 252 89 212

N.S.

1 0.96 0.77 0.69 1.04 0.76 2.60 0.92 2.19

time (sec)

N/A 0.565 0.188 2.516 0.202 0.349 0.184 0.319 0.768

Problem 3

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

77 79 65 54 79 56 168 68 84

N.S.

1 1.03 0.84 0.70 1.03 0.73 2.18 0.88 1.09

time (sec)

N/A 0.391 0.129 1.806 0.198 0.312 0.129 0.303 0.143

Problem 4

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

47 47 44 37 55 38 94 45 50

N.S.

1 1.00 0.94 0.79 1.17 0.81 2.00 0.96 1.06

time (sec)

N/A 0.213 0.077 0.946 0.196 0.368 0.094 0.292 0.120

Problem 5

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

32 32 46 48 47 51 0 79 100

N.S.

1 1.00 1.44 1.50 1.47 1.59 0.00 2.47 3.12

time (sec)

N/A 0.444 0.018 1.482 0.211 0.335 0.000 0.304 0.177

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 43 50 73 79 0 84 100

N.S.

1 1.00 1.34 1.56 2.28 2.47 0.00 2.62 3.12

time (sec)

N/A 0.444 0.018 2.326 0.207 0.395 0.000 0.306 0.179

Problem 7

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

56 59 75 75 95 89 0 124 94

N.S.

1 1.05 1.34 1.34 1.70 1.59 0.00 2.21 1.68

time (sec)

N/A 0.556 0.019 2.917 0.235 0.321 0.000 0.315 0.505

Problem 8

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 87 56 81 127 105 0 154 126

N.S.

1 1.01 0.65 0.94 1.48 1.22 0.00 1.79 1.47

time (sec)

N/A 0.669 0.222 2.976 0.237 0.282 0.000 0.307 1.280

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

106 102 77 119 163 127 0 188 166

N.S.

1 0.96 0.73 1.12 1.54 1.20 0.00 1.77 1.57

time (sec)

N/A 0.698 0.267 3.055 0.242 0.302 0.000 0.312 1.668

Problem 10

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

191 177 134 111 216 130 600 166 315

N.S.

1 0.93 0.70 0.58 1.13 0.68 3.14 0.87 1.65

time (sec)

N/A 1.027 0.399 4.450 0.455 0.320 0.394 0.323 0.991

Problem 11

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

160 151 108 93 178 110 459 137 277

N.S.

1 0.94 0.68 0.58 1.11 0.69 2.87 0.86 1.73

time (sec)

N/A 0.900 0.237 3.520 0.265 0.315 0.296 0.316 0.967

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

129 128 86 74 144 90 338 110 134

N.S.

1 0.99 0.67 0.57 1.12 0.70 2.62 0.85 1.04

time (sec)

N/A 0.579 0.196 2.840 0.248 0.292 0.191 0.319 0.191

Problem 13

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

94 83 84 61 110 70 199 85 98

N.S.

1 0.88 0.89 0.65 1.17 0.74 2.12 0.90 1.04

time (sec)

N/A 0.308 0.322 1.932 0.251 0.279 0.135 0.312 0.138

Problem 14

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 82 96 74 94 79 0 145 141

N.S.

1 1.00 1.17 0.90 1.15 0.96 0.00 1.77 1.72

time (sec)

N/A 0.701 1.025 1.526 0.229 0.292 0.000 0.302 0.215

Problem 15

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 74 143 81 105 108 0 155 161

N.S.

1 1.00 1.93 1.09 1.42 1.46 0.00 2.09 2.18

time (sec)

N/A 0.707 1.341 2.470 0.205 0.292 0.000 0.307 0.192

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

88 88 53 106 142 119 0 154 162

N.S.

1 1.00 0.60 1.20 1.61 1.35 0.00 1.75 1.84

time (sec)

N/A 0.736 0.538 3.292 0.310 0.295 0.000 0.310 0.187

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

113 119 63 120 174 125 0 178 145

N.S.

1 1.05 0.56 1.06 1.54 1.11 0.00 1.58 1.28

time (sec)

N/A 0.879 0.591 4.119 0.210 0.296 0.000 0.319 1.301

Problem 18

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

144 145 81 150 230 145 0 212 183

N.S.

1 1.01 0.56 1.04 1.60 1.01 0.00 1.47 1.27

time (sec)

N/A 1.027 0.816 4.477 0.243 0.311 0.000 0.329 1.943

Problem 19

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

201 197 134 112 262 130 695 166 315

N.S.

1 0.98 0.67 0.56 1.30 0.65 3.46 0.83 1.57

time (sec)

N/A 1.211 0.294 4.290 0.229 0.310 0.408 0.318 1.632

Problem 20

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

154 146 108 93 213 110 530 136 277

N.S.

1 0.95 0.70 0.60 1.38 0.71 3.44 0.88 1.80

time (sec)

N/A 0.628 0.234 3.355 0.212 0.301 0.299 0.310 1.510

Problem 21

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

116 101 116 79 167 90 371 112 134

N.S.

1 0.87 1.00 0.68 1.44 0.78 3.20 0.97 1.16

time (sec)

N/A 0.352 0.390 2.516 0.220 0.285 0.222 0.319 0.303

Problem 22

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

111 117 113 93 141 102 0 180 178

N.S.

1 1.05 1.02 0.84 1.27 0.92 0.00 1.62 1.60

time (sec)

N/A 0.945 1.175 2.550 0.219 0.323 0.000 0.345 0.452

Problem 23

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

110 111 272 120 140 127 0 192 197

N.S.

1 1.01 2.47 1.09 1.27 1.15 0.00 1.75 1.79

time (sec)

N/A 0.944 2.638 2.520 0.366 0.318 0.000 0.316 0.385

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

114 116 208 129 165 137 0 192 207

N.S.

1 1.02 1.82 1.13 1.45 1.20 0.00 1.68 1.82

time (sec)

N/A 0.991 3.261 3.426 0.235 0.303 0.000 0.333 0.397

Problem 25

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

125 131 70 142 212 141 0 189 209

N.S.

1 1.05 0.56 1.14 1.70 1.13 0.00 1.51 1.67

time (sec)

N/A 1.009 1.103 4.017 0.220 0.333 0.000 0.330 0.361

Problem 26

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

154 165 173 178 269 145 0 212 185

N.S.

1 1.07 1.12 1.16 1.75 0.94 0.00 1.38 1.20

time (sec)

N/A 1.204 0.982 4.707 0.220 0.281 0.000 0.351 2.895

Problem 27

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

185 191 101 196 337 165 0 246 224

N.S.

1 1.03 0.55 1.06 1.82 0.89 0.00 1.33 1.21

time (sec)

N/A 1.364 1.761 5.860 0.222 0.312 0.000 0.327 2.964

Problem 28

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

241 242 156 131 356 150 960 193 353

N.S.

1 1.00 0.65 0.54 1.48 0.62 3.98 0.80 1.46

time (sec)

N/A 1.582 0.425 5.701 0.223 0.314 0.592 0.336 1.794

Problem 29

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

185 170 134 111 297 130 765 166 316

N.S.

1 0.92 0.72 0.60 1.61 0.70 4.14 0.90 1.71

time (sec)

N/A 0.664 0.273 4.098 0.238 0.311 0.427 0.345 1.697

Problem 30

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

150 125 133 94 236 110 544 139 278

N.S.

1 0.83 0.89 0.63 1.57 0.73 3.63 0.93 1.85

time (sec)

N/A 0.387 0.578 3.672 0.218 0.310 0.310 0.306 1.642

Problem 31

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

151 162 138 108 198 118 0 214 188

N.S.

1 1.07 0.91 0.72 1.31 0.78 0.00 1.42 1.25

time (sec)

N/A 1.232 1.738 3.459 0.215 0.326 0.000 0.312 0.738

Problem 32

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

150 156 312 140 187 150 0 226 242

N.S.

1 1.04 2.08 0.93 1.25 1.00 0.00 1.51 1.61

time (sec)

N/A 1.293 4.165 3.506 0.229 0.341 0.000 0.340 0.495

Problem 33

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

162 154 343 168 199 156 0 230 243

N.S.

1 0.95 2.12 1.04 1.23 0.96 0.00 1.42 1.50

time (sec)

N/A 1.301 7.850 3.288 0.231 0.321 0.000 0.338 0.488

Problem 34

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

165 172 380 165 235 159 0 227 254

N.S.

1 1.04 2.30 1.00 1.42 0.96 0.00 1.38 1.54

time (sec)

N/A 1.399 9.285 4.061 0.214 0.324 0.000 0.357 0.507

Problem 35

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

173 184 178 203 307 157 0 223 255

N.S.

1 1.06 1.03 1.17 1.77 0.91 0.00 1.29 1.47

time (sec)

N/A 1.384 3.682 4.777 0.233 0.339 0.000 0.367 0.466

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

198 214 217 217 376 165 0 246 224

N.S.

1 1.08 1.10 1.10 1.90 0.83 0.00 1.24 1.13

time (sec)

N/A 1.566 4.345 5.591 0.221 0.309 0.000 0.361 2.938

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

229 240 259 251 464 185 0 280 262

N.S.

1 1.05 1.13 1.10 2.03 0.81 0.00 1.22 1.14

time (sec)

N/A 1.784 5.109 6.185 0.296 0.301 0.000 0.371 2.954

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 134 311 96 394 120 1794 181 170

N.S.

1 0.88 2.03 0.63 2.58 0.78 11.73 1.18 1.11

time (sec)

N/A 0.682 1.442 0.934 0.313 0.329 1.981 0.326 0.404

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 107 249 78 310 98 1161 151 138

N.S.

1 0.88 2.04 0.64 2.54 0.80 9.52 1.24 1.13

time (sec)

N/A 0.556 1.228 0.951 0.298 0.294 1.268 0.312 1.496

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 98 197 61 225 83 665 124 107

N.S.

1 1.09 2.19 0.68 2.50 0.92 7.39 1.38 1.19

time (sec)

N/A 0.400 1.026 0.875 0.303 0.301 0.873 0.293 0.573

Problem 41

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

54 47 93 42 143 61 264 78 65

N.S.

1 0.87 1.72 0.78 2.65 1.13 4.89 1.44 1.20

time (sec)

N/A 0.457 0.373 0.835 0.301 0.293 0.573 0.292 0.323

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 76 28 73 43 49 43 30

N.S.

1 1.00 2.24 0.82 2.15 1.26 1.44 1.26 0.88

time (sec)

N/A 0.271 0.247 0.926 0.289 0.321 0.356 0.296 0.239

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 109 54 99 74 0 71 42

N.S.

1 1.00 2.48 1.23 2.25 1.68 0.00 1.61 0.95

time (sec)

N/A 0.328 0.468 1.269 0.215 0.321 0.000 0.314 0.263

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 70 201 93 196 127 0 110 78

N.S.

1 1.01 2.91 1.35 2.84 1.84 0.00 1.59 1.13

time (sec)

N/A 0.529 1.374 1.209 0.226 0.301 0.000 0.331 0.352

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 100 289 126 282 156 0 157 119

N.S.

1 0.93 2.70 1.18 2.64 1.46 0.00 1.47 1.11

time (sec)

N/A 0.659 2.937 1.215 0.212 0.309 0.000 0.318 0.428

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 118 490 170 368 168 0 182 152

N.S.

1 0.90 3.74 1.30 2.81 1.28 0.00 1.39 1.16

time (sec)

N/A 0.695 3.697 1.404 0.219 0.301 0.000 0.320 0.707

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

170 160 369 108 372 154 1425 192 189

N.S.

1 0.94 2.17 0.64 2.19 0.91 8.38 1.13 1.11

time (sec)

N/A 0.874 1.809 0.973 0.328 0.305 3.177 0.310 0.347

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 152 315 88 283 138 843 164 152

N.S.

1 1.03 2.14 0.60 1.93 0.94 5.73 1.12 1.03

time (sec)

N/A 0.655 1.539 0.964 0.299 0.295 1.813 0.310 0.299

Problem 49

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

99 100 137 73 191 117 411 119 105

N.S.

1 1.01 1.38 0.74 1.93 1.18 4.15 1.20 1.06

time (sec)

N/A 0.769 1.285 1.085 0.320 0.325 1.091 0.322 0.277

Problem 50

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

70 73 153 49 120 91 105 86 65

N.S.

1 1.04 2.19 0.70 1.71 1.30 1.50 1.23 0.93

time (sec)

N/A 0.521 0.750 0.873 0.406 0.286 0.680 0.302 0.242

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 64 43 42 93 58 94 60 45

N.S.

1 0.98 0.66 0.65 1.43 0.89 1.45 0.92 0.69

time (sec)

N/A 0.303 0.100 0.898 0.208 0.292 0.503 0.307 0.195

Problem 52

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

79 80 170 75 145 131 0 113 74

N.S.

1 1.01 2.15 0.95 1.84 1.66 0.00 1.43 0.94

time (sec)

N/A 0.515 0.658 1.239 0.222 0.324 0.000 0.331 0.262

Problem 53

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

107 115 264 126 244 207 0 155 123

N.S.

1 1.07 2.47 1.18 2.28 1.93 0.00 1.45 1.15

time (sec)

N/A 0.792 1.792 1.441 0.261 0.290 0.000 0.345 0.299

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 151 496 158 336 228 0 198 165

N.S.

1 0.99 3.26 1.04 2.21 1.50 0.00 1.30 1.09

time (sec)

N/A 0.962 2.940 1.447 0.257 0.297 0.000 0.332 0.308

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 171 609 196 425 247 0 226 203

N.S.

1 0.96 3.40 1.09 2.37 1.38 0.00 1.26 1.13

time (sec)

N/A 1.018 4.023 1.397 0.228 0.321 0.000 0.352 0.354

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

218 216 491 124 412 205 1584 228 238

N.S.

1 0.99 2.25 0.57 1.89 0.94 7.27 1.05 1.09

time (sec)

N/A 1.209 2.553 0.990 0.305 0.314 5.949 0.333 0.323

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 207 435 106 322 190 966 200 203

N.S.

1 1.07 2.25 0.55 1.67 0.98 5.01 1.04 1.05

time (sec)

N/A 0.972 2.170 0.979 0.290 0.297 3.904 0.329 0.286

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 154 361 89 231 165 496 155 152

N.S.

1 1.05 2.46 0.61 1.57 1.12 3.37 1.05 1.03

time (sec)

N/A 1.114 1.863 1.111 0.294 0.322 2.371 0.337 0.282

Problem 59

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

116 125 241 69 160 137 148 120 134

N.S.

1 1.08 2.08 0.59 1.38 1.18 1.28 1.03 1.16

time (sec)

N/A 0.821 1.207 0.882 0.308 0.308 1.342 0.310 0.420

Problem 60

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

102 104 135 56 115 93 117 75 66

N.S.

1 1.02 1.32 0.55 1.13 0.91 1.15 0.74 0.65

time (sec)

N/A 0.578 0.818 0.906 0.207 0.310 1.006 0.322 0.204

Problem 61

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

102 99 63 56 115 93 114 75 66

N.S.

1 0.97 0.62 0.55 1.13 0.91 1.12 0.74 0.65

time (sec)

N/A 0.411 0.140 1.125 0.364 0.304 0.779 0.301 0.221

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

117 127 197 95 187 185 0 148 130

N.S.

1 1.09 1.68 0.81 1.60 1.58 0.00 1.26 1.11

time (sec)

N/A 0.765 0.936 1.122 0.232 0.303 0.000 0.339 0.260

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 161 482 143 286 272 0 190 168

N.S.

1 1.11 3.32 0.99 1.97 1.88 0.00 1.31 1.16

time (sec)

N/A 1.139 2.776 1.448 0.219 0.318 0.000 0.322 0.294

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

196 203 610 175 377 295 0 233 216

N.S.

1 1.04 3.11 0.89 1.92 1.51 0.00 1.19 1.10

time (sec)

N/A 1.365 4.025 1.344 0.246 0.336 0.000 0.353 0.301

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

229 251 555 123 364 238 1085 233 259

N.S.

1 1.10 2.42 0.54 1.59 1.04 4.74 1.02 1.13

time (sec)

N/A 1.268 5.026 1.159 0.299 0.319 7.966 0.348 0.337

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 202 481 106 271 213 578 188 201

N.S.

1 1.09 2.60 0.57 1.46 1.15 3.12 1.02 1.09

time (sec)

N/A 1.451 4.767 0.969 0.300 0.307 5.071 0.332 0.427

Problem 67

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

154 173 329 89 201 180 192 155 162

N.S.

1 1.12 2.14 0.58 1.31 1.17 1.25 1.01 1.05

time (sec)

N/A 1.113 4.365 0.858 0.305 0.297 3.240 0.324 0.371

Problem 68

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

136 147 193 82 175 124 182 117 86

N.S.

1 1.08 1.42 0.60 1.29 0.91 1.34 0.86 0.63

time (sec)

N/A 0.879 3.090 0.975 0.214 0.287 2.197 0.395 0.278

Problem 69

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

138 137 163 76 174 124 178 117 84

N.S.

1 0.99 1.18 0.55 1.26 0.90 1.29 0.85 0.61

time (sec)

N/A 0.678 1.085 0.970 0.214 0.272 1.628 0.348 0.294

Problem 70

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

138 132 81 80 175 125 177 117 87

N.S.

1 0.96 0.59 0.58 1.27 0.91 1.28 0.85 0.63

time (sec)

N/A 0.516 0.341 1.280 0.221 0.312 1.431 0.329 0.299

Problem 71

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

147 167 239 113 228 236 0 182 199

N.S.

1 1.14 1.63 0.77 1.55 1.61 0.00 1.24 1.35

time (sec)

N/A 1.033 1.444 1.172 0.236 0.302 0.000 0.360 0.428

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

175 199 595 160 326 337 0 224 236

N.S.

1 1.14 3.40 0.91 1.86 1.93 0.00 1.28 1.35

time (sec)

N/A 1.442 4.604 1.473 0.225 0.311 0.000 0.361 0.353

Problem 73

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

232 247 798 192 419 360 0 267 273

N.S.

1 1.06 3.44 0.83 1.81 1.55 0.00 1.15 1.18

time (sec)

N/A 1.736 8.170 1.536 0.213 0.323 0.000 0.385 0.362

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

187 187 103 121 145 99 0 182 0

N.S.

1 1.00 0.55 0.65 0.78 0.53 0.00 0.97 0.00

time (sec)

N/A 0.893 0.395 2.710 0.406 0.305 0.000 0.689 0.000

Problem 75

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

144 146 80 102 118 82 0 147 0

N.S.

1 1.01 0.56 0.71 0.82 0.57 0.00 1.02 0.00

time (sec)

N/A 0.660 0.184 2.756 0.416 0.297 0.000 0.438 0.000

Problem 76

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

101 112 64 83 88 64 0 107 0

N.S.

1 1.11 0.63 0.82 0.87 0.63 0.00 1.06 0.00

time (sec)

N/A 0.601 0.109 2.714 0.372 0.300 0.000 0.332 0.000

Problem 77

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

62 62 46 62 57 47 0 70 0

N.S.

1 1.00 0.74 1.00 0.92 0.76 0.00 1.13 0.00

time (sec)

N/A 0.305 0.057 2.239 0.377 0.282 0.000 0.331 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 66 219 21 127 0 89 0

N.S.

1 1.00 1.00 3.32 0.32 1.92 0.00 1.35 0.00

time (sec)

N/A 0.389 0.069 3.710 0.345 0.317 0.000 0.330 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 85 567 710 153 0 121 0

N.S.

1 1.00 1.25 8.34 10.44 2.25 0.00 1.78 0.00

time (sec)

N/A 0.422 0.135 4.707 0.421 0.320 0.000 0.339 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 109 101 936 3352 178 0 195 0

N.S.

1 0.93 0.86 8.00 28.65 1.52 0.00 1.67 0.00

time (sec)

N/A 0.555 0.568 5.240 3.241 0.302 0.000 0.346 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

160 150 129 1282 5021 197 0 244 0

N.S.

1 0.94 0.81 8.01 31.38 1.23 0.00 1.52 0.00

time (sec)

N/A 0.732 1.188 5.806 3.229 0.322 0.000 0.439 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

234 238 125 142 185 125 0 235 0

N.S.

1 1.02 0.53 0.61 0.79 0.53 0.00 1.00 0.00

time (sec)

N/A 1.251 0.569 2.552 0.395 0.276 0.000 2.301 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 197 103 123 154 107 0 191 0

N.S.

1 1.04 0.54 0.65 0.81 0.57 0.00 1.01 0.00

time (sec)

N/A 0.987 0.301 2.589 0.393 0.279 0.000 1.058 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 146 81 104 123 88 0 155 0

N.S.

1 1.06 0.59 0.75 0.89 0.64 0.00 1.12 0.00

time (sec)

N/A 0.756 0.208 2.603 0.368 0.271 0.000 0.511 0.000

Problem 85

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

101 99 65 85 93 69 0 115 0

N.S.

1 0.98 0.64 0.84 0.92 0.68 0.00 1.14 0.00

time (sec)

N/A 0.412 0.131 2.503 0.368 0.309 0.000 0.359 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 108 85 269 39 149 0 140 0

N.S.

1 1.03 0.81 2.56 0.37 1.42 0.00 1.33 0.00

time (sec)

N/A 0.630 0.150 4.250 0.344 0.288 0.000 0.402 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 109 98 603 1315 172 0 149 0

N.S.

1 1.06 0.95 5.85 12.77 1.67 0.00 1.45 0.00

time (sec)

N/A 0.651 0.208 4.811 0.374 0.324 0.000 0.407 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 118 109 938 3339 182 0 201 0

N.S.

1 0.99 0.92 7.88 28.06 1.53 0.00 1.69 0.00

time (sec)

N/A 0.700 0.354 5.389 0.496 0.335 0.000 0.408 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 160 132 1283 7567 202 0 252 0

N.S.

1 0.98 0.80 7.82 46.14 1.23 0.00 1.54 0.00

time (sec)

N/A 0.879 0.628 5.879 154.990 0.342 0.000 0.444 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

209 201 151 1617 10504 220 0 302 0

N.S.

1 0.96 0.72 7.74 50.26 1.05 0.00 1.44 0.00

time (sec)

N/A 1.103 0.986 6.362 154.623 0.331 0.000 0.484 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

237 249 127 142 207 137 0 257 0

N.S.

1 1.05 0.54 0.60 0.87 0.58 0.00 1.08 0.00

time (sec)

N/A 1.374 0.630 11.388 0.398 0.308 0.000 3.285 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

175 180 105 123 172 116 0 213 0

N.S.

1 1.03 0.60 0.70 0.98 0.66 0.00 1.22 0.00

time (sec)

N/A 0.884 0.377 4.783 0.390 0.285 0.000 1.131 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 133 83 104 139 95 0 169 0

N.S.

1 0.96 0.60 0.75 1.01 0.69 0.00 1.22 0.00

time (sec)

N/A 0.509 0.220 3.231 0.361 0.303 0.000 0.569 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 150 104 310 61 177 0 202 0

N.S.

1 1.06 0.73 2.18 0.43 1.25 0.00 1.42 0.00

time (sec)

N/A 0.862 0.271 6.214 0.336 0.327 0.000 0.692 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 153 120 683 8114 202 0 209 0

N.S.

1 1.06 0.83 4.74 56.35 1.40 0.00 1.45 0.00

time (sec)

N/A 0.920 0.351 15.191 0.647 0.394 0.000 0.657 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 159 126 995 11782 204 0 239 0

N.S.

1 1.02 0.81 6.38 75.53 1.31 0.00 1.53 0.00

time (sec)

N/A 0.963 0.431 54.749 3.425 0.325 0.000 0.687 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 169 131 1282 7994 212 0 268 0

N.S.

1 1.03 0.80 7.82 48.74 1.29 0.00 1.63 0.00

time (sec)

N/A 1.010 0.713 163.576 3.619 0.340 0.000 0.686 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

209 212 152 1650 0 232 0 322 0

N.S.

1 1.01 0.73 7.89 0.00 1.11 0.00 1.54 0.00

time (sec)

N/A 1.207 1.118 2.423 0.000 0.357 0.000 0.732 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

254 253 176 1975 0 252 0 376 0

N.S.

1 1.00 0.69 7.78 0.00 0.99 0.00 1.48 0.00

time (sec)

N/A 1.419 1.422 2.584 0.000 0.348 0.000 0.794 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

202 226 111 281 1604723 184 0 217 0

N.S.

1 1.12 0.55 1.39 7944.17 0.91 0.00 1.07 0.00

time (sec)

N/A 1.303 0.433 4.207 32.549 0.317 0.000 0.727 0.000

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