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2.2.5 Integrals 401 to 500

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 401

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

17 0 502 349 0 70185 0 0 1567

N.S.

1 0.00 29.53 20.53 0.00 4128.53 0.00 0.00 92.18

time (sec)

N/A 0.008 0.372 3.128 0.000 8.354 0.000 0.000 17.893

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A N/A NO TBD TBD TBD TBD TBD TBD

size

26 0 845 398 0 102913 0 0 2500

N.S.

1 0.00 32.50 15.31 0.00 3958.19 0.00 0.00 96.15

time (sec)

N/A 0.029 1.164 6.409 0.000 38.673 0.000 0.000 21.207

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A N/A NO TBD TBD TBD TBD TBD TBD

size

26 0 1158 525 0 133123 0 0 2500

N.S.

1 0.00 44.54 20.19 0.00 5120.12 0.00 0.00 96.15

time (sec)

N/A 0.027 1.263 8.928 0.000 104.276 0.000 0.000 25.437

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 207 176 177 1429 0 360 1931

N.S.

1 1.00 1.58 1.34 1.35 10.91 0.00 2.75 14.74

time (sec)

N/A 0.126 0.183 1.159 0.534 0.605 0.000 0.808 0.774

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 113 189 152 158 1041 0 311 1097

N.S.

1 1.00 1.67 1.35 1.40 9.21 0.00 2.75 9.71

time (sec)

N/A 0.109 0.145 0.834 0.504 0.563 0.000 0.776 15.784

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 160 136 121 631 0 280 489

N.S.

1 1.00 1.68 1.43 1.27 6.64 0.00 2.95 5.15

time (sec)

N/A 0.068 0.062 0.710 0.531 0.463 0.000 0.707 15.811

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 54 68 100 330 129 224 40

N.S.

1 1.00 0.76 0.96 1.41 4.65 1.82 3.15 0.56

time (sec)

N/A 0.039 0.018 0.304 0.502 58.432 2.595 0.696 0.105

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 184 185 167 1329 0 370 2500

N.S.

1 1.00 1.57 1.58 1.43 11.36 0.00 3.16 21.37

time (sec)

N/A 0.109 0.135 0.677 0.543 0.542 0.000 0.739 17.906

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

175 175 255 241 244 2529 0 475 2500

N.S.

1 1.00 1.46 1.38 1.39 14.45 0.00 2.71 14.29

time (sec)

N/A 0.139 0.726 1.262 0.520 0.891 0.000 0.780 19.192

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

249 249 317 322 363 3703 0 630 2500

N.S.

1 1.00 1.27 1.29 1.46 14.87 0.00 2.53 10.04

time (sec)

N/A 0.206 3.747 1.915 0.505 1.585 0.000 0.761 20.572

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

252 252 233 258 0 2948 0 896 2500

N.S.

1 1.00 0.92 1.02 0.00 11.70 0.00 3.56 9.92

time (sec)

N/A 0.315 0.632 1.436 0.000 1.536 0.000 0.871 18.799

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

186 186 200 224 0 2433 0 836 2500

N.S.

1 1.00 1.08 1.20 0.00 13.08 0.00 4.49 13.44

time (sec)

N/A 0.215 0.476 1.075 0.000 1.030 0.000 0.858 17.463

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

155 155 194 179 0 1751 0 995 2500

N.S.

1 1.00 1.25 1.15 0.00 11.30 0.00 6.42 16.13

time (sec)

N/A 0.188 0.333 0.779 0.000 0.766 0.000 0.802 18.042

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 171 148 0 1197 0 906 2500

N.S.

1 1.00 1.35 1.17 0.00 9.43 0.00 7.13 19.69

time (sec)

N/A 0.149 0.181 0.862 0.000 0.613 0.000 0.786 16.400

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 125 158 115 0 541 0 558 1409

N.S.

1 1.00 1.26 0.92 0.00 4.33 0.00 4.46 11.27

time (sec)

N/A 0.074 0.199 0.557 0.000 0.495 0.000 0.829 15.661

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 175 166 0 2589 0 1211 2832

N.S.

1 1.00 1.23 1.17 0.00 18.23 0.00 8.53 19.94

time (sec)

N/A 0.146 0.337 0.769 0.000 0.735 0.000 0.814 16.940

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 205 230 0 4113 0 2183 2500

N.S.

1 1.00 1.27 1.43 0.00 25.55 0.00 13.56 15.53

time (sec)

N/A 0.224 0.706 1.381 0.000 0.919 0.000 0.904 17.739

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

204 204 253 311 0 5587 0 3106 2500

N.S.

1 1.00 1.24 1.52 0.00 27.39 0.00 15.23 12.25

time (sec)

N/A 0.255 0.906 1.457 0.000 1.446 0.000 0.936 18.226

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 0 0 0 0 37 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 1.42 0.00 0.00 -0.04

time (sec)

N/A 0.028 8.275 1.276 0.000 0.720 0.000 0.000 0.000

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

197 191 141 0 0 37 0 0 -1

N.S.

1 0.97 0.72 0.00 0.00 0.19 0.00 0.00 -0.01

time (sec)

N/A 0.148 0.110 0.885 0.000 0.416 0.000 0.000 0.000

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 106 0 0 37 0 0 -1

N.S.

1 1.00 0.76 0.00 0.00 0.26 0.00 0.00 -0.01

time (sec)

N/A 0.067 0.040 1.819 0.000 0.421 0.000 0.000 0.000

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-1) F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 67 0 0 35 0 0 64

N.S.

1 1.00 1.00 0.00 0.00 0.52 0.00 0.00 0.96

time (sec)

N/A 0.029 0.013 0.423 0.000 0.458 0.000 0.000 15.619

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F(-1) F F

verified

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

size

158 158 0 0 0 35 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.22 0.00 0.00 -0.01

time (sec)

N/A 0.105 8.358 0.557 0.000 0.414 0.000 0.000 0.000

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F(-2) F F

verified

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

size

239 239 0 0 0 37 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.15 0.00 0.00 -0.00

time (sec)

N/A 0.152 13.737 0.512 0.000 0.512 0.000 0.000 0.000

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 0 0 0 0 37 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 1.42 0.00 0.00 -0.04

time (sec)

N/A 0.026 5.020 2.292 0.000 0.441 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(-1) A A

verified

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

size

26 0 0 0 0 37 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 1.42 0.00 0.00 -0.04

time (sec)

N/A 0.026 16.646 2.871 0.000 0.458 0.000 0.000 0.000

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

17 0 0 0 0 28 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 1.65 0.00 0.00 -0.06

time (sec)

N/A 0.008 2.269 0.595 0.000 0.405 0.000 0.000 0.000

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 0 0 0 0 37 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 1.42 0.00 0.00 -0.04

time (sec)

N/A 0.026 9.385 0.532 0.000 0.436 0.000 0.000 0.000

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 0 0 0 0 37 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 1.42 0.00 0.00 -0.04

time (sec)

N/A 0.026 12.991 0.541 0.000 0.484 0.000 0.000 0.000

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 0 0 0 0 25 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.96 0.00 0.00 -0.04

time (sec)

N/A 0.031 8.275 0.325 0.000 0.424 0.000 0.000 0.000

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

226 226 155 0 0 25 0 0 -1

N.S.

1 1.00 0.69 0.00 0.00 0.11 0.00 0.00 -0.00

time (sec)

N/A 0.119 0.152 0.329 0.000 0.448 0.000 0.000 0.000

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

148 148 114 0 0 25 0 0 -1

N.S.

1 1.00 0.77 0.00 0.00 0.17 0.00 0.00 -0.01

time (sec)

N/A 0.084 0.069 0.412 0.000 0.393 0.000 0.000 0.000

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 69 0 0 23 0 0 70

N.S.

1 1.00 1.00 0.00 0.00 0.33 0.00 0.00 1.01

time (sec)

N/A 0.033 0.018 0.086 0.000 0.417 0.000 0.000 15.906

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 0 0 0 0 23 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.96 0.00 0.00 -0.04

time (sec)

N/A 0.024 6.819 0.236 0.000 0.404 0.000 0.000 0.000

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 0 0 0 0 25 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.96 0.00 0.00 -0.04

time (sec)

N/A 0.032 13.774 0.265 0.000 0.428 0.000 0.000 0.000

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 0 0 0 0 25 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.96 0.00 0.00 -0.04

time (sec)

N/A 0.031 35.366 0.450 0.000 0.413 0.000 0.000 0.000

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

26 0 0 0 0 25 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.96 0.00 0.00 -0.04

time (sec)

N/A 0.032 21.537 0.315 0.000 0.406 0.000 0.000 0.000

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

17 0 0 0 0 16 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.94 0.00 0.00 -0.06

time (sec)

N/A 0.009 2.637 0.074 0.000 0.371 0.000 0.000 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 0 0 0 0 25 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.96 0.00 0.00 -0.04

time (sec)

N/A 0.032 8.755 0.224 0.000 0.419 0.000 0.000 0.000

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 0 0 0 0 25 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.96 0.00 0.00 -0.04

time (sec)

N/A 0.030 17.584 0.193 0.000 0.392 0.000 0.000 0.000

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

128 128 113 114 273 179 0 603 115

N.S.

1 1.00 0.88 0.89 2.13 1.40 0.00 4.71 0.90

time (sec)

N/A 0.090 0.217 0.492 0.339 0.619 0.000 3.291 14.340

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 78 83 159 118 0 393 90

N.S.

1 1.00 0.83 0.88 1.69 1.26 0.00 4.18 0.96

time (sec)

N/A 0.071 0.186 0.468 0.340 0.485 0.000 1.626 14.353

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 52 58 82 78 0 234 52

N.S.

1 1.00 0.81 0.91 1.28 1.22 0.00 3.66 0.81

time (sec)

N/A 0.051 0.073 0.357 0.343 0.432 0.000 0.759 14.282

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 37 42 43 37 0 110 28

N.S.

1 1.00 0.86 0.98 1.00 0.86 0.00 2.56 0.65

time (sec)

N/A 0.026 0.034 0.376 0.319 0.409 0.000 0.483 14.506

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 38 35 37 35 0 38 41

N.S.

1 1.00 1.00 0.92 0.97 0.92 0.00 1.00 1.08

time (sec)

N/A 0.030 0.018 0.265 0.284 0.416 0.000 0.474 14.430

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 50 101 56 91 0 108 69

N.S.

1 1.00 0.79 1.60 0.89 1.44 0.00 1.71 1.10

time (sec)

N/A 0.051 0.106 0.533 0.305 0.440 0.000 0.554 14.457

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 72 161 92 198 0 205 103

N.S.

1 1.00 0.81 1.81 1.03 2.22 0.00 2.30 1.16

time (sec)

N/A 0.062 0.360 0.542 0.321 0.449 0.000 0.524 14.504

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 100 253 137 371 0 353 138

N.S.

1 1.00 0.83 2.09 1.13 3.07 0.00 2.92 1.14

time (sec)

N/A 0.078 0.183 0.566 0.306 0.502 0.000 0.543 15.351

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 147 120 180 602 0 472 141

N.S.

1 1.00 1.22 1.00 1.50 5.02 0.00 3.93 1.18

time (sec)

N/A 0.090 1.588 0.663 0.538 0.445 0.000 4.925 14.780

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 111 121 130 472 0 296 112

N.S.

1 1.00 1.14 1.25 1.34 4.87 0.00 3.05 1.15

time (sec)

N/A 0.072 0.541 0.550 0.524 0.430 0.000 2.191 15.110

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 75 78 85 366 0 164 83

N.S.

1 1.00 1.01 1.05 1.15 4.95 0.00 2.22 1.12

time (sec)

N/A 0.066 0.232 0.522 0.536 0.449 0.000 1.008 15.184

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

53 53 53 51 51 300 0 86 53

N.S.

1 1.00 1.00 0.96 0.96 5.66 0.00 1.62 1.00

time (sec)

N/A 0.050 0.108 0.496 0.527 0.415 0.000 0.606 14.922

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

52 52 52 55 50 290 0 85 44

N.S.

1 1.00 1.00 1.06 0.96 5.58 0.00 1.63 0.85

time (sec)

N/A 0.043 0.134 0.522 0.508 0.413 0.000 0.501 14.715

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 72 79 76 402 0 120 64

N.S.

1 1.00 1.01 1.11 1.07 5.66 0.00 1.69 0.90

time (sec)

N/A 0.054 0.219 0.570 0.561 0.434 0.000 0.510 15.090

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 101 115 111 576 0 171 82

N.S.

1 1.00 1.05 1.20 1.16 6.00 0.00 1.78 0.85

time (sec)

N/A 0.067 0.616 0.574 0.511 0.434 0.000 0.527 16.150

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 135 155 154 834 0 238 100

N.S.

1 1.00 1.15 1.32 1.32 7.13 0.00 2.03 0.85

time (sec)

N/A 0.081 0.758 0.654 0.518 0.499 0.000 0.516 18.908

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 51 48 72 47 0 136 326

N.S.

1 1.00 0.80 0.75 1.12 0.73 0.00 2.12 5.09

time (sec)

N/A 0.071 0.070 14.026 0.308 0.394 0.000 1.554 19.711

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 29 35 48 34 0 39 69

N.S.

1 1.00 0.76 0.92 1.26 0.89 0.00 1.03 1.82

time (sec)

N/A 0.068 0.062 13.214 0.300 0.376 0.000 0.714 0.716

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 19 21 21 17 0 39 20

N.S.

1 1.00 1.00 1.11 1.11 0.89 0.00 2.05 1.05

time (sec)

N/A 0.042 0.029 0.140 0.537 0.374 0.000 0.492 15.252

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 55 52 74 57 0 55 -1

N.S.

1 1.00 1.10 1.04 1.48 1.14 0.00 1.10 -0.02

time (sec)

N/A 0.055 0.051 11.217 0.516 0.402 0.000 0.451 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 88 78 105 88 0 171 -1

N.S.

1 1.00 1.01 0.90 1.21 1.01 0.00 1.97 -0.01

time (sec)

N/A 0.082 0.301 11.072 0.547 0.392 0.000 0.566 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 75 120 2144 87 0 251 -1

N.S.

1 1.00 0.62 1.00 17.87 0.72 0.00 2.09 -0.01

time (sec)

N/A 0.094 0.232 7.111 2.121 0.413 0.000 1.972 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 55 84 910 77 0 211 -1

N.S.

1 1.00 0.60 0.92 10.00 0.85 0.00 2.32 -0.01

time (sec)

N/A 0.085 0.140 6.997 0.669 0.403 0.000 0.958 0.000

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

57 57 40 54 80 55 0 136 -1

N.S.

1 1.00 0.70 0.95 1.40 0.96 0.00 2.39 -0.02

time (sec)

N/A 0.069 0.034 7.428 0.560 0.413 0.000 0.597 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

57 57 35 43 45 42 0 90 88

N.S.

1 1.00 0.61 0.75 0.79 0.74 0.00 1.58 1.54

time (sec)

N/A 0.074 0.054 4.580 0.522 0.398 0.000 0.506 18.529

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 47 55 61 66 0 132 364

N.S.

1 1.00 0.52 0.60 0.67 0.73 0.00 1.45 4.00

time (sec)

N/A 0.080 0.057 3.918 0.500 0.405 0.000 0.532 18.418

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

124 124 67 65 73 86 0 174 555

N.S.

1 1.00 0.54 0.52 0.59 0.69 0.00 1.40 4.48

time (sec)

N/A 0.082 0.139 4.881 0.526 0.394 0.000 0.550 26.643

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 43 51 72 50 0 71 486

N.S.

1 1.00 0.66 0.78 1.11 0.77 0.00 1.09 7.48

time (sec)

N/A 0.073 0.062 14.434 0.304 0.389 0.000 1.606 23.610

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 31 41 48 40 0 57 100

N.S.

1 1.00 0.74 0.98 1.14 0.95 0.00 1.36 2.38

time (sec)

N/A 0.071 0.052 11.014 0.300 0.410 0.000 0.850 19.497

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

18 18 18 20 69 27 0 41 61

N.S.

1 1.00 1.00 1.11 3.83 1.50 0.00 2.28 3.39

time (sec)

N/A 0.043 0.021 0.128 0.519 0.404 0.000 0.579 0.390

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 49 40 54 84 0 32 -1

N.S.

1 1.00 1.58 1.29 1.74 2.71 0.00 1.03 -0.03

time (sec)

N/A 0.054 0.033 5.461 0.295 0.397 0.000 0.439 0.000

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 80 67 86 79 0 117 -1

N.S.

1 1.00 1.21 1.02 1.30 1.20 0.00 1.77 -0.02

time (sec)

N/A 0.079 0.127 9.309 0.576 0.402 0.000 0.630 0.000

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 66 103 1652 80 0 201 -1

N.S.

1 1.00 0.73 1.13 18.15 0.88 0.00 2.21 -0.01

time (sec)

N/A 0.094 0.095 11.082 0.916 0.432 0.000 1.136 0.000

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 43 65 575 67 0 169 -1

N.S.

1 1.00 0.69 1.05 9.27 1.08 0.00 2.73 -0.02

time (sec)

N/A 0.079 0.034 9.575 0.621 0.403 0.000 0.729 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 25 32 98 36 0 67 37

N.S.

1 1.00 1.00 1.28 3.92 1.44 0.00 2.68 1.48

time (sec)

N/A 0.069 0.021 0.305 0.570 0.386 0.000 0.569 15.063

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 37 44 571 58 0 99 118

N.S.

1 1.00 0.62 0.73 9.52 0.97 0.00 1.65 1.97

time (sec)

N/A 0.080 0.043 3.819 0.629 0.381 0.000 0.666 19.187

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 49 54 1344 79 0 128 491

N.S.

1 1.00 0.51 0.56 14.00 0.82 0.00 1.33 5.11

time (sec)

N/A 0.078 0.050 5.454 0.671 0.436 0.000 0.763 22.470

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 51 51 72 50 0 64 583

N.S.

1 1.00 0.75 0.75 1.06 0.74 0.00 0.94 8.57

time (sec)

N/A 0.082 0.070 13.605 0.325 0.391 0.000 0.818 33.909

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

44 44 34 41 50 40 0 44 389

N.S.

1 1.00 0.77 0.93 1.14 0.91 0.00 1.00 8.84

time (sec)

N/A 0.082 0.080 13.657 0.327 0.382 0.000 0.699 20.209

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 21 21 101 28 0 23 72

N.S.

1 1.00 1.00 1.00 4.81 1.33 0.00 1.10 3.43

time (sec)

N/A 0.049 0.023 0.106 0.558 0.425 0.000 0.661 18.310

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

53 53 55 75 77 58 0 59 -1

N.S.

1 1.00 1.04 1.42 1.45 1.09 0.00 1.11 -0.02

time (sec)

N/A 0.063 0.051 16.431 0.306 0.412 0.000 0.426 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 82 67 106 83 0 129 -1

N.S.

1 1.00 1.24 1.02 1.61 1.26 0.00 1.95 -0.02

time (sec)

N/A 0.086 0.123 8.811 0.285 0.432 0.000 0.731 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 59 104 1666 77 0 84 -1

N.S.

1 1.00 0.56 0.98 15.72 0.73 0.00 0.79 -0.01

time (sec)

N/A 0.107 0.067 8.653 0.867 0.399 0.000 0.733 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 44 65 240 66 0 70 -1

N.S.

1 1.00 0.70 1.03 3.81 1.05 0.00 1.11 -0.02

time (sec)

N/A 0.092 0.056 9.733 0.542 0.420 0.000 0.695 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 29 35 411 50 0 113 88

N.S.

1 1.00 0.76 0.92 10.82 1.32 0.00 2.97 2.32

time (sec)

N/A 0.087 0.026 1.954 0.539 0.387 0.000 0.778 18.687

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 41 67 1146 75 0 151 393

N.S.

1 1.00 0.53 0.87 14.88 0.97 0.00 1.96 5.10

time (sec)

N/A 0.098 0.067 6.493 0.689 0.419 0.000 0.933 20.606

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 51 57 2187 100 0 184 589

N.S.

1 1.00 0.44 0.50 19.02 0.87 0.00 1.60 5.12

time (sec)

N/A 0.102 0.090 4.515 0.591 0.420 0.000 0.960 33.014

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 143 721 237 354 0 2790 -1

N.S.

1 1.00 0.81 4.07 1.34 2.00 0.00 15.76 -0.01

time (sec)

N/A 0.144 0.387 35.185 0.513 0.930 0.000 2.055 0.000

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 84 403 132 234 0 1011 -1

N.S.

1 1.00 0.71 3.42 1.12 1.98 0.00 8.57 -0.01

time (sec)

N/A 0.072 0.280 31.089 0.546 0.628 0.000 0.833 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 60 129 129 145 0 329 -1

N.S.

1 1.00 1.03 2.22 2.22 2.50 0.00 5.67 -0.02

time (sec)

N/A 0.038 0.040 28.333 0.524 0.502 0.000 0.582 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 53 58 45 135 0 49 -1

N.S.

1 1.00 0.98 1.07 0.83 2.50 0.00 0.91 -0.02

time (sec)

N/A 0.043 0.033 8.725 0.303 0.776 0.000 0.513 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 77 122 119 239 0 0 -1

N.S.

1 1.00 0.70 1.11 1.08 2.17 0.00 0.00 -0.01

time (sec)

N/A 0.069 0.138 9.696 0.326 0.963 0.000 0.000 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

165 165 103 212 227 415 0 0 -1

N.S.

1 1.00 0.62 1.28 1.38 2.52 0.00 0.00 -0.01

time (sec)

N/A 0.106 0.391 10.737 0.284 1.244 0.000 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

234 234 198 380 0 27 0 0 -1

N.S.

1 1.00 0.85 1.62 0.00 0.12 0.00 0.00 -0.00

time (sec)

N/A 0.192 1.396 17.988 0.000 0.138 0.000 0.000 0.000

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 140 294 0 27 0 0 -1

N.S.

1 1.00 0.82 1.72 0.00 0.16 0.00 0.00 -0.01

time (sec)

N/A 0.101 0.336 16.095 0.000 0.098 0.000 0.000 0.000

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 61 71 0 18 0 0 -1

N.S.

1 1.00 1.20 1.39 0.00 0.35 0.00 0.00 -0.02

time (sec)

N/A 0.023 0.065 5.293 0.000 0.098 0.000 0.000 0.000

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

174 174 143 156 0 27 0 0 -1

N.S.

1 1.00 0.82 0.90 0.00 0.16 0.00 0.00 -0.01

time (sec)

N/A 0.113 0.390 9.195 0.000 0.129 0.000 0.000 0.000

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

232 232 197 351 0 27 0 0 -1

N.S.

1 1.00 0.85 1.51 0.00 0.12 0.00 0.00 -0.00

time (sec)

N/A 0.176 2.198 10.210 0.000 0.152 0.000 0.000 0.000

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F(-2) F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

220 220 160 711 246 385 0 0 -1

N.S.

1 1.00 0.73 3.23 1.12 1.75 0.00 0.00 -0.00

time (sec)

N/A 0.167 1.338 25.310 0.506 0.785 0.000 0.000 0.000

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F(-1) B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

148 148 116 567 175 265 0 2185 -1

N.S.

1 1.00 0.78 3.83 1.18 1.79 0.00 14.76 -0.01

time (sec)

N/A 0.089 0.342 24.247 0.579 0.624 0.000 1.450 0.000

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