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Integrals 401 to 470

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 Reduce Mupad

grade

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

verified

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

size

165 165 139 450 0 767 0 0 61 0

N.S.

1 1.00 0.84 2.73 0.00 4.65 0.00 0.00 0.37 0.00

time (sec)

N/A 0.477 0.974 4.702 0.000 2.661 0.000 0.000 2.256 0.000

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

89 87 107 193 0 410 0 765 38 0

N.S.

1 0.98 1.20 2.17 0.00 4.61 0.00 8.60 0.43 0.00

time (sec)

N/A 0.311 1.029 11.875 0.000 0.467 0.000 0.689 0.151 0.000

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

56 59 56 154 0 328 0 373 38 0

N.S.

1 1.05 1.00 2.75 0.00 5.86 0.00 6.66 0.68 0.00

time (sec)

N/A 0.279 0.378 4.445 0.000 0.191 0.000 0.501 0.153 0.000

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A F B F B F B

verified

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

size

33 33 33 42 0 261 0 111 36 27

N.S.

1 1.00 1.00 1.27 0.00 7.91 0.00 3.36 1.09 0.82

time (sec)

N/A 0.240 0.078 0.145 0.000 0.139 0.000 0.380 0.164 16.023

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

70 72 294 343 0 1015 0 403 36 0

N.S.

1 1.03 4.20 4.90 0.00 14.50 0.00 5.76 0.51 0.00

time (sec)

N/A 0.293 1.637 0.301 0.000 0.240 0.000 0.657 0.164 0.000

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

116 128 0 1048 0 1550 0 595 38 0

N.S.

1 1.10 0.00 9.03 0.00 13.36 0.00 5.13 0.33 0.00

time (sec)

N/A 0.346 0.000 0.434 0.000 0.417 0.000 0.709 0.169 0.000

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

166 194 0 1978 0 2257 0 924 38 0

N.S.

1 1.17 0.00 11.92 0.00 13.60 0.00 5.57 0.23 0.00

time (sec)

N/A 0.399 0.000 0.487 0.000 1.145 0.000 1.048 0.212 0.000

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

173 181 230 1054 0 1673 0 0 38 0

N.S.

1 1.05 1.33 6.09 0.00 9.67 0.00 0.00 0.22 0.00

time (sec)

N/A 0.491 2.248 12.996 0.000 1.201 0.000 0.000 0.165 0.000

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

120 122 196 732 0 1507 0 0 38 0

N.S.

1 1.02 1.63 6.10 0.00 12.56 0.00 0.00 0.32 0.00

time (sec)

N/A 0.377 1.559 4.362 0.000 0.487 0.000 0.000 0.163 0.000

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

80 78 296 342 0 1259 0 0 38 0

N.S.

1 0.98 3.70 4.28 0.00 15.74 0.00 0.00 0.48 0.00

time (sec)

N/A 0.343 1.505 2.188 0.000 0.333 0.000 0.000 0.160 0.000

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

39 39 87 138 992 408 0 0 30 0

N.S.

1 1.00 2.23 3.54 25.44 10.46 0.00 0.00 0.77 0.00

time (sec)

N/A 0.210 0.050 1.107 0.256 0.196 0.000 0.000 0.153 0.000

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

74 72 127 298 0 525 0 0 38 0

N.S.

1 0.97 1.72 4.03 0.00 7.09 0.00 0.00 0.51 0.00

time (sec)

N/A 0.349 0.147 2.016 0.000 0.236 0.000 0.000 0.152 0.000

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

119 126 168 505 0 723 0 0 38 0

N.S.

1 1.06 1.41 4.24 0.00 6.08 0.00 0.00 0.32 0.00

time (sec)

N/A 0.405 0.935 5.053 0.000 0.479 0.000 0.000 0.185 0.000

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

172 187 199 741 0 987 0 0 38 0

N.S.

1 1.09 1.16 4.31 0.00 5.74 0.00 0.00 0.22 0.00

time (sec)

N/A 0.475 2.089 7.647 0.000 1.581 0.000 0.000 0.356 0.000

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

88 88 121 337 0 458 0 560 54 0

N.S.

1 1.00 1.38 3.83 0.00 5.20 0.00 6.36 0.61 0.00

time (sec)

N/A 0.333 3.419 7.118 0.000 0.627 0.000 0.994 0.164 0.000

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

63 65 62 874 2532 417 0 251 54 0

N.S.

1 1.03 0.98 13.87 40.19 6.62 0.00 3.98 0.86 0.00

time (sec)

N/A 0.298 0.473 0.443 0.401 0.206 0.000 0.839 0.157 0.000

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C A F B A B F B

verified

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

size

57 59 382 62 0 392 75 216 52 49

N.S.

1 1.04 6.70 1.09 0.00 6.88 1.32 3.79 0.91 0.86

time (sec)

N/A 0.261 4.091 0.072 0.000 0.194 5.887 0.650 0.159 17.535

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

100 113 0 2949 0 1569 0 0 52 0

N.S.

1 1.13 0.00 29.49 0.00 15.69 0.00 0.00 0.52 0.00

time (sec)

N/A 0.339 0.000 0.496 0.000 0.429 0.000 0.000 0.156 0.000

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

153 173 0 3946 0 2347 0 1062 54 0

N.S.

1 1.13 0.00 25.79 0.00 15.34 0.00 6.94 0.35 0.00

time (sec)

N/A 0.401 0.000 1.132 0.000 1.340 0.000 1.400 0.165 0.000

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

213 247 0 4962 0 3501 0 1771 54 0

N.S.

1 1.16 0.00 23.30 0.00 16.44 0.00 8.31 0.25 0.00

time (sec)

N/A 0.467 0.000 1.209 0.000 4.402 0.000 2.185 0.522 0.000

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

172 178 247 1296 0 1895 0 0 54 0

N.S.

1 1.03 1.44 7.53 0.00 11.02 0.00 0.00 0.31 0.00

time (sec)

N/A 0.494 6.118 13.582 0.000 1.494 0.000 0.000 0.179 0.000

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

116 121 201 921 0 1655 0 0 54 0

N.S.

1 1.04 1.73 7.94 0.00 14.27 0.00 0.00 0.47 0.00

time (sec)

N/A 0.377 3.076 6.139 0.000 0.568 0.000 0.000 0.173 0.000

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

71 69 169 282 2005 548 0 0 54 0

N.S.

1 0.97 2.38 3.97 28.24 7.72 0.00 0.00 0.76 0.00

time (sec)

N/A 0.340 1.694 2.287 0.348 0.260 0.000 0.000 0.165 0.000

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

77 75 168 465 2055 601 0 0 46 0

N.S.

1 0.97 2.18 6.04 26.69 7.81 0.00 0.00 0.60 0.00

time (sec)

N/A 0.228 0.937 3.418 0.373 0.258 0.000 0.000 0.172 0.000

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

119 124 182 661 0 741 0 0 54 0

N.S.

1 1.04 1.53 5.55 0.00 6.23 0.00 0.00 0.45 0.00

time (sec)

N/A 0.411 2.976 5.640 0.000 0.557 0.000 0.000 0.181 0.000

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

174 184 224 918 0 1061 0 0 54 0

N.S.

1 1.06 1.29 5.28 0.00 6.10 0.00 0.00 0.31 0.00

time (sec)

N/A 0.484 2.663 10.023 0.000 1.815 0.000 0.000 0.247 0.000

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

241 254 237 1161 0 1517 0 0 54 0

N.S.

1 1.05 0.98 4.82 0.00 6.29 0.00 0.00 0.22 0.00

time (sec)

N/A 0.564 4.241 15.240 0.000 6.568 0.000 0.000 2.276 0.000

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

97 96 187 1570 0 564 0 466 70 0

N.S.

1 0.99 1.93 16.19 0.00 5.81 0.00 4.80 0.72 0.00

time (sec)

N/A 0.335 5.572 5.462 0.000 0.787 0.000 1.556 0.175 0.000

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

89 93 522 1541 0 522 0 418 70 0

N.S.

1 1.04 5.87 17.31 0.00 5.87 0.00 4.70 0.79 0.00

time (sec)

N/A 0.306 7.788 1.410 0.000 0.645 0.000 1.304 0.176 0.000

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C A F B A B F B

verified

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

size

83 87 521 86 0 494 100 370 68 68

N.S.

1 1.05 6.28 1.04 0.00 5.95 1.20 4.46 0.82 0.82

time (sec)

N/A 0.264 5.545 0.083 0.000 0.526 10.058 1.073 0.169 19.215

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

137 161 0 9176 0 2279 0 0 68 0

N.S.

1 1.18 0.00 66.98 0.00 16.64 0.00 0.00 0.50 0.00

time (sec)

N/A 0.371 0.000 10.529 0.000 1.245 0.000 0.000 0.164 0.000

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

200 227 0 12014 0 3507 0 2160 70 0

N.S.

1 1.14 0.00 60.07 0.00 17.54 0.00 10.80 0.35 0.00

time (sec)

N/A 0.456 0.000 8.632 0.000 4.476 0.000 2.137 0.181 0.000

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

268 311 0 15443 0 4751 0 3397 70 0

N.S.

1 1.16 0.00 57.62 0.00 17.73 0.00 12.68 0.26 0.00

time (sec)

N/A 0.536 0.000 8.175 0.000 17.468 0.000 2.892 8.843 0.000

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

157 178 316 1423 0 2035 0 0 70 0

N.S.

1 1.13 2.01 9.06 0.00 12.96 0.00 0.00 0.45 0.00

time (sec)

N/A 0.487 9.484 5.409 0.000 1.865 0.000 0.000 0.164 0.000

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

120 122 409 489 0 661 0 0 70 0

N.S.

1 1.02 3.41 4.08 0.00 5.51 0.00 0.00 0.58 0.00

time (sec)

N/A 0.387 4.296 2.838 0.000 0.777 0.000 0.000 0.165 0.000

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

119 120 410 692 0 773 0 0 70 0

N.S.

1 1.01 3.45 5.82 0.00 6.50 0.00 0.00 0.59 0.00

time (sec)

N/A 0.385 3.165 3.877 0.000 0.650 0.000 0.000 0.167 0.000

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

125 135 1927 861 0 881 0 0 62 0

N.S.

1 1.08 15.42 6.89 0.00 7.05 0.00 0.00 0.50 0.00

time (sec)

N/A 0.277 6.292 6.072 0.000 0.552 0.000 0.000 0.166 0.000

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

174 187 247 1109 0 1097 0 0 70 0

N.S.

1 1.07 1.42 6.37 0.00 6.30 0.00 0.00 0.40 0.00

time (sec)

N/A 0.496 4.200 9.801 0.000 1.844 0.000 0.000 0.167 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

236 253 234 1397 0 1579 0 0 70 0

N.S.

1 1.07 0.99 5.92 0.00 6.69 0.00 0.00 0.30 0.00

time (sec)

N/A 0.575 6.127 13.352 0.000 6.705 0.000 0.000 1.948 0.000

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

315 337 272 1698 0 2059 0 0 70 0

N.S.

1 1.07 0.86 5.39 0.00 6.54 0.00 0.00 0.22 0.00

time (sec)

N/A 0.674 9.588 17.253 0.000 22.982 0.000 0.000 30.941 0.000

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

107 105 259 0 0 0 0 0 29 0

N.S.

1 0.98 2.42 0.00 0.00 0.00 0.00 0.00 0.27 0.00

time (sec)

N/A 0.335 2.972 0.000 0.000 0.000 0.000 0.000 0.209 0.000

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

123 113 94 0 0 0 0 0 932 0

N.S.

1 0.92 0.76 0.00 0.00 0.00 0.00 0.00 7.58 0.00

time (sec)

N/A 0.327 0.436 0.000 0.000 0.000 0.000 0.000 0.509 0.000

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

87 83 61 0 0 0 0 0 288 0

N.S.

1 0.95 0.70 0.00 0.00 0.00 0.00 0.00 3.31 0.00

time (sec)

N/A 0.266 0.123 0.000 0.000 0.000 0.000 0.000 0.237 0.000

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

55 54 54 0 0 0 0 0 65 0

N.S.

1 0.98 0.98 0.00 0.00 0.00 0.00 0.00 1.18 0.00

time (sec)

N/A 0.230 0.037 0.000 0.000 0.000 0.000 0.000 0.184 0.000

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

115 110 115 0 0 0 0 0 23 0

N.S.

1 0.96 1.00 0.00 0.00 0.00 0.00 0.00 0.20 0.00

time (sec)

N/A 0.294 1.226 0.000 0.000 0.000 0.000 0.000 0.172 0.000

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

158 163 139 0 0 0 0 0 25 0

N.S.

1 1.03 0.88 0.00 0.00 0.00 0.00 0.00 0.16 0.00

time (sec)

N/A 0.330 2.330 0.000 0.000 0.000 0.000 0.000 0.182 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

90 88 2777 0 0 0 0 0 25 0

N.S.

1 0.98 30.86 0.00 0.00 0.00 0.00 0.00 0.28 0.00

time (sec)

N/A 0.322 16.126 0.000 0.000 0.000 0.000 0.000 0.187 0.000

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

90 88 2465 0 0 0 0 0 25 0

N.S.

1 0.98 27.39 0.00 0.00 0.00 0.00 0.00 0.28 0.00

time (sec)

N/A 0.314 15.155 0.000 0.000 0.000 0.000 0.000 0.197 0.000

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

85 83 1512 0 0 0 0 0 16 0

N.S.

1 0.98 17.79 0.00 0.00 0.00 0.00 0.00 0.19 0.00

time (sec)

N/A 0.232 5.855 0.000 0.000 0.000 0.000 0.000 0.158 0.000

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

86 84 2469 0 0 0 0 0 25 0

N.S.

1 0.98 28.71 0.00 0.00 0.00 0.00 0.00 0.29 0.00

time (sec)

N/A 0.317 15.548 0.000 0.000 0.000 0.000 0.000 0.174 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

90 88 3033 0 0 0 0 0 25 0

N.S.

1 0.98 33.70 0.00 0.00 0.00 0.00 0.00 0.28 0.00

time (sec)

N/A 0.315 16.483 0.000 0.000 0.000 0.000 0.000 200.021 0.000

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

92 77 92 70 73 81 119 74 91 227

N.S.

1 0.84 1.00 0.76 0.79 0.88 1.29 0.80 0.99 2.47

time (sec)

N/A 0.289 0.199 1.914 0.031 0.089 0.791 0.288 0.180 18.513

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

61 55 59 49 51 59 82 52 61 167

N.S.

1 0.90 0.97 0.80 0.84 0.97 1.34 0.85 1.00 2.74

time (sec)

N/A 0.273 0.163 0.938 0.027 0.085 0.383 0.254 0.181 18.447

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

30 28 30 26 28 37 42 39 31 83

N.S.

1 0.93 1.00 0.87 0.93 1.23 1.40 1.30 1.03 2.77

time (sec)

N/A 0.219 0.009 0.434 0.027 0.081 0.181 0.182 0.187 15.982

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

54 51 57 42 45 61 0 52 82 72

N.S.

1 0.94 1.06 0.78 0.83 1.13 0.00 0.96 1.52 1.33

time (sec)

N/A 0.293 0.008 0.414 0.032 0.093 0.000 0.163 0.185 15.392

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

65 63 108 63 62 99 0 78 103 86

N.S.

1 0.97 1.66 0.97 0.95 1.52 0.00 1.20 1.58 1.32

time (sec)

N/A 0.265 0.053 0.804 0.034 0.088 0.000 0.168 0.183 15.172

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C A C F A F B

verified

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

size

219 209 251 233 218 4427 0 229 0 7402

N.S.

1 0.95 1.15 1.06 1.00 20.21 0.00 1.05 0.00 33.80

time (sec)

N/A 0.537 0.536 2.288 0.109 0.828 0.000 0.216 0.523 17.536

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C A C F A F B

verified

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

size

166 156 242 113 159 1052 0 163 25 1620

N.S.

1 0.94 1.46 0.68 0.96 6.34 0.00 0.98 0.15 9.76

time (sec)

N/A 0.424 0.412 2.698 0.112 0.715 0.000 0.178 0.185 18.913

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

23 23 23 35 21 21 139 22 72 114

N.S.

1 1.00 1.00 1.52 0.91 0.91 6.04 0.96 3.13 4.96

time (sec)

N/A 0.217 0.014 1.039 0.031 0.093 17.392 0.156 0.185 15.388

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C A C F A F B

verified

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

size

295 281 215 288 306 6482 0 329 0 11182

N.S.

1 0.95 0.73 0.98 1.04 21.97 0.00 1.12 0.00 37.91

time (sec)

N/A 0.710 0.433 2.096 0.116 0.939 0.000 0.170 0.232 18.409

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C A A C F A F B

verified

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

size

393 375 336 374 488 10746 0 545 0 58699

N.S.

1 0.95 0.85 0.95 1.24 27.34 0.00 1.39 0.00 149.36

time (sec)

N/A 0.844 1.647 5.512 0.126 2.094 0.000 0.209 0.294 30.025

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

27 27 29 27 29 29 26 29 32 31

N.S.

1 1.00 1.07 1.00 1.07 1.07 0.96 1.07 1.19 1.15

time (sec)

N/A 0.239 3.503 0.724 5.802 0.091 98.501 0.735 0.212 14.681

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

229 221 245 0 0 0 0 0 1184 0

N.S.

1 0.97 1.07 0.00 0.00 0.00 0.00 0.00 5.17 0.00

time (sec)

N/A 0.756 8.592 0.000 0.000 0.000 0.000 0.000 0.337 0.000

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

145 141 162 0 0 0 0 0 364 0

N.S.

1 0.97 1.12 0.00 0.00 0.00 0.00 0.00 2.51 0.00

time (sec)

N/A 0.560 3.973 0.000 0.000 0.000 0.000 0.000 0.231 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

60 59 59 0 0 0 0 0 76 0

N.S.

1 0.98 0.98 0.00 0.00 0.00 0.00 0.00 1.27 0.00

time (sec)

N/A 0.272 0.078 0.000 0.000 0.000 0.000 0.000 0.262 0.000

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

23 23 25 23 25 25 22 25 26 27

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.96 1.09 1.13 1.17

time (sec)

N/A 0.226 2.668 0.309 3.642 0.085 9.710 0.461 0.194 15.057

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

25 25 27 25 27 27 0 27 27 29

N.S.

1 1.00 1.08 1.00 1.08 1.08 0.00 1.08 1.08 1.16

time (sec)

N/A 0.235 19.688 0.331 9.315 0.087 0.000 0.856 200.028 15.982

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

25 25 27 25 27 27 24 27 28 29

N.S.

1 1.00 1.08 1.00 1.08 1.08 0.96 1.08 1.12 1.16

time (sec)

N/A 0.239 2.113 0.262 6.092 0.090 18.350 0.740 0.200 14.945

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

16 16 18 16 18 18 15 18 19 20

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.94 1.12 1.19 1.25

time (sec)

N/A 0.189 1.096 0.229 3.849 0.082 1.715 0.366 0.197 14.855

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

25 25 27 25 27 27 24 27 28 29

N.S.

1 1.00 1.08 1.00 1.08 1.08 0.96 1.08 1.12 1.16

time (sec)

N/A 0.229 1.763 0.319 6.227 0.087 48.819 0.920 0.219 15.579

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