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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 B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 56 101 100 95 151 112 98

N.S.

1 1.00 0.73 1.31 1.30 1.23 1.96 1.45 1.27

time (sec)

N/A 0.052 0.109 0.702 0.181 0.297 0.337 0.359 5.136

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 57 21 20 71 73 20 55

N.S.

1 1.00 2.59 0.95 0.91 3.23 3.32 0.91 2.50

time (sec)

N/A 0.020 0.048 0.490 0.180 0.265 0.160 0.332 0.076

Problem 403

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

80 80 67 90 91 93 0 93 65

N.S.

1 1.00 0.84 1.12 1.14 1.16 0.00 1.16 0.81

time (sec)

N/A 0.074 0.084 0.762 0.191 0.301 0.000 0.323 4.991

Problem 404

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

111 111 176 126 98 112 0 114 99

N.S.

1 1.00 1.59 1.14 0.88 1.01 0.00 1.03 0.89

time (sec)

N/A 0.092 0.898 1.158 0.199 0.280 0.000 0.334 4.719

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 94 318 156 136 138 0 139 114

N.S.

1 1.00 3.38 1.66 1.45 1.47 0.00 1.48 1.21

time (sec)

N/A 0.060 2.745 1.253 0.180 0.279 0.000 0.471 4.579

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

158 158 182 145 117 117 348 173 474

N.S.

1 1.00 1.15 0.92 0.74 0.74 2.20 1.09 3.00

time (sec)

N/A 0.153 0.524 1.500 0.189 0.298 0.505 0.609 5.903

Problem 407

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

131 131 107 123 93 98 236 113 356

N.S.

1 1.00 0.82 0.94 0.71 0.75 1.80 0.86 2.72

time (sec)

N/A 0.140 0.806 0.757 0.205 0.274 0.255 0.516 6.086

Problem 408

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

79 79 68 85 70 70 0 123 103

N.S.

1 1.00 0.86 1.08 0.89 0.89 0.00 1.56 1.30

time (sec)

N/A 0.050 0.607 1.560 0.274 0.273 0.000 0.812 5.498

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 84 136 121 80 77 0 128 81

N.S.

1 1.00 1.62 1.44 0.95 0.92 0.00 1.52 0.96

time (sec)

N/A 0.064 0.622 1.596 0.186 0.265 0.000 0.330 4.683

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 135 190 168 105 101 0 243 119

N.S.

1 1.00 1.41 1.24 0.78 0.75 0.00 1.80 0.88

time (sec)

N/A 0.136 0.939 1.847 0.184 0.269 0.000 0.348 4.976

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 165 245 199 124 124 0 358 152

N.S.

1 1.00 1.48 1.21 0.75 0.75 0.00 2.17 0.92

time (sec)

N/A 0.144 1.731 1.968 0.192 0.271 0.000 0.355 5.021

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

192 192 299 230 145 146 0 473 275

N.S.

1 1.00 1.56 1.20 0.76 0.76 0.00 2.46 1.43

time (sec)

N/A 0.150 3.294 2.434 0.180 0.284 0.000 0.366 5.549

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 144 120 316 311 356 614 464 306

N.S.

1 1.00 0.83 2.19 2.16 2.47 4.26 3.22 2.12

time (sec)

N/A 0.155 1.263 4.955 0.184 0.337 3.585 0.438 4.715

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 56 236 233 310 468 272 231

N.S.

1 1.00 0.73 3.06 3.03 4.03 6.08 3.53 3.00

time (sec)

N/A 0.111 0.548 2.986 0.187 0.313 1.908 0.403 4.652

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 137 21 20 257 168 20 135

N.S.

1 1.00 6.23 0.95 0.91 11.68 7.64 0.91 6.14

time (sec)

N/A 0.018 0.261 1.610 0.180 0.315 0.943 0.439 0.120

Problem 416

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

245 245 227 284 317 327 0 378 212

N.S.

1 1.00 0.93 1.16 1.29 1.33 0.00 1.54 0.87

time (sec)

N/A 0.125 0.143 1.766 0.182 0.319 0.000 0.369 4.560

Problem 417

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

284 284 366 356 323 368 0 408 257

N.S.

1 1.00 1.29 1.25 1.14 1.30 0.00 1.44 0.90

time (sec)

N/A 0.164 1.481 2.329 0.184 0.317 0.000 0.409 0.271

Problem 418

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

320 320 514 434 348 366 0 429 305

N.S.

1 1.00 1.61 1.36 1.09 1.14 0.00 1.34 0.95

time (sec)

N/A 0.215 3.312 2.571 0.191 0.341 0.000 0.433 4.951

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

423 423 457 367 336 315 1115 364 467

N.S.

1 1.00 1.08 0.87 0.79 0.74 2.64 0.86 1.10

time (sec)

N/A 0.821 2.064 2.150 0.199 0.313 1.480 0.550 6.877

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

349 349 313 298 348 266 0 799 767

N.S.

1 1.00 0.90 0.85 1.00 0.76 0.00 2.29 2.20

time (sec)

N/A 0.395 2.715 4.161 0.281 0.353 0.000 0.410 7.234

Problem 421

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

369 369 414 371 328 268 0 684 726

N.S.

1 1.00 1.12 1.01 0.89 0.73 0.00 1.85 1.97

time (sec)

N/A 0.436 2.821 4.266 0.288 0.296 0.000 0.438 6.967

Problem 422

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

381 381 472 448 315 281 0 663 665

N.S.

1 1.00 1.24 1.18 0.83 0.74 0.00 1.74 1.75

time (sec)

N/A 0.490 3.006 3.724 0.279 0.317 0.000 0.451 7.033

Problem 423

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

404 404 479 541 310 306 0 726 546

N.S.

1 1.00 1.19 1.34 0.77 0.76 0.00 1.80 1.35

time (sec)

N/A 0.540 4.263 2.327 0.271 0.293 0.000 0.451 8.657

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

236 236 313 587 315 336 0 892 659

N.S.

1 1.00 1.33 2.49 1.33 1.42 0.00 3.78 2.79

time (sec)

N/A 0.263 2.895 3.900 0.202 0.319 0.000 0.504 6.182

Problem 425

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

118 118 103 106 108 107 0 120 109

N.S.

1 1.00 0.87 0.90 0.92 0.91 0.00 1.02 0.92

time (sec)

N/A 0.071 0.142 0.870 0.181 0.293 0.000 0.311 4.437

Problem 426

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

61 61 54 54 55 53 0 56 55

N.S.

1 1.00 0.89 0.89 0.90 0.87 0.00 0.92 0.90

time (sec)

N/A 0.046 0.039 0.473 0.182 0.294 0.000 0.312 0.081

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 19 18 18 41 19 18

N.S.

1 1.00 1.00 1.06 1.00 1.00 2.28 1.06 1.00

time (sec)

N/A 0.018 0.003 0.247 0.180 0.294 0.308 0.323 4.529

Problem 428

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

75 75 64 71 64 62 0 71 69

N.S.

1 1.00 0.85 0.95 0.85 0.83 0.00 0.95 0.92

time (sec)

N/A 0.057 0.014 0.658 0.183 0.305 0.000 0.305 4.511

Problem 429

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

123 123 114 121 139 153 0 177 148

N.S.

1 1.00 0.93 0.98 1.13 1.24 0.00 1.44 1.20

time (sec)

N/A 0.111 0.603 1.043 0.178 0.341 0.000 0.323 4.839

Problem 430

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

195 195 236 190 278 253 0 332 322

N.S.

1 1.00 1.21 0.97 1.43 1.30 0.00 1.70 1.65

time (sec)

N/A 0.177 4.133 1.493 0.195 0.377 0.000 0.336 0.643

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 188 507 382 0 483 0 496 3075

N.S.

1 1.00 2.70 2.03 0.00 2.57 0.00 2.64 16.36

time (sec)

N/A 0.300 5.329 1.285 0.000 0.310 0.000 0.526 7.230

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 127 428 203 0 332 0 226 364

N.S.

1 1.00 3.37 1.60 0.00 2.61 0.00 1.78 2.87

time (sec)

N/A 0.174 3.171 0.899 0.000 0.294 0.000 0.506 5.702

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 361 96 0 214 1923 95 318

N.S.

1 1.00 5.16 1.37 0.00 3.06 27.47 1.36 4.54

time (sec)

N/A 0.080 0.816 0.493 0.000 0.294 119.150 0.533 4.774

Problem 434

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

84 84 152 112 0 305 0 107 149

N.S.

1 1.00 1.81 1.33 0.00 3.63 0.00 1.27 1.77

time (sec)

N/A 0.061 0.167 0.644 0.000 0.311 0.000 0.409 4.784

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 137 202 215 0 466 0 273 387

N.S.

1 1.00 1.47 1.57 0.00 3.40 0.00 1.99 2.82

time (sec)

N/A 0.161 1.138 1.054 0.000 0.300 0.000 0.334 7.610

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

197 197 370 338 0 666 0 584 774

N.S.

1 1.00 1.88 1.72 0.00 3.38 0.00 2.96 3.93

time (sec)

N/A 0.542 2.028 1.602 0.000 0.321 0.000 0.344 7.706

Problem 437

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

184 184 235 205 190 243 0 251 259

N.S.

1 1.00 1.28 1.11 1.03 1.32 0.00 1.36 1.41

time (sec)

N/A 0.216 0.339 1.790 0.190 0.312 0.000 0.326 0.139

Problem 438

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

120 120 127 116 116 156 0 150 118

N.S.

1 1.00 1.06 0.97 0.97 1.30 0.00 1.25 0.98

time (sec)

N/A 0.141 0.452 1.214 0.194 0.303 0.000 0.332 0.090

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 63 52 60 61 78 221 91 69

N.S.

1 1.00 0.83 0.95 0.97 1.24 3.51 1.44 1.10

time (sec)

N/A 0.089 0.032 0.783 0.196 0.285 0.632 0.331 0.093

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 21 20 20 51 20 20

N.S.

1 1.00 1.00 1.05 1.00 1.00 2.55 1.00 1.00

time (sec)

N/A 0.039 0.027 0.369 0.184 0.261 0.535 0.316 4.509

Problem 441

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

104 104 102 93 118 188 0 147 98

N.S.

1 1.00 0.98 0.89 1.13 1.81 0.00 1.41 0.94

time (sec)

N/A 0.160 0.152 0.901 0.188 0.327 0.000 0.321 4.786

Problem 442

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

177 177 222 146 275 381 0 244 227

N.S.

1 1.00 1.25 0.82 1.55 2.15 0.00 1.38 1.28

time (sec)

N/A 0.250 1.364 2.148 0.206 0.363 0.000 0.340 5.130

Problem 443

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

269 269 406 213 505 527 0 460 449

N.S.

1 1.00 1.51 0.79 1.88 1.96 0.00 1.71 1.67

time (sec)

N/A 0.273 6.075 4.299 0.205 0.492 0.000 0.363 5.389

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

187 187 3679 395 0 599 0 469 2530

N.S.

1 1.00 19.67 2.11 0.00 3.20 0.00 2.51 13.53

time (sec)

N/A 0.277 7.270 2.688 0.000 0.327 0.000 0.338 7.304

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 128 448 220 0 411 0 235 601

N.S.

1 1.00 3.50 1.72 0.00 3.21 0.00 1.84 4.70

time (sec)

N/A 0.149 3.930 1.455 0.000 0.314 0.000 0.330 5.935

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 84 414 121 0 388 0 126 329

N.S.

1 1.00 4.93 1.44 0.00 4.62 0.00 1.50 3.92

time (sec)

N/A 0.092 2.016 0.753 0.000 0.296 0.000 0.332 5.098

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 130 162 158 0 538 0 271 303

N.S.

1 1.00 1.25 1.22 0.00 4.14 0.00 2.08 2.33

time (sec)

N/A 0.133 1.026 1.053 0.000 0.295 0.000 0.348 7.097

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 193 336 252 0 782 0 427 727

N.S.

1 1.00 1.74 1.31 0.00 4.05 0.00 2.21 3.77

time (sec)

N/A 0.243 1.626 2.799 0.000 0.335 0.000 0.348 7.929

Problem 449

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

190 190 282 198 200 304 0 245 234

N.S.

1 1.00 1.48 1.04 1.05 1.60 0.00 1.29 1.23

time (sec)

N/A 0.115 0.443 1.920 0.186 0.311 0.000 0.365 0.127

Problem 450

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

127 127 143 117 131 212 0 142 142

N.S.

1 1.00 1.13 0.92 1.03 1.67 0.00 1.12 1.12

time (sec)

N/A 0.078 0.782 1.613 0.190 0.293 0.000 0.338 4.743

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 55 66 76 110 398 62 80

N.S.

1 1.00 0.76 0.92 1.06 1.53 5.53 0.86 1.11

time (sec)

N/A 0.047 0.115 0.966 0.182 0.293 0.761 0.355 0.096

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 22 21 20 43 73 20 39

N.S.

1 1.00 1.00 0.95 0.91 1.95 3.32 0.91 1.77

time (sec)

N/A 0.018 0.036 0.645 0.185 0.268 0.710 0.350 0.061

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

145 145 135 130 223 462 0 242 169

N.S.

1 1.00 0.93 0.90 1.54 3.19 0.00 1.67 1.17

time (sec)

N/A 0.113 0.395 1.428 0.190 0.375 0.000 0.349 4.656

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

226 226 283 184 438 707 0 413 388

N.S.

1 1.00 1.25 0.81 1.94 3.13 0.00 1.83 1.72

time (sec)

N/A 0.186 2.871 3.306 0.198 0.446 0.000 0.365 5.033

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

328 328 388 252 725 895 0 575 688

N.S.

1 1.00 1.18 0.77 2.21 2.73 0.00 1.75 2.10

time (sec)

N/A 0.300 1.999 6.658 0.202 0.641 0.000 0.362 6.156

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

197 197 3889 378 0 752 0 457 1226

N.S.

1 1.00 19.74 1.92 0.00 3.82 0.00 2.32 6.22

time (sec)

N/A 0.265 7.565 3.412 0.000 0.339 0.000 0.381 8.017

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 139 486 238 0 716 0 272 1360

N.S.

1 1.00 3.50 1.71 0.00 5.15 0.00 1.96 9.78

time (sec)

N/A 0.153 6.301 1.940 0.000 0.316 0.000 0.366 7.182

Problem 458

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

115 115 93 201 0 501 0 207 282

N.S.

1 1.00 0.81 1.75 0.00 4.36 0.00 1.80 2.45

time (sec)

N/A 0.086 0.217 1.039 0.000 0.326 0.000 0.544 6.930

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

192 192 193 254 0 894 0 385 650

N.S.

1 1.00 1.01 1.32 0.00 4.66 0.00 2.01 3.39

time (sec)

N/A 0.251 2.293 2.528 0.000 0.332 0.000 0.538 8.448

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

264 264 380 352 0 1200 0 622 1167

N.S.

1 1.00 1.44 1.33 0.00 4.55 0.00 2.36 4.42

time (sec)

N/A 0.430 2.259 4.142 0.000 0.394 0.000 0.603 8.973

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

207 207 171 208 279 382 2530 215 276

N.S.

1 1.00 0.83 1.00 1.35 1.85 12.22 1.04 1.33

time (sec)

N/A 0.111 0.887 7.556 0.200 0.335 9.855 0.541 0.263

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 141 107 127 206 309 1425 117 206

N.S.

1 1.00 0.76 0.90 1.46 2.19 10.11 0.83 1.46

time (sec)

N/A 0.076 0.195 7.481 0.193 0.343 9.689 0.492 0.150

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 54 67 151 254 636 52 152

N.S.

1 1.00 0.70 0.87 1.96 3.30 8.26 0.68 1.97

time (sec)

N/A 0.048 0.120 7.590 0.195 0.342 9.610 0.487 4.736

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 22 21 20 218 167 20 119

N.S.

1 1.00 1.00 0.95 0.91 9.91 7.59 0.91 5.41

time (sec)

N/A 0.018 0.128 7.421 0.183 0.354 9.572 0.456 4.643

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

385 385 365 356 1160 3165 0 1010 937

N.S.

1 1.00 0.95 0.92 3.01 8.22 0.00 2.62 2.43

time (sec)

N/A 0.368 1.667 19.487 0.251 1.744 0.000 0.464 7.282

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

527 527 770 433 1670 3678 0 1327 1443

N.S.

1 1.00 1.46 0.82 3.17 6.98 0.00 2.52 2.74

time (sec)

N/A 0.511 6.475 39.796 0.271 3.168 0.000 0.553 9.610

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

491 491 574 1652 0 3721 0 2326 9647

N.S.

1 1.00 1.17 3.36 0.00 7.58 0.00 4.74 19.65

time (sec)

N/A 0.836 17.168 14.467 0.000 0.734 0.000 0.577 32.388

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

407 407 386 1388 0 2250 0 1650 1868

N.S.

1 1.00 0.95 3.41 0.00 5.53 0.00 4.05 4.59

time (sec)

N/A 0.973 3.757 12.770 0.000 0.478 0.000 0.564 12.130

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

411 411 1167 1533 0 2657 0 1932 2184

N.S.

1 1.00 2.84 3.73 0.00 6.46 0.00 4.70 5.31

time (sec)

N/A 0.567 6.102 14.070 0.000 0.484 0.000 0.518 10.512

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

422 422 1896 1703 0 2972 0 2207 2440

N.S.

1 1.00 4.49 4.04 0.00 7.04 0.00 5.23 5.78

time (sec)

N/A 0.540 6.235 14.275 0.000 0.538 0.000 0.519 9.783

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

529 529 494 1286 0 3882 0 2610 3273

N.S.

1 1.00 0.93 2.43 0.00 7.34 0.00 4.93 6.19

time (sec)

N/A 1.192 3.680 49.675 0.000 0.663 0.000 0.603 54.208

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

653 653 597 1380 0 4500 0 3047 0

N.S.

1 1.00 0.91 2.11 0.00 6.89 0.00 4.67 0.00

time (sec)

N/A 1.377 5.349 111.819 0.000 0.859 0.000 0.715 0.000

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 154 117 150 116 142 0 161 0

N.S.

1 1.00 0.76 0.97 0.75 0.92 0.00 1.05 0.00

time (sec)

N/A 0.075 0.231 0.668 0.184 0.300 0.000 0.307 0.000

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 83 58 62 61 78 0 72 0

N.S.

1 1.00 0.70 0.75 0.73 0.94 0.00 0.87 0.00

time (sec)

N/A 0.057 0.088 0.405 0.183 0.280 0.000 0.300 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 24 21 20 20 83 20 20

N.S.

1 1.00 1.00 0.88 0.83 0.83 3.46 0.83 0.83

time (sec)

N/A 0.023 0.013 0.295 0.191 0.277 0.160 0.288 4.656

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 74 61 0 1729 0 83 0

N.S.

1 1.00 1.00 0.82 0.00 23.36 0.00 1.12 0.00

time (sec)

N/A 0.079 0.045 0.785 0.000 0.546 0.000 0.295 0.000

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 124 143 146 0 2101 0 159 0

N.S.

1 1.00 1.15 1.18 0.00 16.94 0.00 1.28 0.00

time (sec)

N/A 0.120 0.491 1.204 0.000 0.595 0.000 0.317 0.000

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

207 207 224 237 0 2505 0 358 0

N.S.

1 1.00 1.08 1.14 0.00 12.10 0.00 1.73 0.00

time (sec)

N/A 0.229 1.006 2.161 0.000 0.746 0.000 0.322 0.000

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

298 298 233 1189 0 534 0 0 0

N.S.

1 1.00 0.78 3.99 0.00 1.79 0.00 0.00 0.00

time (sec)

N/A 0.385 0.624 3.067 0.000 0.143 0.000 0.000 0.000

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

215 215 185 792 0 448 0 0 0

N.S.

1 1.00 0.86 3.68 0.00 2.08 0.00 0.00 0.00

time (sec)

N/A 0.175 0.591 2.111 0.000 0.125 0.000 0.000 0.000

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 149 127 617 0 418 0 0 0

N.S.

1 1.00 0.85 4.14 0.00 2.81 0.00 0.00 0.00

time (sec)

N/A 0.134 2.737 1.894 0.000 0.115 0.000 0.000 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

248 248 270 1201 0 526 0 0 0

N.S.

1 1.00 1.09 4.84 0.00 2.12 0.00 0.00 0.00

time (sec)

N/A 0.263 2.264 2.457 0.000 0.127 0.000 0.000 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 154 131 150 116 184 0 0 0

N.S.

1 1.00 0.85 0.97 0.75 1.19 0.00 0.00 0.00

time (sec)

N/A 0.078 0.459 0.599 0.195 0.310 0.000 0.000 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 83 58 62 61 111 314 0 0

N.S.

1 1.00 0.70 0.75 0.73 1.34 3.78 0.00 0.00

time (sec)

N/A 0.057 0.122 0.581 0.193 0.284 4.462 0.000 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 24 21 20 53 116 0 20

N.S.

1 1.00 1.00 0.88 0.83 2.21 4.83 0.00 0.83

time (sec)

N/A 0.025 0.016 0.310 0.191 0.281 1.234 0.000 4.742

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 94 89 108 0 1797 0 0 0

N.S.

1 1.00 0.95 1.15 0.00 19.12 0.00 0.00 0.00

time (sec)

N/A 0.116 0.069 0.988 0.000 1.782 0.000 0.000 0.000

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 130 121 154 0 1969 0 0 0

N.S.

1 1.00 0.93 1.18 0.00 15.15 0.00 0.00 0.00

time (sec)

N/A 0.185 0.441 1.339 0.000 0.580 0.000 0.000 0.000

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 188 297 217 0 2397 0 0 0

N.S.

1 1.00 1.58 1.15 0.00 12.75 0.00 0.00 0.00

time (sec)

N/A 0.215 1.617 1.859 0.000 0.653 0.000 0.000 0.000

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

329 329 278 1355 0 583 0 0 0

N.S.

1 1.00 0.84 4.12 0.00 1.77 0.00 0.00 0.00

time (sec)

N/A 0.463 0.789 3.717 0.000 0.137 0.000 0.000 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

247 247 222 943 0 491 0 0 0

N.S.

1 1.00 0.90 3.82 0.00 1.99 0.00 0.00 0.00

time (sec)

N/A 0.307 0.713 2.663 0.000 0.118 0.000 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

168 168 163 633 0 444 0 0 0

N.S.

1 1.00 0.97 3.77 0.00 2.64 0.00 0.00 0.00

time (sec)

N/A 0.138 0.487 2.013 0.000 0.114 0.000 0.000 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

218 218 211 877 0 481 0 0 0

N.S.

1 1.00 0.97 4.02 0.00 2.21 0.00 0.00 0.00

time (sec)

N/A 0.292 1.652 2.339 0.000 0.125 0.000 0.000 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

330 330 364 1519 0 612 0 0 0

N.S.

1 1.00 1.10 4.60 0.00 1.85 0.00 0.00 0.00

time (sec)

N/A 0.477 6.304 4.845 0.000 0.146 0.000 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 154 113 150 116 224 714 0 0

N.S.

1 1.00 0.73 0.97 0.75 1.45 4.64 0.00 0.00

time (sec)

N/A 0.137 0.383 78.859 0.192 0.322 129.113 0.000 0.000

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 83 58 62 61 143 391 0 0

N.S.

1 1.00 0.70 0.75 0.73 1.72 4.71 0.00 0.00

time (sec)

N/A 0.117 0.060 6.902 0.191 0.332 39.224 0.000 0.000

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 24 21 20 77 150 0 20

N.S.

1 1.00 1.00 0.88 0.83 3.21 6.25 0.00 0.83

time (sec)

N/A 0.051 0.019 0.631 0.186 0.304 13.268 0.000 5.365

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 117 105 139 0 1937 0 0 0

N.S.

1 1.00 0.90 1.19 0.00 16.56 0.00 0.00 0.00

time (sec)

N/A 0.300 0.119 1.889 0.000 3.287 0.000 0.000 0.000

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

155 155 147 160 0 2071 0 0 0

N.S.

1 1.00 0.95 1.03 0.00 13.36 0.00 0.00 0.00

time (sec)

N/A 0.353 0.613 34.965 0.000 0.603 0.000 0.000 0.000

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

199 199 307 222 0 2229 0 0 0

N.S.

1 1.00 1.54 1.12 0.00 11.20 0.00 0.00 0.00

time (sec)

N/A 0.382 2.144 1.171 0.000 0.688 0.000 0.000 0.000

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

398 398 321 1619 0 633 0 0 0

N.S.

1 1.00 0.81 4.07 0.00 1.59 0.00 0.00 0.00

time (sec)

N/A 0.793 0.909 23.964 0.000 0.168 0.000 0.000 0.000

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