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2.2.5 Integrals 401 to 500

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 401

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 90 77 59 84 141 112 132 0

N.S.

1 1.05 0.90 0.69 0.98 1.64 1.30 1.53 0.00

time (sec)

N/A 0.185 0.150 1.894 0.220 0.277 2.152 0.307 0.000

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 84 68 57 104 140 105 168 0

N.S.

1 1.02 0.83 0.70 1.27 1.71 1.28 2.05 0.00

time (sec)

N/A 0.194 0.103 1.908 0.207 0.273 2.373 0.312 0.000

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 18 17 46 95 113 71

N.S.

1 1.00 1.00 0.86 0.81 2.19 4.52 5.38 3.38

time (sec)

N/A 0.143 0.072 1.889 0.205 0.257 0.644 0.317 5.141

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 31 28 36 60 121 220 91

N.S.

1 1.00 0.70 0.64 0.82 1.36 2.75 5.00 2.07

time (sec)

N/A 0.158 0.086 1.938 0.202 0.262 0.813 0.301 5.344

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 74 42 39 56 71 481 246 111

N.S.

1 1.09 0.62 0.57 0.82 1.04 7.07 3.62 1.63

time (sec)

N/A 0.177 0.096 1.991 0.197 0.265 1.110 0.295 5.677

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 104 53 50 76 82 721 274 131

N.S.

1 1.13 0.58 0.54 0.83 0.89 7.84 2.98 1.42

time (sec)

N/A 0.199 0.107 2.070 0.222 0.291 1.415 0.331 6.059

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 134 64 61 96 93 1012 300 151

N.S.

1 1.16 0.55 0.53 0.83 0.80 8.72 2.59 1.30

time (sec)

N/A 0.222 0.116 2.206 0.204 0.310 1.762 0.326 6.547

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 164 75 72 116 104 1346 328 171

N.S.

1 1.17 0.54 0.51 0.83 0.74 9.61 2.34 1.22

time (sec)

N/A 0.242 0.127 2.414 0.226 0.371 2.275 0.329 7.118

Problem 409

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

161 166 94 91 153 145 301 113 141

N.S.

1 1.03 0.58 0.57 0.95 0.90 1.87 0.70 0.88

time (sec)

N/A 0.267 0.058 2.127 0.213 0.276 2.827 0.308 4.748

Problem 410

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

140 145 83 80 133 134 277 99 130

N.S.

1 1.04 0.59 0.57 0.95 0.96 1.98 0.71 0.93

time (sec)

N/A 0.252 0.050 1.999 0.201 0.288 2.455 0.292 4.647

Problem 411

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

122 126 72 69 113 123 253 85 119

N.S.

1 1.03 0.59 0.57 0.93 1.01 2.07 0.70 0.98

time (sec)

N/A 0.238 0.039 1.947 0.204 0.266 2.021 0.300 4.680

Problem 412

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

101 105 61 58 93 112 230 71 108

N.S.

1 1.04 0.60 0.57 0.92 1.11 2.28 0.70 1.07

time (sec)

N/A 0.218 0.035 1.889 0.199 0.260 1.650 0.309 4.658

Problem 413

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

80 84 50 47 73 101 204 57 97

N.S.

1 1.05 0.62 0.59 0.91 1.26 2.55 0.71 1.21

time (sec)

N/A 0.203 0.036 1.855 0.203 0.267 1.362 0.292 4.604

Problem 414

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

59 63 39 36 53 90 180 43 86

N.S.

1 1.07 0.66 0.61 0.90 1.53 3.05 0.73 1.46

time (sec)

N/A 0.190 0.031 1.849 0.210 0.269 1.138 0.300 4.729

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 42 28 25 33 78 156 29 29

N.S.

1 1.11 0.74 0.66 0.87 2.05 4.11 0.76 0.76

time (sec)

N/A 0.176 0.033 1.857 0.186 0.260 0.908 0.298 4.624

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 15 14 65 133 14 14

N.S.

1 1.00 1.00 0.83 0.78 3.61 7.39 0.78 0.78

time (sec)

N/A 0.138 0.004 1.836 0.185 0.257 0.675 0.276 4.577

Problem 417

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

108 115 84 75 82 170 160 90 87

N.S.

1 1.06 0.78 0.69 0.76 1.57 1.48 0.83 0.81

time (sec)

N/A 0.207 0.051 1.888 0.204 0.271 10.493 0.291 4.632

Problem 418

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

118 119 90 90 106 188 167 116 95

N.S.

1 1.01 0.76 0.76 0.90 1.59 1.42 0.98 0.81

time (sec)

N/A 0.207 0.083 1.931 0.290 0.265 10.107 0.296 4.899

Problem 419

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

126 125 92 92 136 192 175 124 132

N.S.

1 0.99 0.73 0.73 1.08 1.52 1.39 0.98 1.05

time (sec)

N/A 0.211 0.116 1.939 0.280 0.277 9.624 0.299 5.127

Problem 420

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

126 131 92 92 156 190 175 124 149

N.S.

1 1.04 0.73 0.73 1.24 1.51 1.39 0.98 1.18

time (sec)

N/A 0.209 0.117 1.945 0.205 0.278 9.210 0.290 5.325

Problem 421

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

128 137 92 93 178 189 173 122 105

N.S.

1 1.07 0.72 0.73 1.39 1.48 1.35 0.95 0.82

time (sec)

N/A 0.214 0.128 1.957 0.207 0.275 9.417 0.302 5.777

Problem 422

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

131 143 92 90 201 202 153 121 106

N.S.

1 1.09 0.70 0.69 1.53 1.54 1.17 0.92 0.81

time (sec)

N/A 0.215 0.162 1.978 0.205 0.273 10.168 0.299 6.205

Problem 423

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

155 169 106 100 221 223 204 143 123

N.S.

1 1.09 0.68 0.65 1.43 1.44 1.32 0.92 0.79

time (sec)

N/A 0.223 0.169 2.075 0.209 0.284 46.067 0.284 6.859

Problem 424

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

179 199 117 111 241 245 0 160 140

N.S.

1 1.11 0.65 0.62 1.35 1.37 0.00 0.89 0.78

time (sec)

N/A 0.235 0.200 2.162 0.208 0.324 0.000 0.298 7.473

Problem 425

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

202 229 137 117 161 255 0 133 0

N.S.

1 1.13 0.68 0.58 0.80 1.26 0.00 0.66 0.00

time (sec)

N/A 0.290 0.749 2.052 0.207 0.363 0.000 0.298 0.000

Problem 426

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

178 199 126 106 141 234 0 119 0

N.S.

1 1.12 0.71 0.60 0.79 1.31 0.00 0.67 0.00

time (sec)

N/A 0.277 0.624 1.969 0.201 0.317 0.000 0.430 0.000

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 169 115 95 121 211 204 105 0

N.S.

1 1.10 0.75 0.62 0.79 1.37 1.32 0.68 0.00

time (sec)

N/A 0.251 0.520 1.925 0.212 0.311 46.980 0.401 0.000

Problem 428

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

122 134 93 81 88 190 151 91 37

N.S.

1 1.10 0.76 0.66 0.72 1.56 1.24 0.75 0.30

time (sec)

N/A 0.206 0.116 1.876 0.198 0.299 10.227 0.428 4.565

Problem 429

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

123 132 95 83 91 184 173 115 40

N.S.

1 1.07 0.77 0.67 0.74 1.50 1.41 0.93 0.33

time (sec)

N/A 0.204 0.117 1.954 0.217 0.300 9.720 0.296 6.002

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 132 95 83 120 189 175 160 0

N.S.

1 1.03 0.74 0.65 0.94 1.48 1.37 1.25 0.00

time (sec)

N/A 0.209 0.133 1.927 0.212 0.323 9.538 0.305 0.000

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 136 95 83 140 191 175 200 0

N.S.

1 1.05 0.74 0.64 1.09 1.48 1.36 1.55 0.00

time (sec)

N/A 0.210 0.152 1.938 0.212 0.287 9.783 0.297 0.000

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 138 99 81 160 0 167 240 0

N.S.

1 1.10 0.79 0.64 1.27 0.00 1.33 1.90 0.00

time (sec)

N/A 0.221 0.190 1.968 0.211 0.000 10.320 0.305 0.000

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 126 90 79 180 184 160 276 0

N.S.

1 1.02 0.73 0.64 1.45 1.48 1.29 2.23 0.00

time (sec)

N/A 0.218 0.157 2.007 0.209 0.270 11.160 0.301 0.000

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 18 17 68 150 167 111

N.S.

1 1.00 1.00 0.86 0.81 3.24 7.14 7.95 5.29

time (sec)

N/A 0.139 0.102 2.079 0.219 0.271 1.237 0.319 6.286

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 31 28 36 82 175 328 131

N.S.

1 1.00 0.70 0.64 0.82 1.86 3.98 7.45 2.98

time (sec)

N/A 0.152 0.125 2.163 0.205 0.287 1.526 0.322 6.902

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 74 42 39 56 93 604 354 151

N.S.

1 1.09 0.62 0.57 0.82 1.37 8.88 5.21 2.22

time (sec)

N/A 0.170 0.133 2.243 0.206 0.309 1.958 0.303 7.604

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 104 53 50 76 104 867 382 171

N.S.

1 1.13 0.58 0.54 0.83 1.13 9.42 4.15 1.86

time (sec)

N/A 0.189 0.150 2.423 0.201 0.334 2.438 0.307 8.273

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 134 64 61 96 115 1182 408 191

N.S.

1 1.16 0.55 0.53 0.83 0.99 10.19 3.52 1.65

time (sec)

N/A 0.214 0.166 5.111 0.213 0.386 2.990 0.310 9.120

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 164 75 72 116 126 1540 436 211

N.S.

1 1.17 0.54 0.51 0.83 0.90 11.00 3.11 1.51

time (sec)

N/A 0.231 0.178 12.454 0.207 0.474 3.672 0.314 10.262

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 194 86 83 136 137 1950 462 231

N.S.

1 1.18 0.52 0.51 0.83 0.84 11.89 2.82 1.41

time (sec)

N/A 0.261 0.194 31.504 0.216 0.575 4.461 0.327 10.906

Problem 441

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

46 50 27 24 40 28 61 34 25

N.S.

1 1.09 0.59 0.52 0.87 0.61 1.33 0.74 0.54

time (sec)

N/A 0.167 0.016 1.886 0.270 0.251 0.311 0.300 4.555

Problem 442

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

63 73 49 32 45 42 75 43 30

N.S.

1 1.16 0.78 0.51 0.71 0.67 1.19 0.68 0.48

time (sec)

N/A 0.171 0.035 1.942 0.273 0.250 4.599 0.287 0.031

Problem 443

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

31 35 22 19 26 23 44 23 20

N.S.

1 1.13 0.71 0.61 0.84 0.74 1.42 0.74 0.65

time (sec)

N/A 0.161 0.013 1.866 0.280 0.237 0.158 0.284 0.023

Problem 444

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 50 44 27 31 37 54 36 23

N.S.

1 1.11 0.98 0.60 0.69 0.82 1.20 0.80 0.51

time (sec)

N/A 0.157 0.024 1.914 0.319 0.236 1.862 0.294 0.035

Problem 445

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

15 15 15 12 11 11 27 11 16

N.S.

1 1.00 1.00 0.80 0.73 0.73 1.80 0.73 1.07

time (sec)

N/A 0.129 0.001 1.858 0.210 0.242 0.085 0.275 0.020

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 37 20 19 29 22 29 16

N.S.

1 1.00 1.37 0.74 0.70 1.07 0.81 1.07 0.59

time (sec)

N/A 0.136 0.020 1.894 0.269 0.256 0.086 0.284 0.034

Problem 447

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

30 36 30 25 19 44 39 38 22

N.S.

1 1.20 1.00 0.83 0.63 1.47 1.30 1.27 0.73

time (sec)

N/A 0.152 0.017 1.916 0.292 0.234 0.766 0.274 0.030

Problem 448

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

25 25 35 22 21 35 19 40 19

N.S.

1 1.00 1.40 0.88 0.84 1.40 0.76 1.60 0.76

time (sec)

N/A 0.140 0.025 1.900 0.269 0.238 0.102 0.303 0.030

Problem 449

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

39 41 39 30 35 57 24 43 25

N.S.

1 1.05 1.00 0.77 0.90 1.46 0.62 1.10 0.64

time (sec)

N/A 0.153 0.027 1.917 0.274 0.240 0.958 0.282 0.033

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 15 14 20 34 42 27

N.S.

1 1.00 1.00 0.83 0.78 1.11 1.89 2.33 1.50

time (sec)

N/A 0.131 0.028 1.879 0.272 0.243 0.526 0.276 0.033

Problem 451

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

57 61 46 41 49 64 63 55 45

N.S.

1 1.07 0.81 0.72 0.86 1.12 1.11 0.96 0.79

time (sec)

N/A 0.159 0.041 1.928 0.280 0.242 2.049 0.264 0.033

Problem 452

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

46 50 32 24 40 28 61 52 28

N.S.

1 1.09 0.70 0.52 0.87 0.61 1.33 1.13 0.61

time (sec)

N/A 0.164 0.016 1.883 0.288 0.249 0.315 0.268 4.541

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 73 52 39 45 45 165 33 32

N.S.

1 1.16 0.83 0.62 0.71 0.71 2.62 0.52 0.51

time (sec)

N/A 0.167 0.101 2.034 0.269 0.241 4.810 0.291 4.499

Problem 454

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

31 35 22 19 26 23 44 32 23

N.S.

1 1.13 0.71 0.61 0.84 0.74 1.42 1.03 0.74

time (sec)

N/A 0.157 0.014 1.954 0.272 0.247 0.170 0.280 0.024

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 50 47 32 31 40 122 26 27

N.S.

1 1.11 1.04 0.71 0.69 0.89 2.71 0.58 0.60

time (sec)

N/A 0.154 0.065 1.921 0.276 0.245 1.825 0.290 0.034

Problem 456

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

15 15 15 12 11 18 27 11 18

N.S.

1 1.00 1.00 0.80 0.73 1.20 1.80 0.73 1.20

time (sec)

N/A 0.128 0.002 1.893 0.202 0.247 0.083 0.289 0.022

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 41 20 19 32 22 19 18

N.S.

1 1.00 1.52 0.74 0.70 1.19 0.81 0.70 0.67

time (sec)

N/A 0.138 0.038 1.912 0.296 0.251 0.090 0.296 0.027

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 36 30 25 35 28 75 40 32

N.S.

1 1.20 1.00 0.83 1.17 0.93 2.50 1.33 1.07

time (sec)

N/A 0.151 0.017 1.913 0.300 0.248 0.801 0.297 0.047

Problem 459

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

25 25 39 28 21 36 20 39 21

N.S.

1 1.00 1.56 1.12 0.84 1.44 0.80 1.56 0.84

time (sec)

N/A 0.140 0.032 1.926 0.288 0.240 0.116 0.289 0.030

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 41 39 34 51 38 97 45 35

N.S.

1 1.05 1.00 0.87 1.31 0.97 2.49 1.15 0.90

time (sec)

N/A 0.149 0.030 1.929 0.276 0.244 1.031 0.270 4.506

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 15 14 21 76 73 31

N.S.

1 1.00 1.00 0.83 0.78 1.17 4.22 4.06 1.72

time (sec)

N/A 0.133 0.023 1.882 0.267 0.256 0.550 0.278 0.033

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 61 46 41 65 45 139 57 49

N.S.

1 1.07 0.81 0.72 1.14 0.79 2.44 1.00 0.86

time (sec)

N/A 0.159 0.035 1.918 0.271 0.258 2.126 0.280 0.032

Problem 463

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

46 50 27 24 40 28 61 34 28

N.S.

1 1.09 0.59 0.52 0.87 0.61 1.33 0.74 0.61

time (sec)

N/A 0.161 0.016 1.894 0.290 0.249 0.292 0.312 4.486

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 82 49 42 57 42 165 44 0

N.S.

1 1.14 0.68 0.58 0.79 0.58 2.29 0.61 0.00

time (sec)

N/A 0.185 0.032 1.947 0.279 0.266 4.655 0.279 0.000

Problem 465

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

31 35 22 19 26 23 44 23 23

N.S.

1 1.13 0.71 0.61 0.84 0.74 1.42 0.74 0.74

time (sec)

N/A 0.159 0.014 1.895 0.278 0.240 0.151 0.268 4.486

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 59 44 37 43 37 122 37 0

N.S.

1 1.09 0.81 0.69 0.80 0.69 2.26 0.69 0.00

time (sec)

N/A 0.165 0.025 1.937 0.278 0.252 1.806 0.280 0.000

Problem 467

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

15 15 15 12 11 11 27 11 11

N.S.

1 1.00 1.00 0.80 0.73 0.73 1.80 0.73 0.73

time (sec)

N/A 0.126 0.001 1.887 0.191 0.247 0.079 0.270 0.062

Problem 468

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

36 36 37 30 31 29 31 30 29

N.S.

1 1.00 1.03 0.83 0.86 0.81 0.86 0.83 0.81

time (sec)

N/A 0.144 0.021 1.932 0.285 0.258 0.083 0.280 4.559

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 36 30 25 19 28 80 24 24

N.S.

1 1.20 1.00 0.83 0.63 0.93 2.67 0.80 0.80

time (sec)

N/A 0.151 0.017 1.980 0.275 0.257 0.852 0.286 4.701

Problem 470

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

34 34 35 32 33 35 27 44 39

N.S.

1 1.00 1.03 0.94 0.97 1.03 0.79 1.29 1.15

time (sec)

N/A 0.149 0.025 1.940 0.270 0.252 0.106 0.276 4.998

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 41 39 30 35 38 97 29 29

N.S.

1 1.05 1.00 0.77 0.90 0.97 2.49 0.74 0.74

time (sec)

N/A 0.152 0.026 1.947 0.282 0.254 1.007 0.276 4.697

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 15 14 20 76 42 31

N.S.

1 1.00 1.00 0.83 0.78 1.11 4.22 2.33 1.72

time (sec)

N/A 0.132 0.024 1.901 0.277 0.243 0.546 0.277 4.879

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 61 46 42 49 45 139 41 43

N.S.

1 1.07 0.81 0.74 0.86 0.79 2.44 0.72 0.75

time (sec)

N/A 0.163 0.037 1.948 0.279 0.252 2.046 0.274 5.124

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 50 27 24 40 28 68 34 27

N.S.

1 1.09 0.59 0.52 0.87 0.61 1.48 0.74 0.59

time (sec)

N/A 0.163 0.017 1.900 0.276 0.243 0.337 0.280 5.233

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 82 48 44 45 72 83 0 0

N.S.

1 1.14 0.67 0.61 0.62 1.00 1.15 0.00 0.00

time (sec)

N/A 0.179 0.088 2.024 0.267 0.242 4.702 0.000 0.000

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 35 22 19 26 23 49 23 22

N.S.

1 1.13 0.71 0.61 0.84 0.74 1.58 0.74 0.71

time (sec)

N/A 0.156 0.014 1.945 0.271 0.236 0.164 0.279 5.981

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 59 43 39 31 67 61 0 0

N.S.

1 1.09 0.80 0.72 0.57 1.24 1.13 0.00 0.00

time (sec)

N/A 0.162 0.071 1.915 0.276 0.261 1.836 0.000 0.000

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 12 11 18 31 11 11

N.S.

1 1.00 1.00 0.80 0.73 1.20 2.07 0.73 0.73

time (sec)

N/A 0.123 0.002 1.885 0.198 0.248 0.096 0.284 0.074

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 36 29 19 59 34 0 28

N.S.

1 1.00 1.00 0.81 0.53 1.64 0.94 0.00 0.78

time (sec)

N/A 0.141 0.057 9.025 0.284 0.248 0.184 0.000 5.037

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C C C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 36 30 25 35 52 44 24 24

N.S.

1 1.20 1.00 0.83 1.17 1.73 1.47 0.80 0.80

time (sec)

N/A 0.146 0.015 1.948 0.276 0.253 0.773 0.295 5.005

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 35 34 21 64 32 0 41

N.S.

1 1.00 1.03 1.00 0.62 1.88 0.94 0.00 1.21

time (sec)

N/A 0.149 0.051 1.912 0.277 0.246 0.198 0.000 5.057

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C C C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 41 39 35 51 65 27 29 29

N.S.

1 1.05 1.00 0.90 1.31 1.67 0.69 0.74 0.74

time (sec)

N/A 0.145 0.025 1.935 0.275 0.256 0.973 0.269 5.085

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 15 14 14 37 0 31

N.S.

1 1.00 1.00 0.83 0.78 0.78 2.06 0.00 1.72

time (sec)

N/A 0.130 0.037 1.876 0.267 0.236 0.542 0.000 5.046

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C C C C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 61 46 42 65 72 68 43 43

N.S.

1 1.07 0.81 0.74 1.14 1.26 1.19 0.75 0.75

time (sec)

N/A 0.158 0.031 1.931 0.272 0.263 2.038 0.269 5.156

Problem 485

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

56 61 39 36 53 35 68 46 36

N.S.

1 1.09 0.70 0.64 0.95 0.62 1.21 0.82 0.64

time (sec)

N/A 0.175 0.022 1.891 0.189 0.246 0.206 0.278 5.415

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 79 71 51 51 124 95 54 0

N.S.

1 1.08 0.97 0.70 0.70 1.70 1.30 0.74 0.00

time (sec)

N/A 0.173 0.150 1.908 0.194 0.278 2.446 0.286 0.000

Problem 487

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

36 40 27 24 33 23 44 30 24

N.S.

1 1.11 0.75 0.67 0.92 0.64 1.22 0.83 0.67

time (sec)

N/A 0.162 0.021 1.881 0.187 0.258 0.163 0.282 5.096

Problem 488

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

49 49 57 39 31 93 42 40 56

N.S.

1 1.00 1.16 0.80 0.63 1.90 0.86 0.82 1.14

time (sec)

N/A 0.156 0.106 6.762 0.191 0.254 1.169 0.279 5.203

Problem 489

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

15 15 15 14 13 13 20 13 13

N.S.

1 1.00 1.00 0.93 0.87 0.87 1.33 0.87 0.87

time (sec)

N/A 0.129 0.002 1.863 0.188 0.252 0.069 0.287 4.922

Problem 490

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

25 25 25 21 13 59 17 37 20

N.S.

1 1.00 1.00 0.84 0.52 2.36 0.68 1.48 0.80

time (sec)

N/A 0.139 0.005 6.686 0.195 0.257 0.516 0.288 0.139

Problem 491

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

25 25 25 20 17 60 19 22 19

N.S.

1 1.00 1.00 0.80 0.68 2.40 0.76 0.88 0.76

time (sec)

N/A 0.152 0.019 1.889 0.189 0.270 0.547 0.283 5.150

Problem 492

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

19 19 19 18 17 17 19 30 17

N.S.

1 1.00 1.00 0.95 0.89 0.89 1.00 1.58 0.89

time (sec)

N/A 0.136 0.028 6.751 0.182 0.262 0.378 0.293 4.956

Problem 493

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

50 49 50 43 36 105 42 51 38

N.S.

1 0.98 1.00 0.86 0.72 2.10 0.84 1.02 0.76

time (sec)

N/A 0.163 0.044 1.904 0.187 0.254 1.249 0.267 5.269

Problem 494

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

44 44 31 26 36 27 46 55 25

N.S.

1 1.00 0.70 0.59 0.82 0.61 1.05 1.25 0.57

time (sec)

N/A 0.158 0.040 1.886 0.191 0.250 0.483 0.281 5.103

Problem 495

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

74 79 62 60 56 135 97 75 57

N.S.

1 1.07 0.84 0.81 0.76 1.82 1.31 1.01 0.77

time (sec)

N/A 0.181 0.078 1.921 0.206 0.274 2.507 0.270 5.277

Problem 496

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

55 59 38 35 53 46 68 52 41

N.S.

1 1.07 0.69 0.64 0.96 0.84 1.24 0.95 0.75

time (sec)

N/A 0.181 0.027 1.909 0.192 0.250 0.214 0.260 5.446

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 74 66 54 49 159 71 51 0

N.S.

1 1.09 0.97 0.79 0.72 2.34 1.04 0.75 0.00

time (sec)

N/A 0.177 0.165 1.950 0.198 0.258 1.777 0.292 0.000

Problem 498

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

32 38 24 23 32 34 41 32 22

N.S.

1 1.19 0.75 0.72 1.00 1.06 1.28 1.00 0.69

time (sec)

N/A 0.165 0.022 1.878 0.188 0.244 0.180 0.279 5.427

Problem 499

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

43 43 54 37 29 130 37 39 36

N.S.

1 1.00 1.26 0.86 0.67 3.02 0.86 0.91 0.84

time (sec)

N/A 0.156 0.082 1.924 0.197 0.271 0.900 0.293 0.105

Problem 500

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

16 16 16 15 14 24 24 14 14

N.S.

1 1.00 1.00 0.94 0.88 1.50 1.50 0.88 0.88

time (sec)

N/A 0.132 0.002 1.887 0.195 0.273 0.100 0.273 5.144

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