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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 F F F F(-2) F F(-1)

verified

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

size

66 64 62 0 0 0 0 0 0

N.S.

1 0.97 0.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.334 0.105 0.000 0.000 0.000 0.000 0.000 0.000

Problem 402

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

92 97 43 54 99 46 56 90 63

N.S.

1 1.05 0.47 0.59 1.08 0.50 0.61 0.98 0.68

time (sec)

N/A 0.289 0.070 0.577 0.204 0.288 0.135 0.324 1.583

Problem 403

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

102 108 58 70 159 61 75 113 92

N.S.

1 1.06 0.57 0.69 1.56 0.60 0.74 1.11 0.90

time (sec)

N/A 0.302 0.089 0.569 0.202 0.295 0.156 0.325 1.586

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

160 143 132 642 559 1409 609 1697 380

N.S.

1 0.89 0.82 4.01 3.49 8.81 3.81 10.61 2.38

time (sec)

N/A 0.495 0.051 5.581 0.227 0.324 2.560 0.346 1.838

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

121 110 100 386 317 639 360 772 242

N.S.

1 0.91 0.83 3.19 2.62 5.28 2.98 6.38 2.00

time (sec)

N/A 0.415 0.011 1.512 0.242 0.323 1.138 0.321 1.513

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

78 77 69 165 148 231 178 283 111

N.S.

1 0.99 0.88 2.12 1.90 2.96 2.28 3.63 1.42

time (sec)

N/A 0.335 0.009 0.417 0.211 0.331 0.516 0.333 1.361

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

34 34 34 42 45 50 53 59 41

N.S.

1 1.00 1.00 1.24 1.32 1.47 1.56 1.74 1.21

time (sec)

N/A 0.184 0.007 0.083 0.195 0.304 0.219 0.337 1.320

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

83 85 83 0 0 65 0 78 0

N.S.

1 1.02 1.00 0.00 0.00 0.78 0.00 0.94 0.00

time (sec)

N/A 0.407 0.094 0.000 0.000 0.311 0.000 0.335 0.000

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

123 124 163 0 0 171 0 582 0

N.S.

1 1.01 1.33 0.00 0.00 1.39 0.00 4.73 0.00

time (sec)

N/A 0.500 0.076 0.000 0.000 0.299 0.000 0.336 0.000

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

169 177 189 0 0 444 0 3401 0

N.S.

1 1.05 1.12 0.00 0.00 2.63 0.00 20.12 0.00

time (sec)

N/A 0.606 0.120 0.000 0.000 0.313 0.000 0.381 0.000

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

219 214 190 0 0 0 0 0 0

N.S.

1 0.98 0.87 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.824 0.221 0.000 0.000 0.000 0.000 0.000 0.000

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

176 177 160 0 0 0 0 0 0

N.S.

1 1.01 0.91 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.698 0.054 0.000 0.000 0.000 0.000 0.000 0.000

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

139 140 134 0 0 0 0 0 0

N.S.

1 1.01 0.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.595 0.044 0.000 0.000 0.000 0.000 0.000 0.000

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

104 106 104 0 0 0 0 0 0

N.S.

1 1.02 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.516 0.017 0.000 0.000 0.000 0.000 0.000 0.000

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

147 148 181 0 0 0 0 0 0

N.S.

1 1.01 1.23 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.646 0.171 0.000 0.000 0.000 0.000 0.000 0.000

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

194 203 211 0 0 0 0 0 0

N.S.

1 1.05 1.09 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.787 0.200 0.000 0.000 0.000 0.000 0.000 0.000

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

237 258 272 0 0 0 0 0 0

N.S.

1 1.09 1.15 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.907 0.279 0.000 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 F(-2) A F F F(-1)

verified

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

size

131 135 131 0 0 80 0 0 0

N.S.

1 1.03 1.00 0.00 0.00 0.61 0.00 0.00 0.00

time (sec)

N/A 0.449 0.143 0.000 0.000 0.094 0.000 0.000 0.000

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

109 106 109 0 70 0 0 0 0

N.S.

1 0.97 1.00 0.00 0.64 0.00 0.00 0.00 0.00

time (sec)

N/A 0.418 0.147 0.000 0.061 0.000 0.000 0.000 0.000

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

158 141 232 466 304 405 457 987 370

N.S.

1 0.89 1.47 2.95 1.92 2.56 2.89 6.25 2.34

time (sec)

N/A 0.414 0.210 5.982 0.201 0.364 2.503 0.340 1.541

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 117 156 290 202 268 286 544 225

N.S.

1 0.91 1.22 2.27 1.58 2.09 2.23 4.25 1.76

time (sec)

N/A 0.371 0.127 1.970 0.191 0.305 1.229 0.362 1.592

Problem 422

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

98 93 113 173 112 148 156 236 113

N.S.

1 0.95 1.15 1.77 1.14 1.51 1.59 2.41 1.15

time (sec)

N/A 0.317 0.038 0.438 0.200 0.324 0.587 0.323 1.444

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

34 34 34 42 45 50 53 59 41

N.S.

1 1.00 1.00 1.24 1.32 1.47 1.56 1.74 1.21

time (sec)

N/A 0.183 0.007 0.102 0.183 0.305 0.208 0.322 1.347

Problem 424

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

68 68 67 0 0 0 0 0 0

N.S.

1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.404 0.012 0.000 0.000 0.000 0.000 0.000 0.000

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

80 75 69 139 90 113 357 96 89

N.S.

1 0.94 0.86 1.74 1.12 1.41 4.46 1.20 1.11

time (sec)

N/A 0.290 0.075 1.336 0.194 0.279 3.558 0.321 3.316

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 100 88 305 172 310 1984 221 180

N.S.

1 0.84 0.74 2.56 1.45 2.61 16.67 1.86 1.51

time (sec)

N/A 0.369 0.094 3.759 0.197 0.307 15.248 0.402 3.492

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 126 115 487 306 563 5673 443 293

N.S.

1 0.85 0.77 3.27 2.05 3.78 38.07 2.97 1.97

time (sec)

N/A 0.414 0.123 11.925 0.208 0.319 63.372 0.373 3.742

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

409 343 400 1537 895 1742 1421 3738 1154

N.S.

1 0.84 0.98 3.76 2.19 4.26 3.47 9.14 2.82

time (sec)

N/A 1.143 0.196 16.244 0.228 0.354 5.391 0.387 1.964

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

323 278 277 939 605 1137 894 2106 652

N.S.

1 0.86 0.86 2.91 1.87 3.52 2.77 6.52 2.02

time (sec)

N/A 1.002 0.110 5.678 0.218 0.340 2.594 0.338 1.741

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

211 211 164 540 348 622 466 939 302

N.S.

1 1.00 0.78 2.56 1.65 2.95 2.21 4.45 1.43

time (sec)

N/A 0.642 0.059 1.533 0.214 0.328 1.244 0.324 1.497

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

78 77 69 165 148 231 178 283 111

N.S.

1 0.99 0.88 2.12 1.90 2.96 2.28 3.63 1.42

time (sec)

N/A 0.326 0.013 0.423 0.202 0.287 0.470 0.315 1.309

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

123 117 324 0 0 0 0 0 0

N.S.

1 0.95 2.63 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.684 0.141 0.000 0.000 0.000 0.000 0.000 0.000

Problem 433

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

144 128 200 0 0 0 0 0 0

N.S.

1 0.89 1.39 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.589 0.181 0.000 0.000 0.000 0.000 0.000 0.000

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

222 247 316 0 0 0 0 0 0

N.S.

1 1.11 1.42 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.184 0.314 0.000 0.000 0.000 0.000 0.000 0.000

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

492 492 378 2034 1245 3121 1846 5146 1400

N.S.

1 1.00 0.77 4.13 2.53 6.34 3.75 10.46 2.85

time (sec)

N/A 1.258 0.193 16.190 0.247 0.381 5.381 0.420 2.342

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

306 306 231 1084 732 1692 991 2532 651

N.S.

1 1.00 0.75 3.54 2.39 5.53 3.24 8.27 2.13

time (sec)

N/A 0.824 0.093 5.224 0.232 0.385 2.585 0.379 1.911

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

121 110 100 386 317 639 360 772 242

N.S.

1 0.91 0.83 3.19 2.62 5.28 2.98 6.38 2.00

time (sec)

N/A 0.402 0.018 1.511 0.201 0.299 1.020 0.324 1.428

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

177 166 646 0 0 0 0 0 0

N.S.

1 0.94 3.65 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.903 0.228 0.000 0.000 0.000 0.000 0.000 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

209 177 444 0 0 0 0 0 0

N.S.

1 0.85 2.12 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.889 0.343 0.000 0.000 0.000 0.000 0.000 0.000

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

376 354 660 0 0 0 0 0 0

N.S.

1 0.94 1.76 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.204 0.555 0.000 0.000 0.000 0.000 0.000 0.000

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

160 143 132 642 559 1409 609 1697 380

N.S.

1 0.89 0.82 4.01 3.49 8.81 3.81 10.61 2.38

time (sec)

N/A 0.498 0.034 5.170 0.225 0.309 2.070 0.358 1.600

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

231 214 1095 0 0 0 0 0 0

N.S.

1 0.93 4.74 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.110 0.335 0.000 0.000 0.000 0.000 0.000 0.000

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

274 226 1301 0 0 0 0 0 0

N.S.

1 0.82 4.75 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.132 0.380 0.000 0.000 0.000 0.000 0.000 0.000

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 No Yes Yes TBD TBD TBD TBD TBD

size

29 35 29 41 40 42 48 53 36

N.S.

1 1.21 1.00 1.41 1.38 1.45 1.66 1.83 1.24

time (sec)

N/A 0.243 0.006 0.086 0.194 0.312 0.207 0.328 0.077

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

279 279 252 0 0 243 0 517 0

N.S.

1 1.00 0.90 0.00 0.00 0.87 0.00 1.85 0.00

time (sec)

N/A 1.104 0.550 0.000 0.000 0.303 0.000 0.365 0.000

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

179 179 164 0 0 140 0 248 0

N.S.

1 1.00 0.92 0.00 0.00 0.78 0.00 1.39 0.00

time (sec)

N/A 0.725 0.117 0.000 0.000 0.311 0.000 0.348 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

83 85 83 0 0 65 0 78 0

N.S.

1 1.02 1.00 0.00 0.00 0.78 0.00 0.94 0.00

time (sec)

N/A 0.396 0.036 0.000 0.000 0.294 0.000 0.333 0.000

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

28 28 30 28 30 35 24 30 30

N.S.

1 1.00 1.07 1.00 1.07 1.25 0.86 1.07 1.07

time (sec)

N/A 0.228 0.207 0.157 0.856 0.294 1.503 0.348 1.282

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

28 28 30 28 30 59 26 30 30

N.S.

1 1.00 1.07 1.00 1.07 2.11 0.93 1.07 1.07

time (sec)

N/A 0.225 0.478 0.188 0.858 0.303 3.772 0.347 1.244

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

326 538 1310 0 0 573 0 3975 0

N.S.

1 1.65 4.02 0.00 0.00 1.76 0.00 12.19 0.00

time (sec)

N/A 1.763 0.413 0.000 0.000 0.323 0.000 0.463 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

224 329 269 0 0 328 0 1930 0

N.S.

1 1.47 1.20 0.00 0.00 1.46 0.00 8.62 0.00

time (sec)

N/A 1.267 0.221 0.000 0.000 0.302 0.000 0.392 0.000

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

123 124 163 0 0 171 0 582 0

N.S.

1 1.01 1.33 0.00 0.00 1.39 0.00 4.73 0.00

time (sec)

N/A 0.495 0.074 0.000 0.000 0.308 0.000 0.342 0.000

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

28 28 30 28 267 71 26 30 30

N.S.

1 1.00 1.07 1.00 9.54 2.54 0.93 1.07 1.07

time (sec)

N/A 0.214 0.667 0.181 1.153 0.333 5.011 0.323 1.244

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

28 28 30 28 406 112 27 30 30

N.S.

1 1.00 1.07 1.00 14.50 4.00 0.96 1.07 1.07

time (sec)

N/A 0.217 8.431 0.177 1.136 0.318 31.297 0.359 1.270

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

432 951 438 0 0 1682 0 5889 0

N.S.

1 2.20 1.01 0.00 0.00 3.89 0.00 13.63 0.00

time (sec)

N/A 3.246 1.281 0.000 0.000 0.365 0.000 0.543 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

322 530 322 0 0 931 0 11278 0

N.S.

1 1.65 1.00 0.00 0.00 2.89 0.00 35.02 0.00

time (sec)

N/A 2.034 0.378 0.000 0.000 0.389 0.000 0.553 0.000

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

169 177 189 0 0 444 0 3401 0

N.S.

1 1.05 1.12 0.00 0.00 2.63 0.00 20.12 0.00

time (sec)

N/A 0.616 0.117 0.000 0.000 0.319 0.000 0.399 0.000

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

28 28 30 28 1116 107 26 30 30

N.S.

1 1.00 1.07 1.00 39.86 3.82 0.93 1.07 1.07

time (sec)

N/A 0.219 0.553 0.173 1.570 0.319 17.311 0.348 1.298

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

28 28 30 28 1486 165 27 30 30

N.S.

1 1.00 1.07 1.00 53.07 5.89 0.96 1.07 1.07

time (sec)

N/A 0.218 23.057 0.177 1.579 0.314 135.869 0.398 1.336

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

488 488 458 0 0 0 0 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.032 0.487 0.000 0.000 0.000 0.000 0.000 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

311 311 298 0 0 0 0 0 0

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.254 0.264 0.000 0.000 0.000 0.000 0.000 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

139 140 134 0 0 0 0 0 0

N.S.

1 1.01 0.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.581 0.047 0.000 0.000 0.000 0.000 0.000 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 30 32 28 30 0 26 30 30

N.S.

1 1.00 1.07 0.93 1.00 0.00 0.87 1.00 1.00

time (sec)

N/A 0.249 4.541 0.161 11.956 0.000 0.608 0.429 1.360

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 30 32 28 30 0 27 30 30

N.S.

1 1.00 1.07 0.93 1.00 0.00 0.90 1.00 1.00

time (sec)

N/A 0.304 0.257 0.164 10.690 0.000 2.502 0.402 1.416

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

625 625 545 0 0 0 0 0 0

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.474 0.936 0.000 0.000 0.000 0.000 0.000 0.000

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

396 396 348 0 0 0 0 0 0

N.S.

1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.498 0.386 0.000 0.000 0.000 0.000 0.000 0.000

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

176 177 160 0 0 0 0 0 0

N.S.

1 1.01 0.91 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.675 0.134 0.000 0.000 0.000 0.000 0.000 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 30 32 28 30 0 26 30 30

N.S.

1 1.00 1.07 0.93 1.00 0.00 0.87 1.00 1.00

time (sec)

N/A 0.260 2.657 0.163 10.799 0.000 52.802 0.538 1.449

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 30 32 28 30 0 0 30 30

N.S.

1 1.00 1.07 0.93 1.00 0.00 0.00 1.00 1.00

time (sec)

N/A 0.303 1.276 0.181 10.701 0.000 0.000 0.520 1.387

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

355 355 315 0 0 0 0 0 0

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.660 0.257 0.000 0.000 0.000 0.000 0.000 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

229 229 208 0 0 0 0 0 0

N.S.

1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.060 0.146 0.000 0.000 0.000 0.000 0.000 0.000

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

104 106 104 0 0 0 0 0 0

N.S.

1 1.02 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.505 0.021 0.000 0.000 0.000 0.000 0.000 0.000

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 30 32 28 30 0 27 30 30

N.S.

1 1.00 1.07 0.93 1.00 0.00 0.90 1.00 1.00

time (sec)

N/A 0.258 0.079 0.191 10.492 0.000 1.499 0.490 1.351

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

404 666 1040 0 0 0 0 0 0

N.S.

1 1.65 2.57 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.805 1.522 0.000 0.000 0.000 0.000 0.000 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

275 402 435 0 0 0 0 0 0

N.S.

1 1.46 1.58 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.817 0.727 0.000 0.000 0.000 0.000 0.000 0.000

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

147 148 181 0 0 0 0 0 0

N.S.

1 1.01 1.23 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.646 0.106 0.000 0.000 0.000 0.000 0.000 0.000

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 30 32 28 30 0 27 30 30

N.S.

1 1.00 1.07 0.93 1.00 0.00 0.90 1.00 1.00

time (sec)

N/A 0.281 0.323 0.191 10.750 0.000 24.357 0.511 1.565

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

514 1154 652 0 0 0 0 0 0

N.S.

1 2.25 1.27 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 5.179 3.733 0.000 0.000 0.000 0.000 0.000 0.000

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

380 632 491 0 0 0 0 0 0

N.S.

1 1.66 1.29 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.145 1.274 0.000 0.000 0.000 0.000 0.000 0.000

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

194 203 211 0 0 0 0 0 0

N.S.

1 1.05 1.09 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.776 0.224 0.000 0.000 0.000 0.000 0.000 0.000

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 30 32 28 30 0 0 30 30

N.S.

1 1.00 1.07 0.93 1.00 0.00 0.00 1.00 1.00

time (sec)

N/A 0.275 0.568 0.185 12.525 0.000 0.000 0.835 1.702

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

171 166 153 0 0 624 0 0 0

N.S.

1 0.97 0.89 0.00 0.00 3.65 0.00 0.00 0.00

time (sec)

N/A 0.491 0.247 0.000 0.000 0.341 0.000 0.000 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

139 137 124 0 0 353 0 0 0

N.S.

1 0.99 0.89 0.00 0.00 2.54 0.00 0.00 0.00

time (sec)

N/A 0.404 0.127 0.000 0.000 0.344 0.000 0.000 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 104 89 118 0 201 0 124 0

N.S.

1 1.01 0.86 1.15 0.00 1.95 0.00 1.20 0.00

time (sec)

N/A 0.362 0.182 0.652 0.000 0.298 0.000 0.289 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

86 86 84 0 0 240 0 110 0

N.S.

1 1.00 0.98 0.00 0.00 2.79 0.00 1.28 0.00

time (sec)

N/A 0.335 0.113 0.000 0.000 0.336 0.000 0.310 0.000

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

120 115 91 0 0 467 0 184 0

N.S.

1 0.96 0.76 0.00 0.00 3.89 0.00 1.53 0.00

time (sec)

N/A 0.402 0.118 0.000 0.000 0.349 0.000 0.305 0.000

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

152 151 91 0 0 863 0 324 0

N.S.

1 0.99 0.60 0.00 0.00 5.68 0.00 2.13 0.00

time (sec)

N/A 0.437 0.063 0.000 0.000 0.368 0.000 0.344 0.000

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

184 187 91 0 0 1362 0 0 0

N.S.

1 1.02 0.49 0.00 0.00 7.40 0.00 0.00 0.00

time (sec)

N/A 0.499 0.070 0.000 0.000 0.410 0.000 0.000 0.000

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

635 1036 4354 0 0 0 0 0 0

N.S.

1 1.63 6.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 6.413 18.558 0.000 0.000 0.000 0.000 0.000 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

547 786 1323 0 0 0 0 0 0

N.S.

1 1.44 2.42 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 4.854 11.765 0.000 0.000 0.000 0.000 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

447 570 1407 0 0 0 0 0 0

N.S.

1 1.28 3.15 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.464 12.625 0.000 0.000 0.000 0.000 0.000 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

330 400 785 0 0 0 0 0 0

N.S.

1 1.21 2.38 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.421 2.540 0.000 0.000 0.000 0.000 0.000 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

449 546 1289 0 0 0 0 0 0

N.S.

1 1.22 2.87 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.522 12.812 0.000 0.000 0.000 0.000 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

537 732 1349 0 0 0 0 0 0

N.S.

1 1.36 2.51 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 4.756 9.704 0.000 0.000 0.000 0.000 0.000 0.000

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

625 969 1457 0 0 0 0 0 0

N.S.

1 1.55 2.33 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 6.398 11.041 0.000 0.000 0.000 0.000 0.000 0.000

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

30 30 32 28 30 30 26 30 30

N.S.

1 1.00 1.07 0.93 1.00 1.00 0.87 1.00 1.00

time (sec)

N/A 0.240 0.524 0.191 0.935 0.302 33.766 0.399 1.242

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

30 30 32 28 30 30 26 30 30

N.S.

1 1.00 1.07 0.93 1.00 1.00 0.87 1.00 1.00

time (sec)

N/A 0.227 0.161 0.158 0.938 0.291 0.933 0.376 1.221

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

30 30 32 28 30 43 27 30 30

N.S.

1 1.00 1.07 0.93 1.00 1.43 0.90 1.00 1.00

time (sec)

N/A 0.233 0.519 0.179 0.940 0.312 2.781 0.360 1.308

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

30 30 32 28 30 67 27 30 30

N.S.

1 1.00 1.07 0.93 1.00 2.23 0.90 1.00 1.00

time (sec)

N/A 0.240 0.799 0.187 0.930 0.313 15.332 0.488 1.222

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 32 34 28 30 0 29 30 30

N.S.

1 1.00 1.06 0.88 0.94 0.00 0.91 0.94 0.94

time (sec)

N/A 0.447 1.135 0.180 11.059 0.000 3.559 1.014 1.335

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