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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 C A F C A F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

508 532 52 463 0 58 39 0 0

N.S.

1 1.05 0.10 0.91 0.00 0.11 0.08 0.00 0.00

time (sec)

N/A 0.541 5.241 3.826 0.000 0.076 0.518 0.000 0.000

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

504 530 50 458 0 51 41 0 40

N.S.

1 1.05 0.10 0.91 0.00 0.10 0.08 0.00 0.08

time (sec)

N/A 0.533 6.982 3.869 0.000 0.087 0.535 0.000 6.234

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

505 530 52 458 0 51 46 0 0

N.S.

1 1.05 0.10 0.91 0.00 0.10 0.09 0.00 0.00

time (sec)

N/A 0.527 10.009 3.963 0.000 0.092 0.579 0.000 0.000

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

80 80 50 47 64 46 94 61 73

N.S.

1 1.00 0.62 0.59 0.80 0.58 1.18 0.76 0.91

time (sec)

N/A 0.213 0.031 3.888 0.192 0.248 0.382 0.289 6.142

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

59 61 39 36 47 35 70 47 35

N.S.

1 1.03 0.66 0.61 0.80 0.59 1.19 0.80 0.59

time (sec)

N/A 0.204 0.030 3.717 0.200 0.261 0.279 0.261 5.926

Problem 406

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

38 40 27 25 30 23 46 30 24

N.S.

1 1.05 0.71 0.66 0.79 0.61 1.21 0.79 0.63

time (sec)

N/A 0.184 0.024 3.820 0.191 0.258 0.189 0.264 5.787

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

18 18 18 15 14 14 24 14 14

N.S.

1 1.00 1.00 0.83 0.78 0.78 1.33 0.78 0.78

time (sec)

N/A 0.146 0.012 3.725 0.197 0.254 0.082 0.258 5.806

Problem 408

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 27 27 20 37 63 26 23 40

N.S.

1 1.00 1.00 0.74 1.37 2.33 0.96 0.85 1.48

time (sec)

N/A 0.165 0.021 3.767 0.284 0.272 0.549 0.257 5.922

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

50 49 50 39 68 107 49 51 59

N.S.

1 0.98 1.00 0.78 1.36 2.14 0.98 1.02 1.18

time (sec)

N/A 0.177 0.047 3.617 0.286 0.260 1.199 0.271 5.969

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

74 79 62 51 104 137 104 75 79

N.S.

1 1.07 0.84 0.69 1.41 1.85 1.41 1.01 1.07

time (sec)

N/A 0.196 0.086 3.702 0.278 0.283 2.578 0.271 6.080

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

254 260 79 312 0 47 37 0 0

N.S.

1 1.02 0.31 1.23 0.00 0.19 0.15 0.00 0.00

time (sec)

N/A 0.293 10.027 3.746 0.000 0.080 0.494 0.000 0.000

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

230 230 62 300 0 33 37 0 0

N.S.

1 1.00 0.27 1.30 0.00 0.14 0.16 0.00 0.00

time (sec)

N/A 0.260 10.019 3.742 0.000 0.073 0.445 0.000 0.000

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

207 207 46 283 0 14 36 0 37

N.S.

1 1.00 0.22 1.37 0.00 0.07 0.17 0.00 0.18

time (sec)

N/A 0.230 10.014 3.718 0.000 0.073 0.424 0.000 5.614

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

234 234 51 301 0 34 41 0 0

N.S.

1 1.00 0.22 1.29 0.00 0.15 0.18 0.00 0.00

time (sec)

N/A 0.253 10.009 3.819 0.000 0.079 0.515 0.000 0.000

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

256 264 51 312 0 46 44 0 0

N.S.

1 1.03 0.20 1.22 0.00 0.18 0.17 0.00 0.00

time (sec)

N/A 0.286 10.008 3.877 0.000 0.078 0.586 0.000 0.000

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

514 544 80 466 0 58 37 0 0

N.S.

1 1.06 0.16 0.91 0.00 0.11 0.07 0.00 0.00

time (sec)

N/A 0.537 10.028 3.886 0.000 0.077 0.506 0.000 0.000

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

490 514 64 454 0 43 37 0 0

N.S.

1 1.05 0.13 0.93 0.00 0.09 0.08 0.00 0.00

time (sec)

N/A 0.516 10.023 3.831 0.000 0.075 0.477 0.000 0.000

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

462 484 51 435 0 22 37 0 0

N.S.

1 1.05 0.11 0.94 0.00 0.05 0.08 0.00 0.00

time (sec)

N/A 0.483 10.013 3.758 0.000 0.074 0.430 0.000 0.000

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

484 512 49 453 0 40 39 0 40

N.S.

1 1.06 0.10 0.94 0.00 0.08 0.08 0.00 0.08

time (sec)

N/A 0.519 10.014 4.078 0.000 0.081 0.481 0.000 5.887

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

514 542 51 464 0 54 44 0 0

N.S.

1 1.05 0.10 0.90 0.00 0.11 0.09 0.00 0.00

time (sec)

N/A 0.568 10.010 3.889 0.000 0.081 0.568 0.000 0.000

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

78 78 49 46 64 57 94 69 70

N.S.

1 1.00 0.63 0.59 0.82 0.73 1.21 0.88 0.90

time (sec)

N/A 0.216 0.036 3.789 0.195 0.270 0.434 0.271 5.826

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

59 59 38 35 47 46 70 52 41

N.S.

1 1.00 0.64 0.59 0.80 0.78 1.19 0.88 0.69

time (sec)

N/A 0.198 0.036 3.864 0.212 0.269 0.320 0.267 5.831

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

38 38 27 24 30 35 46 33 24

N.S.

1 1.00 0.71 0.63 0.79 0.92 1.21 0.87 0.63

time (sec)

N/A 0.182 0.029 3.754 0.220 0.257 0.211 0.271 5.604

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

18 18 18 15 14 24 26 14 14

N.S.

1 1.00 1.00 0.83 0.78 1.33 1.44 0.78 0.78

time (sec)

N/A 0.144 0.017 3.797 0.195 0.267 0.103 0.279 5.537

Problem 425

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

46 46 46 39 52 129 184 41 55

N.S.

1 1.00 1.00 0.85 1.13 2.80 4.00 0.89 1.20

time (sec)

N/A 0.174 0.053 3.789 0.278 0.265 0.907 0.259 5.685

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

64 74 57 57 86 173 75 72 74

N.S.

1 1.16 0.89 0.89 1.34 2.70 1.17 1.12 1.16

time (sec)

N/A 0.190 0.069 3.860 0.287 0.278 1.730 0.276 5.988

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

95 104 73 74 122 203 112 88 96

N.S.

1 1.09 0.77 0.78 1.28 2.14 1.18 0.93 1.01

time (sec)

N/A 0.203 0.094 3.784 0.304 0.272 3.767 0.279 6.110

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

251 259 65 320 0 67 37 0 0

N.S.

1 1.03 0.26 1.27 0.00 0.27 0.15 0.00 0.00

time (sec)

N/A 0.288 4.413 4.334 0.000 0.077 0.514 0.000 0.000

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

229 229 55 303 0 51 37 0 0

N.S.

1 1.00 0.24 1.32 0.00 0.22 0.16 0.00 0.00

time (sec)

N/A 0.250 3.892 3.861 0.000 0.077 0.460 0.000 0.000

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

232 232 55 306 0 51 36 0 37

N.S.

1 1.00 0.24 1.32 0.00 0.22 0.16 0.00 0.16

time (sec)

N/A 0.255 3.477 3.819 0.000 0.080 0.501 0.000 5.607

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

255 263 54 321 0 66 41 0 0

N.S.

1 1.03 0.21 1.26 0.00 0.26 0.16 0.00 0.00

time (sec)

N/A 0.282 9.992 4.232 0.000 0.086 0.549 0.000 0.000

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

277 293 54 342 0 80 44 0 0

N.S.

1 1.06 0.19 1.23 0.00 0.29 0.16 0.00 0.00

time (sec)

N/A 0.308 10.012 4.168 0.000 0.083 0.637 0.000 0.000

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

511 543 66 476 0 76 37 0 0

N.S.

1 1.06 0.13 0.93 0.00 0.15 0.07 0.00 0.00

time (sec)

N/A 0.537 4.523 4.306 0.000 0.081 0.542 0.000 0.000

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

487 513 55 457 0 61 37 0 0

N.S.

1 1.05 0.11 0.94 0.00 0.13 0.08 0.00 0.00

time (sec)

N/A 0.513 4.254 3.827 0.000 0.082 0.481 0.000 0.000

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

489 513 54 460 0 61 37 0 0

N.S.

1 1.05 0.11 0.94 0.00 0.12 0.08 0.00 0.00

time (sec)

N/A 0.518 3.465 3.784 0.000 0.079 0.467 0.000 0.000

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

513 541 52 475 0 70 39 0 40

N.S.

1 1.05 0.10 0.93 0.00 0.14 0.08 0.00 0.08

time (sec)

N/A 0.538 6.355 4.190 0.000 0.083 0.554 0.000 5.993

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

535 571 54 496 0 88 44 0 0

N.S.

1 1.07 0.10 0.93 0.00 0.16 0.08 0.00 0.00

time (sec)

N/A 0.576 10.009 4.401 0.000 0.080 0.625 0.000 0.000

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

53 53 30 26 37 26 56 37 46

N.S.

1 1.00 0.57 0.49 0.70 0.49 1.06 0.70 0.87

time (sec)

N/A 0.176 0.021 3.994 0.218 0.260 0.198 0.274 0.051

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

40 42 25 21 28 21 41 28 21

N.S.

1 1.05 0.62 0.52 0.70 0.52 1.02 0.70 0.52

time (sec)

N/A 0.169 0.016 4.018 0.201 0.267 0.134 0.270 0.035

Problem 440

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 18 15 19 14 26 19 14

N.S.

1 1.07 0.67 0.56 0.70 0.52 0.96 0.70 0.52

time (sec)

N/A 0.159 0.012 3.866 0.199 0.280 0.088 0.262 0.024

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

13 13 13 10 9 9 10 9 9

N.S.

1 1.00 1.00 0.77 0.69 0.69 0.77 0.69 0.69

time (sec)

N/A 0.134 0.002 3.908 0.205 0.266 0.059 0.289 0.026

Problem 442

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

14 14 14 11 25 25 12 26 164

N.S.

1 1.00 1.00 0.79 1.79 1.79 0.86 1.86 11.71

time (sec)

N/A 0.144 0.016 4.085 0.197 0.266 0.469 0.296 5.750

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

31 29 31 24 37 44 26 38 176

N.S.

1 0.94 1.00 0.77 1.19 1.42 0.84 1.23 5.68

time (sec)

N/A 0.154 0.035 4.129 0.200 0.264 0.988 0.275 5.682

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

47 50 38 34 64 52 65 50 189

N.S.

1 1.06 0.81 0.72 1.36 1.11 1.38 1.06 4.02

time (sec)

N/A 0.161 0.041 4.190 0.198 0.261 2.108 0.282 0.069

Problem 445

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

63 71 43 41 80 57 85 59 201

N.S.

1 1.13 0.68 0.65 1.27 0.90 1.35 0.94 3.19

time (sec)

N/A 0.171 0.046 4.105 0.206 0.276 6.725 0.277 0.042

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 141 40 17 0 25 29 0 179

N.S.

1 1.04 0.29 0.12 0.00 0.18 0.21 0.00 1.32

time (sec)

N/A 0.224 10.018 3.996 0.000 0.074 0.416 0.000 5.613

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 120 32 17 0 17 29 0 167

N.S.

1 1.00 0.27 0.14 0.00 0.14 0.24 0.00 1.39

time (sec)

N/A 0.197 10.036 4.116 0.000 0.087 0.375 0.000 0.049

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 103 17 14 0 6 27 0 155

N.S.

1 1.00 0.17 0.14 0.00 0.06 0.26 0.00 1.50

time (sec)

N/A 0.182 10.020 3.900 0.000 0.096 0.340 0.000 0.038

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 122 22 17 0 21 32 0 169

N.S.

1 1.00 0.18 0.14 0.00 0.17 0.26 0.00 1.39

time (sec)

N/A 0.197 10.007 3.941 0.000 0.074 0.429 0.000 5.608

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 143 22 17 0 30 36 0 181

N.S.

1 1.04 0.16 0.12 0.00 0.22 0.26 0.00 1.31

time (sec)

N/A 0.223 10.007 4.038 0.000 0.077 0.492 0.000 5.440

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

262 281 42 17 0 30 29 0 239

N.S.

1 1.07 0.16 0.06 0.00 0.11 0.11 0.00 0.91

time (sec)

N/A 0.358 10.018 3.993 0.000 0.072 0.431 0.000 5.437

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

246 260 34 17 0 22 29 0 227

N.S.

1 1.06 0.14 0.07 0.00 0.09 0.12 0.00 0.92

time (sec)

N/A 0.336 10.011 3.962 0.000 0.077 0.378 0.000 5.430

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

224 239 22 17 0 9 29 0 214

N.S.

1 1.07 0.10 0.08 0.00 0.04 0.13 0.00 0.96

time (sec)

N/A 0.319 10.015 3.966 0.000 0.076 0.355 0.000 0.049

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

238 258 20 17 0 22 31 0 227

N.S.

1 1.08 0.08 0.07 0.00 0.09 0.13 0.00 0.95

time (sec)

N/A 0.348 10.017 3.918 0.000 0.082 0.393 0.000 0.072

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

262 279 22 17 0 33 36 0 239

N.S.

1 1.06 0.08 0.06 0.00 0.13 0.14 0.00 0.91

time (sec)

N/A 0.365 10.005 3.948 0.000 0.077 0.473 0.000 5.474

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

61 61 32 28 45 28 58 59 54

N.S.

1 1.00 0.52 0.46 0.74 0.46 0.95 0.97 0.89

time (sec)

N/A 0.193 0.021 3.947 0.199 0.267 0.197 0.267 0.040

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

46 48 27 23 34 23 42 41 23

N.S.

1 1.04 0.59 0.50 0.74 0.50 0.91 0.89 0.50

time (sec)

N/A 0.180 0.019 3.795 0.194 0.263 0.137 0.276 0.031

Problem 458

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 20 17 23 16 27 23 16

N.S.

1 1.06 0.65 0.55 0.74 0.52 0.87 0.74 0.52

time (sec)

N/A 0.170 0.015 3.824 0.192 0.277 0.089 0.271 0.030

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

15 15 15 12 11 11 12 11 11

N.S.

1 1.00 1.00 0.80 0.73 0.73 0.80 0.73 0.73

time (sec)

N/A 0.140 0.011 3.858 0.194 0.318 0.060 0.283 0.023

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 13 29 29 31 30 180

N.S.

1 1.00 1.00 0.81 1.81 1.81 1.94 1.88 11.25

time (sec)

N/A 0.151 0.001 4.053 0.203 0.261 0.505 0.272 5.600

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 35 28 43 50 82 44 195

N.S.

1 1.00 1.00 0.80 1.23 1.43 2.34 1.26 5.57

time (sec)

N/A 0.166 0.032 4.122 0.206 0.266 1.057 0.284 0.072

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 58 42 40 70 58 138 58 209

N.S.

1 1.09 0.79 0.75 1.32 1.09 2.60 1.09 3.94

time (sec)

N/A 0.173 0.032 4.011 0.272 0.280 2.174 0.275 0.044

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 81 47 45 90 63 182 76 223

N.S.

1 1.14 0.66 0.63 1.27 0.89 2.56 1.07 3.14

time (sec)

N/A 0.184 0.055 4.129 0.226 0.285 6.664 0.290 0.034

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 157 40 15 0 27 31 0 199

N.S.

1 1.03 0.26 0.10 0.00 0.18 0.20 0.00 1.31

time (sec)

N/A 0.238 10.019 4.048 0.000 0.074 0.436 0.000 0.043

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 134 32 15 0 19 31 0 185

N.S.

1 1.00 0.24 0.11 0.00 0.14 0.23 0.00 1.38

time (sec)

N/A 0.205 10.028 3.947 0.000 0.078 0.383 0.000 5.436

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 115 15 12 0 6 29 0 172

N.S.

1 1.00 0.13 0.10 0.00 0.05 0.25 0.00 1.50

time (sec)

N/A 0.189 10.020 3.899 0.000 0.088 0.372 0.000 0.034

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 136 20 15 0 26 34 0 187

N.S.

1 1.00 0.15 0.11 0.00 0.19 0.25 0.00 1.38

time (sec)

N/A 0.209 10.004 4.013 0.000 0.077 0.456 0.000 0.055

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 159 20 15 0 33 37 0 201

N.S.

1 1.03 0.13 0.10 0.00 0.21 0.24 0.00 1.31

time (sec)

N/A 0.233 23.990 3.987 0.000 0.079 0.516 0.000 0.044

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

294 313 42 15 0 32 31 0 260

N.S.

1 1.06 0.14 0.05 0.00 0.11 0.11 0.00 0.88

time (sec)

N/A 0.393 10.018 4.091 0.000 0.096 0.446 0.000 0.046

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

276 290 34 15 0 24 31 0 246

N.S.

1 1.05 0.12 0.05 0.00 0.09 0.11 0.00 0.89

time (sec)

N/A 0.380 10.012 4.111 0.000 0.083 0.396 0.000 0.062

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

252 267 20 15 0 9 31 0 231

N.S.

1 1.06 0.08 0.06 0.00 0.04 0.12 0.00 0.92

time (sec)

N/A 0.351 0.001 3.927 0.000 0.084 0.365 0.000 0.040

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

270 287 18 15 0 26 32 0 245

N.S.

1 1.06 0.07 0.06 0.00 0.10 0.12 0.00 0.91

time (sec)

N/A 0.351 10.012 3.966 0.000 0.088 0.408 0.000 5.495

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

294 310 20 15 0 36 37 0 260

N.S.

1 1.05 0.07 0.05 0.00 0.12 0.13 0.00 0.88

time (sec)

N/A 0.402 10.004 3.971 0.000 0.093 0.479 0.000 0.047

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

53 53 30 26 37 26 56 37 46

N.S.

1 1.00 0.57 0.49 0.70 0.49 1.06 0.70 0.87

time (sec)

N/A 0.183 0.017 4.050 0.204 0.277 0.202 0.265 0.037

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

40 42 25 21 28 21 41 28 21

N.S.

1 1.05 0.62 0.52 0.70 0.52 1.02 0.70 0.52

time (sec)

N/A 0.171 0.015 4.063 0.190 0.265 0.143 0.268 0.028

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

27 29 18 15 19 14 26 19 14

N.S.

1 1.07 0.67 0.56 0.70 0.52 0.96 0.70 0.52

time (sec)

N/A 0.163 0.013 3.946 0.217 0.260 0.092 0.276 0.022

Problem 477

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 10 9 9 10 9 9

N.S.

1 1.00 1.00 0.77 0.69 0.69 0.77 0.69 0.69

time (sec)

N/A 0.136 0.009 3.949 0.194 0.269 0.058 0.269 0.024

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 11 10 10 31 10 164

N.S.

1 1.00 1.00 0.79 0.71 0.71 2.21 0.71 11.71

time (sec)

N/A 0.145 0.015 4.496 0.287 0.269 0.493 0.274 0.039

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 28 28 24 23 25 80 23 177

N.S.

1 0.90 0.90 0.77 0.74 0.81 2.58 0.74 5.71

time (sec)

N/A 0.154 0.023 4.289 0.299 0.252 1.034 0.265 5.460

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 49 38 36 48 34 138 35 189

N.S.

1 1.04 0.81 0.77 1.02 0.72 2.94 0.74 4.02

time (sec)

N/A 0.164 0.038 4.264 0.305 0.304 2.174 0.261 5.455

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 70 43 40 66 39 182 44 201

N.S.

1 1.11 0.68 0.63 1.05 0.62 2.89 0.70 3.19

time (sec)

N/A 0.171 0.041 4.282 0.329 0.273 6.624 0.262 0.039

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

153 158 52 33 0 25 27 0 179

N.S.

1 1.03 0.34 0.22 0.00 0.16 0.18 0.00 1.17

time (sec)

N/A 0.232 10.017 4.034 0.000 0.072 0.421 0.000 0.048

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

137 137 44 33 0 17 27 0 167

N.S.

1 1.00 0.32 0.24 0.00 0.12 0.20 0.00 1.22

time (sec)

N/A 0.213 10.030 4.032 0.000 0.080 0.399 0.000 0.046

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

120 120 35 30 0 6 26 0 156

N.S.

1 1.00 0.29 0.25 0.00 0.05 0.22 0.00 1.30

time (sec)

N/A 0.199 10.021 3.931 0.000 0.078 0.359 0.000 0.040

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

139 139 40 33 0 21 31 0 169

N.S.

1 1.00 0.29 0.24 0.00 0.15 0.22 0.00 1.22

time (sec)

N/A 0.208 10.007 3.963 0.000 0.075 0.462 0.000 0.061

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

155 160 40 33 0 30 34 0 181

N.S.

1 1.03 0.26 0.21 0.00 0.19 0.22 0.00 1.17

time (sec)

N/A 0.227 10.009 4.040 0.000 0.087 0.497 0.000 5.381

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

294 312 54 33 0 30 27 0 240

N.S.

1 1.06 0.18 0.11 0.00 0.10 0.09 0.00 0.82

time (sec)

N/A 0.379 10.016 4.070 0.000 0.076 0.439 0.000 5.424

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

278 291 46 33 0 22 27 0 228

N.S.

1 1.05 0.17 0.12 0.00 0.08 0.10 0.00 0.82

time (sec)

N/A 0.347 10.019 3.982 0.000 0.072 0.402 0.000 5.355

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

255 270 40 33 0 9 27 0 215

N.S.

1 1.06 0.16 0.13 0.00 0.04 0.11 0.00 0.84

time (sec)

N/A 0.343 10.024 3.995 0.000 0.090 0.375 0.000 0.049

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

269 289 38 33 0 21 29 0 226

N.S.

1 1.07 0.14 0.12 0.00 0.08 0.11 0.00 0.84

time (sec)

N/A 0.376 10.016 3.885 0.000 0.087 0.414 0.000 5.443

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

294 310 40 33 0 33 34 0 240

N.S.

1 1.05 0.14 0.11 0.00 0.11 0.12 0.00 0.82

time (sec)

N/A 0.384 10.009 3.989 0.000 0.082 0.502 0.000 5.410

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

61 61 32 28 45 28 63 59 54

N.S.

1 1.00 0.52 0.46 0.74 0.46 1.03 0.97 0.89

time (sec)

N/A 0.194 0.023 3.826 0.204 0.266 0.223 0.271 0.036

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

46 48 27 23 34 23 46 41 23

N.S.

1 1.04 0.59 0.50 0.74 0.50 1.00 0.89 0.50

time (sec)

N/A 0.182 0.022 4.784 0.206 0.272 0.142 0.259 0.029

Problem 494

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 20 17 23 16 29 23 16

N.S.

1 1.06 0.65 0.55 0.74 0.52 0.94 0.74 0.52

time (sec)

N/A 0.171 0.015 3.806 0.202 0.269 0.093 0.270 0.030

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

15 15 15 12 11 11 14 11 11

N.S.

1 1.00 1.00 0.80 0.73 0.73 0.93 0.73 0.73

time (sec)

N/A 0.139 0.010 3.894 0.198 0.279 0.065 0.267 0.024

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 13 12 12 12 12 180

N.S.

1 1.00 1.00 0.81 0.75 0.75 0.75 0.75 11.25

time (sec)

N/A 0.154 0.016 4.161 0.279 0.283 0.478 0.260 0.033

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 34 35 28 27 31 29 27 194

N.S.

1 0.97 1.00 0.80 0.77 0.89 0.83 0.77 5.54

time (sec)

N/A 0.157 0.025 4.247 0.275 0.266 1.003 0.269 5.447

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 57 42 38 56 39 66 41 209

N.S.

1 1.08 0.79 0.72 1.06 0.74 1.25 0.77 3.94

time (sec)

N/A 0.173 0.033 4.142 0.278 0.261 2.149 0.262 0.040

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 80 47 44 74 44 90 59 223

N.S.

1 1.13 0.66 0.62 1.04 0.62 1.27 0.83 3.14

time (sec)

N/A 0.185 0.040 4.135 0.278 0.290 6.711 0.261 0.029

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 154 54 18 0 27 32 0 199

N.S.

1 1.03 0.36 0.12 0.00 0.18 0.21 0.00 1.34

time (sec)

N/A 0.239 10.025 3.937 0.000 0.083 0.420 0.000 0.043

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