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

verified

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

size

14 14 502 349 0 70185 15 3 1567

N.S.

1 1.00 35.86 24.93 0.00 5013.21 1.07 0.21 111.93

time (sec)

N/A 0.188 0.609 2.882 0.000 8.471 99.859 4.337 17.023

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 845 398 0 102913 0 3 3148

N.S.

1 1.00 36.74 17.30 0.00 4474.48 0.00 0.13 136.87

time (sec)

N/A 0.223 2.214 6.545 0.000 43.884 0.000 4.343 19.147

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 1158 525 0 133123 0 3 4657

N.S.

1 1.00 50.35 22.83 0.00 5787.96 0.00 0.13 202.48

time (sec)

N/A 0.222 2.255 10.454 0.000 140.116 0.000 4.525 23.827

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 123 207 178 177 1429 0 360 1931

N.S.

1 0.94 1.58 1.36 1.35 10.91 0.00 2.75 14.74

time (sec)

N/A 0.368 0.285 1.972 0.342 0.597 0.000 0.720 0.762

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 108 189 152 158 1041 0 311 1097

N.S.

1 0.96 1.67 1.35 1.40 9.21 0.00 2.75 9.71

time (sec)

N/A 0.346 0.222 1.243 0.311 0.438 0.000 0.638 14.401

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 96 160 136 121 631 0 280 489

N.S.

1 1.01 1.68 1.43 1.27 6.64 0.00 2.95 5.15

time (sec)

N/A 0.290 0.085 0.725 0.295 0.368 0.000 0.859 14.790

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 69 54 48 100 161 129 224 40

N.S.

1 0.97 0.76 0.68 1.41 2.27 1.82 3.15 0.56

time (sec)

N/A 0.251 0.026 0.588 0.290 0.329 2.566 0.847 0.104

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 112 184 185 167 1329 0 370 3891

N.S.

1 0.96 1.57 1.58 1.43 11.36 0.00 3.16 33.26

time (sec)

N/A 0.336 0.196 1.220 0.309 0.423 0.000 0.846 16.540

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

175 164 255 241 244 2529 0 475 7758

N.S.

1 0.94 1.46 1.38 1.39 14.45 0.00 2.71 44.33

time (sec)

N/A 0.402 1.098 2.086 0.300 0.830 0.000 0.824 18.342

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

249 232 317 322 363 3703 0 630 12217

N.S.

1 0.93 1.27 1.29 1.46 14.87 0.00 2.53 49.06

time (sec)

N/A 0.506 5.867 3.402 0.296 1.653 0.000 1.278 19.999

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

252 276 233 258 0 2948 0 896 10319

N.S.

1 1.10 0.92 1.02 0.00 11.70 0.00 3.56 40.95

time (sec)

N/A 0.584 1.607 4.143 0.000 1.633 0.000 1.015 18.627

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

186 200 200 224 0 2433 0 836 8773

N.S.

1 1.08 1.08 1.20 0.00 13.08 0.00 4.49 47.17

time (sec)

N/A 0.471 1.181 2.680 0.000 0.974 0.000 0.950 16.879

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

155 162 194 179 0 1751 0 995 3088

N.S.

1 1.05 1.25 1.15 0.00 11.30 0.00 6.42 19.92

time (sec)

N/A 0.437 0.904 1.579 0.000 0.741 0.000 0.857 16.547

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 131 171 148 0 1197 0 906 4299

N.S.

1 1.03 1.35 1.17 0.00 9.43 0.00 7.13 33.85

time (sec)

N/A 0.395 0.543 0.904 0.000 0.557 0.000 0.797 16.035

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 161 158 73 0 541 0 559 1409

N.S.

1 1.29 1.26 0.58 0.00 4.33 0.00 4.47 11.27

time (sec)

N/A 0.310 0.558 0.720 0.000 0.364 0.000 0.802 14.752

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 137 175 166 0 2589 0 1211 2832

N.S.

1 0.96 1.23 1.17 0.00 18.23 0.00 8.53 19.94

time (sec)

N/A 0.395 0.819 1.474 0.000 0.671 0.000 0.843 15.535

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 153 205 230 0 4113 0 2183 4664

N.S.

1 0.95 1.27 1.43 0.00 25.55 0.00 13.56 28.97

time (sec)

N/A 0.478 1.308 2.290 0.000 0.960 0.000 0.927 16.484

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

204 193 253 311 0 5587 0 3105 6534

N.S.

1 0.95 1.24 1.52 0.00 27.39 0.00 15.22 32.03

time (sec)

N/A 0.531 1.770 3.424 0.000 1.590 0.000 0.997 17.543

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 25 23 25 37 0 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.61 0.00 1.09 1.09

time (sec)

N/A 0.215 6.681 1.306 2.112 0.631 0.000 0.938 18.605

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

197 199 141 0 0 0 0 0 0

N.S.

1 1.01 0.72 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.410 0.161 0.000 0.000 0.000 0.000 0.000 0.000

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

140 138 106 0 0 0 0 0 0

N.S.

1 0.99 0.76 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.311 0.057 0.000 0.000 0.000 0.000 0.000 0.000

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

67 67 67 0 0 0 0 0 64

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.96

time (sec)

N/A 0.230 0.020 0.000 0.000 0.000 0.000 0.000 13.766

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

158 156 0 0 0 0 0 0 0

N.S.

1 0.99 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.358 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

239 234 0 0 0 0 0 0 0

N.S.

1 0.98 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.410 0.000 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 N/A N/A N/A N/A N/A F(-1) N/A N/A

verified

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

size

23 23 25 23 25 37 0 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.61 0.00 1.09 1.09

time (sec)

N/A 0.216 3.462 1.936 3.537 0.309 0.000 0.895 15.247

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 25 23 25 37 0 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.61 0.00 1.09 1.09

time (sec)

N/A 0.216 4.644 1.106 2.112 0.329 0.000 0.908 14.412

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

14 14 16 14 16 28 0 16 16

N.S.

1 1.00 1.14 1.00 1.14 2.00 0.00 1.14 1.14

time (sec)

N/A 0.176 1.158 0.646 1.058 0.283 0.000 0.591 14.142

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 25 23 25 37 0 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.61 0.00 1.09 1.09

time (sec)

N/A 0.210 4.482 1.263 2.146 0.339 0.000 1.167 16.499

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 25 23 25 37 0 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.61 0.00 1.09 1.09

time (sec)

N/A 0.214 7.294 1.493 3.323 0.365 0.000 0.888 17.281

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

23 23 25 23 25 25 22 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.96 1.09 1.09

time (sec)

N/A 0.217 5.131 0.684 3.692 0.301 129.181 4.643 14.783

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

226 221 155 0 0 0 0 0 0

N.S.

1 0.98 0.69 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.410 0.230 0.000 0.000 0.000 0.000 0.000 0.000

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

148 146 114 0 0 0 0 0 0

N.S.

1 0.99 0.77 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.346 0.100 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 B

verified

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

size

69 69 69 0 0 0 0 0 70

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 1.01

time (sec)

N/A 0.238 0.026 0.000 0.000 0.000 0.000 0.000 14.550

Problem 434

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

21 21 23 21 23 23 20 23 25

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.95 1.10 1.19

time (sec)

N/A 0.207 3.853 0.594 2.458 0.315 132.941 0.429 13.648

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 25 23 25 25 0 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.00 1.09 1.09

time (sec)

N/A 0.219 7.648 0.594 2.732 0.288 0.000 0.516 13.285

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 25 23 25 25 0 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.00 1.09 1.09

time (sec)

N/A 0.217 10.215 0.949 7.261 0.308 0.000 10.630 13.494

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

23 23 25 23 25 25 22 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.96 1.09 1.09

time (sec)

N/A 0.217 8.552 0.596 4.698 0.296 43.029 6.960 14.008

Problem 438

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

14 14 16 14 16 16 14 16 16

N.S.

1 1.00 1.14 1.00 1.14 1.14 1.00 1.14 1.14

time (sec)

N/A 0.181 2.036 0.224 2.729 0.307 4.166 3.088 14.016

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 25 23 25 25 0 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.00 1.09 1.09

time (sec)

N/A 0.221 4.770 0.665 2.483 0.288 0.000 3.500 13.735

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 25 23 25 25 0 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.00 1.09 1.09

time (sec)

N/A 0.215 7.894 0.943 3.086 0.286 0.000 3.724 13.749

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 139 113 114 273 179 0 603 115

N.S.

1 1.09 0.88 0.89 2.13 1.40 0.00 4.71 0.90

time (sec)

N/A 0.342 0.309 4.582 0.274 0.561 0.000 4.014 13.911

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 102 78 83 159 118 0 393 90

N.S.

1 1.09 0.83 0.88 1.69 1.26 0.00 4.18 0.96

time (sec)

N/A 0.311 0.282 2.354 0.243 0.392 0.000 2.263 14.172

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 69 52 58 82 78 0 234 52

N.S.

1 1.08 0.81 0.91 1.28 1.22 0.00 3.66 0.81

time (sec)

N/A 0.278 0.105 1.306 0.255 0.352 0.000 0.870 13.585

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 47 37 42 43 37 0 110 28

N.S.

1 1.09 0.86 0.98 1.00 0.86 0.00 2.56 0.65

time (sec)

N/A 0.224 0.039 0.926 0.213 0.317 0.000 0.481 13.444

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

38 39 38 54 37 35 0 38 41

N.S.

1 1.03 1.00 1.42 0.97 0.92 0.00 1.00 1.08

time (sec)

N/A 0.221 0.026 0.958 0.220 0.309 0.000 0.661 13.596

Problem 446

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

63 58 50 101 56 91 0 108 69

N.S.

1 0.92 0.79 1.60 0.89 1.44 0.00 1.71 1.10

time (sec)

N/A 0.268 0.150 1.853 0.224 0.322 0.000 0.406 14.128

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 81 72 161 92 198 0 205 103

N.S.

1 0.91 0.81 1.81 1.03 2.22 0.00 2.30 1.16

time (sec)

N/A 0.291 0.561 3.896 0.217 0.353 0.000 0.425 13.448

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 110 100 253 137 371 0 353 138

N.S.

1 0.91 0.83 2.09 1.13 3.07 0.00 2.92 1.14

time (sec)

N/A 0.320 0.281 7.279 0.206 0.398 0.000 0.448 13.949

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 109 147 120 180 602 0 472 141

N.S.

1 0.91 1.22 1.00 1.50 5.02 0.00 3.93 1.18

time (sec)

N/A 0.319 4.555 6.447 0.307 0.368 0.000 5.089 14.826

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 89 111 121 130 472 0 296 112

N.S.

1 0.92 1.14 1.25 1.34 4.87 0.00 3.05 1.15

time (sec)

N/A 0.293 1.164 3.475 0.326 0.345 0.000 2.208 14.076

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 69 75 78 85 366 0 164 83

N.S.

1 0.93 1.01 1.05 1.15 4.95 0.00 2.22 1.12

time (sec)

N/A 0.289 0.550 1.744 0.351 0.330 0.000 0.913 13.946

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 51 53 51 51 300 0 86 53

N.S.

1 0.96 1.00 0.96 0.96 5.66 0.00 1.62 1.00

time (sec)

N/A 0.243 0.352 1.083 0.338 0.319 0.000 0.496 13.440

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 50 52 55 50 290 0 85 44

N.S.

1 0.96 1.00 1.06 0.96 5.58 0.00 1.63 0.85

time (sec)

N/A 0.244 0.517 1.491 0.353 0.311 0.000 0.466 14.540

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 74 72 79 76 402 0 120 64

N.S.

1 1.04 1.01 1.11 1.07 5.66 0.00 1.69 0.90

time (sec)

N/A 0.257 0.611 2.651 0.328 0.311 0.000 0.526 13.455

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 98 101 115 111 576 0 171 82

N.S.

1 1.02 1.05 1.20 1.16 6.00 0.00 1.78 0.85

time (sec)

N/A 0.280 1.294 5.266 0.305 0.349 0.000 0.535 13.963

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 122 135 155 154 834 0 238 100

N.S.

1 1.04 1.15 1.32 1.32 7.13 0.00 2.03 0.85

time (sec)

N/A 0.298 3.247 10.114 0.331 0.337 0.000 0.588 16.784

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 70 42 49 69 47 0 128 326

N.S.

1 1.09 0.66 0.77 1.08 0.73 0.00 2.00 5.09

time (sec)

N/A 0.363 0.217 0.839 0.247 0.299 0.000 2.141 17.391

Problem 458

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

38 49 29 28 46 34 0 37 69

N.S.

1 1.29 0.76 0.74 1.21 0.89 0.00 0.97 1.82

time (sec)

N/A 0.344 0.131 0.689 0.257 0.319 0.000 0.963 0.671

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 19 21 20 17 0 37 20

N.S.

1 1.00 1.00 1.11 1.05 0.89 0.00 1.95 1.05

time (sec)

N/A 0.291 0.039 0.407 0.384 0.294 0.000 0.369 14.503

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 52 47 54 70 57 0 524 0

N.S.

1 1.04 0.94 1.08 1.40 1.14 0.00 10.48 0.00

time (sec)

N/A 0.317 0.083 0.833 0.323 0.300 0.000 0.557 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 90 97 102 99 88 0 1996 0

N.S.

1 1.03 1.11 1.17 1.14 1.01 0.00 22.94 0.00

time (sec)

N/A 0.348 1.520 0.957 0.306 0.314 0.000 1.187 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 102 75 157 1955 87 0 234 0

N.S.

1 0.85 0.62 1.31 16.29 0.72 0.00 1.95 0.00

time (sec)

N/A 0.420 0.271 1.053 1.131 0.319 0.000 2.315 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 71 55 131 827 77 0 197 0

N.S.

1 0.78 0.60 1.44 9.09 0.85 0.00 2.16 0.00

time (sec)

N/A 0.402 0.217 1.042 0.421 0.299 0.000 1.217 0.000

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 40 40 96 73 55 0 127 0

N.S.

1 0.70 0.70 1.68 1.28 0.96 0.00 2.23 0.00

time (sec)

N/A 0.383 0.054 0.976 0.352 0.322 0.000 0.583 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 38 35 42 42 42 0 1491 88

N.S.

1 0.67 0.61 0.74 0.74 0.74 0.00 26.16 1.54

time (sec)

N/A 0.418 0.075 0.714 0.336 0.289 0.000 0.879 16.809

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 54 47 75 57 66 0 3443 364

N.S.

1 0.59 0.52 0.82 0.63 0.73 0.00 37.84 4.00

time (sec)

N/A 0.408 0.083 0.794 0.326 0.278 0.000 1.820 17.074

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 62 67 85 68 86 0 8626 555

N.S.

1 0.50 0.54 0.69 0.55 0.69 0.00 69.56 4.48

time (sec)

N/A 0.405 0.206 0.704 0.316 0.279 0.000 4.025 24.394

Problem 468

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

65 72 43 48 69 50 0 67 486

N.S.

1 1.11 0.66 0.74 1.06 0.77 0.00 1.03 7.48

time (sec)

N/A 0.357 0.180 0.644 0.213 0.293 0.000 1.661 21.860

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 51 31 38 46 40 0 54 100

N.S.

1 1.21 0.74 0.90 1.10 0.95 0.00 1.29 2.38

time (sec)

N/A 0.345 0.137 0.593 0.239 0.298 0.000 0.711 17.455

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 20 65 27 0 39 61

N.S.

1 1.00 1.00 1.11 3.61 1.50 0.00 2.17 3.39

time (sec)

N/A 0.286 0.029 0.393 0.308 0.269 0.000 0.419 0.388

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 31 31 51 84 0 0 0

N.S.

1 1.00 1.00 1.00 1.65 2.71 0.00 0.00 0.00

time (sec)

N/A 0.303 0.036 0.596 0.212 0.282 0.000 0.000 0.000

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 68 58 83 81 79 0 0 0

N.S.

1 1.03 0.88 1.26 1.23 1.20 0.00 0.00 0.00

time (sec)

N/A 0.340 0.200 0.883 0.332 0.323 0.000 0.000 0.000

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 81 66 132 1518 80 0 188 0

N.S.

1 0.89 0.73 1.45 16.68 0.88 0.00 2.07 0.00

time (sec)

N/A 0.549 0.137 1.157 0.548 0.332 0.000 1.457 0.000

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 55 43 106 527 67 0 158 0

N.S.

1 0.89 0.69 1.71 8.50 1.08 0.00 2.55 0.00

time (sec)

N/A 0.448 0.048 0.937 0.508 0.299 0.000 0.870 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 25 32 90 36 0 0 37

N.S.

1 1.00 1.00 1.28 3.60 1.44 0.00 0.00 1.48

time (sec)

N/A 0.387 0.033 0.496 0.386 0.289 0.000 0.000 13.608

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 46 37 64 525 58 0 0 118

N.S.

1 0.77 0.62 1.07 8.75 0.97 0.00 0.00 1.97

time (sec)

N/A 0.413 0.067 0.781 0.362 0.280 0.000 0.000 18.113

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 56 49 74 1236 79 0 0 491

N.S.

1 0.58 0.51 0.77 12.88 0.82 0.00 0.00 5.11

time (sec)

N/A 0.417 0.076 0.668 0.380 0.296 0.000 0.000 20.956

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 74 51 51 69 50 0 93 583

N.S.

1 1.09 0.75 0.75 1.01 0.74 0.00 1.37 8.57

time (sec)

N/A 0.372 0.229 1.299 0.213 0.299 0.000 2.967 29.967

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 53 34 41 48 40 0 80 389

N.S.

1 1.20 0.77 0.93 1.09 0.91 0.00 1.82 8.84

time (sec)

N/A 0.362 0.174 1.094 0.237 0.288 0.000 0.973 19.297

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 21 95 28 0 54 72

N.S.

1 1.00 1.00 1.00 4.52 1.33 0.00 2.57 3.43

time (sec)

N/A 0.305 0.032 0.362 0.302 0.285 0.000 0.626 17.005

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 55 37 76 73 58 0 0 0

N.S.

1 1.04 0.70 1.43 1.38 1.09 0.00 0.00 0.00

time (sec)

N/A 0.326 0.091 1.092 0.212 0.304 0.000 0.000 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 70 59 67 100 83 0 0 0

N.S.

1 1.06 0.89 1.02 1.52 1.26 0.00 0.00 0.00

time (sec)

N/A 0.363 0.127 0.934 0.206 0.292 0.000 0.000 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 84 59 104 1532 77 0 99 0

N.S.

1 0.79 0.56 0.98 14.45 0.73 0.00 0.93 0.00

time (sec)

N/A 0.579 0.101 0.823 0.527 0.290 0.000 0.831 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 44 44 123 220 66 0 0 0

N.S.

1 0.70 0.70 1.95 3.49 1.05 0.00 0.00 0.00

time (sec)

N/A 0.409 0.079 1.014 0.380 0.302 0.000 0.000 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 29 35 382 50 0 0 88

N.S.

1 1.00 0.76 0.92 10.05 1.32 0.00 0.00 2.32

time (sec)

N/A 0.398 0.042 0.628 0.336 0.283 0.000 0.000 17.716

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 53 41 47 1063 75 0 0 393

N.S.

1 0.69 0.53 0.61 13.81 0.97 0.00 0.00 5.10

time (sec)

N/A 0.425 0.105 0.662 0.354 0.291 0.000 0.000 19.597

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 65 51 57 2026 100 0 0 589

N.S.

1 0.57 0.44 0.50 17.62 0.87 0.00 0.00 5.12

time (sec)

N/A 0.433 0.138 0.662 0.365 0.295 0.000 0.000 30.488

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

177 177 143 721 230 354 0 2646 0

N.S.

1 1.00 0.81 4.07 1.30 2.00 0.00 14.95 0.00

time (sec)

N/A 0.348 0.611 2.150 0.297 0.836 0.000 2.132 0.000

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 113 84 403 127 234 0 959 0

N.S.

1 0.96 0.71 3.42 1.08 1.98 0.00 8.13 0.00

time (sec)

N/A 0.282 0.425 1.591 0.388 0.558 0.000 0.840 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 60 60 129 122 145 0 313 0

N.S.

1 1.03 1.03 2.22 2.10 2.50 0.00 5.40 0.00

time (sec)

N/A 0.230 0.067 1.205 0.305 0.438 0.000 0.432 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 56 51 58 43 135 0 0 0

N.S.

1 1.04 0.94 1.07 0.80 2.50 0.00 0.00 0.00

time (sec)

N/A 0.248 0.046 0.823 0.206 0.732 0.000 0.000 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 100 77 122 113 239 0 0 0

N.S.

1 0.91 0.70 1.11 1.03 2.17 0.00 0.00 0.00

time (sec)

N/A 0.288 0.212 1.050 0.211 0.942 0.000 0.000 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 152 103 212 215 415 0 0 0

N.S.

1 0.92 0.62 1.28 1.30 2.52 0.00 0.00 0.00

time (sec)

N/A 0.324 0.597 1.333 0.212 1.294 0.000 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

234 243 198 380 0 0 0 0 0

N.S.

1 1.04 0.85 1.62 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.474 2.445 4.566 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 A A F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 164 140 222 0 0 0 0 0

N.S.

1 0.96 0.82 1.30 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.363 0.773 3.757 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 A A F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 61 71 0 0 0 0 0

N.S.

1 1.00 1.20 1.39 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.284 0.068 1.567 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 A A F F F F(-1) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

174 167 143 156 0 0 0 0 0

N.S.

1 0.96 0.82 0.90 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.377 0.936 2.925 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 A A F F F F(-1) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

232 238 197 351 0 0 0 0 0

N.S.

1 1.03 0.85 1.51 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.469 3.618 3.455 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 A B A A F(-1) B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

220 202 160 711 238 385 0 3585 0

N.S.

1 0.92 0.73 3.23 1.08 1.75 0.00 16.30 0.00

time (sec)

N/A 0.356 2.119 1.708 0.303 0.693 0.000 3.773 0.000

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 138 116 426 169 265 0 0 0

N.S.

1 0.93 0.78 2.88 1.14 1.79 0.00 0.00 0.00

time (sec)

N/A 0.305 0.535 1.780 0.288 0.526 0.000 0.000 0.000

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