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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 A C F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 154 62 94 117 603 0 111 228

N.S.

1 1.83 0.74 1.12 1.39 7.18 0.00 1.32 2.71

time (sec)

N/A 0.598 0.319 0.083 0.279 0.933 0.000 0.293 1.283

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 31 266 0 137 0 0 0

N.S.

1 1.00 1.00 8.58 0.00 4.42 0.00 0.00 0.00

time (sec)

N/A 0.173 0.059 0.375 0.000 0.279 0.000 0.000 0.000

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 29 98 0 137 0 0 0

N.S.

1 1.00 0.94 3.16 0.00 4.42 0.00 0.00 0.00

time (sec)

N/A 0.178 0.044 0.411 0.000 0.265 0.000 0.000 0.000

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 50 41 171 0 151 0 0 0

N.S.

1 1.11 0.91 3.80 0.00 3.36 0.00 0.00 0.00

time (sec)

N/A 0.235 0.050 2.493 0.000 0.273 0.000 0.000 0.000

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 43 396 0 76 0 0 0

N.S.

1 1.00 0.91 8.43 0.00 1.62 0.00 0.00 0.00

time (sec)

N/A 0.261 0.095 5.267 0.000 0.279 0.000 0.000 0.000

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 69 50 510 0 181 0 0 0

N.S.

1 1.13 0.82 8.36 0.00 2.97 0.00 0.00 0.00

time (sec)

N/A 0.416 0.133 6.089 0.000 0.278 0.000 0.000 0.000

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 68 56 1108 0 205 0 0 0

N.S.

1 1.11 0.92 18.16 0.00 3.36 0.00 0.00 0.00

time (sec)

N/A 0.398 0.107 0.729 0.000 0.268 0.000 0.000 0.000

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 508 0 39 0 0 18

N.S.

1 1.00 1.00 31.75 0.00 2.44 0.00 0.00 1.12

time (sec)

N/A 0.171 0.062 0.654 0.000 0.269 0.000 0.000 0.621

Problem 409

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 Yes TBD TBD TBD TBD TBD

size

31 31 20 2946 0 32 0 0 20

N.S.

1 1.00 0.65 95.03 0.00 1.03 0.00 0.00 0.65

time (sec)

N/A 0.237 0.058 4.941 0.000 0.262 0.000 0.000 0.429

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 31 24 121 0 43 0 0 29

N.S.

1 1.07 0.83 4.17 0.00 1.48 0.00 0.00 1.00

time (sec)

N/A 0.283 0.050 0.375 0.000 0.251 0.000 0.000 0.511

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

68 65 111 761 0 136 0 0 0

N.S.

1 0.96 1.63 11.19 0.00 2.00 0.00 0.00 0.00

time (sec)

N/A 1.007 7.736 1.306 0.000 0.285 0.000 0.000 0.000

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 31 19 16 6 15 0 0 15

N.S.

1 1.63 1.00 0.84 0.32 0.79 0.00 0.00 0.79

time (sec)

N/A 0.252 0.010 0.876 0.300 0.257 0.000 0.000 0.594

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

92 161 66 299 0 628 0 0 0

N.S.

1 1.75 0.72 3.25 0.00 6.83 0.00 0.00 0.00

time (sec)

N/A 0.468 0.132 7.826 0.000 0.416 0.000 0.000 0.000

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

47 53 63 0 13 29 0 0 32

N.S.

1 1.13 1.34 0.00 0.28 0.62 0.00 0.00 0.68

time (sec)

N/A 0.231 0.175 0.000 0.280 0.247 0.000 0.000 4.036

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

70 61 35 0 77 101 0 0 110

N.S.

1 0.87 0.50 0.00 1.10 1.44 0.00 0.00 1.57

time (sec)

N/A 0.341 0.062 0.000 0.288 0.269 0.000 0.000 3.615

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

108 172 75 247 0 479 0 0 0

N.S.

1 1.59 0.69 2.29 0.00 4.44 0.00 0.00 0.00

time (sec)

N/A 1.163 0.502 3.679 0.000 0.459 0.000 0.000 0.000

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

364 781 378 133928 0 0 0 0 0

N.S.

1 2.15 1.04 367.93 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.303 19.658 57.052 0.000 0.000 0.000 0.000 0.000

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

125 151 58 0 60 56 0 0 0

N.S.

1 1.21 0.46 0.00 0.48 0.45 0.00 0.00 0.00

time (sec)

N/A 0.925 0.937 0.000 0.315 0.266 0.000 0.000 0.000

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 83 61 56 55 108 0 55 43

N.S.

1 1.14 0.84 0.77 0.75 1.48 0.00 0.75 0.59

time (sec)

N/A 0.216 0.168 1.084 0.290 0.287 0.000 0.304 0.137

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 79 48 54 53 88 0 41 0

N.S.

1 1.14 0.70 0.78 0.77 1.28 0.00 0.59 0.00

time (sec)

N/A 0.227 0.082 2.151 0.271 0.263 0.000 0.292 0.000

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 63 61 47 36 123 0 41 0

N.S.

1 1.09 1.05 0.81 0.62 2.12 0.00 0.71 0.00

time (sec)

N/A 0.221 0.081 0.261 0.285 0.264 0.000 0.285 0.000

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 60 37 44 43 51 0 30 28

N.S.

1 1.09 0.67 0.80 0.78 0.93 0.00 0.55 0.51

time (sec)

N/A 0.221 0.130 0.336 0.209 0.298 0.000 0.293 0.705

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 39 58 716 100 0 38 0

N.S.

1 1.00 1.00 1.49 18.36 2.56 0.00 0.97 0.00

time (sec)

N/A 0.231 0.110 0.742 0.346 0.288 0.000 0.287 0.000

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 53 63 105 69 131 0 40 0

N.S.

1 1.10 1.31 2.19 1.44 2.73 0.00 0.83 0.00

time (sec)

N/A 0.254 0.453 0.493 0.293 0.272 0.000 0.286 0.000

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 53 28 38 192 42 0 33 28

N.S.

1 1.08 0.57 0.78 3.92 0.86 0.00 0.67 0.57

time (sec)

N/A 0.299 0.096 0.356 0.227 0.271 0.000 0.274 0.627

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

111 119 295 131 115 127 0 0 0

N.S.

1 1.07 2.66 1.18 1.04 1.14 0.00 0.00 0.00

time (sec)

N/A 0.701 7.001 1.760 0.317 0.876 0.000 0.000 0.000

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 112 156 233 0 195 0 0 0

N.S.

1 1.00 1.39 2.08 0.00 1.74 0.00 0.00 0.00

time (sec)

N/A 0.590 0.719 1.150 0.000 0.298 0.000 0.000 0.000

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 35 29 38 25 26 0 35 0

N.S.

1 1.06 0.88 1.15 0.76 0.79 0.00 1.06 0.00

time (sec)

N/A 0.219 0.077 0.471 0.189 0.277 0.000 0.289 0.000

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 37 32 62 488 77 0 27 0

N.S.

1 1.12 0.97 1.88 14.79 2.33 0.00 0.82 0.00

time (sec)

N/A 0.179 0.040 0.472 0.324 0.267 0.000 0.289 0.000

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 72 49 55 790 103 0 48 29

N.S.

1 1.31 0.89 1.00 14.36 1.87 0.00 0.87 0.53

time (sec)

N/A 0.203 0.209 0.401 0.344 0.281 0.000 0.302 0.486

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 39 90 39 0 22 12

N.S.

1 1.00 1.00 2.44 5.62 2.44 0.00 1.38 0.75

time (sec)

N/A 0.168 0.058 0.582 0.306 0.255 0.000 0.293 0.437

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 68 49 100 0 118 0 0 0

N.S.

1 1.39 1.00 2.04 0.00 2.41 0.00 0.00 0.00

time (sec)

N/A 0.232 0.127 0.603 0.000 0.279 0.000 0.000 0.000

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 157 62 180 1359 163 0 55 0

N.S.

1 1.80 0.71 2.07 15.62 1.87 0.00 0.63 0.00

time (sec)

N/A 0.543 0.426 2.613 0.412 0.291 0.000 0.287 0.000

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 71 115 217 0 130 0 0 0

N.S.

1 1.04 1.69 3.19 0.00 1.91 0.00 0.00 0.00

time (sec)

N/A 0.230 0.266 7.204 0.000 0.269 0.000 0.000 0.000

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 40 79 124 0 115 0 0 0

N.S.

1 1.00 1.98 3.10 0.00 2.88 0.00 0.00 0.00

time (sec)

N/A 0.194 0.137 1.365 0.000 0.275 0.000 0.000 0.000

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 100 131 151 0 97 0 0 0

N.S.

1 1.06 1.39 1.61 0.00 1.03 0.00 0.00 0.00

time (sec)

N/A 0.448 0.600 4.208 0.000 0.332 0.000 0.000 0.000

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 41 36 67 63 33 0 135 20

N.S.

1 1.05 0.92 1.72 1.62 0.85 0.00 3.46 0.51

time (sec)

N/A 0.293 0.093 2.726 0.205 0.270 0.000 0.283 0.853

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 129 1498 0 257 0 121 0

N.S.

1 1.00 1.77 20.52 0.00 3.52 0.00 1.66 0.00

time (sec)

N/A 1.222 5.136 2.001 0.000 0.347 0.000 0.328 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 57 116 62 47 84 0 0 113

N.S.

1 1.00 2.04 1.09 0.82 1.47 0.00 0.00 1.98

time (sec)

N/A 0.843 5.350 3.319 0.282 0.275 0.000 0.000 1.612

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 76 49 61 0 50 0 52 90

N.S.

1 1.15 0.74 0.92 0.00 0.76 0.00 0.79 1.36

time (sec)

N/A 0.222 0.081 0.074 0.000 0.275 0.000 0.271 1.623

Problem 441

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

54 63 71 41 0 76 46 36 172

N.S.

1 1.17 1.31 0.76 0.00 1.41 0.85 0.67 3.19

time (sec)

N/A 0.212 0.661 0.056 0.000 0.283 2.317 0.268 0.525

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

133 138 105 0 0 0 0 186 250

N.S.

1 1.04 0.79 0.00 0.00 0.00 0.00 1.40 1.88

time (sec)

N/A 0.308 0.157 0.000 0.000 0.000 0.000 0.308 1.433

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F B F A B

verified

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

size

69 91 69 0 0 117 0 79 101

N.S.

1 1.32 1.00 0.00 0.00 1.70 0.00 1.14 1.46

time (sec)

N/A 0.247 0.171 0.000 0.000 0.628 0.000 0.281 0.750

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

52 59 256 0 71 0 0 73 46

N.S.

1 1.13 4.92 0.00 1.37 0.00 0.00 1.40 0.88

time (sec)

N/A 0.254 0.323 0.000 0.281 0.000 0.000 0.482 0.438

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

54 61 245 0 74 0 0 76 0

N.S.

1 1.13 4.54 0.00 1.37 0.00 0.00 1.41 0.00

time (sec)

N/A 0.258 0.302 0.000 0.287 0.000 0.000 0.410 0.000

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

133 200 1447 0 0 0 0 0 0

N.S.

1 1.50 10.88 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 4.486 25.298 0.000 0.000 0.000 0.000 0.000 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

100 138 169 0 0 271 0 193 0

N.S.

1 1.38 1.69 0.00 0.00 2.71 0.00 1.93 0.00

time (sec)

N/A 1.128 4.996 0.000 0.000 0.303 0.000 0.397 0.000

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 114 47 127 136 185 0 0 0

N.S.

1 1.02 0.42 1.13 1.21 1.65 0.00 0.00 0.00

time (sec)

N/A 0.325 0.038 0.688 0.283 0.285 0.000 0.000 0.000

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

95 159 154 0 145 0 0 146 0

N.S.

1 1.67 1.62 0.00 1.53 0.00 0.00 1.54 0.00

time (sec)

N/A 0.341 0.103 0.000 0.301 0.000 0.000 0.372 0.000

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

49 53 30 0 37 46 0 37 0

N.S.

1 1.08 0.61 0.00 0.76 0.94 0.00 0.76 0.00

time (sec)

N/A 0.264 0.358 0.000 0.199 0.307 0.000 0.281 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 26 86 35 0 25 43

N.S.

1 1.00 1.00 1.30 4.30 1.75 0.00 1.25 2.15

time (sec)

N/A 0.403 0.271 0.184 0.259 0.266 0.000 0.329 0.635

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

27 35 97 0 0 93 0 40 0

N.S.

1 1.30 3.59 0.00 0.00 3.44 0.00 1.48 0.00

time (sec)

N/A 0.977 0.422 0.000 0.000 0.956 0.000 0.310 0.000

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

101 126 89 0 100 461 0 0 0

N.S.

1 1.25 0.88 0.00 0.99 4.56 0.00 0.00 0.00

time (sec)

N/A 1.279 0.452 0.000 0.296 39.137 0.000 0.000 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

25 37 20 0 0 26 0 25 0

N.S.

1 1.48 0.80 0.00 0.00 1.04 0.00 1.00 0.00

time (sec)

N/A 0.215 0.081 0.000 0.000 0.271 0.000 0.293 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

102 189 153 0 0 0 0 120 0

N.S.

1 1.85 1.50 0.00 0.00 0.00 0.00 1.18 0.00

time (sec)

N/A 0.352 0.106 0.000 0.000 0.000 0.000 0.275 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 18 45 78 259 50 0 85 0

N.S.

1 1.06 2.65 4.59 15.24 2.94 0.00 5.00 0.00

time (sec)

N/A 0.212 0.078 0.693 0.304 0.284 0.000 0.291 0.000

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 39 52 143 507 115 0 138 0

N.S.

1 1.22 1.62 4.47 15.84 3.59 0.00 4.31 0.00

time (sec)

N/A 0.201 0.088 6.694 0.472 0.267 0.000 0.365 0.000

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 37 31 24 27 30 24 32 24

N.S.

1 1.19 1.00 0.77 0.87 0.97 0.77 1.03 0.77

time (sec)

N/A 0.152 0.004 0.288 0.203 0.249 0.048 0.275 0.341

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

39 49 39 29 30 32 32 30 30

N.S.

1 1.26 1.00 0.74 0.77 0.82 0.82 0.77 0.77

time (sec)

N/A 0.144 0.010 0.282 0.281 0.266 0.055 0.263 0.036

Problem 460

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

58 64 40 34 46 73 41 42 44

N.S.

1 1.10 0.69 0.59 0.79 1.26 0.71 0.72 0.76

time (sec)

N/A 0.176 0.012 0.304 0.211 0.262 0.061 0.256 0.085

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

52 54 46 35 33 65 984 35 34

N.S.

1 1.04 0.88 0.67 0.63 1.25 18.92 0.67 0.65

time (sec)

N/A 0.150 0.045 0.420 0.282 0.253 1.810 0.263 0.550

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

61 71 49 41 42 47 165 46 46

N.S.

1 1.16 0.80 0.67 0.69 0.77 2.70 0.75 0.75

time (sec)

N/A 0.161 0.039 0.434 0.278 0.255 3.434 0.273 0.488

Problem 463

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 15 15 14 15 15 14 24

N.S.

1 1.00 0.94 0.94 0.88 0.94 0.94 0.88 1.50

time (sec)

N/A 0.123 0.002 0.014 0.209 0.259 0.016 0.258 0.498

Problem 464

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 42 36 30 35 49 32 36 35

N.S.

1 0.91 0.78 0.65 0.76 1.07 0.70 0.78 0.76

time (sec)

N/A 0.158 0.010 0.253 0.201 0.252 0.042 0.267 0.059

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

40 44 23 21 36 36 32 21 36

N.S.

1 1.10 0.58 0.52 0.90 0.90 0.80 0.52 0.90

time (sec)

N/A 0.176 0.006 0.292 0.216 0.253 0.050 0.267 0.070

Problem 466

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 31 25 17 19 21 41 19 20

N.S.

1 1.15 0.93 0.63 0.70 0.78 1.52 0.70 0.74

time (sec)

N/A 0.144 0.016 0.299 0.197 0.240 2.710 0.261 0.439

Problem 467

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

38 42 25 20 28 33 82 26 21

N.S.

1 1.11 0.66 0.53 0.74 0.87 2.16 0.68 0.55

time (sec)

N/A 0.150 0.019 0.295 0.193 0.245 0.794 0.261 0.461

Problem 468

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

33 33 24 20 25 34 61 19 99

N.S.

1 1.00 0.73 0.61 0.76 1.03 1.85 0.58 3.00

time (sec)

N/A 0.128 0.031 0.250 0.203 0.238 0.856 0.275 0.323

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 26 23 51 61 0 21 22

N.S.

1 1.00 0.60 0.53 1.19 1.42 0.00 0.49 0.51

time (sec)

N/A 0.143 0.153 0.351 0.192 0.250 0.000 0.283 0.314

Problem 470

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 52 28 23 35 40 153 62 24

N.S.

1 1.11 0.60 0.49 0.74 0.85 3.26 1.32 0.51

time (sec)

N/A 0.139 0.036 0.291 0.284 0.247 1.175 0.278 0.459

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

28 28 19 16 16 15 24 16 17

N.S.

1 1.00 0.68 0.57 0.57 0.54 0.86 0.57 0.61

time (sec)

N/A 0.136 0.014 0.254 0.195 0.248 0.808 0.267 0.039

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

52 58 49 47 53 74 49 58 51

N.S.

1 1.12 0.94 0.90 1.02 1.42 0.94 1.12 0.98

time (sec)

N/A 0.167 0.018 0.267 0.202 0.242 0.072 0.277 0.362

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 25 22 0 21 0 0 15

N.S.

1 1.00 1.00 0.88 0.00 0.84 0.00 0.00 0.60

time (sec)

N/A 0.171 6.487 0.260 0.000 0.390 0.000 0.000 0.501

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 35 28 79 69 0 98 0

N.S.

1 1.00 0.70 0.56 1.58 1.38 0.00 1.96 0.00

time (sec)

N/A 0.147 0.191 0.336 0.284 0.247 0.000 0.320 0.000

Problem 475

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

24 24 40 22 21 41 49 29 54

N.S.

1 1.00 1.67 0.92 0.88 1.71 2.04 1.21 2.25

time (sec)

N/A 0.129 0.054 0.323 0.286 0.241 0.181 0.273 0.325

Problem 476

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

40 40 46 32 45 45 32 77 33

N.S.

1 1.00 1.15 0.80 1.12 1.12 0.80 1.92 0.82

time (sec)

N/A 0.138 0.056 0.473 0.274 0.264 0.376 0.275 0.042

Problem 477

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

49 54 28 25 37 44 291 35 179

N.S.

1 1.10 0.57 0.51 0.76 0.90 5.94 0.71 3.65

time (sec)

N/A 0.138 0.169 0.298 0.180 0.275 2.995 0.284 0.305

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 31 28 59 47 0 35 29

N.S.

1 1.00 0.66 0.60 1.26 1.00 0.00 0.74 0.62

time (sec)

N/A 0.144 0.135 0.408 0.189 0.244 0.000 0.274 0.358

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

36 36 36 33 32 32 34 32 32

N.S.

1 1.00 1.00 0.92 0.89 0.89 0.94 0.89 0.89

time (sec)

N/A 0.158 0.002 0.381 0.184 0.261 0.021 0.305 0.034

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

39 39 39 30 29 29 34 29 29

N.S.

1 1.00 1.00 0.77 0.74 0.74 0.87 0.74 0.74

time (sec)

N/A 0.155 0.001 0.327 0.182 0.223 0.021 0.265 0.030

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 33 30 59 73 0 27 29

N.S.

1 1.00 0.70 0.64 1.26 1.55 0.00 0.57 0.62

time (sec)

N/A 0.150 0.195 0.377 0.182 0.253 0.000 0.279 0.414

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 33 30 76 73 0 41 29

N.S.

1 1.00 0.73 0.67 1.69 1.62 0.00 0.91 0.64

time (sec)

N/A 0.168 0.310 0.372 0.185 0.234 0.000 0.295 0.184

Problem 483

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

83 113 67 56 55 57 112 55 69

N.S.

1 1.36 0.81 0.67 0.66 0.69 1.35 0.66 0.83

time (sec)

N/A 0.619 0.039 0.530 0.195 0.242 0.368 0.278 0.423

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

73 92 51 50 49 52 92 49 59

N.S.

1 1.26 0.70 0.68 0.67 0.71 1.26 0.67 0.81

time (sec)

N/A 0.632 0.067 0.531 0.193 0.244 0.254 0.312 0.375

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

105 181 70 67 66 72 192 66 88

N.S.

1 1.72 0.67 0.64 0.63 0.69 1.83 0.63 0.84

time (sec)

N/A 0.767 0.059 0.842 0.197 0.257 0.547 0.265 0.418

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

44 48 39 32 35 36 53 35 40

N.S.

1 1.09 0.89 0.73 0.80 0.82 1.20 0.80 0.91

time (sec)

N/A 0.296 0.074 0.448 0.201 0.244 0.178 0.255 0.097

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 33 47 0 45 507 206 56

N.S.

1 1.00 1.00 1.42 0.00 1.36 15.36 6.24 1.70

time (sec)

N/A 0.296 0.025 0.333 0.000 0.249 0.683 0.270 0.635

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 104 43 619 47 551 341 35

N.S.

1 1.00 3.47 1.43 20.63 1.57 18.37 11.37 1.17

time (sec)

N/A 0.191 0.114 0.295 0.283 0.242 0.643 0.427 0.561

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 13 132 15 128 53 16

N.S.

1 1.00 1.00 0.81 8.25 0.94 8.00 3.31 1.00

time (sec)

N/A 0.191 0.024 0.381 0.182 0.243 0.410 0.273 0.384

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 74 57 57 66 113 0 0 0

N.S.

1 1.19 0.92 0.92 1.06 1.82 0.00 0.00 0.00

time (sec)

N/A 0.391 0.023 0.305 0.297 0.264 0.000 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 66 54 59 210 138 0 0 0

N.S.

1 1.12 0.92 1.00 3.56 2.34 0.00 0.00 0.00

time (sec)

N/A 0.339 0.011 0.149 0.289 0.258 0.000 0.000 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 14 44 78 13 0 10 0

N.S.

1 1.00 1.17 3.67 6.50 1.08 0.00 0.83 0.00

time (sec)

N/A 0.229 0.228 3.049 0.278 0.249 0.000 0.276 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 19 20 69 19 66 39 0

N.S.

1 1.00 0.95 1.00 3.45 0.95 3.30 1.95 0.00

time (sec)

N/A 0.224 0.288 0.505 0.199 0.246 0.716 0.286 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 22 23 0 22 42 325 22

N.S.

1 1.00 1.00 1.05 0.00 1.00 1.91 14.77 1.00

time (sec)

N/A 0.165 0.021 0.079 0.000 0.237 0.307 0.278 0.415

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 41 46 42 0 52 0 436 34

N.S.

1 1.21 1.35 1.24 0.00 1.53 0.00 12.82 1.00

time (sec)

N/A 0.359 0.041 0.087 0.000 0.249 0.000 0.331 0.446

Problem 496

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 9 9 8 7 11 7 7 4

N.S.

1 1.00 1.00 0.89 0.78 1.22 0.78 0.78 0.44

time (sec)

N/A 0.132 0.008 0.027 0.187 0.228 0.033 0.272 0.050

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 No Yes Yes TBD TBD TBD TBD TBD

size

22 25 22 17 16 21 17 24 8

N.S.

1 1.14 1.00 0.77 0.73 0.95 0.77 1.09 0.36

time (sec)

N/A 0.168 0.010 0.035 0.200 0.245 0.042 0.262 0.055

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

31 31 30 24 23 24 24 25 23

N.S.

1 1.00 0.97 0.77 0.74 0.77 0.77 0.81 0.74

time (sec)

N/A 0.161 0.027 0.046 0.196 0.231 0.054 0.272 0.349

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

36 38 37 29 28 31 31 36 28

N.S.

1 1.06 1.03 0.81 0.78 0.86 0.86 1.00 0.78

time (sec)

N/A 0.169 0.041 0.049 0.199 0.248 0.067 0.285 0.335

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

48 52 45 0 0 0 0 0 0

N.S.

1 1.08 0.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.185 0.052 0.000 0.000 0.000 0.000 0.000 0.000

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