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2.2.5 Integrals 401 to 500

Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.

In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA

Problem 401

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 51 54 54 53 76 54 53

N.S.

1 1.00 0.70 0.74 0.74 0.73 1.04 0.74 0.73

time (sec)

N/A 0.192 0.042 0.069 0.261 0.302 0.429 0.261 0.047

Problem 402

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

109 109 83 78 77 82 114 77 77

N.S.

1 1.00 0.76 0.72 0.71 0.75 1.05 0.71 0.71

time (sec)

N/A 0.223 0.043 0.227 0.211 0.307 0.989 0.257 0.036

Problem 403

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

109 109 83 78 77 82 114 77 77

N.S.

1 1.00 0.76 0.72 0.71 0.75 1.05 0.71 0.71

time (sec)

N/A 0.227 0.042 0.207 0.213 0.310 0.691 0.258 0.035

Problem 404

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

109 109 83 78 77 82 114 77 77

N.S.

1 1.00 0.76 0.72 0.71 0.75 1.05 0.71 0.71

time (sec)

N/A 0.223 0.038 0.148 0.217 0.330 0.464 0.270 0.035

Problem 405

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

109 109 83 78 77 80 114 77 77

N.S.

1 1.00 0.76 0.72 0.71 0.73 1.05 0.71 0.71

time (sec)

N/A 0.220 0.038 0.145 0.268 0.343 0.731 0.262 0.035

Problem 406

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

107 107 72 77 77 77 112 77 77

N.S.

1 1.00 0.67 0.72 0.72 0.72 1.05 0.72 0.72

time (sec)

N/A 0.223 0.038 0.147 0.244 0.311 0.317 0.272 0.035

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

103 103 81 78 77 77 109 77 77

N.S.

1 1.00 0.79 0.76 0.75 0.75 1.06 0.75 0.75

time (sec)

N/A 0.230 0.061 0.065 0.218 0.405 0.400 0.271 0.037

Problem 408

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

103 103 78 78 77 77 109 77 78

N.S.

1 1.00 0.76 0.76 0.75 0.75 1.06 0.75 0.76

time (sec)

N/A 0.220 0.054 0.076 0.232 0.361 0.427 0.279 0.035

Problem 409

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

103 103 72 78 78 77 109 78 78

N.S.

1 1.00 0.70 0.76 0.76 0.75 1.06 0.76 0.76

time (sec)

N/A 0.224 0.064 0.074 0.211 0.334 0.519 0.288 0.033

Problem 410

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

101 101 70 78 78 77 107 78 78

N.S.

1 1.00 0.69 0.77 0.77 0.76 1.06 0.77 0.77

time (sec)

N/A 0.222 0.052 0.078 0.213 0.404 0.656 0.277 0.033

Problem 411

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

103 103 71 78 78 77 109 78 78

N.S.

1 1.00 0.69 0.76 0.76 0.75 1.06 0.76 0.76

time (sec)

N/A 0.222 0.044 0.079 0.222 0.356 0.803 0.273 0.058

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

292 290 166 240 265 862 291 262 665

N.S.

1 0.99 0.57 0.82 0.91 2.95 1.00 0.90 2.28

time (sec)

N/A 0.547 0.281 0.085 0.315 0.582 14.291 0.290 10.131

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

278 272 157 236 247 772 262 255 601

N.S.

1 0.98 0.56 0.85 0.89 2.78 0.94 0.92 2.16

time (sec)

N/A 0.503 0.235 0.076 0.312 0.370 3.461 0.294 10.152

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

265 258 149 222 246 764 236 249 566

N.S.

1 0.97 0.56 0.84 0.93 2.88 0.89 0.94 2.14

time (sec)

N/A 0.465 0.192 0.068 0.306 0.374 1.619 0.289 10.141

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

254 243 124 214 224 775 231 244 607

N.S.

1 0.96 0.49 0.84 0.88 3.05 0.91 0.96 2.39

time (sec)

N/A 0.433 0.152 0.056 0.338 0.325 1.846 0.312 10.175

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

265 258 149 223 246 767 243 249 602

N.S.

1 0.97 0.56 0.84 0.93 2.89 0.92 0.94 2.27

time (sec)

N/A 0.468 0.247 0.069 0.365 0.292 4.811 0.294 0.243

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

278 271 155 235 244 802 269 258 606

N.S.

1 0.97 0.56 0.85 0.88 2.88 0.97 0.93 2.18

time (sec)

N/A 0.486 0.259 0.072 0.306 0.355 19.670 0.307 10.163

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

292 290 167 239 263 869 296 265 664

N.S.

1 0.99 0.57 0.82 0.90 2.98 1.01 0.91 2.27

time (sec)

N/A 0.519 0.292 0.075 0.302 0.378 66.637 0.303 9.988

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

306 303 175 254 264 884 0 276 678

N.S.

1 0.99 0.57 0.83 0.86 2.89 0.00 0.90 2.22

time (sec)

N/A 0.530 0.345 0.081 0.396 0.328 0.000 0.279 10.169

Problem 420

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

304 297 177 248 283 884 916 283 617

N.S.

1 0.98 0.58 0.82 0.93 2.91 3.01 0.93 2.03

time (sec)

N/A 0.521 0.541 0.125 0.413 0.335 125.865 0.300 10.169

Problem 421

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

289 279 166 250 259 888 937 271 656

N.S.

1 0.97 0.57 0.87 0.90 3.07 3.24 0.94 2.27

time (sec)

N/A 0.502 0.510 0.067 0.464 0.309 60.419 0.292 10.198

Problem 422

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

292 285 167 247 272 901 886 271 652

N.S.

1 0.98 0.57 0.85 0.93 3.09 3.03 0.93 2.23

time (sec)

N/A 0.491 0.674 0.066 0.355 0.422 29.295 0.287 10.139

Problem 423

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

287 276 165 257 256 877 938 273 649

N.S.

1 0.96 0.57 0.90 0.89 3.06 3.27 0.95 2.26

time (sec)

N/A 0.491 0.465 0.066 0.333 0.452 45.449 0.285 10.161

Problem 424

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

304 297 176 248 280 877 1056 281 634

N.S.

1 0.98 0.58 0.82 0.92 2.88 3.47 0.92 2.09

time (sec)

N/A 0.530 0.660 0.105 0.356 0.387 114.020 0.303 10.162

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

317 310 185 259 280 916 0 291 638

N.S.

1 0.98 0.58 0.82 0.88 2.89 0.00 0.92 2.01

time (sec)

N/A 0.560 0.568 0.125 0.308 0.404 0.000 0.286 0.252

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

320 317 186 270 292 986 0 293 686

N.S.

1 0.99 0.58 0.84 0.91 3.08 0.00 0.92 2.14

time (sec)

N/A 0.547 0.765 0.172 0.309 0.739 0.000 0.297 10.208

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

325 325 187 266 312 1031 0 298 697

N.S.

1 1.00 0.58 0.82 0.96 3.17 0.00 0.92 2.14

time (sec)

N/A 0.552 0.856 0.151 0.290 0.366 0.000 0.305 10.225

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

315 310 181 271 289 982 0 289 695

N.S.

1 0.98 0.57 0.86 0.92 3.12 0.00 0.92 2.21

time (sec)

N/A 0.530 0.777 0.089 0.281 0.336 0.000 0.283 10.149

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

331 328 188 266 311 1022 0 297 690

N.S.

1 0.99 0.57 0.80 0.94 3.09 0.00 0.90 2.08

time (sec)

N/A 0.550 0.613 0.083 0.324 0.364 0.000 0.294 10.037

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

320 317 185 303 291 981 0 293 687

N.S.

1 0.99 0.58 0.95 0.91 3.07 0.00 0.92 2.15

time (sec)

N/A 0.545 0.440 0.075 0.297 0.362 0.000 0.303 10.172

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

333 334 198 268 313 958 0 304 673

N.S.

1 1.00 0.59 0.80 0.94 2.88 0.00 0.91 2.02

time (sec)

N/A 0.581 0.717 0.138 0.287 0.298 0.000 0.283 0.295

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 52 23 54 34 33 49 34 20

N.S.

1 1.16 0.51 1.20 0.76 0.73 1.09 0.76 0.44

time (sec)

N/A 0.206 0.033 0.217 0.289 0.276 0.202 0.423 0.134

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

427 414 142 368 0 147 97 0 0

N.S.

1 0.97 0.33 0.86 0.00 0.34 0.23 0.00 0.00

time (sec)

N/A 0.585 10.108 1.037 0.000 0.110 43.639 0.000 0.000

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

397 386 133 360 0 135 97 0 0

N.S.

1 0.97 0.34 0.91 0.00 0.34 0.24 0.00 0.00

time (sec)

N/A 0.524 10.100 0.531 0.000 0.123 15.049 0.000 0.000

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

363 349 118 342 0 106 97 0 0

N.S.

1 0.96 0.33 0.94 0.00 0.29 0.27 0.00 0.00

time (sec)

N/A 0.471 10.060 0.445 0.000 0.113 4.806 0.000 0.000

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

328 321 111 333 0 91 97 0 0

N.S.

1 0.98 0.34 1.02 0.00 0.28 0.30 0.00 0.00

time (sec)

N/A 0.435 10.044 0.381 0.000 0.103 2.381 0.000 0.000

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

297 284 82 312 0 78 97 0 0

N.S.

1 0.96 0.28 1.05 0.00 0.26 0.33 0.00 0.00

time (sec)

N/A 0.387 10.020 0.391 0.000 0.095 2.341 0.000 0.000

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

300 285 80 310 0 82 100 0 0

N.S.

1 0.95 0.27 1.03 0.00 0.27 0.33 0.00 0.00

time (sec)

N/A 0.393 9.033 0.539 0.000 0.098 3.412 0.000 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

298 283 82 303 0 79 104 0 0

N.S.

1 0.95 0.28 1.02 0.00 0.27 0.35 0.00 0.00

time (sec)

N/A 0.395 10.025 0.619 0.000 0.094 5.285 0.000 0.000

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

338 323 83 331 0 95 107 0 0

N.S.

1 0.96 0.25 0.98 0.00 0.28 0.32 0.00 0.00

time (sec)

N/A 0.446 10.026 0.718 0.000 0.108 14.037 0.000 0.000

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

368 358 88 340 0 101 110 0 0

N.S.

1 0.97 0.24 0.92 0.00 0.27 0.30 0.00 0.00

time (sec)

N/A 0.491 10.029 0.881 0.000 0.114 43.622 0.000 0.000

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

438 427 137 384 0 165 199 0 0

N.S.

1 0.97 0.31 0.88 0.00 0.38 0.45 0.00 0.00

time (sec)

N/A 0.581 10.116 0.892 0.000 0.209 42.405 0.000 0.000

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

400 388 124 366 0 132 199 0 0

N.S.

1 0.97 0.31 0.92 0.00 0.33 0.50 0.00 0.00

time (sec)

N/A 0.526 10.092 0.504 0.000 0.104 12.156 0.000 0.000

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

366 362 116 357 0 115 199 0 0

N.S.

1 0.99 0.32 0.98 0.00 0.31 0.54 0.00 0.00

time (sec)

N/A 0.492 10.055 0.432 0.000 0.099 5.325 0.000 0.000

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

333 323 83 338 0 102 199 0 0

N.S.

1 0.97 0.25 1.02 0.00 0.31 0.60 0.00 0.00

time (sec)

N/A 0.441 10.021 0.401 0.000 0.095 5.101 0.000 0.000

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

341 327 81 340 0 106 202 0 0

N.S.

1 0.96 0.24 1.00 0.00 0.31 0.59 0.00 0.00

time (sec)

N/A 0.456 10.024 0.410 0.000 0.103 7.786 0.000 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

341 322 83 325 0 98 206 0 0

N.S.

1 0.94 0.24 0.95 0.00 0.29 0.60 0.00 0.00

time (sec)

N/A 0.436 10.026 0.491 0.000 0.093 10.082 0.000 0.000

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

339 328 84 329 0 98 212 0 0

N.S.

1 0.97 0.25 0.97 0.00 0.29 0.63 0.00 0.00

time (sec)

N/A 0.434 10.026 0.608 0.000 0.097 25.059 0.000 0.000

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

339 329 89 337 0 99 219 0 0

N.S.

1 0.97 0.26 0.99 0.00 0.29 0.65 0.00 0.00

time (sec)

N/A 0.443 10.026 0.641 0.000 0.099 72.490 0.000 0.000

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

437 427 124 390 0 158 301 0 0

N.S.

1 0.98 0.28 0.89 0.00 0.36 0.69 0.00 0.00

time (sec)

N/A 0.570 10.108 1.315 0.000 0.134 27.666 0.000 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

404 399 117 381 0 139 301 0 0

N.S.

1 0.99 0.29 0.94 0.00 0.34 0.75 0.00 0.00

time (sec)

N/A 0.531 10.073 0.693 0.000 0.145 11.314 0.000 0.000

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

369 362 85 362 0 126 301 0 0

N.S.

1 0.98 0.23 0.98 0.00 0.34 0.82 0.00 0.00

time (sec)

N/A 0.480 10.022 0.624 0.000 0.203 10.630 0.000 0.000

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

379 368 83 364 0 132 304 0 0

N.S.

1 0.97 0.22 0.96 0.00 0.35 0.80 0.00 0.00

time (sec)

N/A 0.481 10.024 0.608 0.000 0.139 17.535 0.000 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

378 363 85 359 0 126 308 0 0

N.S.

1 0.96 0.22 0.95 0.00 0.33 0.81 0.00 0.00

time (sec)

N/A 0.484 10.024 0.495 0.000 0.126 18.220 0.000 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

376 369 86 367 0 125 314 0 0

N.S.

1 0.98 0.23 0.98 0.00 0.33 0.84 0.00 0.00

time (sec)

N/A 0.497 10.024 0.716 0.000 0.122 42.810 0.000 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

377 366 91 366 0 124 321 0 0

N.S.

1 0.97 0.24 0.97 0.00 0.33 0.85 0.00 0.00

time (sec)

N/A 0.493 10.032 0.804 0.000 0.105 100.705 0.000 0.000

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

375 366 91 366 0 125 0 0 0

N.S.

1 0.98 0.24 0.98 0.00 0.33 0.00 0.00 0.00

time (sec)

N/A 0.500 10.031 1.187 0.000 0.126 0.000 0.000 0.000

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

388 371 142 344 0 117 94 0 0

N.S.

1 0.96 0.37 0.89 0.00 0.30 0.24 0.00 0.00

time (sec)

N/A 0.525 10.065 0.690 0.000 0.098 29.750 0.000 0.000

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

356 345 133 336 0 105 94 0 0

N.S.

1 0.97 0.37 0.94 0.00 0.29 0.26 0.00 0.00

time (sec)

N/A 0.474 10.058 0.608 0.000 0.110 10.751 0.000 0.000

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

326 310 118 316 0 80 94 0 0

N.S.

1 0.95 0.36 0.97 0.00 0.25 0.29 0.00 0.00

time (sec)

N/A 0.423 10.048 0.238 0.000 0.101 4.196 0.000 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

287 279 109 295 0 67 94 0 0

N.S.

1 0.97 0.38 1.03 0.00 0.23 0.33 0.00 0.00

time (sec)

N/A 0.389 10.031 0.221 0.000 0.102 2.840 0.000 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

253 244 82 175 0 50 94 0 0

N.S.

1 0.96 0.32 0.69 0.00 0.20 0.37 0.00 0.00

time (sec)

N/A 0.342 10.030 0.481 0.000 0.092 1.805 0.000 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

293 279 80 296 0 78 97 0 0

N.S.

1 0.95 0.27 1.01 0.00 0.27 0.33 0.00 0.00

time (sec)

N/A 0.389 10.024 0.548 0.000 0.082 2.267 0.000 0.000

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

327 314 82 306 0 80 100 0 0

N.S.

1 0.96 0.25 0.94 0.00 0.24 0.31 0.00 0.00

time (sec)

N/A 0.433 10.024 0.648 0.000 0.104 4.596 0.000 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

363 356 83 331 0 95 104 0 0

N.S.

1 0.98 0.23 0.91 0.00 0.26 0.29 0.00 0.00

time (sec)

N/A 0.492 10.037 0.561 0.000 0.117 15.749 0.000 0.000

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

360 350 127 318 0 154 94 0 0

N.S.

1 0.97 0.35 0.88 0.00 0.43 0.26 0.00 0.00

time (sec)

N/A 0.481 10.049 1.851 0.000 0.100 142.006 0.000 0.000

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

326 320 120 308 0 143 94 0 0

N.S.

1 0.98 0.37 0.94 0.00 0.44 0.29 0.00 0.00

time (sec)

N/A 0.441 10.044 1.559 0.000 0.104 46.873 0.000 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

296 280 102 290 0 106 94 0 0

N.S.

1 0.95 0.34 0.98 0.00 0.36 0.32 0.00 0.00

time (sec)

N/A 0.390 10.041 0.514 0.000 0.092 15.045 0.000 0.000

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

298 287 113 297 0 111 94 0 0

N.S.

1 0.96 0.38 1.00 0.00 0.37 0.32 0.00 0.00

time (sec)

N/A 0.398 10.045 0.188 0.000 0.089 9.134 0.000 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

290 277 107 288 0 101 94 0 0

N.S.

1 0.96 0.37 0.99 0.00 0.35 0.32 0.00 0.00

time (sec)

N/A 0.382 10.054 0.889 0.000 0.089 12.812 0.000 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

327 318 100 304 0 131 97 0 0

N.S.

1 0.97 0.31 0.93 0.00 0.40 0.30 0.00 0.00

time (sec)

N/A 0.438 10.047 1.181 0.000 0.123 18.886 0.000 0.000

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

357 354 107 307 0 132 100 0 0

N.S.

1 0.99 0.30 0.86 0.00 0.37 0.28 0.00 0.00

time (sec)

N/A 0.489 10.052 1.589 0.000 0.146 31.225 0.000 0.000

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

393 394 107 331 0 154 104 0 0

N.S.

1 1.00 0.27 0.84 0.00 0.39 0.26 0.00 0.00

time (sec)

N/A 0.540 10.049 1.642 0.000 0.113 73.343 0.000 0.000

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

428 426 183 483 0 246 0 0 0

N.S.

1 1.00 0.43 1.13 0.00 0.57 0.00 0.00 0.00

time (sec)

N/A 0.591 10.129 3.320 0.000 0.139 0.000 0.000 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

398 391 165 453 0 225 0 0 0

N.S.

1 0.98 0.41 1.14 0.00 0.57 0.00 0.00 0.00

time (sec)

N/A 0.535 10.103 3.494 0.000 0.119 0.000 0.000 0.000

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

368 361 156 426 0 212 0 0 0

N.S.

1 0.98 0.42 1.16 0.00 0.58 0.00 0.00 0.00

time (sec)

N/A 0.497 10.104 2.056 0.000 0.113 0.000 0.000 0.000

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

339 327 139 400 0 189 0 0 0

N.S.

1 0.96 0.41 1.18 0.00 0.56 0.00 0.00 0.00

time (sec)

N/A 0.453 10.094 0.948 0.000 0.099 0.000 0.000 0.000

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

347 332 149 405 0 201 94 0 0

N.S.

1 0.96 0.43 1.17 0.00 0.58 0.27 0.00 0.00

time (sec)

N/A 0.458 10.090 0.635 0.000 0.102 172.279 0.000 0.000

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

341 321 138 402 0 168 94 0 0

N.S.

1 0.94 0.40 1.18 0.00 0.49 0.28 0.00 0.00

time (sec)

N/A 0.439 10.070 0.868 0.000 0.117 74.380 0.000 0.000

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

342 332 145 397 0 172 94 0 0

N.S.

1 0.97 0.42 1.16 0.00 0.50 0.27 0.00 0.00

time (sec)

N/A 0.453 10.103 0.096 0.000 0.113 43.288 0.000 0.000

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

335 324 140 404 0 164 94 0 0

N.S.

1 0.97 0.42 1.21 0.00 0.49 0.28 0.00 0.00

time (sec)

N/A 0.447 10.095 1.421 0.000 0.096 57.979 0.000 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

373 363 137 437 0 195 97 0 0

N.S.

1 0.97 0.37 1.17 0.00 0.52 0.26 0.00 0.00

time (sec)

N/A 0.499 10.069 2.319 0.000 0.090 105.878 0.000 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

402 393 137 456 0 194 0 0 0

N.S.

1 0.98 0.34 1.13 0.00 0.48 0.00 0.00 0.00

time (sec)

N/A 0.543 10.099 2.964 0.000 0.097 0.000 0.000 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

432 434 137 481 0 216 0 0 0

N.S.

1 1.00 0.32 1.11 0.00 0.50 0.00 0.00 0.00

time (sec)

N/A 0.598 10.083 2.681 0.000 0.145 0.000 0.000 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

217 217 128 1255 208 1051 8032 1778 1075

N.S.

1 1.00 0.59 5.78 0.96 4.84 37.01 8.19 4.95

time (sec)

N/A 0.411 0.581 0.237 0.224 0.385 1.006 0.285 10.681

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 169 101 168 162 649 4398 1102 695

N.S.

1 1.00 0.60 0.99 0.96 3.84 26.02 6.52 4.11

time (sec)

N/A 0.338 0.259 0.161 0.217 0.342 0.692 0.284 10.339

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 121 74 120 116 343 2014 586 371

N.S.

1 1.00 0.61 0.99 0.96 2.83 16.64 4.84 3.07

time (sec)

N/A 0.281 0.110 0.113 0.224 0.341 0.503 0.276 10.141

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 47 72 70 133 658 230 161

N.S.

1 1.00 0.64 0.99 0.96 1.82 9.01 3.15 2.21

time (sec)

N/A 0.217 0.065 0.051 0.211 0.276 0.380 0.276 10.007

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

91 91 82 0 0 0 189 0 0

N.S.

1 1.00 0.90 0.00 0.00 0.00 2.08 0.00 0.00

time (sec)

N/A 0.212 0.065 0.000 0.000 0.000 1.703 0.000 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

91 91 82 0 0 0 770 0 0

N.S.

1 1.00 0.90 0.00 0.00 0.00 8.46 0.00 0.00

time (sec)

N/A 0.206 0.069 0.000 0.000 0.000 16.692 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

91 91 82 0 0 0 2530 0 0

N.S.

1 1.00 0.90 0.00 0.00 0.00 27.80 0.00 0.00

time (sec)

N/A 0.205 0.072 0.000 0.000 0.000 62.796 0.000 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

145 145 111 0 0 0 352 0 0

N.S.

1 1.00 0.77 0.00 0.00 0.00 2.43 0.00 0.00

time (sec)

N/A 0.257 0.425 0.000 0.000 0.000 9.414 0.000 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

141 141 109 0 0 0 233 0 0

N.S.

1 1.00 0.77 0.00 0.00 0.00 1.65 0.00 0.00

time (sec)

N/A 0.247 0.291 0.000 0.000 0.000 3.759 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

139 139 108 0 0 0 114 0 0

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.82 0.00 0.00

time (sec)

N/A 0.244 0.200 0.000 0.000 0.000 1.617 0.000 0.000

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

139 139 108 0 0 0 110 0 0

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.79 0.00 0.00

time (sec)

N/A 0.243 0.226 0.000 0.000 0.000 1.453 0.000 0.000

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

145 145 111 0 0 0 110 0 0

N.S.

1 1.00 0.77 0.00 0.00 0.00 0.76 0.00 0.00

time (sec)

N/A 0.242 0.326 0.000 0.000 0.000 5.132 0.000 0.000

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

145 145 111 0 0 0 110 0 0

N.S.

1 1.00 0.77 0.00 0.00 0.00 0.76 0.00 0.00

time (sec)

N/A 0.247 0.460 0.000 0.000 0.000 69.159 0.000 0.000

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 67 177 0 0 673 0 0

N.S.

1 1.00 0.96 2.53 0.00 0.00 9.61 0.00 0.00

time (sec)

N/A 0.187 0.069 0.948 0.000 0.000 2.837 0.000 0.000

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

70 70 67 0 0 0 313 0 0

N.S.

1 1.00 0.96 0.00 0.00 0.00 4.47 0.00 0.00

time (sec)

N/A 0.183 0.002 0.000 0.000 0.000 1.352 0.000 0.000

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 67 177 0 0 673 0 0

N.S.

1 1.00 0.96 2.53 0.00 0.00 9.61 0.00 0.00

time (sec)

N/A 0.192 0.003 4.827 0.000 0.000 0.930 0.000 0.000

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