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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 B F A F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

346 346 468 1146 0 638 0 1428 0

N.S.

1 1.00 1.35 3.31 0.00 1.84 0.00 4.13 0.00

time (sec)

N/A 0.663 0.269 0.516 0.000 0.324 0.000 0.337 0.000

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

320 320 292 682 0 377 0 831 0

N.S.

1 1.00 0.91 2.13 0.00 1.18 0.00 2.60 0.00

time (sec)

N/A 0.608 0.161 0.364 0.000 0.331 0.000 0.328 0.000

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

255 255 170 356 0 197 0 425 306

N.S.

1 1.00 0.67 1.40 0.00 0.77 0.00 1.67 1.20

time (sec)

N/A 0.519 0.103 0.321 0.000 0.307 0.000 0.437 0.728

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 125 91 150 0 83 0 172 153

N.S.

1 1.00 0.73 1.20 0.00 0.66 0.00 1.38 1.22

time (sec)

N/A 0.344 0.055 0.106 0.000 0.285 0.000 0.288 0.435

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 37 42 0 35 0 50 44

N.S.

1 1.00 1.00 1.14 0.00 0.95 0.00 1.35 1.19

time (sec)

N/A 0.224 0.011 0.027 0.000 0.314 0.000 0.310 0.269

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 62 56 65 0 71 0 483 0

N.S.

1 1.00 0.90 1.05 0.00 1.15 0.00 7.79 0.00

time (sec)

N/A 0.524 0.044 0.328 0.000 0.288 0.000 0.571 0.000

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 111 105 97 0 154 0 330 0

N.S.

1 1.04 0.98 0.91 0.00 1.44 0.00 3.08 0.00

time (sec)

N/A 0.818 0.102 0.325 0.000 0.271 0.000 0.303 0.000

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

240 234 0 240 0 517 0 1733 0

N.S.

1 0.98 0.00 1.00 0.00 2.15 0.00 7.22 0.00

time (sec)

N/A 1.232 0.000 0.375 0.000 0.287 0.000 0.342 0.000

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

322 322 243 553 0 311 0 0 0

N.S.

1 1.00 0.75 1.72 0.00 0.97 0.00 0.00 0.00

time (sec)

N/A 0.611 0.185 0.415 0.000 0.284 0.000 0.000 0.000

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

215 215 176 313 0 196 0 0 0

N.S.

1 1.00 0.82 1.46 0.00 0.91 0.00 0.00 0.00

time (sec)

N/A 0.467 0.118 0.324 0.000 0.289 0.000 0.000 0.000

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 111 85 140 0 122 0 0 0

N.S.

1 1.00 0.77 1.26 0.00 1.10 0.00 0.00 0.00

time (sec)

N/A 0.310 0.088 0.086 0.000 0.297 0.000 0.000 0.000

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 50 48 0 63 0 0 43

N.S.

1 1.00 1.00 0.96 0.00 1.26 0.00 0.00 0.86

time (sec)

N/A 0.246 0.017 0.056 0.000 0.286 0.000 0.000 0.381

Problem 413

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

19 19 21 18 20 31 26 20 20

N.S.

1 1.00 1.11 0.95 1.05 1.63 1.37 1.05 1.05

time (sec)

N/A 0.171 0.027 0.041 0.348 0.293 123.030 0.338 0.304

Problem 414

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

19 19 21 18 20 42 27 1 20

N.S.

1 1.00 1.11 0.95 1.05 2.21 1.42 0.05 1.05

time (sec)

N/A 0.240 0.161 0.044 0.287 0.288 16.221 0.350 0.828

Problem 415

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

19 19 21 18 20 53 1 20 20

N.S.

1 1.00 1.11 0.95 1.05 2.79 0.05 1.05 1.05

time (sec)

N/A 0.238 0.052 0.060 0.301 0.287 0.000 0.333 1.240

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

206 206 195 0 0 349 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 1.69 0.00 0.00 0.00

time (sec)

N/A 0.410 0.103 0.000 0.000 0.099 0.000 0.000 0.000

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

151 151 136 0 0 259 0 0 0

N.S.

1 1.00 0.90 0.00 0.00 1.72 0.00 0.00 0.00

time (sec)

N/A 0.331 0.056 0.000 0.000 0.109 0.000 0.000 0.000

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

92 92 85 0 0 169 0 0 0

N.S.

1 1.00 0.92 0.00 0.00 1.84 0.00 0.00 0.00

time (sec)

N/A 0.242 0.057 0.000 0.000 0.092 0.000 0.000 0.000

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F B F F B

verified

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

size

40 40 40 0 0 89 0 0 61

N.S.

1 1.00 1.00 0.00 0.00 2.22 0.00 0.00 1.52

time (sec)

N/A 0.165 0.005 0.000 0.000 0.117 0.000 0.000 0.671

Problem 420

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

19 19 21 18 20 42 1 20 20

N.S.

1 1.00 1.11 0.95 1.05 2.21 0.05 1.05 1.05

time (sec)

N/A 0.174 0.023 0.043 0.323 0.316 0.000 0.348 0.246

Problem 421

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

19 19 21 18 20 53 1 1 20

N.S.

1 1.00 1.11 0.95 1.05 2.79 0.05 0.05 1.05

time (sec)

N/A 0.228 0.214 0.045 0.357 0.350 0.000 0.631 0.669

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 104 102 436 0 135 0 0 0

N.S.

1 1.00 0.98 4.19 0.00 1.30 0.00 0.00 0.00

time (sec)

N/A 1.707 0.210 0.375 0.000 0.334 0.000 0.000 0.000

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

159 179 0 582 0 220 0 0 0

N.S.

1 1.13 0.00 3.66 0.00 1.38 0.00 0.00 0.00

time (sec)

N/A 2.237 0.000 0.532 0.000 0.325 0.000 0.000 0.000

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

366 355 0 2019 0 755 0 0 0

N.S.

1 0.97 0.00 5.52 0.00 2.06 0.00 0.00 0.00

time (sec)

N/A 4.085 0.000 0.734 0.000 0.366 0.000 0.000 0.000

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

634 612 0 4680 0 2250 0 0 0

N.S.

1 0.97 0.00 7.38 0.00 3.55 0.00 0.00 0.00

time (sec)

N/A 7.904 0.000 1.229 0.000 0.427 0.000 0.000 0.000

Problem 426

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

217 295 122 218 201 114 0 137 153

N.S.

1 1.36 0.56 1.00 0.93 0.53 0.00 0.63 0.71

time (sec)

N/A 0.870 0.219 0.051 0.323 0.348 0.000 0.349 0.553

Problem 427

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

164 170 104 163 166 95 0 108 111

N.S.

1 1.04 0.63 0.99 1.01 0.58 0.00 0.66 0.68

time (sec)

N/A 0.457 0.179 0.039 0.321 0.363 0.000 0.346 0.405

Problem 428

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

81 81 81 79 107 73 0 80 71

N.S.

1 1.00 1.00 0.98 1.32 0.90 0.00 0.99 0.88

time (sec)

N/A 0.248 0.102 0.026 0.310 0.328 0.000 0.328 0.331

Problem 429

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

56 56 56 50 50 55 0 50 49

N.S.

1 1.00 1.00 0.89 0.89 0.98 0.00 0.89 0.88

time (sec)

N/A 0.194 0.033 0.027 0.210 0.342 0.000 0.385 0.182

Problem 430

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

16 16 18 16 18 18 14 18 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.88 1.12 1.12

time (sec)

N/A 0.174 0.163 0.006 0.271 0.336 0.335 0.429 0.218

Problem 431

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

16 16 18 16 18 18 15 18 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.94 1.12 1.12

time (sec)

N/A 0.352 0.342 0.006 0.274 0.355 0.286 0.379 0.309

Problem 432

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

181 242 91 154 181 89 0 104 112

N.S.

1 1.34 0.50 0.85 1.00 0.49 0.00 0.57 0.62

time (sec)

N/A 0.795 0.268 0.065 0.331 0.324 0.000 0.335 0.299

Problem 433

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

134 140 79 111 151 72 0 80 80

N.S.

1 1.04 0.59 0.83 1.13 0.54 0.00 0.60 0.60

time (sec)

N/A 0.427 0.182 0.036 0.332 0.335 0.000 0.317 0.211

Problem 434

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

66 66 68 53 98 57 0 58 58

N.S.

1 1.00 1.03 0.80 1.48 0.86 0.00 0.88 0.88

time (sec)

N/A 0.237 0.101 0.023 0.279 0.351 0.000 0.333 0.149

Problem 435

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 44 46 34 32 36 41 38 40

N.S.

1 1.00 1.05 0.77 0.73 0.82 0.93 0.86 0.91

time (sec)

N/A 0.187 0.033 0.013 0.210 0.290 0.285 0.316 0.036

Problem 436

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

17 17 19 16 18 18 17 18 18

N.S.

1 1.00 1.12 0.94 1.06 1.06 1.00 1.06 1.06

time (sec)

N/A 0.174 0.170 0.007 0.289 0.313 2.411 0.308 0.218

Problem 437

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

17 17 19 16 18 18 19 18 18

N.S.

1 1.00 1.12 0.94 1.06 1.06 1.12 1.06 1.06

time (sec)

N/A 0.351 0.325 0.007 0.273 0.306 2.059 0.321 0.269

Problem 438

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

297 392 191 368 267 212 0 250 230

N.S.

1 1.32 0.64 1.24 0.90 0.71 0.00 0.84 0.77

time (sec)

N/A 1.651 0.507 0.080 0.339 0.339 0.000 0.305 0.570

Problem 439

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

216 225 144 212 221 148 0 152 150

N.S.

1 1.04 0.67 0.98 1.02 0.69 0.00 0.70 0.69

time (sec)

N/A 0.788 0.329 0.049 0.368 0.334 0.000 0.334 0.296

Problem 440

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

107 107 116 102 143 107 0 104 95

N.S.

1 1.00 1.08 0.95 1.34 1.00 0.00 0.97 0.89

time (sec)

N/A 0.348 0.147 0.024 0.338 0.309 0.000 0.349 0.375

Problem 441

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

68 68 68 57 58 74 0 68 60

N.S.

1 1.00 1.00 0.84 0.85 1.09 0.00 1.00 0.88

time (sec)

N/A 0.223 0.025 0.013 0.245 0.349 0.000 0.414 0.039

Problem 442

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

17 17 19 16 18 26 29 18 18

N.S.

1 1.00 1.12 0.94 1.06 1.53 1.71 1.06 1.06

time (sec)

N/A 0.284 0.299 0.010 0.326 0.325 6.761 0.324 0.224

Problem 443

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

17 17 19 16 18 26 31 18 18

N.S.

1 1.00 1.12 0.94 1.06 1.53 1.82 1.06 1.06

time (sec)

N/A 0.719 0.603 0.012 0.297 0.323 9.045 0.333 0.335

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

266 345 169 550 539 204 0 240 251

N.S.

1 1.30 0.64 2.07 2.03 0.77 0.00 0.90 0.94

time (sec)

N/A 0.960 0.437 0.296 0.445 0.356 0.000 0.334 0.602

Problem 445

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

189 195 123 307 332 130 0 143 153

N.S.

1 1.03 0.65 1.62 1.76 0.69 0.00 0.76 0.81

time (sec)

N/A 0.496 0.314 0.364 0.351 0.352 0.000 0.311 0.488

Problem 446

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

90 90 96 131 160 83 0 89 80

N.S.

1 1.00 1.07 1.46 1.78 0.92 0.00 0.99 0.89

time (sec)

N/A 0.254 0.202 0.037 0.305 0.362 0.000 0.328 0.375

Problem 447

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

20 20 22 20 22 22 17 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.85 1.10 1.10

time (sec)

N/A 0.179 0.326 0.023 0.291 0.299 0.336 0.307 0.432

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

20 20 22 20 22 33 19 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.65 0.95 1.10 1.10

time (sec)

N/A 0.418 0.696 0.027 0.283 0.294 0.541 0.437 1.382

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

20 20 22 20 22 44 19 22 22

N.S.

1 1.00 1.10 1.00 1.10 2.20 0.95 1.10 1.10

time (sec)

N/A 0.633 0.989 0.023 0.301 0.330 0.744 0.329 3.346

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 31 45 539 41 85 798 44

N.S.

1 1.00 0.69 1.00 11.98 0.91 1.89 17.73 0.98

time (sec)

N/A 0.236 0.384 0.244 0.449 0.329 0.073 0.333 0.427

Problem 451

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

78 78 86 99 332 74 0 88 92

N.S.

1 1.00 1.10 1.27 4.26 0.95 0.00 1.13 1.18

time (sec)

N/A 0.261 0.364 0.366 0.380 0.337 0.000 0.331 0.376

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 17 18 17 17 24 17 17

N.S.

1 1.00 1.00 1.06 1.00 1.00 1.41 1.00 1.00

time (sec)

N/A 0.164 0.069 0.017 0.206 0.338 0.055 0.306 0.280

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 39 40 0 47 0 0 0

N.S.

1 1.00 1.00 1.03 0.00 1.21 0.00 0.00 0.00

time (sec)

N/A 0.192 0.181 0.286 0.000 0.327 0.000 0.000 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 84 96 101 0 85 0 0 76

N.S.

1 1.00 1.14 1.20 0.00 1.01 0.00 0.00 0.90

time (sec)

N/A 0.267 0.459 0.372 0.000 0.311 0.000 0.000 0.766

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 69 79 88 0 106 0 0 0

N.S.

1 1.00 1.14 1.28 0.00 1.54 0.00 0.00 0.00

time (sec)

N/A 0.255 0.406 0.373 0.000 0.303 0.000 0.000 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 29 42 536 40 83 742 43

N.S.

1 1.00 0.67 0.98 12.47 0.93 1.93 17.26 1.00

time (sec)

N/A 0.228 0.153 0.352 0.503 0.304 0.080 0.346 0.296

Problem 457

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

75 75 84 90 329 68 0 77 86

N.S.

1 1.00 1.12 1.20 4.39 0.91 0.00 1.03 1.15

time (sec)

N/A 0.265 0.135 0.275 0.333 0.324 0.000 0.322 0.301

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

16 16 16 15 16 16 22 16 16

N.S.

1 1.00 1.00 0.94 1.00 1.00 1.38 1.00 1.00

time (sec)

N/A 0.166 0.030 0.026 0.198 0.355 0.055 0.276 0.241

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 37 33 0 42 0 0 0

N.S.

1 1.00 1.00 0.89 0.00 1.14 0.00 0.00 0.00

time (sec)

N/A 0.186 0.048 0.345 0.000 0.320 0.000 0.000 0.000

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 81 94 87 0 79 0 0 73

N.S.

1 1.00 1.16 1.07 0.00 0.98 0.00 0.00 0.90

time (sec)

N/A 0.250 0.137 0.302 0.000 0.348 0.000 0.000 0.429

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 77 74 0 100 0 0 0

N.S.

1 1.00 1.17 1.12 0.00 1.52 0.00 0.00 0.00

time (sec)

N/A 0.246 0.133 0.466 0.000 0.283 0.000 0.000 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 145 121 142 0 128 0 0 0

N.S.

1 1.00 0.83 0.98 0.00 0.88 0.00 0.00 0.00

time (sec)

N/A 0.479 0.360 0.427 0.000 0.285 0.000 0.000 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 111 93 112 0 80 0 0 0

N.S.

1 1.00 0.84 1.01 0.00 0.72 0.00 0.00 0.00

time (sec)

N/A 0.428 0.187 0.422 0.000 0.297 0.000 0.000 0.000

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 118 94 102 0 98 0 0 0

N.S.

1 1.00 0.80 0.86 0.00 0.83 0.00 0.00 0.00

time (sec)

N/A 0.318 0.087 0.430 0.000 0.311 0.000 0.000 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 100 83 100 0 72 0 0 0

N.S.

1 1.00 0.83 1.00 0.00 0.72 0.00 0.00 0.00

time (sec)

N/A 0.308 0.119 0.424 0.000 0.299 0.000 0.000 0.000

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 132 120 127 0 106 0 0 0

N.S.

1 1.00 0.91 0.96 0.00 0.80 0.00 0.00 0.00

time (sec)

N/A 0.411 0.138 0.437 0.000 0.341 0.000 0.000 0.000

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

212 212 320 561 0 313 0 0 0

N.S.

1 1.00 1.51 2.65 0.00 1.48 0.00 0.00 0.00

time (sec)

N/A 0.730 0.883 0.629 0.000 0.347 0.000 0.000 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 169 163 363 0 241 0 0 0

N.S.

1 1.00 0.96 2.15 0.00 1.43 0.00 0.00 0.00

time (sec)

N/A 0.562 0.367 0.437 0.000 0.312 0.000 0.000 0.000

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 138 127 169 0 192 0 0 0

N.S.

1 1.00 0.92 1.22 0.00 1.39 0.00 0.00 0.00

time (sec)

N/A 0.383 0.008 0.433 0.000 0.293 0.000 0.000 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

158 158 153 350 0 224 0 0 0

N.S.

1 1.00 0.97 2.22 0.00 1.42 0.00 0.00 0.00

time (sec)

N/A 0.402 0.326 0.431 0.000 0.315 0.000 0.000 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

186 186 217 561 0 267 0 0 0

N.S.

1 1.00 1.17 3.02 0.00 1.44 0.00 0.00 0.00

time (sec)

N/A 0.546 0.890 0.608 0.000 0.270 0.000 0.000 0.000

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

232 232 268 755 0 330 0 0 0

N.S.

1 1.00 1.16 3.25 0.00 1.42 0.00 0.00 0.00

time (sec)

N/A 0.649 0.457 0.556 0.000 0.275 0.000 0.000 0.000

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 27 27 33 30 25 41 0 26

N.S.

1 0.90 0.90 1.10 1.00 0.83 1.37 0.00 0.87

time (sec)

N/A 0.199 0.095 0.048 0.276 0.360 0.151 0.000 0.313

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

30 27 27 28 30 25 31 31 26

N.S.

1 0.90 0.90 0.93 1.00 0.83 1.03 1.03 0.87

time (sec)

N/A 0.200 0.001 0.033 0.186 0.294 0.077 0.325 0.264

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 29 26 35 33 27 44 0 27

N.S.

1 0.91 0.81 1.09 1.03 0.84 1.38 0.00 0.84

time (sec)

N/A 0.205 0.111 0.039 0.261 0.353 0.166 0.000 0.291

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

32 29 26 30 33 27 34 34 27

N.S.

1 0.91 0.81 0.94 1.03 0.84 1.06 1.06 0.84

time (sec)

N/A 0.206 0.001 0.033 0.182 0.310 0.084 0.333 0.277

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 58 36 50 59 39 75 0 0

N.S.

1 1.00 0.62 0.86 1.02 0.67 1.29 0.00 0.00

time (sec)

N/A 0.231 0.107 0.043 0.325 0.309 0.170 0.000 0.000

Problem 478

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 58 36 41 59 39 66 48 47

N.S.

1 1.00 0.62 0.71 1.02 0.67 1.14 0.83 0.81

time (sec)

N/A 0.233 0.001 0.036 0.198 0.336 0.101 0.301 0.307

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 60 38 50 58 41 75 0 0

N.S.

1 1.03 0.66 0.86 1.00 0.71 1.29 0.00 0.00

time (sec)

N/A 0.231 0.104 0.037 0.282 0.331 0.188 0.000 0.000

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

58 60 38 42 58 41 66 50 47

N.S.

1 1.03 0.66 0.72 1.00 0.71 1.14 0.86 0.81

time (sec)

N/A 0.228 0.001 0.037 0.197 0.280 0.099 0.303 0.282

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 30 53 21 86 29 0 22

N.S.

1 1.00 1.00 1.77 0.70 2.87 0.97 0.00 0.73

time (sec)

N/A 0.182 0.040 0.046 0.284 0.278 0.197 0.000 0.309

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 30 22 21 86 24 21 22

N.S.

1 1.00 1.00 0.73 0.70 2.87 0.80 0.70 0.73

time (sec)

N/A 0.181 0.001 0.046 0.265 0.326 0.081 0.291 0.263

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 30 49 45 86 29 0 22

N.S.

1 1.00 1.00 1.63 1.50 2.87 0.97 0.00 0.73

time (sec)

N/A 0.181 0.041 0.042 0.281 0.366 0.174 0.000 0.453

Problem 484

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

30 30 30 22 45 86 24 24 22

N.S.

1 1.00 1.00 0.73 1.50 2.87 0.80 0.80 0.73

time (sec)

N/A 0.183 0.002 0.037 0.287 0.280 0.088 0.290 0.419

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 40 40 74 68 102 54 0 35

N.S.

1 0.93 0.93 1.72 1.58 2.37 1.26 0.00 0.81

time (sec)

N/A 0.201 0.042 0.066 0.286 0.324 0.259 0.000 0.295

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

43 40 40 36 39 102 39 38 35

N.S.

1 0.93 0.93 0.84 0.91 2.37 0.91 0.88 0.81

time (sec)

N/A 0.203 0.001 0.066 0.268 0.315 0.113 0.469 0.118

Problem 487

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

43 40 40 70 88 103 54 0 35

N.S.

1 0.93 0.93 1.63 2.05 2.40 1.26 0.00 0.81

time (sec)

N/A 0.199 0.041 0.047 0.274 0.296 0.223 0.000 0.329

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 40 40 36 65 103 39 39 35

N.S.

1 0.93 0.93 0.84 1.51 2.40 0.91 0.91 0.81

time (sec)

N/A 0.202 0.001 0.045 0.266 0.306 0.120 0.282 0.328

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F A A F B

verified

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

size

31 33 33 0 0 77 61 0 28

N.S.

1 1.06 1.06 0.00 0.00 2.48 1.97 0.00 0.90

time (sec)

N/A 0.188 0.060 0.000 0.000 0.317 0.416 0.000 0.455

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 33 33 29 22 77 61 31 28

N.S.

1 1.06 1.06 0.94 0.71 2.48 1.97 1.00 0.90

time (sec)

N/A 0.196 0.001 0.019 0.190 0.323 0.398 0.325 0.384

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F A A F B

verified

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

size

32 34 34 0 0 92 66 0 33

N.S.

1 1.06 1.06 0.00 0.00 2.88 2.06 0.00 1.03

time (sec)

N/A 0.195 0.080 0.000 0.000 0.317 0.434 0.000 0.484

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

32 34 34 29 22 92 66 36 33

N.S.

1 1.06 1.06 0.91 0.69 2.88 2.06 1.12 1.03

time (sec)

N/A 0.195 0.001 0.018 0.265 0.354 0.453 0.322 0.392

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 35 40 19 30 0 0 24

N.S.

1 1.00 1.46 1.67 0.79 1.25 0.00 0.00 1.00

time (sec)

N/A 0.197 0.055 0.046 0.318 0.288 0.000 0.000 0.278

Problem 494

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

24 24 35 40 24 30 0 29 24

N.S.

1 1.00 1.46 1.67 1.00 1.25 0.00 1.21 1.00

time (sec)

N/A 0.189 0.001 0.046 0.186 0.298 0.000 0.278 0.227

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 38 44 21 32 0 0 25

N.S.

1 1.00 1.52 1.76 0.84 1.28 0.00 0.00 1.00

time (sec)

N/A 0.192 0.052 0.037 0.309 0.289 0.000 0.000 0.268

Problem 496

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

25 25 38 44 25 32 0 33 25

N.S.

1 1.00 1.52 1.76 1.00 1.28 0.00 1.32 1.00

time (sec)

N/A 0.191 0.001 0.035 0.229 0.297 0.000 0.294 0.262

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 41 29 29 68 27 56 0 28

N.S.

1 0.93 0.66 0.66 1.55 0.61 1.27 0.00 0.64

time (sec)

N/A 0.202 0.062 0.017 0.259 0.302 0.327 0.000 0.345

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

44 41 29 29 38 27 58 31 28

N.S.

1 0.93 0.66 0.66 0.86 0.61 1.32 0.70 0.64

time (sec)

N/A 0.202 0.001 0.035 0.184 0.299 0.313 0.289 0.268

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 43 30 29 71 28 58 0 28

N.S.

1 0.93 0.65 0.63 1.54 0.61 1.26 0.00 0.61

time (sec)

N/A 0.202 0.062 0.016 0.275 0.328 0.325 0.000 0.335

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

46 43 30 29 40 28 60 33 28

N.S.

1 0.93 0.65 0.63 0.87 0.61 1.30 0.72 0.61

time (sec)

N/A 0.200 0.002 0.035 0.190 0.304 0.332 0.330 0.302

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