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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

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.017 0.045 0.519 0.273 4.600 0.560 0.578 0.048

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.026 0.045 0.530 0.265 2.483 2.362 0.989 0.037

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.025 0.041 0.525 0.262 2.818 0.908 0.828 0.034

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.026 0.039 0.577 0.282 3.064 0.601 1.001 0.034

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.027 0.040 0.521 0.275 2.852 1.657 0.620 0.036

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

107 107 72 78 77 77 112 77 77

N.S.

1 1.00 0.67 0.73 0.72 0.72 1.05 0.72 0.72

time (sec)

N/A 0.025 0.040 0.512 0.295 2.266 0.375 0.614 0.036

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.026 0.066 0.513 0.273 2.477 0.504 0.834 0.038

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.026 0.058 0.513 0.275 4.562 0.571 0.774 0.033

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.025 0.059 0.522 0.282 4.431 0.693 0.893 0.032

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.027 0.057 0.607 0.265 2.993 0.869 0.687 0.031

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.025 0.046 0.585 0.270 2.952 1.057 0.594 0.060

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

292 292 166 242 265 862 291 262 665

N.S.

1 1.00 0.57 0.83 0.91 2.95 1.00 0.90 2.28

time (sec)

N/A 0.239 0.288 0.541 0.485 2.594 17.847 0.624 1.256

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

278 278 157 238 247 772 262 255 601

N.S.

1 1.00 0.56 0.86 0.89 2.78 0.94 0.92 2.16

time (sec)

N/A 0.197 0.259 0.546 0.500 2.886 3.557 0.825 0.248

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

265 265 149 223 246 764 236 249 566

N.S.

1 1.00 0.56 0.84 0.93 2.88 0.89 0.94 2.14

time (sec)

N/A 0.169 0.203 0.543 0.495 4.305 1.853 0.774 1.258

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

254 254 124 214 224 775 231 244 607

N.S.

1 1.00 0.49 0.84 0.88 3.05 0.91 0.96 2.39

time (sec)

N/A 0.135 0.157 0.510 0.502 2.951 1.917 0.745 1.265

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

265 265 149 223 246 767 243 249 602

N.S.

1 1.00 0.56 0.84 0.93 2.89 0.92 0.94 2.27

time (sec)

N/A 0.157 0.255 0.587 0.492 2.515 6.093 1.042 0.235

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

278 278 155 239 244 802 269 258 606

N.S.

1 1.00 0.56 0.86 0.88 2.88 0.97 0.93 2.18

time (sec)

N/A 0.189 0.276 0.536 0.486 3.423 22.070 0.765 1.254

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

292 292 167 243 263 869 296 265 664

N.S.

1 1.00 0.57 0.83 0.90 2.98 1.01 0.91 2.27

time (sec)

N/A 0.221 0.301 0.547 0.537 3.003 70.521 0.856 1.247

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

306 306 175 261 264 884 316 276 678

N.S.

1 1.00 0.57 0.85 0.86 2.89 1.03 0.90 2.22

time (sec)

N/A 0.257 0.363 0.544 0.487 5.241 197.665 0.680 1.266

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

304 304 177 248 283 884 916 283 617

N.S.

1 1.00 0.58 0.82 0.93 2.91 3.01 0.93 2.03

time (sec)

N/A 0.213 0.611 0.549 0.484 3.353 131.109 0.716 1.275

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

289 289 166 250 259 888 937 271 656

N.S.

1 1.00 0.57 0.87 0.90 3.07 3.24 0.94 2.27

time (sec)

N/A 0.169 0.535 0.610 0.493 4.550 66.767 0.608 1.286

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

292 292 167 247 272 901 886 271 652

N.S.

1 1.00 0.57 0.85 0.93 3.09 3.03 0.93 2.23

time (sec)

N/A 0.150 0.730 0.568 0.488 3.068 32.158 0.643 1.277

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

287 287 165 257 256 877 938 273 649

N.S.

1 1.00 0.57 0.90 0.89 3.06 3.27 0.95 2.26

time (sec)

N/A 0.163 0.504 0.520 0.490 3.217 47.692 0.567 1.277

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

304 304 176 248 280 877 1056 281 634

N.S.

1 1.00 0.58 0.82 0.92 2.88 3.47 0.92 2.09

time (sec)

N/A 0.205 0.694 0.595 0.487 3.033 114.130 0.632 0.248

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

317 317 185 262 280 916 0 291 638

N.S.

1 1.00 0.58 0.83 0.88 2.89 0.00 0.92 2.01

time (sec)

N/A 0.234 0.598 0.563 0.503 2.318 0.000 0.503 0.245

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

320 320 186 270 292 986 0 293 686

N.S.

1 1.00 0.58 0.84 0.91 3.08 0.00 0.92 2.14

time (sec)

N/A 0.209 0.778 0.510 0.508 4.802 0.000 0.547 1.293

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD 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 0.195 0.911 0.540 0.487 3.329 0.000 0.576 1.285

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

315 315 181 271 289 982 0 289 695

N.S.

1 1.00 0.57 0.86 0.92 3.12 0.00 0.92 2.21

time (sec)

N/A 0.192 0.788 0.518 0.495 4.341 0.000 0.534 1.288

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

331 331 188 266 311 1022 0 297 690

N.S.

1 1.00 0.57 0.80 0.94 3.09 0.00 0.90 2.08

time (sec)

N/A 0.194 0.630 0.559 0.512 3.215 0.000 0.587 1.286

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

320 320 185 303 291 981 0 293 687

N.S.

1 1.00 0.58 0.95 0.91 3.07 0.00 0.92 2.15

time (sec)

N/A 0.208 0.446 0.609 0.500 2.419 0.000 0.579 1.278

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

333 333 198 268 313 958 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 0.241 0.718 0.591 0.507 3.120 0.000 0.535 0.281

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 23 112 34 33 49 34 20

N.S.

1 1.00 0.51 2.49 0.76 0.73 1.09 0.76 0.44

time (sec)

N/A 0.022 0.032 0.547 0.500 3.293 0.458 0.569 0.125

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

427 427 142 368 0 123 97 0 -1

N.S.

1 1.00 0.33 0.86 0.00 0.29 0.23 0.00 -0.00

time (sec)

N/A 0.400 10.114 0.646 0.000 0.433 78.411 0.000 0.000

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

397 397 133 360 0 113 97 0 -1

N.S.

1 1.00 0.34 0.91 0.00 0.28 0.24 0.00 -0.00

time (sec)

N/A 0.335 10.094 0.591 0.000 0.474 24.193 0.000 0.000

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

363 363 118 342 0 100 97 0 -1

N.S.

1 1.00 0.33 0.94 0.00 0.28 0.27 0.00 -0.00

time (sec)

N/A 0.282 10.072 0.679 0.000 0.371 8.133 0.000 0.000

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

328 328 111 333 0 90 95 0 -1

N.S.

1 1.00 0.34 1.02 0.00 0.27 0.29 0.00 -0.00

time (sec)

N/A 0.232 10.046 0.668 0.000 0.439 2.762 0.000 0.000

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

297 297 82 312 0 71 97 0 -1

N.S.

1 1.00 0.28 1.05 0.00 0.24 0.33 0.00 -0.00

time (sec)

N/A 0.186 10.024 0.578 0.000 0.364 2.838 0.000 0.000

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

300 300 80 310 0 74 100 0 -1

N.S.

1 1.00 0.27 1.03 0.00 0.25 0.33 0.00 -0.00

time (sec)

N/A 0.171 9.793 0.588 0.000 0.550 3.086 0.000 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

298 298 82 303 0 72 104 0 -1

N.S.

1 1.00 0.28 1.02 0.00 0.24 0.35 0.00 -0.00

time (sec)

N/A 0.194 10.031 0.585 0.000 0.856 6.220 0.000 0.000

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

338 338 83 331 0 87 107 0 -1

N.S.

1 1.00 0.25 0.98 0.00 0.26 0.32 0.00 -0.00

time (sec)

N/A 0.233 10.028 0.724 0.000 0.502 21.424 0.000 0.000

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

368 368 88 340 0 92 110 0 -1

N.S.

1 1.00 0.24 0.92 0.00 0.25 0.30 0.00 -0.00

time (sec)

N/A 0.281 10.037 0.695 0.000 0.556 71.454 0.000 0.000

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

438 438 137 384 0 137 199 0 -1

N.S.

1 1.00 0.31 0.88 0.00 0.31 0.45 0.00 -0.00

time (sec)

N/A 0.391 10.123 0.585 0.000 0.684 64.171 0.000 0.000

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

400 400 124 366 0 124 199 0 -1

N.S.

1 1.00 0.31 0.92 0.00 0.31 0.50 0.00 -0.00

time (sec)

N/A 0.338 10.100 0.589 0.000 0.592 19.629 0.000 0.000

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

366 366 116 357 0 114 197 0 -1

N.S.

1 1.00 0.32 0.98 0.00 0.31 0.54 0.00 -0.00

time (sec)

N/A 0.282 10.060 0.589 0.000 0.491 5.915 0.000 0.000

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

333 333 83 338 0 95 199 0 -1

N.S.

1 1.00 0.25 1.02 0.00 0.29 0.60 0.00 -0.00

time (sec)

N/A 0.238 10.031 0.597 0.000 0.619 6.681 0.000 0.000

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

341 341 81 340 0 98 202 0 -1

N.S.

1 1.00 0.24 1.00 0.00 0.29 0.59 0.00 -0.00

time (sec)

N/A 0.229 10.027 0.599 0.000 0.643 6.834 0.000 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

341 341 83 325 0 91 206 0 -1

N.S.

1 1.00 0.24 0.95 0.00 0.27 0.60 0.00 -0.00

time (sec)

N/A 0.223 10.024 0.681 0.000 0.552 11.488 0.000 0.000

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

339 339 84 329 0 90 212 0 -1

N.S.

1 1.00 0.25 0.97 0.00 0.27 0.63 0.00 -0.00

time (sec)

N/A 0.235 10.030 0.706 0.000 0.648 35.142 0.000 0.000

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

339 339 89 337 0 90 219 0 -1

N.S.

1 1.00 0.26 0.99 0.00 0.27 0.65 0.00 -0.00

time (sec)

N/A 0.236 10.039 0.608 0.000 0.564 95.925 0.000 0.000

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

437 437 124 390 0 148 301 0 -1

N.S.

1 1.00 0.28 0.89 0.00 0.34 0.69 0.00 -0.00

time (sec)

N/A 0.393 10.116 0.563 0.000 0.467 35.514 0.000 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

404 404 117 381 0 138 299 0 -1

N.S.

1 1.00 0.29 0.94 0.00 0.34 0.74 0.00 -0.00

time (sec)

N/A 0.338 10.090 0.618 0.000 0.940 9.133 0.000 0.000

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

369 369 85 362 0 119 301 0 -1

N.S.

1 1.00 0.23 0.98 0.00 0.32 0.82 0.00 -0.00

time (sec)

N/A 0.279 10.034 0.589 0.000 0.977 10.559 0.000 0.000

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

379 379 83 364 0 124 304 0 -1

N.S.

1 1.00 0.22 0.96 0.00 0.33 0.80 0.00 -0.00

time (sec)

N/A 0.283 10.040 0.597 0.000 2.173 11.447 0.000 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

378 378 85 359 0 119 308 0 -1

N.S.

1 1.00 0.22 0.95 0.00 0.31 0.81 0.00 -0.00

time (sec)

N/A 0.268 10.028 0.685 0.000 1.062 14.786 0.000 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

376 376 86 367 0 117 314 0 -1

N.S.

1 1.00 0.23 0.98 0.00 0.31 0.84 0.00 -0.00

time (sec)

N/A 0.282 10.032 0.605 0.000 0.644 38.287 0.000 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

377 377 91 366 0 115 321 0 -1

N.S.

1 1.00 0.24 0.97 0.00 0.31 0.85 0.00 -0.00

time (sec)

N/A 0.290 10.032 0.600 0.000 0.636 130.069 0.000 0.000

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

375 375 91 366 0 114 0 0 -1

N.S.

1 1.00 0.24 0.98 0.00 0.30 0.00 0.00 -0.00

time (sec)

N/A 0.294 10.038 0.620 0.000 0.766 0.000 0.000 0.000

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

388 388 142 344 0 99 94 0 -1

N.S.

1 1.00 0.37 0.89 0.00 0.26 0.24 0.00 -0.00

time (sec)

N/A 0.329 10.071 0.556 0.000 0.663 44.810 0.000 0.000

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

356 356 133 336 0 89 94 0 -1

N.S.

1 1.00 0.37 0.94 0.00 0.25 0.26 0.00 -0.00

time (sec)

N/A 0.274 10.067 0.560 0.000 0.897 13.935 0.000 0.000

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

326 326 118 316 0 76 94 0 -1

N.S.

1 1.00 0.36 0.97 0.00 0.23 0.29 0.00 -0.00

time (sec)

N/A 0.227 10.060 0.626 0.000 0.723 4.538 0.000 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

287 287 109 296 0 66 92 0 -1

N.S.

1 1.00 0.38 1.03 0.00 0.23 0.32 0.00 -0.00

time (sec)

N/A 0.173 10.033 0.568 0.000 0.565 2.789 0.000 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

253 253 82 175 0 45 94 0 -1

N.S.

1 1.00 0.32 0.69 0.00 0.18 0.37 0.00 -0.00

time (sec)

N/A 0.131 10.037 0.528 0.000 0.911 1.365 0.000 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

293 293 80 296 0 70 97 0 -1

N.S.

1 1.00 0.27 1.01 0.00 0.24 0.33 0.00 -0.00

time (sec)

N/A 0.171 10.036 0.562 0.000 0.557 3.041 0.000 0.000

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

327 327 82 306 0 73 100 0 -1

N.S.

1 1.00 0.25 0.94 0.00 0.22 0.31 0.00 -0.00

time (sec)

N/A 0.223 10.037 0.565 0.000 0.310 6.003 0.000 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

363 363 83 331 0 87 104 0 -1

N.S.

1 1.00 0.23 0.91 0.00 0.24 0.29 0.00 -0.00

time (sec)

N/A 0.268 10.034 0.558 0.000 0.574 20.919 0.000 0.000

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

360 360 127 318 0 130 94 0 -1

N.S.

1 1.00 0.35 0.88 0.00 0.36 0.26 0.00 -0.00

time (sec)

N/A 0.276 10.059 0.668 0.000 0.478 188.188 0.000 0.000

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

326 326 120 308 0 122 94 0 -1

N.S.

1 1.00 0.37 0.94 0.00 0.37 0.29 0.00 -0.00

time (sec)

N/A 0.227 10.049 0.584 0.000 0.356 52.260 0.000 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

296 296 102 290 0 100 94 0 -1

N.S.

1 1.00 0.34 0.98 0.00 0.34 0.32 0.00 -0.00

time (sec)

N/A 0.183 10.063 0.539 0.000 0.514 12.642 0.000 0.000

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

298 298 113 297 0 111 94 0 -1

N.S.

1 1.00 0.38 1.00 0.00 0.37 0.32 0.00 -0.00

time (sec)

N/A 0.169 10.047 0.539 0.000 1.002 6.380 0.000 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

290 290 107 288 0 95 94 0 -1

N.S.

1 1.00 0.37 0.99 0.00 0.33 0.32 0.00 -0.00

time (sec)

N/A 0.184 10.042 0.536 0.000 0.524 6.360 0.000 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

327 327 100 304 0 121 97 0 -1

N.S.

1 1.00 0.31 0.93 0.00 0.37 0.30 0.00 -0.00

time (sec)

N/A 0.227 10.046 0.575 0.000 0.516 12.124 0.000 0.000

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

357 357 107 307 0 122 100 0 -1

N.S.

1 1.00 0.30 0.86 0.00 0.34 0.28 0.00 -0.00

time (sec)

N/A 0.276 10.048 0.645 0.000 0.511 27.846 0.000 0.000

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

393 393 107 331 0 144 104 0 -1

N.S.

1 1.00 0.27 0.84 0.00 0.37 0.26 0.00 -0.00

time (sec)

N/A 0.331 10.051 0.595 0.000 0.407 76.094 0.000 0.000

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

428 428 183 637 0 207 0 0 -1

N.S.

1 1.00 0.43 1.49 0.00 0.48 0.00 0.00 -0.00

time (sec)

N/A 0.383 10.123 0.640 0.000 1.378 0.000 0.000 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

398 398 165 615 0 189 0 0 -1

N.S.

1 1.00 0.41 1.55 0.00 0.47 0.00 0.00 -0.00

time (sec)

N/A 0.326 10.113 0.627 0.000 0.917 0.000 0.000 0.000

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

368 368 156 607 0 179 0 0 -1

N.S.

1 1.00 0.42 1.65 0.00 0.49 0.00 0.00 -0.00

time (sec)

N/A 0.275 10.110 0.626 0.000 0.879 0.000 0.000 0.000

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

339 339 139 584 0 159 0 0 -1

N.S.

1 1.00 0.41 1.72 0.00 0.47 0.00 0.00 -0.00

time (sec)

N/A 0.226 10.113 0.567 0.000 0.555 0.000 0.000 0.000

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

347 347 149 601 0 171 94 0 -1

N.S.

1 1.00 0.43 1.73 0.00 0.49 0.27 0.00 -0.00

time (sec)

N/A 0.227 10.129 0.554 0.000 0.462 190.402 0.000 0.000

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

341 341 137 583 0 158 94 0 -1

N.S.

1 1.00 0.40 1.71 0.00 0.46 0.28 0.00 -0.00

time (sec)

N/A 0.232 10.124 0.612 0.000 0.527 74.571 0.000 0.000

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

342 342 145 596 0 172 94 0 -1

N.S.

1 1.00 0.42 1.74 0.00 0.50 0.27 0.00 -0.00

time (sec)

N/A 0.230 10.116 0.547 0.000 0.597 38.281 0.000 0.000

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

335 335 140 581 0 157 94 0 -1

N.S.

1 1.00 0.42 1.73 0.00 0.47 0.28 0.00 -0.00

time (sec)

N/A 0.241 10.093 0.546 0.000 0.910 50.942 0.000 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

373 373 137 605 0 182 97 0 -1

N.S.

1 1.00 0.37 1.62 0.00 0.49 0.26 0.00 -0.00

time (sec)

N/A 0.289 10.067 0.615 0.000 0.650 96.953 0.000 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

402 402 137 602 0 181 100 0 -1

N.S.

1 1.00 0.34 1.50 0.00 0.45 0.25 0.00 -0.00

time (sec)

N/A 0.337 10.070 0.617 0.000 0.477 180.526 0.000 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

432 432 137 632 0 203 0 0 -1

N.S.

1 1.00 0.32 1.46 0.00 0.47 0.00 0.00 -0.00

time (sec)

N/A 0.386 10.073 0.624 0.000 0.592 0.000 0.000 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

217 217 128 1255 217 1052 8032 1778 1075

N.S.

1 1.00 0.59 5.78 1.00 4.85 37.01 8.19 4.95

time (sec)

N/A 0.105 0.514 0.559 0.281 2.922 1.858 1.462 1.793

Problem 486

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

169 169 101 168 169 650 4398 1102 695

N.S.

1 1.00 0.60 0.99 1.00 3.85 26.02 6.52 4.11

time (sec)

N/A 0.071 0.235 0.520 0.284 3.282 0.672 1.212 1.481

Problem 487

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

121 121 74 120 121 344 2014 586 371

N.S.

1 1.00 0.61 0.99 1.00 2.84 16.64 4.84 3.07

time (sec)

N/A 0.042 0.094 0.508 0.309 3.885 0.432 1.074 1.280

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 47 72 73 134 658 230 161

N.S.

1 1.00 0.64 0.99 1.00 1.84 9.01 3.15 2.21

time (sec)

N/A 0.022 0.055 0.037 0.286 5.206 0.251 1.316 1.146

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 82 0 0 0 192 0 -1

N.S.

1 1.00 0.90 0.00 0.00 0.00 2.11 0.00 -0.01

time (sec)

N/A 0.028 0.053 0.106 0.000 0.000 2.985 0.000 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 82 0 0 0 770 0 -1

N.S.

1 1.00 0.90 0.00 0.00 0.00 8.46 0.00 -0.01

time (sec)

N/A 0.029 0.055 0.110 0.000 0.000 17.959 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 82 0 0 0 2509 0 -1

N.S.

1 1.00 0.90 0.00 0.00 0.00 27.57 0.00 -0.01

time (sec)

N/A 0.027 0.061 0.147 0.000 0.000 68.766 0.000 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 111 0 0 0 360 0 -1

N.S.

1 1.00 0.77 0.00 0.00 0.00 2.48 0.00 -0.01

time (sec)

N/A 0.054 0.435 0.090 0.000 0.000 11.888 0.000 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 109 0 0 0 238 0 -1

N.S.

1 1.00 0.77 0.00 0.00 0.00 1.69 0.00 -0.01

time (sec)

N/A 0.049 0.256 0.095 0.000 0.000 5.581 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 108 0 0 0 116 0 -1

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.83 0.00 -0.01

time (sec)

N/A 0.047 0.205 0.090 0.000 0.000 1.758 0.000 0.000

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 108 0 0 0 112 0 -1

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.81 0.00 -0.01

time (sec)

N/A 0.045 0.238 0.095 0.000 0.000 2.524 0.000 0.000

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 111 0 0 0 112 0 -1

N.S.

1 1.00 0.77 0.00 0.00 0.00 0.77 0.00 -0.01

time (sec)

N/A 0.050 0.306 0.116 0.000 0.000 5.042 0.000 0.000

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 111 0 0 0 112 0 -1

N.S.

1 1.00 0.77 0.00 0.00 0.00 0.77 0.00 -0.01

time (sec)

N/A 0.048 0.471 0.092 0.000 0.000 75.165 0.000 0.000

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 67 177 0 0 673 0 -1

N.S.

1 1.00 0.96 2.53 0.00 0.00 9.61 0.00 -0.01

time (sec)

N/A 0.017 0.063 0.562 0.000 0.000 3.786 0.000 0.000

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 67 0 0 0 313 0 -1

N.S.

1 1.00 0.96 0.00 0.00 0.00 4.47 0.00 -0.01

time (sec)

N/A 0.013 0.006 0.174 0.000 0.000 1.127 0.000 0.000

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 67 177 0 0 673 0 -1

N.S.

1 1.00 0.96 2.53 0.00 0.00 9.61 0.00 -0.01

time (sec)

N/A 0.016 0.006 0.626 0.000 0.000 1.347 0.000 0.000

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