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

verified

N/A N/A No N/A TBD TBD TBD TBD TBD

size

1443 0 5147 0 0 18801 0 0 0

N.S.

1 0.00 3.57 0.00 0.00 13.03 0.00 0.00 0.00

time (sec)

N/A 0.000 11.067 0.000 0.000 0.529 0.000 0.000 0.000

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1049 0 1811 0 0 11318 0 0 0

N.S.

1 0.00 1.73 0.00 0.00 10.79 0.00 0.00 0.00

time (sec)

N/A 0.000 9.732 0.000 0.000 0.415 0.000 0.000 0.000

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

641 0 2704 1363 0 5548 0 0 0

N.S.

1 0.00 4.22 2.13 0.00 8.66 0.00 0.00 0.00

time (sec)

N/A 0.000 8.518 187.964 0.000 0.334 0.000 0.000 0.000

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 125 123 144 300 1660 0 258 307

N.S.

1 0.89 0.87 1.02 2.13 11.77 0.00 1.83 2.18

time (sec)

N/A 0.374 0.265 99.050 0.223 0.282 0.000 0.338 1.470

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

36 36 38 36 551 44 0 38 38

N.S.

1 1.00 1.06 1.00 15.31 1.22 0.00 1.06 1.06

time (sec)

N/A 0.332 28.684 0.799 0.559 0.244 0.000 0.576 1.292

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1519 0 4239 0 0 4522 0 0 0

N.S.

1 0.00 2.79 0.00 0.00 2.98 0.00 0.00 0.00

time (sec)

N/A 0.000 11.355 0.000 0.000 0.365 0.000 0.000 0.000

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1067 0 3418 0 0 2775 0 0 0

N.S.

1 0.00 3.20 0.00 0.00 2.60 0.00 0.00 0.00

time (sec)

N/A 0.000 10.878 0.000 0.000 0.342 0.000 0.000 0.000

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

631 570 637 4066 0 1410 0 0 0

N.S.

1 0.90 1.01 6.44 0.00 2.23 0.00 0.00 0.00

time (sec)

N/A 3.597 8.635 3.147 0.000 0.312 0.000 0.000 0.000

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 97 91 169 147 288 0 145 249

N.S.

1 1.09 1.02 1.90 1.65 3.24 0.00 1.63 2.80

time (sec)

N/A 0.405 0.147 1.602 0.314 0.270 0.000 0.313 2.529

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 34 36 34 322 42 31 0 36

N.S.

1 1.00 1.06 1.00 9.47 1.24 0.91 0.00 1.06

time (sec)

N/A 0.289 39.989 1.193 0.514 0.317 2.043 0.000 2.219

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1294 0 1111 0 0 7331 0 0 0

N.S.

1 0.00 0.86 0.00 0.00 5.67 0.00 0.00 0.00

time (sec)

N/A 0.000 5.130 0.000 0.000 0.403 0.000 0.000 0.000

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

904 0 665 0 0 4196 0 0 0

N.S.

1 0.00 0.74 0.00 0.00 4.64 0.00 0.00 0.00

time (sec)

N/A 0.000 2.924 0.000 0.000 0.366 0.000 0.000 0.000

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

454 0 358 1897 0 1571 0 0 0

N.S.

1 0.00 0.79 4.18 0.00 3.46 0.00 0.00 0.00

time (sec)

N/A 0.000 5.672 2.356 0.000 0.306 0.000 0.000 0.000

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

121 127 96 125 141 459 0 128 468

N.S.

1 1.05 0.79 1.03 1.17 3.79 0.00 1.06 3.87

time (sec)

N/A 0.692 0.813 1.099 0.306 0.260 0.000 0.328 2.868

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 34 36 34 411 42 31 0 36

N.S.

1 1.00 1.06 1.00 12.09 1.24 0.91 0.00 1.06

time (sec)

N/A 0.291 37.650 0.577 0.498 0.307 2.111 0.000 3.394

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A N/A No N/A TBD TBD TBD TBD TBD

size

1479 0 3368 0 0 10574 0 0 0

N.S.

1 0.00 2.28 0.00 0.00 7.15 0.00 0.00 0.00

time (sec)

N/A 0.000 11.934 0.000 0.000 0.457 0.000 0.000 0.000

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

894 0 834 2284 0 4729 0 0 0

N.S.

1 0.00 0.93 2.55 0.00 5.29 0.00 0.00 0.00

time (sec)

N/A 0.000 9.102 2.710 0.000 0.372 0.000 0.000 0.000

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 146 152 210 217 896 0 279 381

N.S.

1 1.22 1.27 1.75 1.81 7.47 0.00 2.32 3.18

time (sec)

N/A 0.382 0.352 1.428 0.306 0.283 0.000 0.340 3.221

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

28 28 30 28 1095 36 24 0 30

N.S.

1 1.00 1.07 1.00 39.11 1.29 0.86 0.00 1.07

time (sec)

N/A 0.252 60.757 0.661 1.936 4.200 1.759 0.000 3.818

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

451 532 1914 0 0 1228 0 0 0

N.S.

1 1.18 4.24 0.00 0.00 2.72 0.00 0.00 0.00

time (sec)

N/A 2.304 9.793 0.000 0.000 0.289 0.000 0.000 0.000

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

325 397 1296 0 0 813 0 0 0

N.S.

1 1.22 3.99 0.00 0.00 2.50 0.00 0.00 0.00

time (sec)

N/A 1.844 5.700 0.000 0.000 0.271 0.000 0.000 0.000

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

205 263 431 451 0 476 0 0 0

N.S.

1 1.28 2.10 2.20 0.00 2.32 0.00 0.00 0.00

time (sec)

N/A 1.138 2.244 1.930 0.000 0.305 0.000 0.000 0.000

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 28 53 75 67 0 61 254

N.S.

1 1.00 0.82 1.56 2.21 1.97 0.00 1.79 7.47

time (sec)

N/A 0.220 0.026 1.126 0.227 0.273 0.000 0.295 0.450

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

26 26 28 26 28 34 22 28 28

N.S.

1 1.00 1.08 1.00 1.08 1.31 0.85 1.08 1.08

time (sec)

N/A 0.224 10.619 0.796 0.454 0.285 2.559 0.641 1.114

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

638 0 781 0 0 1470 0 0 0

N.S.

1 0.00 1.22 0.00 0.00 2.30 0.00 0.00 0.00

time (sec)

N/A 0.000 1.086 0.000 0.000 0.323 0.000 0.000 0.000

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

462 0 490 0 0 992 0 0 0

N.S.

1 0.00 1.06 0.00 0.00 2.15 0.00 0.00 0.00

time (sec)

N/A 0.000 0.713 0.000 0.000 0.283 0.000 0.000 0.000

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

286 368 298 970 0 598 0 0 0

N.S.

1 1.29 1.04 3.39 0.00 2.09 0.00 0.00 0.00

time (sec)

N/A 2.185 1.359 1.953 0.000 0.310 0.000 0.000 0.000

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

71 80 94 109 126 209 0 113 384

N.S.

1 1.13 1.32 1.54 1.77 2.94 0.00 1.59 5.41

time (sec)

N/A 0.558 0.315 1.542 0.279 0.292 0.000 0.321 1.208

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 32 34 32 167 40 29 0 34

N.S.

1 1.00 1.06 1.00 5.22 1.25 0.91 0.00 1.06

time (sec)

N/A 0.256 8.266 0.560 0.400 0.282 2.904 0.000 1.312

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

656 0 3089 0 0 3344 0 0 0

N.S.

1 0.00 4.71 0.00 0.00 5.10 0.00 0.00 0.00

time (sec)

N/A 0.000 10.255 0.000 0.000 0.340 0.000 0.000 0.000

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

486 0 1462 0 0 2101 0 0 0

N.S.

1 0.00 3.01 0.00 0.00 4.32 0.00 0.00 0.00

time (sec)

N/A 0.000 8.327 0.000 0.000 0.321 0.000 0.000 0.000

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

322 422 487 932 0 1108 0 0 0

N.S.

1 1.31 1.51 2.89 0.00 3.44 0.00 0.00 0.00

time (sec)

N/A 2.910 3.950 3.235 0.000 0.290 0.000 0.000 0.000

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 55 48 133 130 203 0 94 360

N.S.

1 0.96 0.84 2.33 2.28 3.56 0.00 1.65 6.32

time (sec)

N/A 0.308 0.068 2.345 0.232 0.266 0.000 0.301 1.507

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 34 36 34 249 42 31 0 36

N.S.

1 1.00 1.06 1.00 7.32 1.24 0.91 0.00 1.06

time (sec)

N/A 0.280 44.853 1.041 0.548 0.275 5.532 0.000 2.321

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1049 910 3862 0 0 2448 0 0 0

N.S.

1 0.87 3.68 0.00 0.00 2.33 0.00 0.00 0.00

time (sec)

N/A 4.034 12.012 0.000 0.000 0.357 0.000 0.000 0.000

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

734 651 3730 0 0 1535 0 0 0

N.S.

1 0.89 5.08 0.00 0.00 2.09 0.00 0.00 0.00

time (sec)

N/A 3.125 13.223 0.000 0.000 0.315 0.000 0.000 0.000

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

439 402 788 1065 0 808 0 0 0

N.S.

1 0.92 1.79 2.43 0.00 1.84 0.00 0.00 0.00

time (sec)

N/A 1.939 8.367 3.666 0.000 0.306 0.000 0.000 0.000

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 104 92 108 138 134 0 147 0

N.S.

1 1.16 1.02 1.20 1.53 1.49 0.00 1.63 0.00

time (sec)

N/A 0.365 0.102 1.707 0.316 0.304 0.000 0.291 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

32 32 34 32 34 40 29 34 38

N.S.

1 1.00 1.06 1.00 1.06 1.25 0.91 1.06 1.19

time (sec)

N/A 0.258 19.563 0.942 0.557 0.832 67.651 6.619 1.637

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1164 991 1441 0 0 9707 0 0 0

N.S.

1 0.85 1.24 0.00 0.00 8.34 0.00 0.00 0.00

time (sec)

N/A 4.926 9.074 0.000 0.000 0.508 0.000 0.000 0.000

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

795 695 928 0 0 5562 0 0 0

N.S.

1 0.87 1.17 0.00 0.00 7.00 0.00 0.00 0.00

time (sec)

N/A 3.744 8.304 0.000 0.000 0.397 0.000 0.000 0.000

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

442 388 428 1815 0 2176 0 0 0

N.S.

1 0.88 0.97 4.11 0.00 4.92 0.00 0.00 0.00

time (sec)

N/A 2.180 7.942 10.704 0.000 0.324 0.000 0.000 0.000

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 126 233 106 168 581 0 146 668

N.S.

1 1.12 2.06 0.94 1.49 5.14 0.00 1.29 5.91

time (sec)

N/A 0.489 1.109 4.800 0.313 0.329 0.000 0.312 6.868

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 34 36 34 463 42 0 0 38

N.S.

1 1.00 1.06 1.00 13.62 1.24 0.00 0.00 1.12

time (sec)

N/A 0.273 49.809 0.806 0.645 0.569 0.000 0.000 5.660

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

1185 993 4072 0 0 16670 0 0 0

N.S.

1 0.84 3.44 0.00 0.00 14.07 0.00 0.00 0.00

time (sec)

N/A 4.521 13.163 0.000 0.000 0.563 0.000 0.000 0.000

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

746 627 1080 2580 0 7645 0 0 0

N.S.

1 0.84 1.45 3.46 0.00 10.25 0.00 0.00 0.00

time (sec)

N/A 2.603 10.908 30.793 0.000 0.491 0.000 0.000 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

160 181 196 230 265 1279 0 343 0

N.S.

1 1.13 1.22 1.44 1.66 7.99 0.00 2.14 0.00

time (sec)

N/A 0.441 0.538 15.007 0.329 0.442 0.000 0.289 0.000

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 34 36 34 1214 42 0 0 38

N.S.

1 1.00 1.06 1.00 35.71 1.24 0.00 0.00 1.12

time (sec)

N/A 0.278 102.423 0.910 2.430 19.432 0.000 0.000 12.251

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

601 681 2598 0 0 4313 0 0 0

N.S.

1 1.13 4.32 0.00 0.00 7.18 0.00 0.00 0.00

time (sec)

N/A 3.979 11.106 0.000 0.000 0.356 0.000 0.000 0.000

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

419 492 1735 0 0 2528 0 0 0

N.S.

1 1.17 4.14 0.00 0.00 6.03 0.00 0.00 0.00

time (sec)

N/A 2.706 10.383 0.000 0.000 0.316 0.000 0.000 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

243 304 621 528 0 1221 0 0 0

N.S.

1 1.25 2.56 2.17 0.00 5.02 0.00 0.00 0.00

time (sec)

N/A 1.599 8.150 2.331 0.000 0.288 0.000 0.000 0.000

Problem 452

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

50 49 50 35 110 211 0 110 409

N.S.

1 0.98 1.00 0.70 2.20 4.22 0.00 2.20 8.18

time (sec)

N/A 0.275 0.039 0.674 0.212 0.283 0.000 0.313 2.066

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 32 34 32 316 40 29 0 36

N.S.

1 1.00 1.06 1.00 9.88 1.25 0.91 0.00 1.12

time (sec)

N/A 0.243 76.912 0.692 0.521 0.314 5.559 0.000 1.823

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

721 0 1490 0 0 4612 0 0 0

N.S.

1 0.00 2.07 0.00 0.00 6.40 0.00 0.00 0.00

time (sec)

N/A 0.000 7.174 0.000 0.000 0.369 0.000 0.000 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

517 0 917 0 0 2729 0 0 0

N.S.

1 0.00 1.77 0.00 0.00 5.28 0.00 0.00 0.00

time (sec)

N/A 0.000 6.907 0.000 0.000 0.333 0.000 0.000 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

294 0 347 1017 0 1338 0 0 0

N.S.

1 0.00 1.18 3.46 0.00 4.55 0.00 0.00 0.00

time (sec)

N/A 0.000 3.279 2.442 0.000 0.292 0.000 0.000 0.000

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

77 88 112 105 134 360 0 120 380

N.S.

1 1.14 1.45 1.36 1.74 4.68 0.00 1.56 4.94

time (sec)

N/A 0.663 0.537 1.285 0.286 0.268 0.000 0.309 1.474

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

28 28 30 28 311 36 24 0 30

N.S.

1 1.00 1.07 1.00 11.11 1.29 0.86 0.00 1.07

time (sec)

N/A 0.253 67.271 0.685 0.532 0.301 2.524 0.000 1.357

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

718 0 2696 0 0 5829 0 0 0

N.S.

1 0.00 3.75 0.00 0.00 8.12 0.00 0.00 0.00

time (sec)

N/A 0.000 10.565 0.000 0.000 0.361 0.000 0.000 0.000

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

518 0 1806 0 0 3506 0 0 0

N.S.

1 0.00 3.49 0.00 0.00 6.77 0.00 0.00 0.00

time (sec)

N/A 0.000 10.065 0.000 0.000 0.321 0.000 0.000 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

324 0 504 938 0 1735 0 0 0

N.S.

1 0.00 1.56 2.90 0.00 5.35 0.00 0.00 0.00

time (sec)

N/A 0.000 7.165 3.019 0.000 0.287 0.000 0.000 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 52 128 131 299 0 121 356

N.S.

1 1.00 0.88 2.17 2.22 5.07 0.00 2.05 6.03

time (sec)

N/A 0.323 0.067 1.689 0.232 0.264 0.000 0.344 1.542

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 34 36 34 353 42 31 0 36

N.S.

1 1.00 1.06 1.00 10.38 1.24 0.91 0.00 1.06

time (sec)

N/A 0.283 54.219 0.813 0.621 0.449 5.161 0.000 3.912

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1428 1259 4139 0 0 9763 0 0 0

N.S.

1 0.88 2.90 0.00 0.00 6.84 0.00 0.00 0.00

time (sec)

N/A 6.186 11.132 0.000 0.000 0.491 0.000 0.000 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

982 889 2323 0 0 5664 0 0 0

N.S.

1 0.91 2.37 0.00 0.00 5.77 0.00 0.00 0.00

time (sec)

N/A 4.685 10.202 0.000 0.000 0.379 0.000 0.000 0.000

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

591 529 864 1529 0 2593 0 0 0

N.S.

1 0.90 1.46 2.59 0.00 4.39 0.00 0.00 0.00

time (sec)

N/A 2.844 8.954 8.332 0.000 0.354 0.000 0.000 0.000

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 118 160 140 173 441 0 200 142

N.S.

1 1.13 1.54 1.35 1.66 4.24 0.00 1.92 1.37

time (sec)

N/A 0.367 0.425 3.765 0.312 0.324 0.000 0.311 4.065

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 34 36 34 472 42 0 0 38

N.S.

1 1.00 1.06 1.00 13.88 1.24 0.00 0.00 1.12

time (sec)

N/A 0.283 41.564 0.866 0.804 6.704 0.000 0.000 3.662

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

914 818 2029 0 0 10432 0 0 0

N.S.

1 0.89 2.22 0.00 0.00 11.41 0.00 0.00 0.00

time (sec)

N/A 5.683 9.328 0.000 0.000 0.508 0.000 0.000 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

499 444 1295 3717 0 4086 0 0 0

N.S.

1 0.89 2.60 7.45 0.00 8.19 0.00 0.00 0.00

time (sec)

N/A 3.019 8.795 22.306 0.000 0.368 0.000 0.000 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 144 152 139 208 1040 0 185 768

N.S.

1 1.00 1.06 0.97 1.44 7.22 0.00 1.28 5.33

time (sec)

N/A 0.544 1.696 10.363 0.283 0.331 0.000 0.636 6.546

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

36 36 38 36 626 44 0 0 38

N.S.

1 1.00 1.06 1.00 17.39 1.22 0.00 0.00 1.06

time (sec)

N/A 0.318 52.114 0.816 0.766 0.700 0.000 0.000 6.309

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

978 803 1437 3280 0 15223 0 0 0

N.S.

1 0.82 1.47 3.35 0.00 15.57 0.00 0.00 0.00

time (sec)

N/A 3.816 11.642 60.273 0.000 0.615 0.000 0.000 0.000

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

180 207 227 249 350 2568 0 458 398

N.S.

1 1.15 1.26 1.38 1.94 14.27 0.00 2.54 2.21

time (sec)

N/A 0.470 0.800 28.203 0.299 0.494 0.000 0.301 8.673

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

36 36 38 36 1586 44 0 0 38

N.S.

1 1.00 1.06 1.00 44.06 1.22 0.00 0.00 1.06

time (sec)

N/A 0.315 109.979 0.804 2.436 157.055 0.000 0.000 20.549

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

752 0 3254 0 0 11595 0 0 0

N.S.

1 0.00 4.33 0.00 0.00 15.42 0.00 0.00 0.00

time (sec)

N/A 0.000 11.719 0.000 0.000 0.409 0.000 0.000 0.000

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

502 565 1816 0 0 6479 0 0 0

N.S.

1 1.13 3.62 0.00 0.00 12.91 0.00 0.00 0.00

time (sec)

N/A 3.733 10.325 0.000 0.000 0.344 0.000 0.000 0.000

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

298 350 713 649 0 2899 0 0 0

N.S.

1 1.17 2.39 2.18 0.00 9.73 0.00 0.00 0.00

time (sec)

N/A 2.166 8.402 2.163 0.000 0.320 0.000 0.000 0.000

Problem 479

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

72 68 60 54 161 545 0 145 470

N.S.

1 0.94 0.83 0.75 2.24 7.57 0.00 2.01 6.53

time (sec)

N/A 0.289 0.084 0.647 0.208 0.255 0.000 0.284 1.690

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 34 36 34 684 42 31 0 36

N.S.

1 1.00 1.06 1.00 20.12 1.24 0.91 0.00 1.06

time (sec)

N/A 0.283 142.621 0.593 0.782 0.769 16.470 0.000 1.877

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A N/A No N/A TBD TBD TBD TBD TBD

size

1038 0 2799 0 0 13504 0 0 0

N.S.

1 0.00 2.70 0.00 0.00 13.01 0.00 0.00 0.00

time (sec)

N/A 0.000 9.494 0.000 0.000 0.519 0.000 0.000 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

714 0 1530 0 0 7726 0 0 0

N.S.

1 0.00 2.14 0.00 0.00 10.82 0.00 0.00 0.00

time (sec)

N/A 0.000 8.338 0.000 0.000 0.374 0.000 0.000 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

413 0 615 1284 0 3585 0 0 0

N.S.

1 0.00 1.49 3.11 0.00 8.68 0.00 0.00 0.00

time (sec)

N/A 0.000 8.832 1.960 0.000 0.344 0.000 0.000 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

111 136 167 140 217 892 0 182 628

N.S.

1 1.23 1.50 1.26 1.95 8.04 0.00 1.64 5.66

time (sec)

N/A 1.046 2.093 1.192 0.275 0.291 0.000 0.317 1.406

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 34 36 34 762 42 31 0 38

N.S.

1 1.00 1.06 1.00 22.41 1.24 0.91 0.00 1.12

time (sec)

N/A 0.280 70.685 0.595 0.998 0.342 15.211 0.000 1.600

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

972 0 3868 0 0 13683 0 0 0

N.S.

1 0.00 3.98 0.00 0.00 14.08 0.00 0.00 0.00

time (sec)

N/A 0.000 12.727 0.000 0.000 0.482 0.000 0.000 0.000

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

689 0 2403 0 0 7775 0 0 0

N.S.

1 0.00 3.49 0.00 0.00 11.28 0.00 0.00 0.00

time (sec)

N/A 0.000 10.697 0.000 0.000 0.355 0.000 0.000 0.000

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A N/A No Yes TBD TBD TBD TBD TBD

size

435 0 766 1098 0 3547 0 0 0

N.S.

1 0.00 1.76 2.52 0.00 8.15 0.00 0.00 0.00

time (sec)

N/A 0.000 8.631 1.979 0.000 0.309 0.000 0.000 0.000

Problem 489

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

80 76 64 143 173 617 0 184 1329

N.S.

1 0.95 0.80 1.79 2.16 7.71 0.00 2.30 16.61

time (sec)

N/A 0.285 0.095 1.416 0.202 0.272 0.000 0.341 1.774

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

28 28 30 28 751 36 24 0 30

N.S.

1 1.00 1.07 1.00 26.82 1.29 0.86 0.00 1.07

time (sec)

N/A 0.247 139.403 0.653 0.960 0.900 4.902 0.000 1.985

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

1795 1596 5813 0 0 23903 0 0 0

N.S.

1 0.89 3.24 0.00 0.00 13.32 0.00 0.00 0.00

time (sec)

N/A 8.159 12.835 0.000 0.000 0.773 0.000 0.000 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

1219 1118 2784 0 0 13309 0 0 0

N.S.

1 0.92 2.28 0.00 0.00 10.92 0.00 0.00 0.00

time (sec)

N/A 6.158 10.382 0.000 0.000 0.497 0.000 0.000 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

762 673 1009 1478 0 5731 0 0 0

N.S.

1 0.88 1.32 1.94 0.00 7.52 0.00 0.00 0.00

time (sec)

N/A 4.094 9.431 15.114 0.000 0.416 0.000 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 144 164 186 236 1035 0 263 196

N.S.

1 1.11 1.26 1.43 1.82 7.96 0.00 2.02 1.51

time (sec)

N/A 0.411 0.308 7.069 0.286 0.353 0.000 0.294 4.634

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 34 36 34 912 42 0 0 38

N.S.

1 1.00 1.06 1.00 26.82 1.24 0.00 0.00 1.12

time (sec)

N/A 0.284 112.918 0.724 1.261 37.808 0.000 0.000 11.508

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A N/A No N/A TBD TBD TBD TBD TBD

size

1245 0 2346 0 0 29722 0 0 0

N.S.

1 0.00 1.88 0.00 0.00 23.87 0.00 0.00 0.00

time (sec)

N/A 0.000 9.786 0.000 0.000 0.777 0.000 0.000 0.000

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

699 611 798 2767 0 11126 0 0 0

N.S.

1 0.87 1.14 3.96 0.00 15.92 0.00 0.00 0.00

time (sec)

N/A 4.390 9.436 37.578 0.000 0.549 0.000 0.000 0.000

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

206 231 212 183 334 2653 0 224 531

N.S.

1 1.12 1.03 0.89 1.62 12.88 0.00 1.09 2.58

time (sec)

N/A 0.627 3.371 18.533 0.282 0.450 0.000 0.282 4.489

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

36 36 38 36 1426 44 0 0 38

N.S.

1 1.00 1.06 1.00 39.61 1.22 0.00 0.00 1.06

time (sec)

N/A 0.329 79.402 0.608 1.389 1.889 0.000 0.000 18.741

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

1122 943 1552 3563 0 16848 0 0 0

N.S.

1 0.84 1.38 3.18 0.00 15.02 0.00 0.00 0.00

time (sec)

N/A 5.599 10.268 89.783 0.000 0.669 0.000 0.000 0.000

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