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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 C A F B F F(-1) B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

187 215 90 233 0 328 0 0 103

N.S.

1 1.15 0.48 1.25 0.00 1.75 0.00 0.00 0.55

time (sec)

N/A 0.673 0.236 0.567 0.000 0.250 0.000 0.000 5.157

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 165 67 209 0 299 0 0 69

N.S.

1 1.15 0.47 1.46 0.00 2.09 0.00 0.00 0.48

time (sec)

N/A 0.420 0.038 0.623 0.000 0.246 0.000 0.000 0.277

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F B F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

161 183 83 2130 0 336 0 0 85

N.S.

1 1.14 0.52 13.23 0.00 2.09 0.00 0.00 0.53

time (sec)

N/A 0.793 0.077 117.358 0.000 0.263 0.000 0.000 0.176

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F B F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

215 246 125 3819 0 416 0 0 147

N.S.

1 1.14 0.58 17.76 0.00 1.93 0.00 0.00 0.68

time (sec)

N/A 1.218 0.358 179.787 0.000 0.257 0.000 0.000 5.064

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F B F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

269 310 169 4783 0 436 0 0 197

N.S.

1 1.15 0.63 17.78 0.00 1.62 0.00 0.00 0.73

time (sec)

N/A 1.690 1.524 133.826 0.000 0.262 0.000 0.000 4.842

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

311 339 112 326 0 340 0 0 101

N.S.

1 1.09 0.36 1.05 0.00 1.09 0.00 0.00 0.32

time (sec)

N/A 0.837 0.857 0.746 0.000 0.250 0.000 0.000 0.603

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

257 277 80 311 0 318 0 0 86

N.S.

1 1.08 0.31 1.21 0.00 1.24 0.00 0.00 0.33

time (sec)

N/A 0.538 0.113 0.813 0.000 0.247 0.000 0.000 0.316

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

240 259 66 296 0 299 0 276 71

N.S.

1 1.08 0.28 1.23 0.00 1.25 0.00 1.15 0.30

time (sec)

N/A 0.439 0.030 1.042 0.000 0.250 0.000 0.640 4.763

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F A F A B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

280 306 101 2372 0 391 0 336 117

N.S.

1 1.09 0.36 8.47 0.00 1.40 0.00 1.20 0.42

time (sec)

N/A 1.040 0.276 142.990 0.000 0.263 0.000 0.843 0.228

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F A F A B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

339 370 147 4582 0 426 0 363 170

N.S.

1 1.09 0.43 13.52 0.00 1.26 0.00 1.07 0.50

time (sec)

N/A 1.386 0.673 174.237 0.000 0.262 0.000 0.763 5.147

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

161 159 0 0 0 0 0 0 0

N.S.

1 0.99 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.363 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 93 95 79 81 80 97 887 76

N.S.

1 1.00 1.02 0.85 0.87 0.86 1.04 9.54 0.82

time (sec)

N/A 0.629 0.340 0.266 0.307 0.253 0.138 2.499 4.542

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 79 68 70 69 83 666 65

N.S.

1 1.00 1.03 0.88 0.91 0.90 1.08 8.65 0.84

time (sec)

N/A 0.526 0.227 0.224 0.416 0.240 0.119 1.341 4.907

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 67 57 59 58 70 475 54

N.S.

1 1.00 1.12 0.95 0.98 0.97 1.17 7.92 0.90

time (sec)

N/A 0.420 0.142 0.234 0.387 0.232 0.104 0.788 4.822

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 51 45 47 47 56 297 43

N.S.

1 1.00 1.16 1.02 1.07 1.07 1.27 6.75 0.98

time (sec)

N/A 0.325 0.113 0.240 0.418 0.244 0.096 0.565 4.335

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 38 34 37 35 41 154 32

N.S.

1 1.00 1.31 1.17 1.28 1.21 1.41 5.31 1.10

time (sec)

N/A 0.240 0.026 0.221 0.306 0.243 0.080 0.361 4.877

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

17 17 17 22 16 27 24 18 21

N.S.

1 1.00 1.00 1.29 0.94 1.59 1.41 1.06 1.24

time (sec)

N/A 0.151 0.011 0.185 0.197 0.243 0.059 0.304 4.755

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 18 28 34 38 35 42 42 79

N.S.

1 1.12 1.75 2.12 2.38 2.19 2.62 2.62 4.94

time (sec)

N/A 0.238 0.022 0.450 0.318 0.246 0.148 0.337 5.351

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 31 55 42 48 59 66 83 70

N.S.

1 1.07 1.90 1.45 1.66 2.03 2.28 2.86 2.41

time (sec)

N/A 0.327 0.032 0.444 0.322 0.248 0.216 0.414 4.695

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 48 66 53 58 72 80 113 83

N.S.

1 1.04 1.43 1.15 1.26 1.57 1.74 2.46 1.80

time (sec)

N/A 0.438 0.325 0.465 0.297 0.239 0.409 0.446 5.291

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 62 70 65 71 89 94 140 96

N.S.

1 1.03 1.17 1.08 1.18 1.48 1.57 2.33 1.60

time (sec)

N/A 0.540 0.328 0.429 0.411 0.243 0.621 0.525 4.772

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 77 91 76 82 100 107 169 107

N.S.

1 1.03 1.21 1.01 1.09 1.33 1.43 2.25 1.43

time (sec)

N/A 0.649 0.044 0.521 0.371 0.250 0.856 0.589 5.038

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 95 91 87 93 111 121 198 116

N.S.

1 1.02 0.98 0.94 1.00 1.19 1.30 2.13 1.25

time (sec)

N/A 0.772 0.051 0.470 0.359 0.245 1.365 0.620 4.964

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 120 110 118 110 109 139 1255 146

N.S.

1 1.00 0.92 0.98 0.92 0.91 1.16 10.46 1.22

time (sec)

N/A 0.763 0.669 0.219 0.349 0.240 0.157 2.032 5.056

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 98 113 98 91 90 134 1162 90

N.S.

1 1.00 1.15 1.00 0.93 0.92 1.37 11.86 0.92

time (sec)

N/A 0.624 0.477 0.278 0.300 0.244 0.128 1.497 5.205

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 63 99 80 78 77 94 635 108

N.S.

1 1.00 1.57 1.27 1.24 1.22 1.49 10.08 1.71

time (sec)

N/A 0.366 0.324 0.245 0.320 0.240 0.108 0.764 4.750

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 58 162 61 58 58 85 494 57

N.S.

1 1.00 2.79 1.05 1.00 1.00 1.47 8.52 0.98

time (sec)

N/A 0.351 0.125 0.246 0.318 0.243 0.093 0.624 5.480

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 69 43 41 44 48 181 136

N.S.

1 1.00 1.77 1.10 1.05 1.13 1.23 4.64 3.49

time (sec)

N/A 0.252 0.148 0.211 0.325 0.243 0.077 0.357 4.675

Problem 429

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

35 37 49 38 49 56 70 50 61

N.S.

1 1.06 1.40 1.09 1.40 1.60 2.00 1.43 1.74

time (sec)

N/A 0.276 0.051 0.753 0.338 0.244 0.196 0.492 5.638

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 43 82 46 58 67 83 98 79

N.S.

1 1.05 2.00 1.12 1.41 1.63 2.02 2.39 1.93

time (sec)

N/A 0.365 0.168 0.516 0.319 0.250 0.302 0.622 4.954

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 60 92 61 78 86 129 154 97

N.S.

1 1.03 1.59 1.05 1.34 1.48 2.22 2.66 1.67

time (sec)

N/A 0.485 0.289 0.757 0.409 0.239 0.531 0.682 5.323

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 80 103 75 91 107 124 191 112

N.S.

1 1.03 1.32 0.96 1.17 1.37 1.59 2.45 1.44

time (sec)

N/A 0.632 0.770 0.691 0.403 0.245 0.824 0.757 4.913

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 100 96 87 111 128 177 248 129

N.S.

1 1.02 0.98 0.89 1.13 1.31 1.81 2.53 1.32

time (sec)

N/A 0.746 0.583 0.863 0.370 0.251 1.064 0.938 5.259

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 122 132 103 124 141 170 287 145

N.S.

1 1.02 1.10 0.86 1.03 1.18 1.42 2.39 1.21

time (sec)

N/A 0.908 0.072 0.871 0.384 0.254 1.802 1.103 5.266

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 160 161 146 137 136 194 1877 182

N.S.

1 1.09 1.10 0.99 0.93 0.93 1.32 12.77 1.24

time (sec)

N/A 0.889 0.855 0.300 0.307 0.242 0.165 2.797 4.930

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 94 97 121 114 113 160 1385 154

N.S.

1 1.00 1.03 1.29 1.21 1.20 1.70 14.73 1.64

time (sec)

N/A 0.503 1.126 0.331 0.313 0.245 0.135 1.957 5.277

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 97 100 95 95 94 128 913 135

N.S.

1 1.00 1.03 0.98 0.98 0.97 1.32 9.41 1.39

time (sec)

N/A 0.494 0.620 0.339 0.325 0.246 0.116 1.185 4.889

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 79 73 78 71 94 543 106

N.S.

1 1.00 1.10 1.01 1.08 0.99 1.31 7.54 1.47

time (sec)

N/A 0.376 0.254 0.243 0.297 0.248 0.100 0.578 5.371

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 64 79 69 71 78 92 72 75

N.S.

1 1.03 1.27 1.11 1.15 1.26 1.48 1.16 1.21

time (sec)

N/A 0.413 0.217 0.645 0.389 0.250 0.287 0.814 4.622

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 71 80 74 74 97 112 88 78

N.S.

1 1.03 1.16 1.07 1.07 1.41 1.62 1.28 1.13

time (sec)

N/A 0.434 0.162 0.603 0.374 0.253 0.434 0.923 5.579

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 89 96 93 92 99 144 171 102

N.S.

1 1.07 1.16 1.12 1.11 1.19 1.73 2.06 1.23

time (sec)

N/A 0.593 0.381 0.521 0.419 0.243 0.785 1.074 4.922

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 115 120 116 117 126 175 236 124

N.S.

1 1.11 1.15 1.12 1.12 1.21 1.68 2.27 1.19

time (sec)

N/A 0.759 1.241 0.528 0.331 0.247 1.047 1.343 5.503

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 141 118 137 135 152 206 301 145

N.S.

1 1.08 0.91 1.05 1.04 1.17 1.58 2.32 1.12

time (sec)

N/A 0.931 1.707 0.569 0.286 0.245 1.757 1.613 4.944

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 166 152 152 158 173 240 370 166

N.S.

1 1.06 0.97 0.97 1.01 1.10 1.53 2.36 1.06

time (sec)

N/A 1.142 1.040 0.585 0.291 0.250 2.277 1.963 5.505

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

181 193 190 181 171 170 277 3175 225

N.S.

1 1.07 1.05 1.00 0.94 0.94 1.53 17.54 1.24

time (sec)

N/A 1.103 1.240 0.356 0.291 0.247 0.199 5.024 4.956

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 128 122 158 149 148 214 2161 221

N.S.

1 1.00 0.95 1.23 1.16 1.16 1.67 16.88 1.73

time (sec)

N/A 0.685 0.760 0.297 0.302 0.251 0.175 2.849 5.236

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 130 123 130 124 123 187 1736 168

N.S.

1 1.00 0.95 1.00 0.95 0.95 1.44 13.35 1.29

time (sec)

N/A 0.674 1.794 0.307 0.369 0.244 0.140 2.214 5.025

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 103 105 103 113 100 131 991 167

N.S.

1 1.00 1.02 1.00 1.10 0.97 1.27 9.62 1.62

time (sec)

N/A 0.531 0.398 0.244 0.378 0.243 0.118 0.807 5.165

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 94 94 93 89 101 133 90 92

N.S.

1 1.02 1.02 1.01 0.97 1.10 1.45 0.98 1.00

time (sec)

N/A 0.632 0.445 0.532 0.426 0.259 0.424 1.231 5.251

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 99 94 83 88 114 131 102 94

N.S.

1 1.02 0.97 0.86 0.91 1.18 1.35 1.05 0.97

time (sec)

N/A 0.663 0.290 0.969 0.369 0.257 0.709 1.417 5.028

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 101 90 93 99 126 168 132 102

N.S.

1 1.02 0.91 0.94 1.00 1.27 1.70 1.33 1.03

time (sec)

N/A 0.682 0.332 0.552 0.314 0.249 1.019 1.671 5.494

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 123 125 123 122 131 185 246 127

N.S.

1 1.05 1.07 1.05 1.04 1.12 1.58 2.10 1.09

time (sec)

N/A 0.884 1.164 0.607 0.292 0.237 1.720 1.865 5.016

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 152 147 144 149 162 250 335 150

N.S.

1 1.08 1.04 1.02 1.06 1.15 1.77 2.38 1.06

time (sec)

N/A 1.098 2.266 0.694 0.294 0.243 2.269 1.731 5.411

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

170 176 154 173 170 186 264 416 174

N.S.

1 1.04 0.91 1.02 1.00 1.09 1.55 2.45 1.02

time (sec)

N/A 1.284 0.472 0.676 0.295 0.250 4.004 1.205 5.247

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

198 207 178 195 195 214 338 506 202

N.S.

1 1.05 0.90 0.98 0.98 1.08 1.71 2.56 1.02

time (sec)

N/A 1.508 0.557 0.641 0.401 0.253 5.386 1.344 5.643

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 182 167 138 146 181 947 158 165

N.S.

1 1.18 1.08 0.90 0.95 1.18 6.15 1.03 1.07

time (sec)

N/A 1.361 1.842 0.474 0.397 0.282 2.347 2.077 5.381

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 147 155 119 123 159 821 129 138

N.S.

1 1.18 1.24 0.95 0.98 1.27 6.57 1.03 1.10

time (sec)

N/A 1.025 0.681 0.477 0.670 0.258 1.073 1.518 5.456

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 113 107 92 99 134 677 100 109

N.S.

1 1.16 1.10 0.95 1.02 1.38 6.98 1.03 1.12

time (sec)

N/A 0.744 0.459 0.271 0.311 0.260 0.771 0.898 5.265

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 87 91 79 85 111 554 86 94

N.S.

1 1.10 1.15 1.00 1.08 1.41 7.01 1.09 1.19

time (sec)

N/A 0.537 0.468 0.434 0.320 0.271 0.576 0.628 5.440

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 75 78 56 72 89 405 73 78

N.S.

1 1.14 1.18 0.85 1.09 1.35 6.14 1.11 1.18

time (sec)

N/A 0.475 0.093 0.288 0.315 0.253 0.488 0.469 5.123

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 66 48 68 63 255 73 76

N.S.

1 1.00 1.43 1.04 1.48 1.37 5.54 1.59 1.65

time (sec)

N/A 0.309 0.250 0.277 0.298 0.243 0.419 0.364 5.598

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 76 48 69 62 241 74 73

N.S.

1 1.00 1.69 1.07 1.53 1.38 5.36 1.64 1.62

time (sec)

N/A 0.298 0.078 0.273 0.300 0.250 0.400 0.301 5.063

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 68 91 79 84 98 626 88 95

N.S.

1 1.03 1.38 1.20 1.27 1.48 9.48 1.33 1.44

time (sec)

N/A 0.398 0.188 0.576 0.464 0.249 0.824 0.443 5.586

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 90 96 94 100 140 1080 116 108

N.S.

1 1.11 1.19 1.16 1.23 1.73 13.33 1.43 1.33

time (sec)

N/A 0.594 0.486 0.529 0.380 0.258 1.473 0.500 5.130

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 123 106 114 122 180 1336 155 137

N.S.

1 1.15 0.99 1.07 1.14 1.68 12.49 1.45 1.28

time (sec)

N/A 0.824 0.690 0.608 0.658 0.258 2.087 0.584 5.535

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 155 131 137 145 207 1533 187 153

N.S.

1 1.17 0.98 1.03 1.09 1.56 11.53 1.41 1.15

time (sec)

N/A 1.135 1.653 0.563 0.307 0.267 2.782 0.706 4.720

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

239 247 242 168 206 387 3279 251 213

N.S.

1 1.03 1.01 0.70 0.86 1.62 13.72 1.05 0.89

time (sec)

N/A 1.744 6.254 0.362 0.311 0.296 2.539 2.159 5.831

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

197 209 182 142 180 340 2837 221 185

N.S.

1 1.06 0.92 0.72 0.91 1.73 14.40 1.12 0.94

time (sec)

N/A 1.339 3.040 0.418 0.340 0.299 1.543 1.606 4.866

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

155 172 158 125 164 288 2312 201 158

N.S.

1 1.11 1.02 0.81 1.06 1.86 14.92 1.30 1.02

time (sec)

N/A 0.955 1.113 0.328 0.322 0.271 1.119 1.016 5.655

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 138 112 114 155 226 1992 181 137

N.S.

1 1.21 0.98 1.00 1.36 1.98 17.47 1.59 1.20

time (sec)

N/A 0.664 3.075 0.342 0.363 0.274 0.876 0.658 4.764

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 99 183 101 137 153 1314 165 126

N.S.

1 1.12 2.08 1.15 1.56 1.74 14.93 1.88 1.43

time (sec)

N/A 0.512 0.546 0.369 0.405 0.251 0.776 0.568 5.448

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 93 181 104 139 157 1476 173 133

N.S.

1 1.13 2.21 1.27 1.70 1.91 18.00 2.11 1.62

time (sec)

N/A 0.474 0.498 0.368 0.482 0.249 0.733 0.430 4.581

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 93 106 97 131 154 1260 159 121

N.S.

1 1.13 1.29 1.18 1.60 1.88 15.37 1.94 1.48

time (sec)

N/A 0.453 1.308 0.336 0.404 0.257 0.729 0.331 5.246

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 132 154 126 164 235 2961 206 152

N.S.

1 1.23 1.44 1.18 1.53 2.20 27.67 1.93 1.42

time (sec)

N/A 0.722 0.750 0.490 0.295 0.273 1.618 0.605 4.915

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 180 136 140 200 323 4083 235 183

N.S.

1 1.20 0.91 0.93 1.33 2.15 27.22 1.57 1.22

time (sec)

N/A 1.030 0.797 0.764 0.302 0.275 2.036 0.715 5.727

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 225 146 166 240 386 5263 272 222

N.S.

1 1.19 0.77 0.88 1.27 2.04 27.85 1.44 1.17

time (sec)

N/A 1.371 1.338 0.754 0.292 0.288 2.605 0.866 4.929

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

283 309 243 203 308 628 0 345 284

N.S.

1 1.09 0.86 0.72 1.09 2.22 0.00 1.22 1.00

time (sec)

N/A 1.920 4.113 0.423 0.317 0.317 0.000 2.360 5.713

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

239 270 211 186 293 549 0 325 263

N.S.

1 1.13 0.88 0.78 1.23 2.30 0.00 1.36 1.10

time (sec)

N/A 1.505 2.561 0.577 0.409 0.294 0.000 1.798 4.889

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 216 150 169 279 481 0 304 240

N.S.

1 1.18 0.82 0.92 1.52 2.63 0.00 1.66 1.31

time (sec)

N/A 1.032 3.049 0.431 0.473 0.297 0.000 1.114 5.151

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 179 269 158 262 317 0 282 236

N.S.

1 1.20 1.81 1.06 1.76 2.13 0.00 1.89 1.58

time (sec)

N/A 0.822 5.797 0.306 0.687 0.254 0.000 0.820 5.203

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 150 200 150 256 326 0 263 224

N.S.

1 1.16 1.55 1.16 1.98 2.53 0.00 2.04 1.74

time (sec)

N/A 0.717 4.114 0.290 0.294 0.256 0.000 0.687 5.004

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 151 234 147 253 328 0 275 224

N.S.

1 1.17 1.81 1.14 1.96 2.54 0.00 2.13 1.74

time (sec)

N/A 0.678 4.108 0.362 0.302 0.248 0.000 0.551 4.761

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 144 127 140 248 321 0 265 215

N.S.

1 1.18 1.04 1.15 2.03 2.63 0.00 2.17 1.76

time (sec)

N/A 0.647 1.904 0.327 0.296 0.268 0.000 0.370 4.651

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

168 210 209 182 290 494 0 328 256

N.S.

1 1.25 1.24 1.08 1.73 2.94 0.00 1.95 1.52

time (sec)

N/A 1.125 4.558 0.667 0.312 0.285 0.000 0.870 5.694

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

211 257 178 201 349 585 0 357 293

N.S.

1 1.22 0.84 0.95 1.65 2.77 0.00 1.69 1.39

time (sec)

N/A 1.490 4.620 1.074 0.409 0.295 0.000 0.861 5.172

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

315 360 280 249 444 886 0 472 387

N.S.

1 1.14 0.89 0.79 1.41 2.81 0.00 1.50 1.23

time (sec)

N/A 2.106 2.461 0.575 0.462 0.320 0.000 2.470 5.546

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

256 303 213 234 433 784 0 451 373

N.S.

1 1.18 0.83 0.91 1.69 3.06 0.00 1.76 1.46

time (sec)

N/A 1.556 5.117 0.460 0.610 0.313 0.000 2.045 5.078

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

208 251 236 211 410 510 0 409 359

N.S.

1 1.21 1.13 1.01 1.97 2.45 0.00 1.97 1.73

time (sec)

N/A 1.229 2.771 0.428 0.311 0.281 0.000 1.234 5.479

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 233 387 206 402 526 0 400 359

N.S.

1 1.23 2.05 1.09 2.13 2.78 0.00 2.12 1.90

time (sec)

N/A 1.092 6.252 0.460 0.307 0.260 0.000 0.902 4.944

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 204 324 190 389 531 0 376 326

N.S.

1 1.21 1.92 1.12 2.30 3.14 0.00 2.22 1.93

time (sec)

N/A 0.990 6.229 0.432 0.352 0.271 0.000 0.758 5.343

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

172 205 319 191 394 528 0 401 355

N.S.

1 1.19 1.85 1.11 2.29 3.07 0.00 2.33 2.06

time (sec)

N/A 0.940 6.252 0.547 0.305 0.255 0.000 0.632 4.709

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 198 176 183 385 511 0 370 333

N.S.

1 1.20 1.07 1.11 2.33 3.10 0.00 2.24 2.02

time (sec)

N/A 0.921 3.266 0.457 0.431 0.267 0.000 0.405 5.229

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

226 281 243 246 444 793 0 476 385

N.S.

1 1.24 1.08 1.09 1.96 3.51 0.00 2.11 1.70

time (sec)

N/A 1.598 2.113 0.887 0.429 0.314 0.000 0.836 5.029

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

278 337 241 264 516 925 0 502 430

N.S.

1 1.21 0.87 0.95 1.86 3.33 0.00 1.81 1.55

time (sec)

N/A 2.021 3.711 1.467 0.618 0.326 0.000 1.062 7.096

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 65 35 39 46 46 40 49

N.S.

1 1.00 2.10 1.13 1.26 1.48 1.48 1.29 1.58

time (sec)

N/A 0.266 0.043 0.254 0.309 0.247 0.081 0.297 4.581

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 55 67 55 53 83 190 64 64

N.S.

1 1.10 1.34 1.10 1.06 1.66 3.80 1.28 1.28

time (sec)

N/A 0.379 0.292 0.273 0.314 0.249 0.271 0.318 5.359

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 79 84 69 73 120 442 74 84

N.S.

1 1.14 1.22 1.00 1.06 1.74 6.41 1.07 1.22

time (sec)

N/A 0.496 0.637 0.299 0.347 0.245 0.379 0.344 4.437

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 103 87 83 93 157 790 84 104

N.S.

1 1.17 0.99 0.94 1.06 1.78 8.98 0.95 1.18

time (sec)

N/A 0.603 1.160 0.350 0.309 0.248 0.466 0.374 5.451

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 65 35 39 46 46 40 49

N.S.

1 1.00 2.10 1.13 1.26 1.48 1.48 1.29 1.58

time (sec)

N/A 0.260 0.045 0.242 0.413 0.245 0.081 0.295 4.543

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 55 67 55 53 83 190 64 64

N.S.

1 1.10 1.34 1.10 1.06 1.66 3.80 1.28 1.28

time (sec)

N/A 0.370 0.277 0.311 0.396 0.238 0.273 0.311 5.154

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