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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 A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 65 61 49 66 149 0 53 72

N.S.

1 1.02 0.95 0.77 1.03 2.33 0.00 0.83 1.12

time (sec)

N/A 0.192 0.107 4.243 0.281 0.297 0.000 0.276 8.118

Problem 402

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

88 100 83 78 0 226 0 79 76

N.S.

1 1.14 0.94 0.89 0.00 2.57 0.00 0.90 0.86

time (sec)

N/A 0.235 0.146 4.525 0.000 0.314 0.000 0.290 8.252

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

124 142 97 98 0 278 0 113 117

N.S.

1 1.15 0.78 0.79 0.00 2.24 0.00 0.91 0.94

time (sec)

N/A 0.265 0.291 4.629 0.000 0.333 0.000 0.287 8.433

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 184 112 116 0 310 0 105 154

N.S.

1 1.12 0.68 0.71 0.00 1.89 0.00 0.64 0.94

time (sec)

N/A 0.302 0.373 4.637 0.000 0.328 0.000 0.280 8.702

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

663 671 176 897 0 2568 0 0 0

N.S.

1 1.01 0.27 1.35 0.00 3.87 0.00 0.00 0.00

time (sec)

N/A 1.118 7.094 5.543 0.000 8.825 0.000 0.000 0.000

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

641 641 167 877 0 2397 0 0 0

N.S.

1 1.00 0.26 1.37 0.00 3.74 0.00 0.00 0.00

time (sec)

N/A 1.017 10.153 4.566 0.000 1.735 0.000 0.000 0.000

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

644 640 164 883 0 2496 0 0 0

N.S.

1 0.99 0.25 1.37 0.00 3.88 0.00 0.00 0.00

time (sec)

N/A 1.024 10.105 4.488 0.000 0.402 0.000 0.000 0.000

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

665 669 179 898 0 2390 0 0 0

N.S.

1 1.01 0.27 1.35 0.00 3.59 0.00 0.00 0.00

time (sec)

N/A 1.103 11.126 5.668 0.000 0.500 0.000 0.000 0.000

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

687 698 199 919 0 2549 0 0 0

N.S.

1 1.02 0.29 1.34 0.00 3.71 0.00 0.00 0.00

time (sec)

N/A 1.134 10.154 5.649 0.000 1.434 0.000 0.000 0.000

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

711 728 209 938 0 2582 0 0 0

N.S.

1 1.02 0.29 1.32 0.00 3.63 0.00 0.00 0.00

time (sec)

N/A 1.243 10.160 5.512 0.000 2.939 0.000 0.000 0.000

Problem 411

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

134 157 103 109 119 239 0 127 147

N.S.

1 1.17 0.77 0.81 0.89 1.78 0.00 0.95 1.10

time (sec)

N/A 0.280 0.223 4.776 0.295 0.305 0.000 0.281 8.316

Problem 412

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

119 135 93 98 107 219 0 111 127

N.S.

1 1.13 0.78 0.82 0.90 1.84 0.00 0.93 1.07

time (sec)

N/A 0.244 0.194 4.640 0.305 0.322 0.000 0.271 8.266

Problem 413

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

97 112 81 79 93 192 0 93 107

N.S.

1 1.15 0.84 0.81 0.96 1.98 0.00 0.96 1.10

time (sec)

N/A 0.225 0.167 4.414 0.331 0.306 0.000 0.277 8.045

Problem 414

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

77 84 72 63 79 162 0 69 87

N.S.

1 1.09 0.94 0.82 1.03 2.10 0.00 0.90 1.13

time (sec)

N/A 0.208 0.130 4.488 0.318 0.304 0.000 0.282 8.000

Problem 415

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

85 94 85 64 0 220 0 70 101

N.S.

1 1.11 1.00 0.75 0.00 2.59 0.00 0.82 1.19

time (sec)

N/A 0.232 0.133 4.531 0.000 0.315 0.000 0.272 8.754

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 136 97 99 0 280 0 114 110

N.S.

1 1.12 0.80 0.82 0.00 2.31 0.00 0.94 0.91

time (sec)

N/A 0.265 0.264 4.642 0.000 0.409 0.000 0.284 8.215

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 178 112 118 0 310 0 129 151

N.S.

1 1.11 0.70 0.73 0.00 1.93 0.00 0.80 0.94

time (sec)

N/A 0.309 0.339 4.654 0.000 0.362 0.000 0.287 8.588

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

681 687 191 921 0 2580 0 0 0

N.S.

1 1.01 0.28 1.35 0.00 3.79 0.00 0.00 0.00

time (sec)

N/A 1.148 8.442 5.508 0.000 17.752 0.000 0.000 0.000

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

657 661 176 897 0 2568 0 0 0

N.S.

1 1.01 0.27 1.37 0.00 3.91 0.00 0.00 0.00

time (sec)

N/A 1.093 10.176 5.523 0.000 3.788 0.000 0.000 0.000

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

638 631 141 874 0 2335 0 0 0

N.S.

1 0.99 0.22 1.37 0.00 3.66 0.00 0.00 0.00

time (sec)

N/A 1.027 10.194 4.489 0.000 0.994 0.000 0.000 0.000

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

522 547 242 483 0 68 0 0 0

N.S.

1 1.05 0.46 0.93 0.00 0.13 0.00 0.00 0.00

time (sec)

N/A 0.560 11.739 5.352 0.000 0.101 0.000 0.000 0.000

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

684 692 199 919 0 2549 0 0 0

N.S.

1 1.01 0.29 1.34 0.00 3.73 0.00 0.00 0.00

time (sec)

N/A 1.203 10.153 5.615 0.000 0.896 0.000 0.000 0.000

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

708 722 212 938 0 2582 0 0 0

N.S.

1 1.02 0.30 1.32 0.00 3.65 0.00 0.00 0.00

time (sec)

N/A 1.253 10.169 5.837 0.000 1.946 0.000 0.000 0.000

Problem 424

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

95 105 81 79 93 195 0 93 107

N.S.

1 1.11 0.85 0.83 0.98 2.05 0.00 0.98 1.13

time (sec)

N/A 0.229 0.186 4.575 0.302 0.280 0.000 0.269 8.046

Problem 425

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

83 93 70 63 79 167 0 69 87

N.S.

1 1.12 0.84 0.76 0.95 2.01 0.00 0.83 1.05

time (sec)

N/A 0.221 0.127 4.393 0.297 0.286 0.000 0.263 8.043

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

64 68 63 50 67 155 0 58 72

N.S.

1 1.06 0.98 0.78 1.05 2.42 0.00 0.91 1.12

time (sec)

N/A 0.193 0.119 4.352 0.291 0.302 0.000 0.282 7.963

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

67 71 64 52 72 153 0 59 75

N.S.

1 1.06 0.96 0.78 1.07 2.28 0.00 0.88 1.12

time (sec)

N/A 0.200 0.092 4.246 0.284 0.276 0.000 0.277 7.921

Problem 428

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

88 100 83 78 0 226 0 79 80

N.S.

1 1.14 0.94 0.89 0.00 2.57 0.00 0.90 0.91

time (sec)

N/A 0.235 0.144 4.512 0.000 0.294 0.000 0.280 7.999

Problem 429

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

124 142 97 99 0 280 0 114 117

N.S.

1 1.15 0.78 0.80 0.00 2.26 0.00 0.92 0.94

time (sec)

N/A 0.272 0.285 4.639 0.000 0.308 0.000 0.276 8.119

Problem 430

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

164 184 112 118 0 310 0 128 155

N.S.

1 1.12 0.68 0.72 0.00 1.89 0.00 0.78 0.95

time (sec)

N/A 0.306 0.359 4.642 0.000 0.307 0.000 0.273 8.434

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

641 641 167 877 0 2397 0 0 0

N.S.

1 1.00 0.26 1.37 0.00 3.74 0.00 0.00 0.00

time (sec)

N/A 0.997 10.167 4.691 0.000 3.665 0.000 0.000 0.000

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

647 646 166 886 0 2538 0 0 0

N.S.

1 1.00 0.26 1.37 0.00 3.92 0.00 0.00 0.00

time (sec)

N/A 1.001 10.115 4.886 0.000 0.452 0.000 0.000 0.000

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

644 641 164 883 0 2540 0 0 0

N.S.

1 1.00 0.25 1.37 0.00 3.94 0.00 0.00 0.00

time (sec)

N/A 1.023 10.105 4.318 0.000 0.567 0.000 0.000 0.000

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

665 669 180 898 0 2391 0 0 0

N.S.

1 1.01 0.27 1.35 0.00 3.60 0.00 0.00 0.00

time (sec)

N/A 1.118 11.132 5.487 0.000 0.677 0.000 0.000 0.000

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

687 698 196 919 0 2549 0 0 0

N.S.

1 1.02 0.29 1.34 0.00 3.71 0.00 0.00 0.00

time (sec)

N/A 1.148 10.163 5.596 0.000 2.066 0.000 0.000 0.000

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

711 728 212 938 0 2582 0 0 0

N.S.

1 1.02 0.30 1.32 0.00 3.63 0.00 0.00 0.00

time (sec)

N/A 1.246 10.165 5.797 0.000 4.286 0.000 0.000 0.000

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

66 66 239 723 0 2425 0 0 0

N.S.

1 1.00 3.62 10.95 0.00 36.74 0.00 0.00 0.00

time (sec)

N/A 0.218 10.327 4.505 0.000 0.718 0.000 0.000 0.000

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

66 66 237 732 0 2548 0 0 0

N.S.

1 1.00 3.59 11.09 0.00 38.61 0.00 0.00 0.00

time (sec)

N/A 0.221 10.216 4.582 0.000 0.899 0.000 0.000 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

64 64 237 729 0 2498 0 0 0

N.S.

1 1.00 3.70 11.39 0.00 39.03 0.00 0.00 0.00

time (sec)

N/A 0.193 10.199 4.481 0.000 0.874 0.000 0.000 0.000

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

66 66 266 744 0 0 0 0 0

N.S.

1 1.00 4.03 11.27 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.220 10.209 5.565 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 B C F B F F F(-1)

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

66 66 279 765 0 2561 0 0 0

N.S.

1 1.00 4.23 11.59 0.00 38.80 0.00 0.00 0.00

time (sec)

N/A 0.216 10.217 5.559 0.000 4.252 0.000 0.000 0.000

Problem 442

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

95 107 99 75 98 233 0 88 111

N.S.

1 1.13 1.04 0.79 1.03 2.45 0.00 0.93 1.17

time (sec)

N/A 0.227 0.184 4.582 0.286 0.313 0.000 0.294 8.308

Problem 443

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

83 95 71 61 81 223 0 67 94

N.S.

1 1.14 0.86 0.73 0.98 2.69 0.00 0.81 1.13

time (sec)

N/A 0.215 0.177 4.769 0.283 0.337 0.000 0.279 8.362

Problem 444

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

85 97 73 61 83 223 0 76 96

N.S.

1 1.14 0.86 0.72 0.98 2.62 0.00 0.89 1.13

time (sec)

N/A 0.204 0.152 4.381 0.291 0.352 0.000 0.296 8.278

Problem 445

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

88 100 73 62 85 219 0 72 97

N.S.

1 1.14 0.83 0.70 0.97 2.49 0.00 0.82 1.10

time (sec)

N/A 0.216 0.153 4.274 0.302 0.315 0.000 0.288 8.252

Problem 446

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

106 126 93 92 0 316 0 93 101

N.S.

1 1.19 0.88 0.87 0.00 2.98 0.00 0.88 0.95

time (sec)

N/A 0.266 0.202 4.554 0.000 0.353 0.000 0.289 8.347

Problem 447

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

143 168 109 113 0 368 0 129 133

N.S.

1 1.17 0.76 0.79 0.00 2.57 0.00 0.90 0.93

time (sec)

N/A 0.292 0.352 4.701 0.000 0.316 0.000 0.299 8.478

Problem 448

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

185 210 123 135 0 398 0 149 171

N.S.

1 1.14 0.66 0.73 0.00 2.15 0.00 0.81 0.92

time (sec)

N/A 0.336 0.431 4.497 0.000 0.328 0.000 0.293 8.821

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

668 669 168 910 0 2681 0 0 0

N.S.

1 1.00 0.25 1.36 0.00 4.01 0.00 0.00 0.00

time (sec)

N/A 1.083 10.125 4.591 0.000 0.596 0.000 0.000 0.000

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

671 676 169 910 0 2723 0 0 0

N.S.

1 1.01 0.25 1.36 0.00 4.06 0.00 0.00 0.00

time (sec)

N/A 1.084 10.120 4.619 0.000 0.650 0.000 0.000 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

665 669 167 904 0 2684 0 0 0

N.S.

1 1.01 0.25 1.36 0.00 4.04 0.00 0.00 0.00

time (sec)

N/A 1.093 10.119 4.528 0.000 0.762 0.000 0.000 0.000

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

686 698 180 920 0 2534 0 0 0

N.S.

1 1.02 0.26 1.34 0.00 3.69 0.00 0.00 0.00

time (sec)

N/A 1.177 11.154 6.327 0.000 0.909 0.000 0.000 0.000

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

708 727 198 943 0 2692 0 0 0

N.S.

1 1.03 0.28 1.33 0.00 3.80 0.00 0.00 0.00

time (sec)

N/A 1.255 10.163 6.309 0.000 2.796 0.000 0.000 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

732 757 210 962 0 2725 0 0 0

N.S.

1 1.03 0.29 1.31 0.00 3.72 0.00 0.00 0.00

time (sec)

N/A 1.304 10.185 6.671 0.000 5.575 0.000 0.000 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

256 66 189 339 0 89 0 0 0

N.S.

1 0.26 0.74 1.32 0.00 0.35 0.00 0.00 0.00

time (sec)

N/A 0.214 10.562 4.401 0.000 0.102 0.000 0.000 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

66 66 242 754 0 2713 0 0 0

N.S.

1 1.00 3.67 11.42 0.00 41.11 0.00 0.00 0.00

time (sec)

N/A 0.218 10.291 4.422 0.000 1.067 0.000 0.000 0.000

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

64 64 253 748 0 2640 0 0 0

N.S.

1 1.00 3.95 11.69 0.00 41.25 0.00 0.00 0.00

time (sec)

N/A 0.190 10.265 4.546 0.000 0.975 0.000 0.000 0.000

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

66 66 259 764 0 2650 0 0 0

N.S.

1 1.00 3.92 11.58 0.00 40.15 0.00 0.00 0.00

time (sec)

N/A 0.215 10.246 6.045 0.000 2.074 0.000 0.000 0.000

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

66 66 283 787 0 2698 0 0 0

N.S.

1 1.00 4.29 11.92 0.00 40.88 0.00 0.00 0.00

time (sec)

N/A 0.218 10.242 6.209 0.000 5.324 0.000 0.000 0.000

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 164 126 129 0 469 0 136 202

N.S.

1 1.02 0.78 0.80 0.00 2.91 0.00 0.84 1.25

time (sec)

N/A 0.302 0.434 4.801 0.000 0.314 0.000 0.290 10.881

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 132 98 98 0 334 0 102 152

N.S.

1 0.97 0.72 0.72 0.00 2.46 0.00 0.75 1.12

time (sec)

N/A 0.259 0.291 4.666 0.000 0.407 0.000 0.278 10.135

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 80 80 65 0 255 0 79 125

N.S.

1 1.00 1.00 0.81 0.00 3.19 0.00 0.99 1.56

time (sec)

N/A 0.210 0.229 4.457 0.000 0.351 0.000 0.273 9.669

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 126 111 120 0 856 0 114 182

N.S.

1 1.04 0.92 0.99 0.00 7.07 0.00 0.94 1.50

time (sec)

N/A 0.261 0.630 4.442 0.000 0.393 0.000 0.277 12.814

Problem 464

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

161 170 132 151 0 870 0 183 438

N.S.

1 1.06 0.82 0.94 0.00 5.40 0.00 1.14 2.72

time (sec)

N/A 0.328 0.781 4.761 0.000 0.397 0.000 0.286 14.409

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

64 64 235 748 0 0 0 0 0

N.S.

1 1.00 3.67 11.69 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.216 10.218 4.743 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 B C F F(-1) F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

64 64 153 908 0 0 0 0 0

N.S.

1 1.00 2.39 14.19 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.204 10.109 4.557 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 B C F F(-1) F F F(-1)

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

59 59 232 753 0 0 0 0 0

N.S.

1 1.00 3.93 12.76 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.189 10.226 4.395 0.000 0.000 0.000 0.000 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

62 62 172 920 0 0 0 0 0

N.S.

1 1.00 2.77 14.84 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.211 10.151 6.387 0.000 0.000 0.000 0.000 0.000

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

64 64 338 766 0 0 0 0 0

N.S.

1 1.00 5.28 11.97 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.206 10.323 6.576 0.000 0.000 0.000 0.000 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 195 162 169 0 443 0 211 331

N.S.

1 1.03 0.86 0.89 0.00 2.34 0.00 1.12 1.75

time (sec)

N/A 0.324 0.562 4.651 0.000 0.384 0.000 0.287 12.037

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 163 125 133 0 314 0 173 229

N.S.

1 1.00 0.77 0.82 0.00 1.93 0.00 1.06 1.40

time (sec)

N/A 0.271 0.361 4.725 0.000 0.322 0.000 0.276 11.577

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 104 94 108 0 234 0 122 170

N.S.

1 1.11 1.00 1.15 0.00 2.49 0.00 1.30 1.81

time (sec)

N/A 0.231 0.311 4.259 0.000 0.315 0.000 0.274 11.373

Problem 473

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

131 140 122 140 0 686 0 155 214

N.S.

1 1.07 0.93 1.07 0.00 5.24 0.00 1.18 1.63

time (sec)

N/A 0.289 0.524 4.657 0.000 0.423 0.000 0.278 13.944

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

170 197 154 165 0 838 0 216 531

N.S.

1 1.16 0.91 0.97 0.00 4.93 0.00 1.27 3.12

time (sec)

N/A 0.382 0.929 4.725 0.000 0.351 0.000 0.286 15.795

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

65 65 338 808 0 0 0 0 0

N.S.

1 1.00 5.20 12.43 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.212 10.466 6.478 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 B C F F(-1) F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

65 65 177 955 0 0 0 0 0

N.S.

1 1.00 2.72 14.69 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.207 10.199 4.767 0.000 0.000 0.000 0.000 0.000

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

60 60 339 801 0 0 0 0 0

N.S.

1 1.00 5.65 13.35 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.189 10.323 4.568 0.000 0.000 0.000 0.000 0.000

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

63 63 190 970 0 0 0 0 0

N.S.

1 1.00 3.02 15.40 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.216 10.253 6.316 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 B C F F(-1) F(-1) F F(-1)

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

65 65 370 815 0 0 0 0 0

N.S.

1 1.00 5.69 12.54 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.213 10.408 6.813 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 A F(-2) B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 144 130 132 0 475 0 134 160

N.S.

1 1.17 1.06 1.07 0.00 3.86 0.00 1.09 1.30

time (sec)

N/A 0.279 0.616 4.600 0.000 0.288 0.000 0.287 11.608

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 98 100 83 0 348 0 116 111

N.S.

1 0.99 1.01 0.84 0.00 3.52 0.00 1.17 1.12

time (sec)

N/A 0.231 0.286 4.638 0.000 0.320 0.000 0.276 11.036

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 86 86 90 0 302 0 93 104

N.S.

1 0.99 0.99 1.03 0.00 3.47 0.00 1.07 1.20

time (sec)

N/A 0.217 0.260 4.440 0.000 0.269 0.000 0.279 10.663

Problem 483

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

132 155 124 146 0 862 0 139 162

N.S.

1 1.17 0.94 1.11 0.00 6.53 0.00 1.05 1.23

time (sec)

N/A 0.291 0.549 4.571 0.000 0.341 0.000 0.271 14.692

Problem 484

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

185 213 163 191 0 1236 0 257 355

N.S.

1 1.15 0.88 1.03 0.00 6.68 0.00 1.39 1.92

time (sec)

N/A 0.376 1.019 4.803 0.000 0.405 0.000 0.268 15.994

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

64 64 238 764 0 0 0 0 0

N.S.

1 1.00 3.72 11.94 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.213 10.225 4.511 0.000 0.000 0.000 0.000 0.000

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

64 64 172 923 0 0 0 0 0

N.S.

1 1.00 2.69 14.42 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.204 10.175 4.560 0.000 0.000 0.000 0.000 0.000

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

59 59 392 769 0 0 0 0 0

N.S.

1 1.00 6.64 13.03 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.189 10.277 4.666 0.000 0.000 0.000 0.000 0.000

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

62 62 226 963 0 0 0 0 0

N.S.

1 1.00 3.65 15.53 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.210 10.263 6.403 0.000 0.000 0.000 0.000 0.000

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

64 64 411 809 0 0 0 0 0

N.S.

1 1.00 6.42 12.64 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.209 10.634 6.312 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 A A F(-2) B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 162 133 146 0 746 0 195 367

N.S.

1 1.08 0.89 0.97 0.00 4.97 0.00 1.30 2.45

time (sec)

N/A 0.312 0.662 4.394 0.000 0.352 0.000 0.272 12.269

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 138 110 124 0 630 0 181 247

N.S.

1 1.03 0.82 0.93 0.00 4.70 0.00 1.35 1.84

time (sec)

N/A 0.259 0.473 4.446 0.000 0.376 0.000 0.278 11.733

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 125 101 86 0 450 0 153 199

N.S.

1 1.16 0.94 0.80 0.00 4.17 0.00 1.42 1.84

time (sec)

N/A 0.241 0.376 4.479 0.000 0.334 0.000 0.266 11.305

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

172 208 157 199 0 1819 0 226 288

N.S.

1 1.21 0.91 1.16 0.00 10.58 0.00 1.31 1.67

time (sec)

N/A 0.368 1.179 4.550 0.000 0.602 0.000 0.270 16.413

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

241 283 223 250 0 2384 0 367 18847

N.S.

1 1.17 0.93 1.04 0.00 9.89 0.00 1.52 78.20

time (sec)

N/A 0.458 1.464 4.892 0.000 0.722 0.000 0.288 23.902

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

67 67 381 787 0 0 0 0 0

N.S.

1 1.00 5.69 11.75 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.221 10.323 4.435 0.000 0.000 0.000 0.000 0.000

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

67 67 216 986 0 0 0 0 0

N.S.

1 1.00 3.22 14.72 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.204 10.283 4.383 0.000 0.000 0.000 0.000 0.000

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

62 62 381 830 0 0 0 0 0

N.S.

1 1.00 6.15 13.39 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.194 10.518 4.412 0.000 0.000 0.000 0.000 0.000

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

65 65 308 1019 0 0 0 0 0

N.S.

1 1.00 4.74 15.68 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.218 10.421 7.528 0.000 0.000 0.000 0.000 0.000

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

67 67 515 863 0 0 0 0 0

N.S.

1 1.00 7.69 12.88 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.214 10.917 7.337 0.000 0.000 0.000 0.000 0.000

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

134 134 113 0 0 0 379 0 0

N.S.

1 1.00 0.84 0.00 0.00 0.00 2.83 0.00 0.00

time (sec)

N/A 0.279 0.956 0.000 0.000 0.000 18.960 0.000 0.000

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