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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 40 16 15 20 14 15 14 13

N.S.

1 2.00 0.80 0.75 1.00 0.70 0.75 0.70 0.65

time (sec)

N/A 0.172 0.016 0.134 0.211 0.242 0.063 0.261 14.260

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 138 22 30 108 34 37 45 16

N.S.

1 9.20 1.47 2.00 7.20 2.27 2.47 3.00 1.07

time (sec)

N/A 0.322 0.083 0.271 0.192 0.254 0.119 0.258 14.638

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A B B

verified

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

size

20 0 19 18 17 34 14 81 17

N.S.

1 0.00 0.95 0.90 0.85 1.70 0.70 4.05 0.85

time (sec)

N/A 0.000 0.936 0.706 0.416 0.312 0.239 0.256 15.960

Problem 404

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 12 12 11 10 12 7 11 10

N.S.

1 1.00 1.00 0.92 0.83 1.00 0.58 0.92 0.83

time (sec)

N/A 0.175 0.005 1.075 0.194 0.260 0.039 0.252 0.051

Problem 405

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

24 0 23 24 122 22 19 22 22

N.S.

1 0.00 0.96 1.00 5.08 0.92 0.79 0.92 0.92

time (sec)

N/A 0.000 0.528 0.569 0.360 0.252 0.105 0.262 0.306

Problem 406

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

35 0 38 42 37 44 39 44 0

N.S.

1 0.00 1.09 1.20 1.06 1.26 1.11 1.26 0.00

time (sec)

N/A 0.000 0.094 2.110 0.279 0.275 0.164 0.445 0.000

Problem 407

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 24 24 22 21 21 22 21 24

N.S.

1 0.92 0.92 0.85 0.81 0.81 0.85 0.81 0.92

time (sec)

N/A 0.174 0.055 0.079 0.208 0.260 0.076 0.257 0.136

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 0 113 69 59 54 75 68 0

N.S.

1 0.00 5.38 3.29 2.81 2.57 3.57 3.24 0.00

time (sec)

N/A 0.000 5.482 3.835 0.334 0.274 0.151 0.296 0.000

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 70 23 24 23 23 20 0 24

N.S.

1 2.33 0.77 0.80 0.77 0.77 0.67 0.00 0.80

time (sec)

N/A 0.382 0.523 0.150 0.277 0.262 0.104 0.000 15.145

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 69 49 48 0 51 51 63 56

N.S.

1 2.09 1.48 1.45 0.00 1.55 1.55 1.91 1.70

time (sec)

N/A 1.163 0.450 0.108 0.000 0.249 0.126 0.280 14.446

Problem 411

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

35 0 31 46 42 38 26 42 32

N.S.

1 0.00 0.89 1.31 1.20 1.09 0.74 1.20 0.91

time (sec)

N/A 0.000 0.231 27.393 0.376 0.257 0.378 0.449 14.099

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

12 11 11 7 6 6 5 6 6

N.S.

1 0.92 0.92 0.58 0.50 0.50 0.42 0.50 0.50

time (sec)

N/A 0.136 0.001 0.099 0.192 0.237 0.033 0.247 0.038

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

27 0 29 74 72 73 82 71 0

N.S.

1 0.00 1.07 2.74 2.67 2.70 3.04 2.63 0.00

time (sec)

N/A 0.000 0.750 4.592 0.686 0.278 0.185 19.152 0.000

Problem 414

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

31 0 32 26 30 26 24 27 0

N.S.

1 0.00 1.03 0.84 0.97 0.84 0.77 0.87 0.00

time (sec)

N/A 0.000 5.171 2.181 0.369 0.250 0.136 0.436 0.000

Problem 415

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 32 41 46 44 44 110

N.S.

1 0.00 1.03 1.03 1.32 1.48 1.42 1.42 3.55

time (sec)

N/A 0.000 0.115 1.905 0.350 0.270 0.146 0.340 14.657

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 55 24 36 34 38 34 36 27

N.S.

1 2.50 1.09 1.64 1.55 1.73 1.55 1.64 1.23

time (sec)

N/A 0.611 0.148 2.122 0.237 0.249 0.046 0.268 14.222

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

20 17 17 18 17 21 17 17 18

N.S.

1 0.85 0.85 0.90 0.85 1.05 0.85 0.85 0.90

time (sec)

N/A 0.177 0.004 0.060 0.190 0.237 0.067 0.255 14.482

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 30 19 15 30 14 12 14 12

N.S.

1 1.15 0.73 0.58 1.15 0.54 0.46 0.54 0.46

time (sec)

N/A 0.202 0.056 0.079 0.198 0.252 0.040 0.255 0.056

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 16 12 16 15 15 14 15 11

N.S.

1 1.33 1.00 1.33 1.25 1.25 1.17 1.25 0.92

time (sec)

N/A 0.205 0.049 0.043 0.199 0.245 0.042 0.251 14.870

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

31 0 51 58 92 55 54 0 57

N.S.

1 0.00 1.65 1.87 2.97 1.77 1.74 0.00 1.84

time (sec)

N/A 0.000 0.406 116.989 0.439 0.270 3.302 0.000 15.597

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 79 16 60 51 52 58 55 21

N.S.

1 3.95 0.80 3.00 2.55 2.60 2.90 2.75 1.05

time (sec)

N/A 0.306 0.063 0.168 0.207 0.255 0.072 0.273 13.741

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B A A B B

verified

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

size

26 0 29 32 95 30 29 52 377

N.S.

1 0.00 1.12 1.23 3.65 1.15 1.12 2.00 14.50

time (sec)

N/A 0.000 0.608 0.524 0.365 0.236 0.138 0.350 14.446

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 16 18 13 13 13 14 13 12

N.S.

1 0.80 0.90 0.65 0.65 0.65 0.70 0.65 0.60

time (sec)

N/A 0.130 0.002 0.092 0.201 0.229 0.023 0.272 0.043

Problem 424

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 16 14 11 11 11 10 11 10

N.S.

1 1.33 1.17 0.92 0.92 0.92 0.83 0.92 0.83

time (sec)

N/A 0.131 0.000 0.109 0.187 0.230 0.020 0.262 13.938

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 34 32 34 0 50 32 60 38

N.S.

1 1.17 1.10 1.17 0.00 1.72 1.10 2.07 1.31

time (sec)

N/A 0.756 0.211 0.211 0.000 0.260 0.143 0.284 13.851

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

17 16 18 17 15 27 10 16 15

N.S.

1 0.94 1.06 1.00 0.88 1.59 0.59 0.94 0.88

time (sec)

N/A 0.208 0.018 1.915 0.201 0.250 0.047 0.265 13.288

Problem 427

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 28 28 44 32 31 46 27

N.S.

1 0.00 0.93 0.93 1.47 1.07 1.03 1.53 0.90

time (sec)

N/A 0.000 0.677 2.102 0.324 0.263 0.088 0.274 14.393

Problem 428

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 36 37 58 58 31 37 60

N.S.

1 0.00 1.09 1.12 1.76 1.76 0.94 1.12 1.82

time (sec)

N/A 0.000 0.059 1.105 0.234 0.294 0.103 0.274 14.094

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 25 12 14 14 14 15 14 13

N.S.

1 1.47 0.71 0.82 0.82 0.82 0.88 0.82 0.76

time (sec)

N/A 0.140 0.007 0.112 0.202 0.272 0.067 0.258 0.039

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F B A B B B B B

verified

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

size

28 0 59 52 84 81 70 93 547

N.S.

1 0.00 2.11 1.86 3.00 2.89 2.50 3.32 19.54

time (sec)

N/A 0.000 0.159 2.747 0.240 0.304 0.164 0.289 15.134

Problem 431

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

16 21 14 21 32 16 22 20 16

N.S.

1 1.31 0.88 1.31 2.00 1.00 1.38 1.25 1.00

time (sec)

N/A 0.208 0.097 0.086 0.250 0.303 0.102 0.264 14.568

Problem 432

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

33 90 84 66 84 92 94 94 77

N.S.

1 2.73 2.55 2.00 2.55 2.79 2.85 2.85 2.33

time (sec)

N/A 0.565 0.073 0.264 0.191 0.380 0.908 0.268 14.304

Problem 433

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 16 15 13 17 15 15

N.S.

1 0.89 0.89 0.89 0.83 0.72 0.94 0.83 0.83

time (sec)

N/A 0.171 0.010 0.066 0.197 0.316 0.074 0.262 13.615

Problem 434

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 23 21 15 29 20 32 21

N.S.

1 0.00 0.92 0.84 0.60 1.16 0.80 1.28 0.84

time (sec)

N/A 0.000 0.295 0.513 0.248 0.305 0.103 0.260 14.676

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 234 40 30 59 57 54 64 79

N.S.

1 9.36 1.60 1.20 2.36 2.28 2.16 2.56 3.16

time (sec)

N/A 0.719 0.133 1.378 0.200 0.300 0.146 0.267 0.336

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 90 85 31 35 29 27 0 33

N.S.

1 3.60 3.40 1.24 1.40 1.16 1.08 0.00 1.32

time (sec)

N/A 0.553 0.244 1.194 0.398 0.303 0.106 0.000 15.086

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 36 14 14 37 37 27 37 15

N.S.

1 1.89 0.74 0.74 1.95 1.95 1.42 1.95 0.79

time (sec)

N/A 0.162 0.009 0.096 0.194 0.307 0.022 0.263 0.080

Problem 438

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

13 18 12 13 0 11 12 11 11

N.S.

1 1.38 0.92 1.00 0.00 0.85 0.92 0.85 0.85

time (sec)

N/A 0.257 0.254 1.419 0.000 0.275 0.059 0.260 14.826

Problem 439

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 33 30 24 23 30 20 23 23

N.S.

1 1.06 0.97 0.77 0.74 0.97 0.65 0.74 0.74

time (sec)

N/A 0.190 0.005 0.177 0.199 0.286 0.043 0.265 0.040

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F F A B A B B B

verified

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

size

31 0 0 55 122 56 51 124 54

N.S.

1 0.00 0.00 1.77 3.94 1.81 1.65 4.00 1.74

time (sec)

N/A 0.000 0.000 12.651 0.259 0.278 0.487 2.608 14.810

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 8 8 9 8 8 10 9 8

N.S.

1 0.53 0.53 0.60 0.53 0.53 0.67 0.60 0.53

time (sec)

N/A 0.129 0.001 0.071 0.204 0.244 0.024 0.255 0.048

Problem 442

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

15 15 15 14 44 31 14 0 14

N.S.

1 1.00 1.00 0.93 2.93 2.07 0.93 0.00 0.93

time (sec)

N/A 0.318 0.048 0.245 0.216 0.267 0.197 0.000 13.071

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A F B A B B

verified

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

size

22 0 32 27 0 103 22 124 37

N.S.

1 0.00 1.45 1.23 0.00 4.68 1.00 5.64 1.68

time (sec)

N/A 0.000 3.413 1.645 0.000 0.257 0.147 0.648 14.052

Problem 444

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 45 44 40 40 66 42 45

N.S.

1 0.00 1.36 1.33 1.21 1.21 2.00 1.27 1.36

time (sec)

N/A 0.000 0.578 1.754 0.254 0.235 0.181 0.298 15.868

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B B B B B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 89 66 72 336 99 76 0 62

N.S.

1 4.24 3.14 3.43 16.00 4.71 3.62 0.00 2.95

time (sec)

N/A 1.192 0.108 0.264 0.250 0.254 0.164 0.000 15.128

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 29 29 30 29 29 27 29 29

N.S.

1 0.97 0.97 1.00 0.97 0.97 0.90 0.97 0.97

time (sec)

N/A 0.603 0.034 2.117 0.228 0.232 0.112 0.281 14.982

Problem 447

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

33 0 35 37 33 32 44 34 0

N.S.

1 0.00 1.06 1.12 1.00 0.97 1.33 1.03 0.00

time (sec)

N/A 0.000 0.165 46.286 0.272 0.249 0.807 0.659 0.000

Problem 448

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

24 23 23 27 31 31 37 79 23

N.S.

1 0.96 0.96 1.12 1.29 1.29 1.54 3.29 0.96

time (sec)

N/A 0.231 0.021 0.296 0.206 0.305 0.623 0.265 0.243

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

36 43 43 41 40 40 34 40 45

N.S.

1 1.19 1.19 1.14 1.11 1.11 0.94 1.11 1.25

time (sec)

N/A 4.698 0.400 4.729 0.531 0.378 166.788 23.503 14.795

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

15 16 16 15 14 14 15 26 14

N.S.

1 1.07 1.07 1.00 0.93 0.93 1.00 1.73 0.93

time (sec)

N/A 0.235 0.035 0.125 0.256 0.323 1.613 0.270 13.892

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

28 0 46 58 196 236 158 302 0

N.S.

1 0.00 1.64 2.07 7.00 8.43 5.64 10.79 0.00

time (sec)

N/A 0.000 0.259 7.483 0.352 0.330 0.253 0.418 0.000

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 40 23 27 42 23 26 24 22

N.S.

1 1.74 1.00 1.17 1.83 1.00 1.13 1.04 0.96

time (sec)

N/A 0.245 0.092 1.191 0.249 0.323 0.131 0.281 15.594

Problem 453

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 24 23 25 22 24 19 24 23

N.S.

1 1.14 1.10 1.19 1.05 1.14 0.90 1.14 1.10

time (sec)

N/A 0.510 0.128 0.198 0.271 0.313 0.084 0.271 15.311

Problem 454

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 39 31 24 152 32 29 32 39

N.S.

1 1.62 1.29 1.00 6.33 1.33 1.21 1.33 1.62

time (sec)

N/A 0.399 0.396 0.162 0.261 0.404 0.085 0.271 0.144

Problem 455

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 25 23 22 22 19 22 47

N.S.

1 0.00 1.00 0.92 0.88 0.88 0.76 0.88 1.88

time (sec)

N/A 0.000 0.732 2.008 0.330 0.325 0.061 0.293 14.055

Problem 456

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

17 0 15 17 15 15 14 15 15

N.S.

1 0.00 0.88 1.00 0.88 0.88 0.82 0.88 0.88

time (sec)

N/A 0.000 0.232 1.457 0.319 0.318 0.062 0.286 14.232

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

22 42 25 20 22 22 20 33 22

N.S.

1 1.91 1.14 0.91 1.00 1.00 0.91 1.50 1.00

time (sec)

N/A 0.280 0.013 0.074 0.204 0.338 0.149 0.274 14.558

Problem 458

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

16 28 21 22 29 29 22 21 22

N.S.

1 1.75 1.31 1.38 1.81 1.81 1.38 1.31 1.38

time (sec)

N/A 0.261 0.036 0.156 0.219 0.357 0.044 0.281 14.495

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 31 31 28 45 42 26 27 37

N.S.

1 0.97 0.97 0.88 1.41 1.31 0.81 0.84 1.16

time (sec)

N/A 0.690 0.068 0.076 0.255 0.330 0.096 0.264 14.422

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A C A A F B

verified

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

size

35 0 28 32 33 30 26 0 25

N.S.

1 0.00 0.80 0.91 0.94 0.86 0.74 0.00 0.71

time (sec)

N/A 0.000 0.433 0.291 0.294 0.288 0.110 0.000 15.550

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

31 0 52 35 48 34 0 0 33

N.S.

1 0.00 1.68 1.13 1.55 1.10 0.00 0.00 1.06

time (sec)

N/A 0.000 1.022 7.088 0.478 0.284 0.000 0.000 16.456

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 0 0 24 26 24 22 26 0

N.S.

1 0.00 0.00 1.04 1.13 1.04 0.96 1.13 0.00

time (sec)

N/A 0.000 0.000 1.575 0.318 0.270 0.111 0.329 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 45 53 34 27 28 49 35 19

N.S.

1 1.80 2.12 1.36 1.08 1.12 1.96 1.40 0.76

time (sec)

N/A 0.800 0.073 0.391 0.327 0.289 0.134 0.278 0.397

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

28 0 32 38 36 32 51 36 0

N.S.

1 0.00 1.14 1.36 1.29 1.14 1.82 1.29 0.00

time (sec)

N/A 0.000 4.029 0.479 0.268 0.279 0.170 0.287 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 14 20 12 11 11 12 12 11

N.S.

1 0.93 1.33 0.80 0.73 0.73 0.80 0.80 0.73

time (sec)

N/A 0.148 0.008 0.744 0.196 0.262 0.044 0.261 14.829

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A B B B A A B

verified

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

size

28 0 28 103 78 63 29 39 184

N.S.

1 0.00 1.00 3.68 2.79 2.25 1.04 1.39 6.57

time (sec)

N/A 0.000 0.150 4.065 0.268 0.290 0.186 0.568 16.187

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 95 26 24 24 23 22 0 32

N.S.

1 3.39 0.93 0.86 0.86 0.82 0.79 0.00 1.14

time (sec)

N/A 0.447 1.047 1.546 0.283 0.290 0.111 0.000 15.578

Problem 468

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

21 38 28 30 37 57 36 59 112

N.S.

1 1.81 1.33 1.43 1.76 2.71 1.71 2.81 5.33

time (sec)

N/A 0.298 0.040 1.382 0.191 0.289 0.172 0.265 14.741

Problem 469

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

23 53 29 30 39 29 27 39 28

N.S.

1 2.30 1.26 1.30 1.70 1.26 1.17 1.70 1.22

time (sec)

N/A 0.187 0.050 0.144 0.199 0.276 0.069 0.268 0.100

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A B B B

verified

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

size

23 0 28 35 32 35 53 73 34

N.S.

1 0.00 1.22 1.52 1.39 1.52 2.30 3.17 1.48

time (sec)

N/A 0.000 0.548 1.429 0.339 0.292 0.127 0.401 14.798

Problem 471

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

32 0 28 44 28 46 41 42 164

N.S.

1 0.00 0.88 1.38 0.88 1.44 1.28 1.31 5.12

time (sec)

N/A 0.000 0.105 3.826 0.343 0.268 0.143 0.406 16.205

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C C B B B B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 902 949 50 399 49 49 0 49

N.S.

1 32.21 33.89 1.79 14.25 1.75 1.75 0.00 1.75

time (sec)

N/A 2.956 0.426 0.494 2.908 0.267 3.878 0.000 37.890

Problem 473

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 18 16 14 13 13 12 13 13

N.S.

1 0.82 0.73 0.64 0.59 0.59 0.55 0.59 0.59

time (sec)

N/A 0.142 0.003 0.062 0.193 0.282 0.036 0.264 0.053

Problem 474

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 18 18 18 17 24 17 24 17

N.S.

1 0.67 0.67 0.67 0.63 0.89 0.63 0.89 0.63

time (sec)

N/A 0.184 0.031 0.113 0.204 0.284 0.072 0.264 15.096

Problem 475

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 26 25 27 27 24 27 27

N.S.

1 2.04 1.04 1.00 1.08 1.08 0.96 1.08 1.08

time (sec)

N/A 0.745 0.473 0.936 0.368 0.278 0.142 0.439 14.868

Problem 476

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 17 15 16 22 18 10 34 15

N.S.

1 0.85 0.75 0.80 1.10 0.90 0.50 1.70 0.75

time (sec)

N/A 0.338 0.021 0.834 0.331 0.287 0.061 0.273 14.803

Problem 477

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

27 0 30 28 39 40 37 34 0

N.S.

1 0.00 1.11 1.04 1.44 1.48 1.37 1.26 0.00

time (sec)

N/A 0.000 3.821 1.013 0.268 0.279 0.217 0.279 0.000

Problem 478

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

26 73 31 25 32 28 31 28 23

N.S.

1 2.81 1.19 0.96 1.23 1.08 1.19 1.08 0.88

time (sec)

N/A 0.598 0.469 2.144 0.366 0.285 0.058 0.275 14.426

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

17 15 14 10 18 8 10 19 10

N.S.

1 0.88 0.82 0.59 1.06 0.47 0.59 1.12 0.59

time (sec)

N/A 0.133 0.002 0.119 0.211 0.269 0.022 0.259 0.041

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 0 21 23 29 23 0 37 22

N.S.

1 0.00 0.88 0.96 1.21 0.96 0.00 1.54 0.92

time (sec)

N/A 0.000 0.124 1.674 0.259 0.269 0.000 0.303 14.284

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F B B F B B F B

verified

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

size

31 0 71 77 0 71 76 0 38

N.S.

1 0.00 2.29 2.48 0.00 2.29 2.45 0.00 1.23

time (sec)

N/A 0.000 0.082 7.768 0.000 0.258 0.334 0.000 16.158

Problem 482

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 18 18 13 18 21 17 18 18

N.S.

1 1.29 1.29 0.93 1.29 1.50 1.21 1.29 1.29

time (sec)

N/A 0.523 0.048 3.079 0.244 0.257 0.088 0.269 16.728

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B A A B B

verified

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

size

21 0 21 18 47 17 19 104 519

N.S.

1 0.00 1.00 0.86 2.24 0.81 0.90 4.95 24.71

time (sec)

N/A 0.000 0.390 37.667 0.332 0.254 0.231 0.319 15.961

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 104 28 30 30 34 31 0 0

N.S.

1 3.71 1.00 1.07 1.07 1.21 1.11 0.00 0.00

time (sec)

N/A 0.531 0.446 4.480 0.490 0.247 0.274 0.000 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 14 13 13 14 13 13

N.S.

1 1.00 1.00 0.88 0.81 0.81 0.88 0.81 0.81

time (sec)

N/A 0.416 0.131 0.263 0.232 0.262 0.070 0.270 14.709

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 0 0 43 36 55 32 55 0

N.S.

1 0.00 0.00 1.65 1.38 2.12 1.23 2.12 0.00

time (sec)

N/A 0.000 0.000 2.977 0.369 0.257 1.198 0.512 0.000

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 11 11 12 11 11 10 12 11

N.S.

1 0.85 0.85 0.92 0.85 0.85 0.77 0.92 0.85

time (sec)

N/A 0.145 0.001 0.108 0.211 0.234 0.035 0.264 13.964

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

15 16 21 16 15 12 15 18 15

N.S.

1 1.07 1.40 1.07 1.00 0.80 1.00 1.20 1.00

time (sec)

N/A 0.200 0.022 0.586 0.231 0.258 0.106 0.262 14.094

Problem 489

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

35 0 42 46 43 51 39 1129 0

N.S.

1 0.00 1.20 1.31 1.23 1.46 1.11 32.26 0.00

time (sec)

N/A 0.000 0.317 46.305 0.689 0.266 0.418 3.211 0.000

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

20 17 16 11 13 13 19 13 10

N.S.

1 0.85 0.80 0.55 0.65 0.65 0.95 0.65 0.50

time (sec)

N/A 0.149 0.003 0.166 0.201 0.241 0.023 0.260 0.032

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 53 21 20 21 19 22 19 0

N.S.

1 2.41 0.95 0.91 0.95 0.86 1.00 0.86 0.00

time (sec)

N/A 0.271 0.152 0.263 0.271 0.235 0.146 0.275 0.000

Problem 492

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

27 0 23 27 22 25 20 25 22

N.S.

1 0.00 0.85 1.00 0.81 0.93 0.74 0.93 0.81

time (sec)

N/A 0.000 0.589 0.138 0.241 0.254 0.101 0.266 15.202

Problem 493

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

31 0 48 49 53 43 34 0 58

N.S.

1 0.00 1.55 1.58 1.71 1.39 1.10 0.00 1.87

time (sec)

N/A 0.000 0.216 1.159 0.476 0.242 1.875 0.000 14.814

Problem 494

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

14 0 14 21 18 20 12 14 60

N.S.

1 0.00 1.00 1.50 1.29 1.43 0.86 1.00 4.29

time (sec)

N/A 0.000 0.114 1.534 0.254 0.225 0.141 0.287 14.609

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B A C B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 51 46 34 103 36 36 41 37

N.S.

1 2.55 2.30 1.70 5.15 1.80 1.80 2.05 1.85

time (sec)

N/A 0.274 0.397 0.359 0.248 0.244 0.079 0.277 14.172

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 40 27 24 55 27 22 55 44

N.S.

1 1.33 0.90 0.80 1.83 0.90 0.73 1.83 1.47

time (sec)

N/A 0.248 0.759 0.547 0.383 0.242 0.092 0.281 0.150

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

18 32 31 23 27 28 29 27 27

N.S.

1 1.78 1.72 1.28 1.50 1.56 1.61 1.50 1.50

time (sec)

N/A 0.167 0.008 1.302 0.206 0.263 0.134 0.264 14.011

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

28 0 53 0 0 40 39 0 40

N.S.

1 0.00 1.89 0.00 0.00 1.43 1.39 0.00 1.43

time (sec)

N/A 0.000 0.488 0.000 0.000 0.249 5.944 0.000 14.461

Problem 499

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

26 0 27 25 23 25 19 48 25

N.S.

1 0.00 1.04 0.96 0.88 0.96 0.73 1.85 0.96

time (sec)

N/A 0.000 0.633 1.231 0.224 0.251 0.082 0.293 0.368

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 81 81 22 21 21 20 21 23

N.S.

1 2.70 2.70 0.73 0.70 0.70 0.67 0.70 0.77

time (sec)

N/A 0.289 0.142 0.187 0.195 0.308 0.075 0.276 0.087

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