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2.2.5 Integrals 401 to 500

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 401

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 131 0 104 113 128 271 111

N.S.

1 1.00 0.98 0.00 0.78 0.84 0.96 2.02 0.83

time (sec)

N/A 0.067 0.065 0.013 0.284 0.392 3.825 5.634 0.421

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 107 0 84 88 100 185 85

N.S.

1 1.00 1.05 0.00 0.82 0.86 0.98 1.81 0.83

time (sec)

N/A 0.049 0.026 0.014 0.281 0.378 1.902 4.158 0.409

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 60 53 59 60 66 107 52

N.S.

1 1.00 1.00 0.88 0.98 1.00 1.10 1.78 0.87

time (sec)

N/A 0.029 0.023 0.042 0.326 0.398 0.685 4.827 0.431

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 53 0 122 0 0 0 -1

N.S.

1 1.00 1.04 0.00 2.39 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.035 0.005 0.025 0.408 0.000 0.000 0.000 0.000

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 67 0 66 64 410 187 58

N.S.

1 1.00 0.96 0.00 0.94 0.91 5.86 2.67 0.83

time (sec)

N/A 0.039 0.035 0.012 0.271 0.392 14.690 3.943 0.802

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

109 109 104 0 84 95 493 366 83

N.S.

1 1.00 0.95 0.00 0.77 0.87 4.52 3.36 0.76

time (sec)

N/A 0.052 0.029 0.014 0.290 0.366 107.565 4.836 0.634

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 132 0 104 120 0 542 110

N.S.

1 1.00 0.94 0.00 0.74 0.85 0.00 3.84 0.78

time (sec)

N/A 0.066 0.093 0.014 0.274 0.374 0.000 4.914 0.756

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

480 480 341 0 317 451 0 956 434

N.S.

1 1.00 0.71 0.00 0.66 0.94 0.00 1.99 0.90

time (sec)

N/A 0.334 0.244 0.025 0.286 0.378 0.000 4.053 1.782

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

342 342 269 0 256 333 0 642 420

N.S.

1 1.00 0.79 0.00 0.75 0.97 0.00 1.88 1.23

time (sec)

N/A 0.243 0.165 0.031 0.294 0.385 0.000 4.238 0.563

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

195 195 150 0 184 213 0 361 186

N.S.

1 1.00 0.77 0.00 0.94 1.09 0.00 1.85 0.95

time (sec)

N/A 0.126 0.059 0.019 0.282 0.398 0.000 5.500 0.474

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 195 0 0 0 0 0 -1

N.S.

1 1.00 2.10 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.088 0.076 0.025 0.000 0.000 0.000 0.000 0.000

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

155 155 188 0 0 0 0 0 -1

N.S.

1 1.00 1.21 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.192 0.120 0.020 0.000 0.000 0.000 0.000 0.000

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

293 293 353 0 0 0 0 0 -1

N.S.

1 1.00 1.20 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.397 0.229 0.035 0.000 0.000 0.000 0.000 0.000

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

408 408 538 0 0 0 0 0 -1

N.S.

1 1.00 1.32 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.618 0.201 0.027 0.000 0.000 0.000 0.000 0.000

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

907 907 661 0 655 1098 0 2223 976

N.S.

1 1.00 0.73 0.00 0.72 1.21 0.00 2.45 1.08

time (sec)

N/A 0.666 0.449 0.043 0.323 0.436 0.000 4.968 8.180

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

595 595 517 0 537 798 0 1483 840

N.S.

1 1.00 0.87 0.00 0.90 1.34 0.00 2.49 1.41

time (sec)

N/A 0.404 0.321 0.037 0.314 0.445 0.000 4.574 0.771

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

284 284 241 0 394 496 0 763 350

N.S.

1 1.00 0.85 0.00 1.39 1.75 0.00 2.69 1.23

time (sec)

N/A 0.168 0.144 0.011 0.302 0.419 0.000 2.593 0.602

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 333 0 0 0 0 0 -1

N.S.

1 1.00 2.47 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.135 0.093 0.038 0.000 0.000 0.000 0.000 0.000

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

263 263 536 0 0 0 0 0 -1

N.S.

1 1.00 2.04 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.326 0.542 0.040 0.000 0.000 0.000 0.000 0.000

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

573 573 841 0 0 0 0 0 -1

N.S.

1 1.00 1.47 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.853 0.772 0.048 0.000 0.000 0.000 0.000 0.000

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 158 0 115 176 162 272 140

N.S.

1 1.00 0.92 0.00 0.67 1.03 0.95 1.59 0.82

time (sec)

N/A 0.085 0.096 0.014 0.289 0.383 59.311 4.712 0.977

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 130 0 95 152 134 236 106

N.S.

1 1.00 0.94 0.00 0.68 1.09 0.96 1.70 0.76

time (sec)

N/A 0.068 0.063 0.022 0.300 0.381 21.147 3.093 0.694

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

107 107 102 0 75 127 88 81 86

N.S.

1 1.00 0.95 0.00 0.70 1.19 0.82 0.76 0.80

time (sec)

N/A 0.048 0.023 0.016 0.312 0.391 7.493 4.255 0.831

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

53 53 62 94 52 93 76 56 44

N.S.

1 1.00 1.17 1.77 0.98 1.75 1.43 1.06 0.83

time (sec)

N/A 0.026 0.025 0.054 0.287 0.388 3.458 4.148 0.380

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 53 0 127 0 0 0 -1

N.S.

1 1.00 1.04 0.00 2.49 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.034 0.004 0.026 0.690 0.000 0.000 0.000 0.000

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 68 63 76 67 360 162 60

N.S.

1 1.00 1.05 0.97 1.17 1.03 5.54 2.49 0.92

time (sec)

N/A 0.035 0.025 0.028 0.285 0.360 51.831 3.446 0.425

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 109 0 94 91 0 349 87

N.S.

1 1.00 1.05 0.00 0.90 0.88 0.00 3.36 0.84

time (sec)

N/A 0.050 0.050 0.017 0.276 0.379 0.000 3.320 0.417

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 133 0 114 116 0 535 113

N.S.

1 1.00 0.98 0.00 0.84 0.85 0.00 3.93 0.83

time (sec)

N/A 0.063 0.062 0.014 0.294 0.428 0.000 4.291 0.442

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

404 404 379 0 0 0 0 0 -1

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.621 0.724 0.025 0.000 0.000 0.000 0.000 0.000

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

288 288 307 0 0 0 0 0 -1

N.S.

1 1.00 1.07 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.369 0.370 0.030 0.000 0.000 0.000 0.000 0.000

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 170 0 0 0 0 0 -1

N.S.

1 1.00 1.12 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.195 0.093 0.016 0.000 0.000 0.000 0.000 0.000

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 386 0 0 0 0 0 -1

N.S.

1 1.00 4.15 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.084 0.225 0.026 0.000 0.000 0.000 0.000 0.000

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

195 195 298 0 252 227 0 503 193

N.S.

1 1.00 1.53 0.00 1.29 1.16 0.00 2.58 0.99

time (sec)

N/A 0.128 0.213 0.028 0.280 0.373 0.000 5.204 0.474

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

341 341 473 0 319 342 0 1071 424

N.S.

1 1.00 1.39 0.00 0.94 1.00 0.00 3.14 1.24

time (sec)

N/A 0.246 0.246 0.030 0.307 0.373 0.000 4.361 0.559

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

480 480 692 0 379 460 0 1639 440

N.S.

1 1.00 1.44 0.00 0.79 0.96 0.00 3.41 0.92

time (sec)

N/A 0.324 0.232 0.030 0.327 0.384 0.000 3.755 1.772

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

569 569 777 0 0 0 0 0 -1

N.S.

1 1.00 1.37 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.868 0.608 0.058 0.000 0.000 0.000 0.000 0.000

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

260 260 476 0 0 0 0 0 -1

N.S.

1 1.00 1.83 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.341 0.431 0.040 0.000 0.000 0.000 0.000 0.000

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 532 0 0 0 0 0 -1

N.S.

1 1.00 3.94 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.128 0.207 0.059 0.000 0.000 0.000 0.000 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

285 285 558 0 579 519 0 1127 357

N.S.

1 1.00 1.96 0.00 2.03 1.82 0.00 3.95 1.25

time (sec)

N/A 0.185 0.372 0.060 0.335 0.401 0.000 4.677 0.625

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

595 595 766 0 731 815 0 2389 846

N.S.

1 1.00 1.29 0.00 1.23 1.37 0.00 4.02 1.42

time (sec)

N/A 0.413 0.635 0.065 0.320 0.434 0.000 4.605 0.800

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

907 907 950 0 851 1115 0 3651 989

N.S.

1 1.00 1.05 0.00 0.94 1.23 0.00 4.03 1.09

time (sec)

N/A 0.637 1.030 0.359 0.335 0.425 0.000 6.086 8.179

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

234 234 219 0 164 186 216 529 189

N.S.

1 1.00 0.94 0.00 0.70 0.79 0.92 2.26 0.81

time (sec)

N/A 0.121 0.163 0.012 0.278 0.454 44.141 3.652 0.652

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

185 185 176 0 134 149 173 400 150

N.S.

1 1.00 0.95 0.00 0.72 0.81 0.94 2.16 0.81

time (sec)

N/A 0.090 0.100 0.015 0.272 0.380 9.844 5.900 0.506

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 133 0 104 114 131 271 111

N.S.

1 1.00 0.98 0.00 0.76 0.84 0.96 1.99 0.82

time (sec)

N/A 0.063 0.071 0.012 0.285 0.399 2.698 4.374 0.416

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 77 66 70 71 82 135 65

N.S.

1 1.00 1.00 0.86 0.91 0.92 1.06 1.75 0.84

time (sec)

N/A 0.039 0.033 0.025 0.269 0.376 0.746 4.377 0.342

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 53 0 183 0 0 0 -1

N.S.

1 1.00 1.04 0.00 3.59 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.034 0.004 0.011 0.435 0.000 0.000 0.000 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 84 0 77 79 450 280 74

N.S.

1 1.00 0.97 0.00 0.89 0.91 5.17 3.22 0.85

time (sec)

N/A 0.046 0.028 0.022 0.275 0.496 106.562 4.200 0.592

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

143 143 134 0 104 120 0 542 109

N.S.

1 1.00 0.94 0.00 0.73 0.84 0.00 3.79 0.76

time (sec)

N/A 0.062 0.100 0.011 0.275 0.373 0.000 3.933 0.657

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

192 192 177 0 135 156 0 808 154

N.S.

1 1.00 0.92 0.00 0.70 0.81 0.00 4.21 0.80

time (sec)

N/A 0.085 0.137 0.024 0.278 0.393 0.000 6.250 0.612

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

680 680 458 0 407 623 0 1427 608

N.S.

1 1.00 0.67 0.00 0.60 0.92 0.00 2.10 0.89

time (sec)

N/A 0.465 0.378 0.018 0.293 0.426 0.000 3.773 4.703

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

480 480 347 0 316 452 0 956 431

N.S.

1 1.00 0.72 0.00 0.66 0.94 0.00 1.99 0.90

time (sec)

N/A 0.311 0.255 0.023 0.307 0.402 0.000 3.286 1.720

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

267 267 249 0 217 272 0 479 290

N.S.

1 1.00 0.93 0.00 0.81 1.02 0.00 1.79 1.09

time (sec)

N/A 0.199 0.102 0.011 0.282 0.371 0.000 4.153 0.511

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 195 0 0 0 0 0 -1

N.S.

1 1.00 2.10 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.090 0.066 0.021 0.000 0.000 0.000 0.000 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

231 231 274 0 0 0 0 0 -1

N.S.

1 1.00 1.19 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.288 0.163 0.024 0.000 0.000 0.000 0.000 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

405 405 533 0 0 0 0 0 -1

N.S.

1 1.00 1.32 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.627 0.195 0.017 0.000 0.000 0.000 0.000 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

1835 1835 1117 0 1017 1985 0 4443 1802

N.S.

1 1.00 0.61 0.00 0.55 1.08 0.00 2.42 0.98

time (sec)

N/A 1.434 1.049 0.039 0.318 0.490 0.000 4.077 8.472

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

1357 1357 895 0 835 1544 0 3333 1386

N.S.

1 1.00 0.66 0.00 0.62 1.14 0.00 2.46 1.02

time (sec)

N/A 1.019 0.708 0.028 0.311 0.455 0.000 3.780 8.254

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

907 907 673 0 657 1100 0 2223 979

N.S.

1 1.00 0.74 0.00 0.72 1.21 0.00 2.45 1.08

time (sec)

N/A 0.633 0.497 0.048 0.296 0.412 0.000 3.033 8.059

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

438 438 463 0 459 646 0 1105 558

N.S.

1 1.00 1.06 0.00 1.05 1.47 0.00 2.52 1.27

time (sec)

N/A 0.288 0.255 0.014 0.307 0.404 0.000 3.350 0.688

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 333 0 0 0 0 0 -1

N.S.

1 1.00 2.47 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.126 0.104 0.046 0.000 0.000 0.000 0.000 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

439 439 733 0 0 0 0 0 -1

N.S.

1 1.00 1.67 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.551 0.562 0.048 0.000 0.000 0.000 0.000 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

765 765 1074 0 0 0 0 0 -1

N.S.

1 1.00 1.40 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.732 1.151 0.050 0.000 0.000 0.000 0.000 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 135 0 106 121 0 261 113

N.S.

1 1.00 0.98 0.00 0.77 0.88 0.00 1.89 0.82

time (sec)

N/A 0.071 0.085 0.015 0.285 0.378 0.000 4.407 0.446

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-1) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

130 130 135 0 95 307 0 104 -1

N.S.

1 1.00 1.04 0.00 0.73 2.36 0.00 0.80 -0.01

time (sec)

N/A 0.057 0.072 0.013 0.512 0.420 0.000 3.088 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 94 0 76 77 95 82 74

N.S.

1 1.00 1.06 0.00 0.85 0.87 1.07 0.92 0.83

time (sec)

N/A 0.043 0.023 0.022 0.269 0.404 54.921 4.971 0.390

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 72 62 61 218 124 68 56

N.S.

1 1.00 1.00 0.86 0.85 3.03 1.72 0.94 0.78

time (sec)

N/A 0.037 0.022 0.028 0.506 0.383 2.403 4.112 0.394

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 55 0 128 0 0 0 -1

N.S.

1 1.00 1.00 0.00 2.33 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.035 0.011 0.017 0.409 0.000 0.000 0.000 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F A A F(-1) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 59 0 56 210 0 61 -1

N.S.

1 1.00 0.87 0.00 0.82 3.09 0.00 0.90 -0.01

time (sec)

N/A 0.027 0.015 0.015 0.501 0.384 0.000 4.897 0.000

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 91 0 79 84 0 95 74

N.S.

1 1.00 0.97 0.00 0.84 0.89 0.00 1.01 0.79

time (sec)

N/A 0.047 0.027 0.024 0.270 0.366 0.000 5.206 0.610

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F A A F(-2) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 65 0 88 303 0 94 -1

N.S.

1 1.00 0.53 0.00 0.72 2.46 0.00 0.76 -0.01

time (sec)

N/A 0.052 0.012 0.015 0.505 0.395 0.000 4.921 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

482 482 328 0 323 473 0 933 440

N.S.

1 1.00 0.68 0.00 0.67 0.98 0.00 1.94 0.91

time (sec)

N/A 0.329 0.261 0.022 0.318 0.437 0.000 4.442 1.754

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

275 275 239 0 232 286 0 316 299

N.S.

1 1.00 0.87 0.00 0.84 1.04 0.00 1.15 1.09

time (sec)

N/A 0.209 0.110 0.030 0.297 0.405 0.000 4.878 0.529

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F A F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 199 0 156 0 0 0 -1

N.S.

1 1.00 2.09 0.00 1.64 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.092 0.071 0.027 0.341 0.000 0.000 0.000 0.000

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

238 238 264 0 0 0 0 0 -1

N.S.

1 1.00 1.11 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.281 0.207 0.029 0.000 0.000 0.000 0.000 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

412 412 539 0 0 0 0 0 -1

N.S.

1 1.00 1.31 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.609 0.196 0.024 0.000 0.000 0.000 0.000 0.000

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

547 547 438 0 0 0 0 0 -1

N.S.

1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.503 0.331 0.024 0.000 0.000 0.000 0.000 0.000

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

364 364 319 0 0 0 0 0 -1

N.S.

1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.305 0.153 0.020 0.000 0.000 0.000 0.000 0.000

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

298 298 247 0 0 0 0 0 -1

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.267 0.132 0.026 0.000 0.000 0.000 0.000 0.000

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F F F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

476 476 473 0 0 0 0 0 -1

N.S.

1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.406 0.372 0.018 0.000 0.000 0.000 0.000 0.000

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

640 640 678 0 0 0 0 0 -1

N.S.

1 1.00 1.06 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.627 0.747 0.026 0.000 0.000 0.000 0.000 0.000

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

913 913 598 0 669 1142 0 2174 992

N.S.

1 1.00 0.65 0.00 0.73 1.25 0.00 2.38 1.09

time (sec)

N/A 0.672 0.721 0.030 0.310 0.454 0.000 4.297 8.104

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

449 449 428 0 489 671 0 778 575

N.S.

1 1.00 0.95 0.00 1.09 1.49 0.00 1.73 1.28

time (sec)

N/A 0.297 0.293 0.045 0.309 0.459 0.000 4.914 0.723

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 339 0 297 0 0 0 -1

N.S.

1 1.00 2.44 0.00 2.14 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.134 0.119 0.052 0.383 0.000 0.000 0.000 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

451 451 764 0 690 0 0 0 -1

N.S.

1 1.00 1.69 0.00 1.53 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.569 0.552 0.036 0.409 0.000 0.000 0.000 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

794 0 3146 0 0 0 0 0 -1

N.S.

1 0.00 3.96 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.940 8.185 0.046 0.000 0.000 0.000 0.000 0.000

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

486 0 598 0 0 0 0 0 -1

N.S.

1 0.00 1.23 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.708 0.897 0.013 0.000 0.000 0.000 0.000 0.000

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

319 0 1028 0 0 0 0 0 -1

N.S.

1 0.00 3.22 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.326 5.015 0.053 0.000 0.000 0.000 0.000 0.000

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

632 0 803 0 0 0 0 0 -1

N.S.

1 0.00 1.27 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.198 2.528 0.051 0.000 0.000 0.000 0.000 0.000

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

239 239 218 0 155 225 0 161 191

N.S.

1 1.00 0.91 0.00 0.65 0.94 0.00 0.67 0.80

time (sec)

N/A 0.118 0.162 0.013 0.285 0.379 0.000 4.401 0.796

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

190 190 175 0 125 188 180 131 153

N.S.

1 1.00 0.92 0.00 0.66 0.99 0.95 0.69 0.81

time (sec)

N/A 0.087 0.093 0.015 0.290 0.376 62.179 4.729 0.677

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 132 0 95 152 138 101 112

N.S.

1 1.00 0.94 0.00 0.67 1.08 0.98 0.72 0.79

time (sec)

N/A 0.063 0.068 0.013 0.289 0.382 13.524 4.464 0.792

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 79 115 62 109 92 66 59

N.S.

1 1.00 1.13 1.64 0.89 1.56 1.31 0.94 0.84

time (sec)

N/A 0.033 0.035 0.049 0.273 0.386 3.670 4.642 0.470

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 53 0 183 0 0 0 -1

N.S.

1 1.00 1.04 0.00 3.59 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.034 0.004 0.034 0.730 0.000 0.000 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 85 0 86 94 398 95 73

N.S.

1 1.00 1.04 0.00 1.05 1.15 4.85 1.16 0.89

time (sec)

N/A 0.047 0.028 0.015 0.280 0.350 237.547 3.987 0.430

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 135 0 114 149 0 123 113

N.S.

1 1.00 0.98 0.00 0.83 1.08 0.00 0.89 0.82

time (sec)

N/A 0.066 0.066 0.024 0.322 0.391 0.000 4.582 0.464

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

187 187 178 0 144 196 0 153 152

N.S.

1 1.00 0.95 0.00 0.77 1.05 0.00 0.82 0.81

time (sec)

N/A 0.088 0.111 0.014 0.291 0.394 0.000 3.428 0.526

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

572 572 495 0 0 0 0 0 -1

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.078 1.064 0.029 0.000 0.000 0.000 0.000 0.000

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

400 400 383 0 0 0 0 0 -1

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.623 0.642 0.040 0.000 0.000 0.000 0.000 0.000

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

227 227 336 0 0 0 0 0 -1

N.S.

1 1.00 1.48 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.304 0.271 0.017 0.000 0.000 0.000 0.000 0.000

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 389 0 0 0 0 0 -1

N.S.

1 1.00 4.18 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.089 0.137 0.030 0.000 0.000 0.000 0.000 0.000

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