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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 F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 124 140 90 0 94 0 390 179

N.S.

1 0.84 0.95 0.61 0.00 0.64 0.00 2.65 1.22

time (sec)

N/A 0.314 0.470 0.070 0.000 0.287 0.000 0.356 16.565

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 86 101 66 0 70 0 206 129

N.S.

1 0.91 1.06 0.69 0.00 0.74 0.00 2.17 1.36

time (sec)

N/A 0.269 0.357 0.058 0.000 0.276 0.000 0.351 16.944

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 41 35 40 0 29 136 75 79

N.S.

1 0.87 0.74 0.85 0.00 0.62 2.89 1.60 1.68

time (sec)

N/A 0.238 0.215 0.018 0.000 0.275 0.364 0.342 16.852

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 88 160 73 0 318 0 1015 2983

N.S.

1 0.91 1.65 0.75 0.00 3.28 0.00 10.46 30.75

time (sec)

N/A 0.262 0.504 0.025 0.000 0.317 0.000 0.509 32.295

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 96 187 88 0 399 0 1192 2642

N.S.

1 0.93 1.82 0.85 0.00 3.87 0.00 11.57 25.65

time (sec)

N/A 0.258 0.816 0.034 0.000 0.307 0.000 2.443 35.038

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

228 206 188 604 0 196 0 797 1358

N.S.

1 0.90 0.82 2.65 0.00 0.86 0.00 3.50 5.96

time (sec)

N/A 0.516 0.526 0.042 0.000 0.290 0.000 0.356 146.996

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 151 133 431 0 149 0 445 1012

N.S.

1 0.92 0.81 2.61 0.00 0.90 0.00 2.70 6.13

time (sec)

N/A 0.389 0.318 0.035 0.000 0.317 0.000 0.341 75.361

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 106 82 184 0 103 388 189 110

N.S.

1 1.68 1.30 2.92 0.00 1.63 6.16 3.00 1.75

time (sec)

N/A 0.292 0.205 0.035 0.000 0.326 0.418 0.310 0.242

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 106 137 258 0 290 0 194 524

N.S.

1 0.80 1.03 1.94 0.00 2.18 0.00 1.46 3.94

time (sec)

N/A 0.400 0.276 0.039 0.000 0.354 0.000 0.422 25.540

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 114 128 274 0 367 0 311 7637

N.S.

1 0.81 0.91 1.94 0.00 2.60 0.00 2.21 54.16

time (sec)

N/A 0.398 0.522 0.038 0.000 0.307 0.000 0.772 44.379

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

375 285 138 294 0 208 0 1447 529

N.S.

1 0.76 0.37 0.78 0.00 0.55 0.00 3.86 1.41

time (sec)

N/A 0.543 0.751 0.098 0.000 0.271 0.000 0.695 16.436

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

261 199 93 222 0 159 942 866 385

N.S.

1 0.76 0.36 0.85 0.00 0.61 3.61 3.32 1.48

time (sec)

N/A 0.426 0.586 0.096 0.000 0.276 0.754 0.354 16.830

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 117 55 146 0 106 384 427 252

N.S.

1 1.83 0.86 2.28 0.00 1.66 6.00 6.67 3.94

time (sec)

N/A 0.304 0.483 0.064 0.000 0.286 0.727 0.346 16.640

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 123 244 181 0 516 0 2649 4060

N.S.

1 0.78 1.55 1.15 0.00 3.29 0.00 16.87 25.86

time (sec)

N/A 0.401 0.939 0.025 0.000 0.323 0.000 0.925 42.361

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

162 175 187 252 0 675 0 2594 4681

N.S.

1 1.08 1.15 1.56 0.00 4.17 0.00 16.01 28.90

time (sec)

N/A 0.446 10.455 0.041 0.000 0.309 0.000 7.563 51.541

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 14 0 13 63 13 21

N.S.

1 1.00 1.00 0.67 0.00 0.62 3.00 0.62 1.00

time (sec)

N/A 0.146 0.007 0.033 0.000 0.264 0.163 0.325 16.606

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 14 0 13 63 13 21

N.S.

1 1.00 1.00 0.67 0.00 0.62 3.00 0.62 1.00

time (sec)

N/A 0.144 0.067 0.029 0.000 0.264 0.174 0.296 16.345

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 27 23 16 0 15 51 15 15

N.S.

1 1.17 1.00 0.70 0.00 0.65 2.22 0.65 0.65

time (sec)

N/A 0.196 0.113 0.018 0.000 0.281 0.191 0.317 0.044

Problem 419

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

38 38 44 33 31 32 0 77 45

N.S.

1 1.00 1.16 0.87 0.82 0.84 0.00 2.03 1.18

time (sec)

N/A 0.282 0.283 0.913 0.275 0.278 0.000 0.341 16.506

Problem 420

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

48 48 67 59 34 51 0 76 563

N.S.

1 1.00 1.40 1.23 0.71 1.06 0.00 1.58 11.73

time (sec)

N/A 0.265 0.250 0.923 0.275 0.288 0.000 0.344 29.813

Problem 421

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 25 24 15 23 0 51 33

N.S.

1 1.00 1.32 1.26 0.79 1.21 0.00 2.68 1.74

time (sec)

N/A 0.230 0.159 0.905 0.269 0.290 0.000 0.341 16.820

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 45 58 17 40 44 48 206

N.S.

1 1.00 2.37 3.05 0.89 2.11 2.32 2.53 10.84

time (sec)

N/A 0.205 0.136 0.968 0.278 0.317 0.904 0.358 21.699

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 72 51 41 41 0 130 122

N.S.

1 1.00 2.25 1.59 1.28 1.28 0.00 4.06 3.81

time (sec)

N/A 0.267 0.146 0.941 0.271 0.342 0.000 0.395 17.759

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 49 50 24 44 0 149 120

N.S.

1 1.00 1.88 1.92 0.92 1.69 0.00 5.73 4.62

time (sec)

N/A 0.255 0.138 0.922 0.264 0.326 0.000 0.313 17.690

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 147 58 54 44 0 235 189

N.S.

1 1.00 4.32 1.71 1.59 1.29 0.00 6.91 5.56

time (sec)

N/A 0.274 0.274 0.921 0.382 0.305 0.000 0.402 19.567

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 124 1832 90 0 122 0 451 179

N.S.

1 0.84 12.46 0.61 0.00 0.83 0.00 3.07 1.22

time (sec)

N/A 0.311 5.983 0.076 0.000 0.314 0.000 0.387 17.613

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 86 113 66 0 92 0 255 129

N.S.

1 0.91 1.19 0.69 0.00 0.97 0.00 2.68 1.36

time (sec)

N/A 0.279 0.866 0.067 0.000 0.312 0.000 0.372 16.540

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 71 40 0 50 0 107 79

N.S.

1 1.00 1.51 0.85 0.00 1.06 0.00 2.28 1.68

time (sec)

N/A 0.210 0.514 0.017 0.000 0.317 0.000 0.337 16.554

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 77 121 73 0 158 0 1093 213

N.S.

1 0.79 1.25 0.75 0.00 1.63 0.00 11.27 2.20

time (sec)

N/A 0.274 0.649 0.020 0.000 0.330 0.000 0.535 18.156

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 96 135 88 0 182 0 1402 1637

N.S.

1 0.93 1.31 0.85 0.00 1.77 0.00 13.61 15.89

time (sec)

N/A 0.258 10.169 0.038 0.000 0.318 0.000 2.749 24.654

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 144 75 120 0 243 0 1895 1610

N.S.

1 0.84 0.44 0.70 0.00 1.42 0.00 11.08 9.42

time (sec)

N/A 0.286 10.091 0.036 0.000 0.369 0.000 6.129 26.553

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

195 181 182 517 0 479 0 511 1107

N.S.

1 0.93 0.93 2.65 0.00 2.46 0.00 2.62 5.68

time (sec)

N/A 0.504 1.202 0.041 0.000 0.331 0.000 0.795 45.026

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 134 175 187 0 372 0 272 129

N.S.

1 0.94 1.23 1.32 0.00 2.62 0.00 1.92 0.91

time (sec)

N/A 0.412 0.827 0.037 0.000 0.322 0.000 0.835 0.247

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 108 254 266 0 346 0 359 5098

N.S.

1 0.80 1.88 1.97 0.00 2.56 0.00 2.66 37.76

time (sec)

N/A 0.379 1.191 0.046 0.000 0.348 0.000 0.918 34.870

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 111 239 269 0 317 0 438 4285

N.S.

1 0.80 1.73 1.95 0.00 2.30 0.00 3.17 31.05

time (sec)

N/A 0.333 1.144 0.040 0.000 0.381 0.000 0.968 33.209

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 115 109 313 0 126 0 532 787

N.S.

1 0.93 0.89 2.54 0.00 1.02 0.00 4.33 6.40

time (sec)

N/A 0.394 0.814 0.041 0.000 0.318 0.000 2.835 30.043

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

174 160 153 457 0 182 0 802 1290

N.S.

1 0.92 0.88 2.63 0.00 1.05 0.00 4.61 7.41

time (sec)

N/A 0.442 10.182 0.040 0.000 0.342 0.000 2.460 48.119

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

277 215 2321 246 0 225 0 932 429

N.S.

1 0.78 8.38 0.89 0.00 0.81 0.00 3.36 1.55

time (sec)

N/A 0.498 6.819 0.101 0.000 0.320 0.000 1.061 17.552

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 129 197 172 0 167 0 480 268

N.S.

1 0.79 1.21 1.06 0.00 1.02 0.00 2.94 1.64

time (sec)

N/A 0.392 1.076 0.062 0.000 0.313 0.000 1.021 16.856

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

155 121 1004 148 0 321 0 2374 762

N.S.

1 0.78 6.48 0.95 0.00 2.07 0.00 15.32 4.92

time (sec)

N/A 0.405 5.569 0.024 0.000 0.322 0.000 1.576 20.353

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 175 690 237 0 260 0 2318 559

N.S.

1 1.11 4.39 1.51 0.00 1.66 0.00 14.76 3.56

time (sec)

N/A 0.426 10.678 0.036 0.000 0.316 0.000 9.204 21.489

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 213 182 300 0 297 0 2766 287

N.S.

1 1.30 1.11 1.83 0.00 1.81 0.00 16.87 1.75

time (sec)

N/A 0.404 10.213 0.047 0.000 0.334 0.000 17.839 19.715

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 45 63 23 44 48 54 209

N.S.

1 1.00 1.45 2.03 0.74 1.42 1.55 1.74 6.74

time (sec)

N/A 0.237 0.008 0.937 0.270 0.295 1.035 0.297 21.797

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

38 38 44 33 31 32 0 77 42

N.S.

1 1.00 1.16 0.87 0.82 0.84 0.00 2.03 1.11

time (sec)

N/A 0.509 0.013 0.946 0.257 0.321 0.000 0.319 17.648

Problem 445

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

48 48 68 59 34 51 0 76 381

N.S.

1 1.00 1.42 1.23 0.71 1.06 0.00 1.58 7.94

time (sec)

N/A 0.490 0.017 0.953 0.266 0.321 0.000 0.298 26.488

Problem 446

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

21 21 25 26 17 25 0 54 25

N.S.

1 1.00 1.19 1.24 0.81 1.19 0.00 2.57 1.19

time (sec)

N/A 0.345 0.004 0.949 0.272 0.315 0.000 0.287 17.276

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 46 59 20 41 48 49 205

N.S.

1 1.00 2.09 2.68 0.91 1.86 2.18 2.23 9.32

time (sec)

N/A 0.283 0.005 0.945 0.263 0.328 1.061 0.284 17.973

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 72 51 41 41 0 130 122

N.S.

1 1.00 2.25 1.59 1.28 1.28 0.00 4.06 3.81

time (sec)

N/A 0.412 0.008 0.959 0.263 0.293 0.000 0.337 18.142

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 49 50 24 44 0 149 118

N.S.

1 1.00 1.88 1.92 0.92 1.69 0.00 5.73 4.54

time (sec)

N/A 0.418 0.010 1.019 0.263 0.327 0.000 0.346 17.875

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 148 57 51 43 0 233 186

N.S.

1 1.00 4.48 1.73 1.55 1.30 0.00 7.06 5.64

time (sec)

N/A 0.431 0.028 1.000 0.262 0.316 0.000 0.421 19.134

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 69 68 48 0 36 0 123 93

N.S.

1 2.46 2.43 1.71 0.00 1.29 0.00 4.39 3.32

time (sec)

N/A 0.560 0.164 0.952 0.000 0.326 0.000 0.369 19.041

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A B F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 79 46 62 0 37 223 41 200

N.S.

1 2.39 1.39 1.88 0.00 1.12 6.76 1.24 6.06

time (sec)

N/A 0.354 0.089 0.919 0.000 0.288 11.609 0.296 27.821

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

121 116 86 0 0 0 0 0 0

N.S.

1 0.96 0.71 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.270 0.396 0.000 0.000 0.000 0.000 0.000 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

175 168 192 341 293 161 459 171 0

N.S.

1 0.96 1.10 1.95 1.67 0.92 2.62 0.98 0.00

time (sec)

N/A 0.286 0.763 0.932 0.197 0.287 0.604 0.372 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 131 113 124 107 114 185 107 210

N.S.

1 0.96 0.83 0.91 0.79 0.84 1.36 0.79 1.54

time (sec)

N/A 0.270 0.559 0.876 0.184 0.365 0.529 0.369 18.794

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 80 75 54 74 54 68 136

N.S.

1 1.00 1.18 1.10 0.79 1.09 0.79 1.00 2.00

time (sec)

N/A 0.197 0.137 0.983 0.191 0.292 1.069 0.361 17.640

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 111 337 651 0 187 0 299 0

N.S.

1 0.95 2.88 5.56 0.00 1.60 0.00 2.56 0.00

time (sec)

N/A 0.275 0.858 0.064 0.000 0.357 0.000 0.501 0.000

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 146 228 3182 0 284 0 146 0

N.S.

1 0.97 1.51 21.07 0.00 1.88 0.00 0.97 0.00

time (sec)

N/A 0.284 0.700 0.084 0.000 0.377 0.000 0.458 0.000

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 182 278 11352 0 536 0 182 0

N.S.

1 0.94 1.44 58.82 0.00 2.78 0.00 0.94 0.00

time (sec)

N/A 0.313 1.906 0.133 0.000 0.551 0.000 1.222 0.000

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

225 219 212 0 0 416 0 0 0

N.S.

1 0.97 0.94 0.00 0.00 1.85 0.00 0.00 0.00

time (sec)

N/A 0.408 1.407 0.000 0.000 0.388 0.000 0.000 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

183 181 170 0 0 337 0 0 0

N.S.

1 0.99 0.93 0.00 0.00 1.84 0.00 0.00 0.00

time (sec)

N/A 0.371 1.236 0.000 0.000 0.366 0.000 0.000 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

147 147 142 0 0 301 0 0 0

N.S.

1 1.00 0.97 0.00 0.00 2.05 0.00 0.00 0.00

time (sec)

N/A 0.315 0.871 0.000 0.000 0.369 0.000 0.000 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

147 151 141 0 0 298 0 0 0

N.S.

1 1.03 0.96 0.00 0.00 2.03 0.00 0.00 0.00

time (sec)

N/A 0.278 0.852 0.000 0.000 0.381 0.000 0.000 0.000

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

158 160 169 0 0 487 0 0 0

N.S.

1 1.01 1.07 0.00 0.00 3.08 0.00 0.00 0.00

time (sec)

N/A 0.314 1.309 0.000 0.000 0.465 0.000 0.000 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

199 196 209 0 0 812 0 0 0

N.S.

1 0.98 1.05 0.00 0.00 4.08 0.00 0.00 0.00

time (sec)

N/A 0.375 1.371 0.000 0.000 0.657 0.000 0.000 0.000

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

41 45 41 0 0 26 0 0 0

N.S.

1 1.10 1.00 0.00 0.00 0.63 0.00 0.00 0.00

time (sec)

N/A 0.181 0.039 0.000 0.000 0.305 0.000 0.000 0.000

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

69 70 69 0 0 59 0 0 0

N.S.

1 1.01 1.00 0.00 0.00 0.86 0.00 0.00 0.00

time (sec)

N/A 0.228 0.396 0.000 0.000 0.330 0.000 0.000 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 35 60 0 34 415 0 0

N.S.

1 1.00 0.78 1.33 0.00 0.76 9.22 0.00 0.00

time (sec)

N/A 0.170 0.057 0.051 0.000 0.338 0.708 0.000 0.000

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 31 55 0 28 197 0 0

N.S.

1 1.00 0.76 1.34 0.00 0.68 4.80 0.00 0.00

time (sec)

N/A 0.161 0.060 0.052 0.000 0.325 0.657 0.000 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 31 64 0 30 197 0 0

N.S.

1 1.00 0.76 1.56 0.00 0.73 4.80 0.00 0.00

time (sec)

N/A 0.164 0.048 0.050 0.000 0.327 0.671 0.000 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

66 66 72 0 0 70 0 0 0

N.S.

1 1.00 1.09 0.00 0.00 1.06 0.00 0.00 0.00

time (sec)

N/A 0.209 3.997 0.000 0.000 0.398 0.000 0.000 0.000

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

166 168 134 0 0 0 0 0 0

N.S.

1 1.01 0.81 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.359 0.969 0.000 0.000 0.000 0.000 0.000 0.000

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

303 312 260 809 0 345 1363 397 0

N.S.

1 1.03 0.86 2.67 0.00 1.14 4.50 1.31 0.00

time (sec)

N/A 0.520 1.271 1.261 0.000 0.334 1.136 0.349 0.000

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

237 246 176 300 0 219 490 236 0

N.S.

1 1.04 0.74 1.27 0.00 0.92 2.07 1.00 0.00

time (sec)

N/A 0.438 0.918 1.152 0.000 0.282 0.707 0.354 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 118 180 123 0 123 197 119 0

N.S.

1 1.00 1.53 1.04 0.00 1.04 1.67 1.01 0.00

time (sec)

N/A 0.252 0.348 1.246 0.000 0.268 0.297 0.303 0.000

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

215 222 266 1263 0 371 0 0 0

N.S.

1 1.03 1.24 5.87 0.00 1.73 0.00 0.00 0.00

time (sec)

N/A 0.401 0.746 0.082 0.000 2.519 0.000 0.000 0.000

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

266 275 427 6303 0 826 0 1618 0

N.S.

1 1.03 1.61 23.70 0.00 3.11 0.00 6.08 0.00

time (sec)

N/A 0.455 1.448 0.106 0.000 1.667 0.000 6.663 0.000

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

330 339 300 29133 0 1954 0 0 0

N.S.

1 1.03 0.91 88.28 0.00 5.92 0.00 0.00 0.00

time (sec)

N/A 0.502 10.506 0.292 0.000 12.004 0.000 0.000 0.000

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

370 377 985 0 0 923 0 0 0

N.S.

1 1.02 2.66 0.00 0.00 2.49 0.00 0.00 0.00

time (sec)

N/A 0.840 4.555 0.000 0.000 0.447 0.000 0.000 0.000

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

302 309 443 0 0 657 0 0 0

N.S.

1 1.02 1.47 0.00 0.00 2.18 0.00 0.00 0.00

time (sec)

N/A 0.651 2.570 0.000 0.000 0.441 0.000 0.000 0.000

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

233 243 327 0 0 692 0 0 0

N.S.

1 1.04 1.40 0.00 0.00 2.97 0.00 0.00 0.00

time (sec)

N/A 0.484 1.361 0.000 0.000 0.432 0.000 0.000 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

244 276 341 0 0 716 0 0 0

N.S.

1 1.13 1.40 0.00 0.00 2.93 0.00 0.00 0.00

time (sec)

N/A 0.438 1.511 0.000 0.000 0.432 0.000 0.000 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

269 281 395 0 0 1456 0 0 0

N.S.

1 1.04 1.47 0.00 0.00 5.41 0.00 0.00 0.00

time (sec)

N/A 0.483 2.408 0.000 0.000 0.785 0.000 0.000 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

335 354 557 0 0 2514 0 0 0

N.S.

1 1.06 1.66 0.00 0.00 7.50 0.00 0.00 0.00

time (sec)

N/A 0.656 3.340 0.000 0.000 1.961 0.000 0.000 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 155 138 216 0 158 0 0 0

N.S.

1 0.95 0.84 1.32 0.00 0.96 0.00 0.00 0.00

time (sec)

N/A 0.288 0.395 0.965 0.000 0.280 0.000 0.000 0.000

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 103 92 167 0 78 15302 0 0

N.S.

1 0.95 0.85 1.55 0.00 0.72 141.69 0.00 0.00

time (sec)

N/A 0.247 0.223 0.036 0.000 0.300 14.579 0.000 0.000

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 51 43 120 0 32 2236 0 0

N.S.

1 0.98 0.83 2.31 0.00 0.62 43.00 0.00 0.00

time (sec)

N/A 0.189 0.127 0.026 0.000 0.280 1.711 0.000 0.000

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

59 59 61 0 0 0 0 0 0

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.214 0.159 0.000 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 A F F F F F F(-1)

verified

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

size

59 59 61 0 0 0 0 0 0

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.211 0.166 0.000 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 F F A F F F(-1)

verified

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

size

176 167 150 0 0 159 0 0 0

N.S.

1 0.95 0.85 0.00 0.00 0.90 0.00 0.00 0.00

time (sec)

N/A 0.277 0.409 0.000 0.000 0.282 0.000 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

116 111 100 0 0 79 0 0 0

N.S.

1 0.96 0.86 0.00 0.00 0.68 0.00 0.00 0.00

time (sec)

N/A 0.233 0.226 0.000 0.000 0.275 0.000 0.000 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

56 55 50 0 0 33 0 0 0

N.S.

1 0.98 0.89 0.00 0.00 0.59 0.00 0.00 0.00

time (sec)

N/A 0.183 0.141 0.000 0.000 0.273 0.000 0.000 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

63 63 65 0 0 0 0 0 0

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.213 0.157 0.000 0.000 0.000 0.000 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

63 63 65 0 0 0 0 0 0

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.212 0.163 0.000 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 F F A F(-2) F F(-1)

verified

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

size

187 176 157 0 0 201 0 0 0

N.S.

1 0.94 0.84 0.00 0.00 1.07 0.00 0.00 0.00

time (sec)

N/A 0.302 0.341 0.000 0.000 0.286 0.000 0.000 0.000

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

131 124 111 0 0 110 0 0 0

N.S.

1 0.95 0.85 0.00 0.00 0.84 0.00 0.00 0.00

time (sec)

N/A 0.273 0.223 0.000 0.000 0.283 0.000 0.000 0.000

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

75 72 65 0 0 48 0 0 0

N.S.

1 0.96 0.87 0.00 0.00 0.64 0.00 0.00 0.00

time (sec)

N/A 0.235 0.182 0.000 0.000 0.280 0.000 0.000 0.000

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 17 16 0 15 311 15 15

N.S.

1 1.00 1.00 0.94 0.00 0.88 18.29 0.88 0.88

time (sec)

N/A 0.189 0.023 0.854 0.000 0.276 1.509 0.310 16.967

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

59 59 61 0 0 0 0 0 0

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.216 0.075 0.000 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 F F F(-1)

verified

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

size

59 59 61 0 0 0 0 0 0

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.221 0.087 0.000 0.000 0.000 0.000 0.000 0.000

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