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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 B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 22 22 24 23 23 20 23 21

N.S.

1 1.10 1.10 1.20 1.15 1.15 1.00 1.15 1.05

time (sec)

N/A 1.017 0.958 2.919 0.310 0.258 0.118 0.488 12.275

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 24 60 21 24 19 0 23

N.S.

1 1.00 1.00 2.50 0.88 1.00 0.79 0.00 0.96

time (sec)

N/A 0.917 0.072 2.956 0.313 0.248 0.166 0.000 12.400

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A B B B B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 113 26 48 173 48 49 0 29

N.S.

1 5.65 1.30 2.40 8.65 2.40 2.45 0.00 1.45

time (sec)

N/A 0.702 0.121 0.157 0.221 0.248 0.160 0.000 12.481

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

18 0 16 16 16 13 19 13 13

N.S.

1 0.00 0.89 0.89 0.89 0.72 1.06 0.72 0.72

time (sec)

N/A 0.000 0.701 0.222 0.283 0.256 1.335 0.286 12.805

Problem 405

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

21 20 20 19 33 18 15 18 13

N.S.

1 0.95 0.95 0.90 1.57 0.86 0.71 0.86 0.62

time (sec)

N/A 0.158 0.008 0.047 0.170 0.258 0.049 0.317 12.253

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 12 12 0 11 0 0 11

N.S.

1 1.00 1.00 1.00 0.00 0.92 0.00 0.00 0.92

time (sec)

N/A 0.479 0.169 0.335 0.000 0.258 0.000 0.000 12.487

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B C A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 143 66 45 75 43 37 42 43

N.S.

1 4.93 2.28 1.55 2.59 1.48 1.28 1.45 1.48

time (sec)

N/A 0.666 0.183 0.146 0.227 0.249 0.115 0.283 12.493

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 67 61 88 63 69 56 59 63

N.S.

1 3.05 2.77 4.00 2.86 3.14 2.55 2.68 2.86

time (sec)

N/A 1.357 5.092 0.317 0.205 0.248 0.202 0.293 13.532

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

13 0 19 16 16 16 12 17 17

N.S.

1 0.00 1.46 1.23 1.23 1.23 0.92 1.31 1.31

time (sec)

N/A 0.000 0.423 0.103 0.208 0.246 0.099 0.268 13.244

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 0 21 75 30 30 0 30 25

N.S.

1 0.00 0.64 2.27 0.91 0.91 0.00 0.91 0.76

time (sec)

N/A 0.000 5.107 0.447 0.320 0.250 0.000 0.306 12.815

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 83 29 25 23 29 32 23 26

N.S.

1 2.96 1.04 0.89 0.82 1.04 1.14 0.82 0.93

time (sec)

N/A 0.255 0.034 0.098 0.265 0.257 0.112 0.308 13.456

Problem 412

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 16 16 17 16 26 12 17 16

N.S.

1 0.64 0.64 0.68 0.64 1.04 0.48 0.68 0.64

time (sec)

N/A 0.245 0.012 0.042 0.167 0.227 0.041 0.284 13.603

Problem 413

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 13 11 10 9 12 10 9 9

N.S.

1 0.68 0.58 0.53 0.47 0.63 0.53 0.47 0.47

time (sec)

N/A 0.145 0.002 0.025 0.171 0.234 0.037 0.295 0.028

Problem 414

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 49 33 31 49 56 26 48 105

N.S.

1 1.58 1.06 1.00 1.58 1.81 0.84 1.55 3.39

time (sec)

N/A 1.469 0.096 0.585 0.235 0.255 0.115 0.298 14.094

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A F B

verified

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

size

15 0 15 15 14 14 15 0 14

N.S.

1 0.00 1.00 1.00 0.93 0.93 1.00 0.00 0.93

time (sec)

N/A 0.000 5.074 247.202 0.268 0.267 171.529 0.000 14.473

Problem 416

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 25 25 37 32 32 32 36 36

N.S.

1 0.93 0.93 1.37 1.19 1.19 1.19 1.33 1.33

time (sec)

N/A 3.936 4.905 41.549 1.742 0.258 4.625 0.324 14.718

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 61 51 28 28 26 29 28 30

N.S.

1 2.65 2.22 1.22 1.22 1.13 1.26 1.22 1.30

time (sec)

N/A 0.332 0.084 0.112 0.176 0.249 0.405 0.299 0.165

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 51 21 26 25 21 19 21 27

N.S.

1 2.04 0.84 1.04 1.00 0.84 0.76 0.84 1.08

time (sec)

N/A 0.991 2.806 0.345 0.250 0.250 0.087 0.299 14.081

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A F A A F B

verified

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

size

32 0 37 41 0 48 36 0 67

N.S.

1 0.00 1.16 1.28 0.00 1.50 1.12 0.00 2.09

time (sec)

N/A 0.000 0.393 3.563 0.000 0.255 1.458 0.000 14.520

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 470 76 243 526 203 267 400 153

N.S.

1 15.67 2.53 8.10 17.53 6.77 8.90 13.33 5.10

time (sec)

N/A 0.776 0.425 0.252 0.208 0.258 0.239 0.300 14.746

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

10 10 10 8 7 7 8 7 7

N.S.

1 1.00 1.00 0.80 0.70 0.70 0.80 0.70 0.70

time (sec)

N/A 0.124 0.000 0.110 0.193 0.233 0.020 0.292 15.147

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

17 17 18 17 17 16 15 20 16

N.S.

1 1.00 1.06 1.00 1.00 0.94 0.88 1.18 0.94

time (sec)

N/A 0.211 0.007 0.044 0.172 0.259 0.049 0.288 14.076

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 21 16 26 102 27 29 21 30

N.S.

1 1.05 0.80 1.30 5.10 1.35 1.45 1.05 1.50

time (sec)

N/A 0.412 0.082 0.524 0.300 0.250 0.096 0.289 13.342

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 13 9 9 15 8 7 8 8

N.S.

1 1.44 1.00 1.00 1.67 0.89 0.78 0.89 0.89

time (sec)

N/A 0.175 0.051 0.025 0.197 0.254 0.046 0.269 13.244

Problem 425

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 29 29 24 30 23 20 30 30

N.S.

1 1.07 1.07 0.89 1.11 0.85 0.74 1.11 1.11

time (sec)

N/A 0.473 0.026 0.663 0.285 0.271 0.094 0.320 14.655

Problem 426

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 38 26 24 27 39 22 26 21

N.S.

1 1.41 0.96 0.89 1.00 1.44 0.81 0.96 0.78

time (sec)

N/A 0.661 0.045 0.440 0.173 0.276 0.122 0.267 13.811

Problem 427

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

13 12 12 13 12 12 12 12 12

N.S.

1 0.92 0.92 1.00 0.92 0.92 0.92 0.92 0.92

time (sec)

N/A 0.338 0.006 0.069 0.171 0.290 0.080 0.265 13.894

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 84 28 32 57 25 0 0 37

N.S.

1 3.00 1.00 1.14 2.04 0.89 0.00 0.00 1.32

time (sec)

N/A 1.899 0.151 34.668 0.386 0.269 0.000 0.000 13.647

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 69 27 27 50 31 26 0 0

N.S.

1 2.56 1.00 1.00 1.85 1.15 0.96 0.00 0.00

time (sec)

N/A 0.584 0.760 0.661 0.231 0.255 7.518 0.000 0.000

Problem 430

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 33 27 28 28 29 27 28 28

N.S.

1 1.22 1.00 1.04 1.04 1.07 1.00 1.04 1.04

time (sec)

N/A 0.198 0.030 0.096 0.171 0.253 0.060 0.262 12.119

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

27 0 29 37 34 34 39 0 0

N.S.

1 0.00 1.07 1.37 1.26 1.26 1.44 0.00 0.00

time (sec)

N/A 0.000 5.076 1.061 0.267 0.275 0.250 0.000 0.000

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 0 32 76 28 65 22 0 0

N.S.

1 0.00 0.94 2.24 0.82 1.91 0.65 0.00 0.00

time (sec)

N/A 0.000 0.365 0.514 0.514 0.261 10.874 0.000 0.000

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 12 12 24 24 37 9 9

N.S.

1 1.00 0.86 0.86 1.71 1.71 2.64 0.64 0.64

time (sec)

N/A 0.156 0.003 0.099 0.173 0.244 0.136 0.246 0.082

Problem 434

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

21 20 20 20 19 19 17 19 15

N.S.

1 0.95 0.95 0.95 0.90 0.90 0.81 0.90 0.71

time (sec)

N/A 0.192 0.080 0.070 0.178 0.246 0.052 0.261 12.293

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 28 60 41 28 41 26 57 0

N.S.

1 0.97 2.07 1.41 0.97 1.41 0.90 1.97 0.00

time (sec)

N/A 0.312 0.034 0.692 0.190 0.259 0.313 0.259 0.000

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 24 18 15 14 31 15 31 14

N.S.

1 1.26 0.95 0.79 0.74 1.63 0.79 1.63 0.74

time (sec)

N/A 0.176 0.010 0.109 0.185 0.254 0.083 0.263 12.054

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B A A A B

verified

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

size

22 0 23 25 39 38 22 17 17

N.S.

1 0.00 1.05 1.14 1.77 1.73 1.00 0.77 0.77

time (sec)

N/A 0.000 0.170 0.455 0.215 0.267 0.213 0.254 12.590

Problem 438

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

20 29 32 24 25 25 29 25 26

N.S.

1 1.45 1.60 1.20 1.25 1.25 1.45 1.25 1.30

time (sec)

N/A 0.163 0.004 0.059 0.177 0.240 0.028 0.273 12.905

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 48 21 24 0 23 24 49 24

N.S.

1 2.29 1.00 1.14 0.00 1.10 1.14 2.33 1.14

time (sec)

N/A 0.409 0.115 0.393 0.000 0.258 0.119 0.263 12.773

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 29 21 22 34 19 27 21 21

N.S.

1 1.53 1.11 1.16 1.79 1.00 1.42 1.11 1.11

time (sec)

N/A 0.250 0.237 0.040 0.209 0.268 0.064 0.246 0.062

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

29 0 34 31 34 43 36 32 32

N.S.

1 0.00 1.17 1.07 1.17 1.48 1.24 1.10 1.10

time (sec)

N/A 0.000 0.627 0.113 0.281 0.262 0.187 0.264 12.386

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

26 26 27 25 22 26 24 25 24

N.S.

1 1.00 1.04 0.96 0.85 1.00 0.92 0.96 0.92

time (sec)

N/A 0.193 0.014 0.091 0.175 0.262 0.051 0.263 12.066

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 0 17 18 27 19 20 35 0

N.S.

1 0.00 0.81 0.86 1.29 0.90 0.95 1.67 0.00

time (sec)

N/A 0.000 0.270 2.618 0.310 0.266 0.453 0.321 0.000

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 111 21 15 45 12 24 0 12

N.S.

1 5.29 1.00 0.71 2.14 0.57 1.14 0.00 0.57

time (sec)

N/A 0.667 0.087 2.237 0.299 0.254 18.177 0.000 11.705

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 27 24 21 27 20 19 20 22

N.S.

1 1.12 1.00 0.88 1.12 0.83 0.79 0.83 0.92

time (sec)

N/A 0.202 0.114 0.177 0.223 0.271 0.075 0.258 0.083

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

25 0 22 22 21 30 22 34 34

N.S.

1 0.00 0.88 0.88 0.84 1.20 0.88 1.36 1.36

time (sec)

N/A 0.000 0.325 0.130 0.299 0.251 0.073 0.263 0.164

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A B C B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 101 36 102 237 79 82 134 107

N.S.

1 3.74 1.33 3.78 8.78 2.93 3.04 4.96 3.96

time (sec)

N/A 0.468 0.061 0.565 0.235 0.256 0.191 0.280 11.320

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F C A A A A A B

verified

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

size

18 0 109 26 25 25 24 28 25

N.S.

1 0.00 6.06 1.44 1.39 1.39 1.33 1.56 1.39

time (sec)

N/A 0.000 0.046 0.091 0.173 0.238 0.347 0.262 11.205

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

19 20 18 14 16 16 27 16 13

N.S.

1 1.05 0.95 0.74 0.84 0.84 1.42 0.84 0.68

time (sec)

N/A 0.149 0.003 0.043 0.181 0.241 0.020 0.261 0.032

Problem 450

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

20 20 15 15 19 19 17 19 20

N.S.

1 1.00 0.75 0.75 0.95 0.95 0.85 0.95 1.00

time (sec)

N/A 0.182 0.058 0.046 0.180 0.266 0.045 0.265 0.067

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

19 0 17 18 16 28 17 16 15

N.S.

1 0.00 0.89 0.95 0.84 1.47 0.89 0.84 0.79

time (sec)

N/A 0.000 0.390 49.670 0.323 0.263 0.625 0.295 11.766

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 54 26 26 0 25 24 32 26

N.S.

1 2.25 1.08 1.08 0.00 1.04 1.00 1.33 1.08

time (sec)

N/A 0.325 0.377 0.539 0.000 0.250 0.089 0.267 11.364

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 1206 29 24 138 34 20 23 25

N.S.

1 48.24 1.16 0.96 5.52 1.36 0.80 0.92 1.00

time (sec)

N/A 2.509 0.641 0.199 0.321 0.260 0.112 0.284 11.503

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

24 33 24 18 22 18 20 22 16

N.S.

1 1.38 1.00 0.75 0.92 0.75 0.83 0.92 0.67

time (sec)

N/A 0.176 0.006 0.049 0.170 0.254 0.064 0.271 11.551

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

27 0 23 42 122 122 112 277 0

N.S.

1 0.00 0.85 1.56 4.52 4.52 4.15 10.26 0.00

time (sec)

N/A 0.000 2.337 0.912 0.229 0.265 0.348 0.314 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 95 28 26 101 31 37 55 25

N.S.

1 3.17 0.93 0.87 3.37 1.03 1.23 1.83 0.83

time (sec)

N/A 0.494 0.213 0.545 0.309 0.247 0.524 0.271 11.331

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

12 14 12 9 8 8 8 8 9

N.S.

1 1.17 1.00 0.75 0.67 0.67 0.67 0.67 0.75

time (sec)

N/A 0.143 0.015 0.095 0.170 0.256 0.056 0.267 0.048

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 226 27 35 36 31 26 34 24

N.S.

1 8.37 1.00 1.30 1.33 1.15 0.96 1.26 0.89

time (sec)

N/A 1.699 0.062 1.073 0.220 0.274 0.285 0.280 11.553

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B A F B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 127 72 59 0 62 82 67 64

N.S.

1 3.85 2.18 1.79 0.00 1.88 2.48 2.03 1.94

time (sec)

N/A 1.384 2.663 0.722 0.000 0.251 0.200 0.275 0.696

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 75 15 18 18 17 14 18 15

N.S.

1 5.00 1.00 1.20 1.20 1.13 0.93 1.20 1.00

time (sec)

N/A 0.714 0.414 0.444 0.281 0.245 0.066 0.280 11.458

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B B B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 32 48 32 30 63 31 17 31

N.S.

1 2.13 3.20 2.13 2.00 4.20 2.07 1.13 2.07

time (sec)

N/A 0.281 0.045 0.128 0.185 0.268 0.216 0.258 11.276

Problem 462

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

18 16 16 14 13 13 14 13 13

N.S.

1 0.89 0.89 0.78 0.72 0.72 0.78 0.72 0.72

time (sec)

N/A 0.179 0.122 0.135 0.213 0.253 0.085 0.261 11.150

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

33 0 51 54 53 53 48 57 52

N.S.

1 0.00 1.55 1.64 1.61 1.61 1.45 1.73 1.58

time (sec)

N/A 0.000 0.226 1.379 0.225 0.253 0.253 1.140 13.062

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

31 0 42 42 49 49 49 0 454

N.S.

1 0.00 1.35 1.35 1.58 1.58 1.58 0.00 14.65

time (sec)

N/A 0.000 0.161 1.783 0.300 0.274 0.194 0.000 13.449

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 28 26 47 95 78 80 95 106

N.S.

1 0.93 0.87 1.57 3.17 2.60 2.67 3.17 3.53

time (sec)

N/A 3.688 5.016 10.835 0.571 0.256 0.532 0.564 12.813

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 182 0 35 0 34 0 74 0

N.S.

1 6.07 0.00 1.17 0.00 1.13 0.00 2.47 0.00

time (sec)

N/A 18.748 0.000 0.223 0.000 0.263 0.000 0.359 0.000

Problem 467

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

14 4 4 5 4 4 3 5 4

N.S.

1 0.29 0.29 0.36 0.29 0.29 0.21 0.36 0.29

time (sec)

N/A 0.110 0.001 0.025 0.169 0.243 0.020 0.266 0.014

Problem 468

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

23 43 43 120 48 43 42 44 46

N.S.

1 1.87 1.87 5.22 2.09 1.87 1.83 1.91 2.00

time (sec)

N/A 2.535 0.731 5.265 0.315 0.272 0.404 0.689 12.328

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

31 0 32 25 24 24 22 24 24

N.S.

1 0.00 1.03 0.81 0.77 0.77 0.71 0.77 0.77

time (sec)

N/A 0.000 3.761 0.324 0.217 0.270 0.094 0.256 0.411

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A B A B

verified

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

size

33 0 24 29 24 24 70 26 64

N.S.

1 0.00 0.73 0.88 0.73 0.73 2.12 0.79 1.94

time (sec)

N/A 0.000 0.336 1.427 0.222 0.270 0.158 0.302 13.436

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 25 16 18 38 35 12 0 14

N.S.

1 1.56 1.00 1.12 2.38 2.19 0.75 0.00 0.88

time (sec)

N/A 0.202 0.022 0.207 0.200 0.250 0.171 0.000 12.851

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A F B

verified

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

size

22 0 21 20 19 19 17 0 20

N.S.

1 0.00 0.95 0.91 0.86 0.86 0.77 0.00 0.91

time (sec)

N/A 0.000 0.034 0.311 0.224 0.254 0.105 0.000 12.943

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 28 26 25 0 22 34 24 24

N.S.

1 1.33 1.24 1.19 0.00 1.05 1.62 1.14 1.14

time (sec)

N/A 0.279 1.552 0.150 0.000 0.262 0.142 0.254 13.606

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B B B B B

verified

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

size

21 0 25 38 74 76 185 74 371

N.S.

1 0.00 1.19 1.81 3.52 3.62 8.81 3.52 17.67

time (sec)

N/A 0.000 1.941 1.090 0.266 0.262 0.296 0.274 14.563

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

28 0 34 32 33 33 29 33 31

N.S.

1 0.00 1.21 1.14 1.18 1.18 1.04 1.18 1.11

time (sec)

N/A 0.000 2.911 0.096 0.219 0.272 0.105 0.262 13.938

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

19 20 18 21 20 20 20 136 24

N.S.

1 1.05 0.95 1.11 1.05 1.05 1.05 7.16 1.26

time (sec)

N/A 0.218 0.115 0.270 0.175 0.256 0.073 0.268 0.206

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 0 23 63 47 51 0 43 26

N.S.

1 0.00 1.00 2.74 2.04 2.22 0.00 1.87 1.13

time (sec)

N/A 0.000 4.207 5.423 0.221 0.257 0.000 0.293 13.779

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

30 0 23 25 32 32 27 33 27

N.S.

1 0.00 0.77 0.83 1.07 1.07 0.90 1.10 0.90

time (sec)

N/A 0.000 2.136 0.102 0.230 0.261 0.103 0.281 13.941

Problem 479

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

21 19 18 12 13 19 8 13 13

N.S.

1 0.90 0.86 0.57 0.62 0.90 0.38 0.62 0.62

time (sec)

N/A 0.169 0.011 0.573 0.169 0.249 0.040 0.268 0.047

Problem 480

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

26 38 35 36 34 33 32 38 33

N.S.

1 1.46 1.35 1.38 1.31 1.27 1.23 1.46 1.27

time (sec)

N/A 0.428 0.034 0.154 0.174 0.254 1.200 0.277 13.836

Problem 481

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

12 11 9 8 9 7 8 9 8

N.S.

1 0.92 0.75 0.67 0.75 0.58 0.67 0.75 0.67

time (sec)

N/A 0.124 0.000 0.003 0.175 0.248 0.020 0.265 0.002

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 51 26 17 0 22 17 16 16

N.S.

1 1.24 0.63 0.41 0.00 0.54 0.41 0.39 0.39

time (sec)

N/A 0.227 0.028 0.328 0.000 0.266 0.099 0.278 13.164

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

22 0 17 38 19 21 19 19 15

N.S.

1 0.00 0.77 1.73 0.86 0.95 0.86 0.86 0.68

time (sec)

N/A 0.000 0.225 0.205 0.200 0.260 0.078 0.268 0.132

Problem 484

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

19 26 20 21 26 25 24 26 18

N.S.

1 1.37 1.05 1.11 1.37 1.32 1.26 1.37 0.95

time (sec)

N/A 0.170 0.004 0.099 0.168 0.258 0.058 0.259 12.132

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

33 0 33 31 31 38 34 33 138

N.S.

1 0.00 1.00 0.94 0.94 1.15 1.03 1.00 4.18

time (sec)

N/A 0.000 0.350 186.652 0.301 0.260 1.041 0.335 13.039

Problem 486

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

22 17 12 12 11 11 10 11 11

N.S.

1 0.77 0.55 0.55 0.50 0.50 0.45 0.50 0.50

time (sec)

N/A 0.130 0.000 0.038 0.198 0.257 0.020 0.276 0.043

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

18 18 18 16 15 15 15 15 15

N.S.

1 1.00 1.00 0.89 0.83 0.83 0.83 0.83 0.83

time (sec)

N/A 0.151 0.026 0.041 0.174 0.245 0.055 0.255 0.068

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

23 15 15 16 15 18 12 16 15

N.S.

1 0.65 0.65 0.70 0.65 0.78 0.52 0.70 0.65

time (sec)

N/A 0.212 0.008 0.458 0.174 0.252 0.042 0.259 0.051

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B A B F B

verified

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

size

28 0 29 55 60 49 48 0 68

N.S.

1 0.00 1.04 1.96 2.14 1.75 1.71 0.00 2.43

time (sec)

N/A 0.000 4.320 0.800 0.264 0.254 0.177 0.000 12.554

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

30 41 36 36 38 38 32 35 35

N.S.

1 1.37 1.20 1.20 1.27 1.27 1.07 1.17 1.17

time (sec)

N/A 1.218 0.175 16.209 0.290 0.262 1.534 0.686 14.497

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

30 21 21 20 19 19 19 19 19

N.S.

1 0.70 0.70 0.67 0.63 0.63 0.63 0.63 0.63

time (sec)

N/A 0.148 0.011 0.054 0.174 0.254 0.050 0.265 0.069

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

22 5 5 6 5 5 3 5 5

N.S.

1 0.23 0.23 0.27 0.23 0.23 0.14 0.23 0.23

time (sec)

N/A 0.117 0.000 0.033 0.166 0.253 0.029 0.261 0.014

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

33 34 34 151 0 38 0 0 33

N.S.

1 1.03 1.03 4.58 0.00 1.15 0.00 0.00 1.00

time (sec)

N/A 3.783 0.291 0.921 0.000 0.264 0.000 0.000 13.953

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 0 29 30 34 29 24 29 0

N.S.

1 0.00 1.00 1.03 1.17 1.00 0.83 1.00 0.00

time (sec)

N/A 0.000 0.095 71.693 0.232 0.262 0.179 0.567 0.000

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A F A A B B

verified

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

size

22 0 22 26 0 25 24 375 28

N.S.

1 0.00 1.00 1.18 0.00 1.14 1.09 17.05 1.27

time (sec)

N/A 0.000 4.539 0.658 0.000 0.272 0.217 0.386 0.267

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 50 33 30 30 30 27 30 23

N.S.

1 2.17 1.43 1.30 1.30 1.30 1.17 1.30 1.00

time (sec)

N/A 0.216 0.018 0.052 0.188 0.249 0.056 0.262 12.680

Problem 497

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

13 13 13 11 10 10 10 10 10

N.S.

1 1.00 1.00 0.85 0.77 0.77 0.77 0.77 0.77

time (sec)

N/A 0.141 0.005 0.017 0.175 0.249 0.042 0.256 0.051

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 107 33 28 170 32 26 31 25

N.S.

1 3.69 1.14 0.97 5.86 1.10 0.90 1.07 0.86

time (sec)

N/A 0.839 0.257 0.198 0.737 0.260 0.102 0.278 12.961

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 0 18 17 16 16 17 0 0

N.S.

1 0.00 0.90 0.85 0.80 0.80 0.85 0.00 0.00

time (sec)

N/A 0.000 1.437 2.370 0.224 0.257 0.131 0.000 0.000

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

15 10 10 11 10 10 8 10 10

N.S.

1 0.67 0.67 0.73 0.67 0.67 0.53 0.67 0.67

time (sec)

N/A 0.140 0.004 0.054 0.172 0.290 0.045 0.262 12.194

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