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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 20 20 18 17 17 15 17 17

N.S.

1 1.00 1.00 0.90 0.85 0.85 0.75 0.85 0.85

time (sec)

N/A 0.160 0.022 0.022 0.186 0.240 0.037 0.300 7.596

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A C A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 90 18 23 48 22 19 77 18

N.S.

1 5.00 1.00 1.28 2.67 1.22 1.06 4.28 1.00

time (sec)

N/A 0.566 0.023 0.091 0.218 0.263 0.085 0.293 7.612

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 15 15 14 13 29 10 13 13

N.S.

1 0.88 0.88 0.82 0.76 1.71 0.59 0.76 0.76

time (sec)

N/A 0.151 0.057 0.023 0.229 0.237 0.050 0.285 0.095

Problem 404

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

27 99 72 84 87 87 92 87 84

N.S.

1 3.67 2.67 3.11 3.22 3.22 3.41 3.22 3.11

time (sec)

N/A 0.247 0.029 0.026 0.183 0.232 0.032 0.295 7.180

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

17 12 14 13 14 12 10 14 12

N.S.

1 0.71 0.82 0.76 0.82 0.71 0.59 0.82 0.71

time (sec)

N/A 0.164 0.008 0.018 0.189 0.223 0.034 0.284 0.036

Problem 406

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

24 0 0 30 41 36 31 28 0

N.S.

1 0.00 0.00 1.25 1.71 1.50 1.29 1.17 0.00

time (sec)

N/A 0.000 0.000 0.603 0.303 0.235 0.276 0.313 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

14 13 13 14 13 13 8 13 12

N.S.

1 0.93 0.93 1.00 0.93 0.93 0.57 0.93 0.86

time (sec)

N/A 0.347 0.056 0.041 0.218 0.235 0.066 0.287 0.119

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 16 16 15 14 14 14 14 0

N.S.

1 0.89 0.89 0.83 0.78 0.78 0.78 0.78 0.00

time (sec)

N/A 0.437 0.027 0.372 0.218 0.229 0.072 0.334 0.000

Problem 409

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 24 11 11 11 10 8 10 10

N.S.

1 1.50 0.69 0.69 0.69 0.62 0.50 0.62 0.62

time (sec)

N/A 0.177 0.023 0.122 0.176 0.230 0.033 0.295 7.628

Problem 410

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

35 37 36 30 28 53 24 30 27

N.S.

1 1.06 1.03 0.86 0.80 1.51 0.69 0.86 0.77

time (sec)

N/A 0.416 0.034 0.053 0.182 0.236 0.531 0.291 0.136

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 0 34 103 72 54 24 77 0

N.S.

1 0.00 1.06 3.22 2.25 1.69 0.75 2.41 0.00

time (sec)

N/A 0.000 0.188 5.267 0.283 0.240 0.231 1.135 0.000

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 0 31 31 79 30 0 0 78

N.S.

1 0.00 1.07 1.07 2.72 1.03 0.00 0.00 2.69

time (sec)

N/A 0.000 0.397 0.037 0.657 0.241 0.000 0.000 8.681

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

28 0 27 32 0 46 31 0 28

N.S.

1 0.00 0.96 1.14 0.00 1.64 1.11 0.00 1.00

time (sec)

N/A 0.000 0.294 5.978 0.000 0.242 0.821 0.000 7.890

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 0 0 33 50 51 34 56 0

N.S.

1 0.00 0.00 1.10 1.67 1.70 1.13 1.87 0.00

time (sec)

N/A 0.000 0.000 0.343 0.314 0.258 0.094 0.328 0.000

Problem 415

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

24 74 35 19 168 18 29 41 26

N.S.

1 3.08 1.46 0.79 7.00 0.75 1.21 1.71 1.08

time (sec)

N/A 0.754 0.087 0.143 0.323 0.235 0.113 0.325 8.359

Problem 416

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 52 52 66 82 73 58 442 90

N.S.

1 2.36 2.36 3.00 3.73 3.32 2.64 20.09 4.09

time (sec)

N/A 0.221 0.013 0.104 0.190 0.235 0.054 0.299 0.114

Problem 417

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

23 147 23 72 133 95 80 125 76

N.S.

1 6.39 1.00 3.13 5.78 4.13 3.48 5.43 3.30

time (sec)

N/A 0.336 0.205 0.080 0.181 0.250 0.159 0.292 7.719

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

7 7 7 7 6 6 5 6 6

N.S.

1 1.00 1.00 1.00 0.86 0.86 0.71 0.86 0.86

time (sec)

N/A 0.135 0.016 0.015 0.173 0.220 0.032 0.278 0.036

Problem 419

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 37 42 45 38 36 38 35

N.S.

1 0.00 1.32 1.50 1.61 1.36 1.29 1.36 1.25

time (sec)

N/A 0.000 0.120 0.135 0.254 0.255 0.108 0.338 0.294

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 381 51 74 207 138 87 174 126

N.S.

1 11.91 1.59 2.31 6.47 4.31 2.72 5.44 3.94

time (sec)

N/A 2.793 0.264 0.234 0.317 0.249 0.106 0.312 0.228

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

24 21 30 22 21 26 19 22 19

N.S.

1 0.88 1.25 0.92 0.88 1.08 0.79 0.92 0.79

time (sec)

N/A 0.164 0.013 0.152 0.174 0.239 0.092 0.282 0.184

Problem 422

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

31 0 31 27 27 27 22 566 168

N.S.

1 0.00 1.00 0.87 0.87 0.87 0.71 18.26 5.42

time (sec)

N/A 0.000 0.464 56.897 0.312 0.249 0.216 0.568 7.968

Problem 423

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

26 71 39 46 46 46 42 51 48

N.S.

1 2.73 1.50 1.77 1.77 1.77 1.62 1.96 1.85

time (sec)

N/A 0.402 0.638 0.046 0.199 0.239 0.072 0.295 0.143

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A C A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 87 31 59 86 55 70 63 28

N.S.

1 2.64 0.94 1.79 2.61 1.67 2.12 1.91 0.85

time (sec)

N/A 0.432 0.278 0.095 0.241 0.246 0.102 0.286 7.523

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

22 29 22 23 25 28 19 29 23

N.S.

1 1.32 1.00 1.05 1.14 1.27 0.86 1.32 1.05

time (sec)

N/A 0.192 0.070 0.023 0.182 0.243 0.050 0.285 7.685

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A B A B B

verified

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

size

30 0 31 36 47 108 31 129 49

N.S.

1 0.00 1.03 1.20 1.57 3.60 1.03 4.30 1.63

time (sec)

N/A 0.000 0.708 14.226 0.372 0.253 5.161 2.946 8.842

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

28 24 24 21 20 20 20 20 22

N.S.

1 0.86 0.86 0.75 0.71 0.71 0.71 0.71 0.79

time (sec)

N/A 0.235 0.101 0.067 0.192 0.247 0.059 0.273 0.165

Problem 428

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

33 33 33 30 28 30 31 28 28

N.S.

1 1.00 1.00 0.91 0.85 0.91 0.94 0.85 0.85

time (sec)

N/A 0.196 0.004 0.019 0.180 0.245 0.035 0.276 8.241

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

26 52 48 39 36 57 34 47 45

N.S.

1 2.00 1.85 1.50 1.38 2.19 1.31 1.81 1.73

time (sec)

N/A 0.411 0.350 0.115 0.189 0.247 0.067 0.301 8.145

Problem 430

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

18 56 56 57 63 53 53 56 19

N.S.

1 3.11 3.11 3.17 3.50 2.94 2.94 3.11 1.06

time (sec)

N/A 0.215 0.017 0.033 0.191 0.251 0.069 0.289 8.341

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B B A F B

verified

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

size

21 0 17 25 49 74 22 0 40

N.S.

1 0.00 0.81 1.19 2.33 3.52 1.05 0.00 1.90

time (sec)

N/A 0.000 5.302 1.254 0.724 0.276 0.658 0.000 8.464

Problem 432

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

32 0 48 51 80 49 44 67 110

N.S.

1 0.00 1.50 1.59 2.50 1.53 1.38 2.09 3.44

time (sec)

N/A 0.000 0.256 0.528 0.509 0.240 0.275 0.907 8.850

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 180 34 41 36 32 37 0 40

N.S.

1 5.14 0.97 1.17 1.03 0.91 1.06 0.00 1.14

time (sec)

N/A 16.688 0.303 8.575 0.309 0.236 0.203 0.000 8.683

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 73 31 45 27 41 26 54 0

N.S.

1 2.61 1.11 1.61 0.96 1.46 0.93 1.93 0.00

time (sec)

N/A 1.340 1.349 1.412 0.243 0.240 0.165 0.287 0.000

Problem 435

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 62 21 27 29 29 24 30 21

N.S.

1 2.70 0.91 1.17 1.26 1.26 1.04 1.30 0.91

time (sec)

N/A 2.184 0.373 4.567 0.213 0.237 0.257 0.288 8.368

Problem 436

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

27 0 26 30 26 27 31 0 47

N.S.

1 0.00 0.96 1.11 0.96 1.00 1.15 0.00 1.74

time (sec)

N/A 0.000 0.118 15.949 0.397 0.242 2.061 0.000 9.626

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A B B B B B B

verified

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

size

25 0 43 53 173 53 41 53 48

N.S.

1 0.00 1.72 2.12 6.92 2.12 1.64 2.12 1.92

time (sec)

N/A 0.000 0.081 0.502 0.302 0.233 0.068 0.463 8.259

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B B A F B

verified

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

size

27 0 30 21 59 56 49 0 65

N.S.

1 0.00 1.11 0.78 2.19 2.07 1.81 0.00 2.41

time (sec)

N/A 0.000 5.102 0.214 0.525 0.233 0.265 0.000 8.963

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A C A A B B

verified

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

size

28 0 39 32 77 23 49 46 43

N.S.

1 0.00 1.39 1.14 2.75 0.82 1.75 1.64 1.54

time (sec)

N/A 0.000 0.192 0.036 0.225 0.248 0.055 0.280 8.165

Problem 440

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

21 0 21 21 21 21 19 0 20

N.S.

1 0.00 1.00 1.00 1.00 1.00 0.90 0.00 0.95

time (sec)

N/A 0.000 2.599 0.676 0.215 0.230 0.094 0.000 8.648

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 12 10 11 10 10 7 10 10

N.S.

1 0.80 0.67 0.73 0.67 0.67 0.47 0.67 0.67

time (sec)

N/A 0.158 0.006 0.034 0.176 0.230 0.037 0.319 8.533

Problem 442

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 27 28 44 56 24 56 34

N.S.

1 0.00 0.90 0.93 1.47 1.87 0.80 1.87 1.13

time (sec)

N/A 0.000 1.835 0.050 0.208 0.239 0.066 0.278 9.344

Problem 443

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 13 11 12 11 11 10 11 9

N.S.

1 0.93 0.79 0.86 0.79 0.79 0.71 0.79 0.64

time (sec)

N/A 0.141 0.003 0.018 0.169 0.227 0.033 0.288 0.056

Problem 444

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

9 15 13 11 15 9 8 13 9

N.S.

1 1.67 1.44 1.22 1.67 1.00 0.89 1.44 1.00

time (sec)

N/A 0.151 0.004 0.012 0.171 0.232 0.042 0.283 9.229

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 0 33 52 0 51 42 0 141

N.S.

1 0.00 1.03 1.62 0.00 1.59 1.31 0.00 4.41

time (sec)

N/A 0.000 0.481 157.885 0.000 0.238 7.757 0.000 10.134

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 0 0 32 61 29 36 0 0

N.S.

1 0.00 0.00 1.60 3.05 1.45 1.80 0.00 0.00

time (sec)

N/A 0.000 0.000 0.421 0.298 0.237 0.207 0.000 0.000

Problem 447

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 19 15 41 44 17 14 14

N.S.

1 2.17 0.83 0.65 1.78 1.91 0.74 0.61 0.61

time (sec)

N/A 0.363 0.043 0.344 0.328 0.239 0.164 0.286 0.199

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C B A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 2439 69 32 243 55 26 32 239

N.S.

1 78.68 2.23 1.03 7.84 1.77 0.84 1.03 7.71

time (sec)

N/A 4.980 5.096 0.161 0.487 0.248 0.194 0.285 8.496

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A C B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 241 35 32 259 75 90 82 31

N.S.

1 10.48 1.52 1.39 11.26 3.26 3.91 3.57 1.35

time (sec)

N/A 0.524 0.038 0.073 0.182 0.243 0.113 0.272 8.111

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

19 16 21 20 18 20 17 18 19

N.S.

1 0.84 1.11 1.05 0.95 1.05 0.89 0.95 1.00

time (sec)

N/A 0.132 0.000 0.013 0.192 0.231 0.016 0.270 0.002

Problem 451

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 16 16 16 15 15 12 15 15

N.S.

1 0.67 0.67 0.67 0.62 0.62 0.50 0.62 0.62

time (sec)

N/A 0.155 0.019 0.014 0.177 0.230 0.039 0.269 0.063

Problem 452

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

23 0 23 24 41 42 19 42 139

N.S.

1 0.00 1.00 1.04 1.78 1.83 0.83 1.83 6.04

time (sec)

N/A 0.000 0.111 0.401 0.289 0.239 0.124 0.346 0.682

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

13 13 16 14 13 13 14 13 13

N.S.

1 1.00 1.23 1.08 1.00 1.00 1.08 1.00 1.00

time (sec)

N/A 0.180 0.000 0.011 0.178 0.227 0.014 0.260 0.002

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 79 21 16 0 15 0 0 15

N.S.

1 3.95 1.05 0.80 0.00 0.75 0.00 0.00 0.75

time (sec)

N/A 0.250 2.447 0.107 0.000 0.242 0.000 0.000 8.114

Problem 455

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

28 44 30 27 26 20 32 26 24

N.S.

1 1.57 1.07 0.96 0.93 0.71 1.14 0.93 0.86

time (sec)

N/A 0.487 0.060 0.186 0.214 0.258 0.129 0.274 8.229

Problem 456

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 11 11

N.S.

1 0.85 0.85 0.92 0.85 0.85 0.77 0.85 0.85

time (sec)

N/A 0.135 0.004 0.554 0.178 0.244 0.033 0.273 7.993

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 22 19 23 65 22 19 0 19

N.S.

1 1.05 0.90 1.10 3.10 1.05 0.90 0.00 0.90

time (sec)

N/A 0.424 0.028 0.694 0.219 0.245 0.126 0.000 9.371

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 0 23 40 19 47 0 0 24

N.S.

1 0.00 1.00 1.74 0.83 2.04 0.00 0.00 1.04

time (sec)

N/A 0.000 0.295 0.359 0.240 0.248 0.000 0.000 8.424

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

29 27 27 26 19 27 19 21 17

N.S.

1 0.93 0.93 0.90 0.66 0.93 0.66 0.72 0.59

time (sec)

N/A 0.291 0.184 33.135 0.301 0.235 0.253 0.358 9.574

Problem 460

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

17 21 21 20 33 19 19 19 12

N.S.

1 1.24 1.24 1.18 1.94 1.12 1.12 1.12 0.71

time (sec)

N/A 0.183 0.010 0.023 0.184 0.235 0.046 0.282 8.149

Problem 461

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 16 7 16 7

N.S.

1 1.00 1.00 0.80 0.70 1.60 0.70 1.60 0.70

time (sec)

N/A 0.128 0.001 0.025 0.185 0.237 0.028 0.265 7.699

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

14 13 21 15 14 14 14 14 14

N.S.

1 0.93 1.50 1.07 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.178 0.009 0.157 0.195 0.256 0.043 0.271 0.062

Problem 463

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

18 32 28 23 31 24 26 24 17

N.S.

1 1.78 1.56 1.28 1.72 1.33 1.44 1.33 0.94

time (sec)

N/A 0.235 0.067 0.079 0.222 0.240 0.065 0.272 8.085

Problem 464

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

30 0 97 88 99 116 71 89 0

N.S.

1 0.00 3.23 2.93 3.30 3.87 2.37 2.97 0.00

time (sec)

N/A 0.000 0.210 0.174 0.252 0.253 2.387 0.364 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

16 21 10 8 16 8 10 7 7

N.S.

1 1.31 0.62 0.50 1.00 0.50 0.62 0.44 0.44

time (sec)

N/A 0.168 0.028 0.025 0.185 0.239 0.036 0.269 8.321

Problem 466

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 49 27 22 22 21 26 31 22

N.S.

1 2.13 1.17 0.96 0.96 0.91 1.13 1.35 0.96

time (sec)

N/A 0.309 0.032 0.132 0.225 0.234 0.430 0.271 0.231

Problem 467

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

32 0 31 28 89 30 26 65 68

N.S.

1 0.00 0.97 0.88 2.78 0.94 0.81 2.03 2.12

time (sec)

N/A 0.000 1.787 0.256 0.438 0.237 0.529 0.273 10.076

Problem 468

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 11 11 12 11 11 12 12 11

N.S.

1 0.65 0.65 0.71 0.65 0.65 0.71 0.71 0.65

time (sec)

N/A 0.305 0.102 0.255 0.183 0.233 0.139 0.301 8.522

Problem 469

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

8 8 8 6 5 5 5 5 5

N.S.

1 1.00 1.00 0.75 0.62 0.62 0.62 0.62 0.62

time (sec)

N/A 0.130 0.000 0.023 0.195 0.232 0.014 0.297 0.024

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A C A A A B

verified

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

size

22 0 23 16 19 23 12 23 15

N.S.

1 0.00 1.05 0.73 0.86 1.05 0.55 1.05 0.68

time (sec)

N/A 0.000 0.153 0.074 0.235 0.247 0.100 0.277 7.425

Problem 471

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 38 26 23 32 30 22 33 23

N.S.

1 1.58 1.08 0.96 1.33 1.25 0.92 1.38 0.96

time (sec)

N/A 0.221 0.010 0.092 0.210 0.252 0.069 0.294 7.377

Problem 472

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 19 19 16 18 18 14 18 15

N.S.

1 0.86 0.86 0.73 0.82 0.82 0.64 0.82 0.68

time (sec)

N/A 0.155 0.000 0.018 0.170 0.236 0.024 0.273 0.034

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 0 62 64 0 58 0 0 75

N.S.

1 0.00 1.94 2.00 0.00 1.81 0.00 0.00 2.34

time (sec)

N/A 0.000 0.429 28.659 0.000 0.267 0.000 0.000 7.992

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

29 37 16 17 16 16 12 16 16

N.S.

1 1.28 0.55 0.59 0.55 0.55 0.41 0.55 0.55

time (sec)

N/A 0.332 0.010 0.036 0.185 0.248 0.043 0.272 7.458

Problem 475

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 13 10 13 17 7 13 9

N.S.

1 0.68 0.68 0.53 0.68 0.89 0.37 0.68 0.47

time (sec)

N/A 0.166 0.009 0.198 0.196 0.241 0.032 0.280 0.042

Problem 476

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 30 28 27 27 24 27 28

N.S.

1 0.00 0.97 0.90 0.87 0.87 0.77 0.87 0.90

time (sec)

N/A 0.000 1.462 0.064 0.214 0.248 0.076 0.286 7.474

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 65 49 45 0 70 68 165 41

N.S.

1 2.32 1.75 1.61 0.00 2.50 2.43 5.89 1.46

time (sec)

N/A 0.665 0.660 0.253 0.000 0.256 0.106 0.296 7.443

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F B A B B B F B

verified

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

size

32 0 107 58 120 62 65 0 138

N.S.

1 0.00 3.34 1.81 3.75 1.94 2.03 0.00 4.31

time (sec)

N/A 0.000 1.575 298.026 0.527 0.266 16.591 0.000 8.129

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

22 26 22 20 22 20 20 22 23

N.S.

1 1.18 1.00 0.91 1.00 0.91 0.91 1.00 1.05

time (sec)

N/A 0.153 0.008 0.036 0.170 0.243 0.062 0.270 7.328

Problem 480

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

23 0 23 24 25 23 53 35 20

N.S.

1 0.00 1.00 1.04 1.09 1.00 2.30 1.52 0.87

time (sec)

N/A 0.000 1.905 1.877 0.288 0.258 10.760 0.361 7.546

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A B A F B

verified

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

size

21 0 21 16 21 61 22 0 22

N.S.

1 0.00 1.00 0.76 1.00 2.90 1.05 0.00 1.05

time (sec)

N/A 0.000 3.215 1.316 0.360 0.268 1.316 0.000 7.355

Problem 482

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

15 0 15 16 15 15 10 15 15

N.S.

1 0.00 1.00 1.07 1.00 1.00 0.67 1.00 1.00

time (sec)

N/A 0.000 0.387 0.990 0.208 0.240 0.044 0.279 0.226

Problem 483

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

20 47 17 18 29 17 17 32 17

N.S.

1 2.35 0.85 0.90 1.45 0.85 0.85 1.60 0.85

time (sec)

N/A 0.606 0.116 0.355 0.207 0.250 0.122 0.278 7.459

Problem 484

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 16 15 13 14 15 15

N.S.

1 1.00 1.00 1.00 0.94 0.81 0.88 0.94 0.94

time (sec)

N/A 0.203 0.023 0.053 0.209 0.256 0.093 0.275 7.583

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 65 22 37 55 39 51 74 25

N.S.

1 2.95 1.00 1.68 2.50 1.77 2.32 3.36 1.14

time (sec)

N/A 0.211 0.024 0.240 0.175 0.250 0.099 0.274 7.545

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F F A B A A A B

verified

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

size

28 0 0 27 50 25 22 29 25

N.S.

1 0.00 0.00 0.96 1.79 0.89 0.79 1.04 0.89

time (sec)

N/A 0.000 0.000 0.133 0.288 0.252 0.163 0.676 7.886

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

22 18 18 17 18 18 15 20 18

N.S.

1 0.82 0.82 0.77 0.82 0.82 0.68 0.91 0.82

time (sec)

N/A 0.337 0.118 0.240 0.280 0.250 0.072 0.282 7.704

Problem 488

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

25 0 23 20 21 19 17 139 19

N.S.

1 0.00 0.92 0.80 0.84 0.76 0.68 5.56 0.76

time (sec)

N/A 0.000 0.250 0.198 0.289 0.254 0.087 0.309 7.719

Problem 489

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

24 0 27 22 25 25 22 67 31

N.S.

1 0.00 1.12 0.92 1.04 1.04 0.92 2.79 1.29

time (sec)

N/A 0.000 0.641 0.343 0.280 0.254 0.123 0.328 7.833

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 36 21 22 35 30 46 44 20

N.S.

1 1.71 1.00 1.05 1.67 1.43 2.19 2.10 0.95

time (sec)

N/A 0.196 0.006 0.038 0.173 0.235 0.057 0.297 0.072

Problem 491

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

18 17 17 16 15 41 15 41 15

N.S.

1 0.94 0.94 0.89 0.83 2.28 0.83 2.28 0.83

time (sec)

N/A 0.190 0.029 0.033 0.169 0.263 0.066 0.282 7.330

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

14 14 14 13 15 15 14 23 17

N.S.

1 1.00 1.00 0.93 1.07 1.07 1.00 1.64 1.21

time (sec)

N/A 0.163 0.008 0.026 0.197 0.239 0.082 0.284 7.243

Problem 493

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 13 8 13 8 11 8 8 8

N.S.

1 0.87 0.53 0.87 0.53 0.73 0.53 0.53 0.53

time (sec)

N/A 0.131 0.000 0.004 0.179 0.232 0.015 0.287 0.002

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F F C F A A F B

verified

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

size

31 0 0 192 0 40 31 0 30

N.S.

1 0.00 0.00 6.19 0.00 1.29 1.00 0.00 0.97

time (sec)

N/A 0.000 0.000 0.148 0.000 0.249 51.404 0.000 8.240

Problem 495

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 22 18 22 20 21 20 23 16

N.S.

1 1.38 1.12 1.38 1.25 1.31 1.25 1.44 1.00

time (sec)

N/A 0.171 0.016 0.084 0.176 0.250 0.112 0.278 7.491

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

14 39 14 14 13 13 10 13 13

N.S.

1 2.79 1.00 1.00 0.93 0.93 0.71 0.93 0.93

time (sec)

N/A 0.465 0.018 0.186 0.217 0.245 0.075 0.277 7.694

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

14 17 17 18 17 15 14 17 17

N.S.

1 1.21 1.21 1.29 1.21 1.07 1.00 1.21 1.21

time (sec)

N/A 0.165 0.003 0.028 0.172 0.244 0.048 0.275 7.361

Problem 498

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

28 23 37 23 38 45 36 38 44

N.S.

1 0.82 1.32 0.82 1.36 1.61 1.29 1.36 1.57

time (sec)

N/A 0.268 0.027 0.059 0.204 0.243 0.410 0.273 7.527

Problem 499

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

23 0 20 46 55 49 42 57 0

N.S.

1 0.00 0.87 2.00 2.39 2.13 1.83 2.48 0.00

time (sec)

N/A 0.000 5.032 0.116 0.219 0.252 0.166 0.296 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

22 16 16 22 21 21 24 22 16

N.S.

1 0.73 0.73 1.00 0.95 0.95 1.09 1.00 0.73

time (sec)

N/A 0.163 0.004 0.033 0.178 0.244 0.047 0.280 0.060

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