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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

97 97 93 90 85 90 136 94 78

N.S.

1 1.00 0.96 0.93 0.88 0.93 1.40 0.97 0.80

time (sec)

N/A 0.227 0.067 2.728 0.192 0.243 0.620 0.273 0.033

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

97 97 93 90 85 88 110 94 78

N.S.

1 1.00 0.96 0.93 0.88 0.91 1.13 0.97 0.80

time (sec)

N/A 0.222 0.062 2.739 0.201 0.236 0.733 0.277 0.032

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

95 95 93 90 85 87 134 94 78

N.S.

1 1.00 0.98 0.95 0.89 0.92 1.41 0.99 0.82

time (sec)

N/A 0.228 0.067 2.718 0.192 0.244 0.404 0.277 0.033

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

95 95 92 95 85 87 134 94 78

N.S.

1 1.00 0.97 1.00 0.89 0.92 1.41 0.99 0.82

time (sec)

N/A 0.225 0.053 2.718 0.195 0.247 0.489 0.286 0.038

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

95 95 93 95 85 87 133 94 78

N.S.

1 1.00 0.98 1.00 0.89 0.92 1.40 0.99 0.82

time (sec)

N/A 0.225 0.053 2.810 0.192 0.246 0.537 0.283 0.066

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

95 95 93 89 87 87 133 96 86

N.S.

1 1.00 0.98 0.94 0.92 0.92 1.40 1.01 0.91

time (sec)

N/A 0.230 0.084 2.794 0.195 0.249 0.690 0.270 0.115

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

139 139 126 128 127 132 192 135 119

N.S.

1 1.00 0.91 0.92 0.91 0.95 1.38 0.97 0.86

time (sec)

N/A 0.267 0.102 3.072 0.215 0.243 1.780 0.301 4.923

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

139 139 126 128 127 132 192 135 119

N.S.

1 1.00 0.91 0.92 0.91 0.95 1.38 0.97 0.86

time (sec)

N/A 0.265 0.099 2.931 0.199 0.236 1.305 0.286 0.043

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

139 139 126 128 127 132 192 135 119

N.S.

1 1.00 0.91 0.92 0.91 0.95 1.38 0.97 0.86

time (sec)

N/A 0.267 0.081 2.710 0.207 0.236 0.943 0.278 0.041

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

139 139 126 128 127 130 155 135 119

N.S.

1 1.00 0.91 0.92 0.91 0.94 1.12 0.97 0.86

time (sec)

N/A 0.261 0.098 2.745 0.197 0.250 0.991 0.285 0.040

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

137 137 126 128 127 129 190 135 119

N.S.

1 1.00 0.92 0.93 0.93 0.94 1.39 0.99 0.87

time (sec)

N/A 0.261 0.089 2.745 0.212 0.242 0.641 0.272 0.040

Problem 412

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

137 137 126 136 127 129 189 135 119

N.S.

1 1.00 0.92 0.99 0.93 0.94 1.38 0.99 0.87

time (sec)

N/A 0.261 0.070 2.816 0.195 0.250 0.731 0.276 0.048

Problem 413

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

137 137 126 136 127 129 189 135 119

N.S.

1 1.00 0.92 0.99 0.93 0.94 1.38 0.99 0.87

time (sec)

N/A 0.262 0.101 2.803 0.193 0.243 0.809 0.281 0.042

Problem 414

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

137 137 126 132 129 129 185 137 125

N.S.

1 1.00 0.92 0.96 0.94 0.94 1.35 1.00 0.91

time (sec)

N/A 0.260 0.084 2.802 0.201 0.249 0.965 0.275 0.043

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

311 311 219 230 360 1193 561 436 1202

N.S.

1 1.00 0.70 0.74 1.16 3.84 1.80 1.40 3.86

time (sec)

N/A 0.526 0.297 2.798 0.335 0.265 82.271 0.318 0.426

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

290 290 187 191 263 1393 0 385 435

N.S.

1 1.00 0.64 0.66 0.91 4.80 0.00 1.33 1.50

time (sec)

N/A 0.465 0.237 2.794 0.306 0.271 0.000 0.310 5.461

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

288 288 187 190 324 1131 488 385 1175

N.S.

1 1.00 0.65 0.66 1.12 3.93 1.69 1.34 4.08

time (sec)

N/A 0.463 0.229 2.729 0.287 0.263 16.128 0.295 4.908

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

268 268 156 153 229 1330 386 361 390

N.S.

1 1.00 0.58 0.57 0.85 4.96 1.44 1.35 1.46

time (sec)

N/A 0.431 0.203 2.798 0.295 0.268 48.896 0.297 0.183

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

266 266 155 155 291 1102 423 360 1107

N.S.

1 1.00 0.58 0.58 1.09 4.14 1.59 1.35 4.16

time (sec)

N/A 0.419 0.203 2.818 0.280 0.265 4.427 0.303 5.160

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

260 262 154 153 223 1335 357 344 416

N.S.

1 1.01 0.59 0.59 0.86 5.13 1.37 1.32 1.60

time (sec)

N/A 0.486 0.237 2.824 0.309 0.279 20.535 0.304 4.959

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

260 262 155 155 286 1112 408 344 1201

N.S.

1 1.01 0.60 0.60 1.10 4.28 1.57 1.32 4.62

time (sec)

N/A 0.471 0.216 2.835 0.296 0.268 8.758 0.302 0.232

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

267 268 158 158 229 1352 372 353 417

N.S.

1 1.00 0.59 0.59 0.86 5.06 1.39 1.32 1.56

time (sec)

N/A 0.490 0.218 2.833 0.330 0.274 57.906 0.305 4.866

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

269 270 159 156 293 1117 449 354 1209

N.S.

1 1.00 0.59 0.58 1.09 4.15 1.67 1.32 4.49

time (sec)

N/A 0.480 0.217 2.831 0.291 0.275 63.904 0.297 4.966

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

288 287 192 186 263 1383 0 390 451

N.S.

1 1.00 0.67 0.65 0.91 4.80 0.00 1.35 1.57

time (sec)

N/A 0.509 0.285 2.839 0.293 0.293 0.000 0.306 0.195

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

375 325 255 216 377 1248 0 440 1367

N.S.

1 0.87 0.68 0.58 1.01 3.33 0.00 1.17 3.65

time (sec)

N/A 0.554 0.750 2.806 0.303 0.298 0.000 0.312 4.942

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

346 309 223 177 272 1444 0 413 160

N.S.

1 0.89 0.64 0.51 0.79 4.17 0.00 1.19 0.46

time (sec)

N/A 0.531 0.660 2.809 0.308 0.308 0.000 0.317 5.470

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

346 307 221 175 336 1204 1280 408 1238

N.S.

1 0.89 0.64 0.51 0.97 3.48 3.70 1.18 3.58

time (sec)

N/A 0.524 0.664 2.753 0.341 0.274 66.759 0.321 0.277

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

310 289 204 168 258 1441 0 388 137

N.S.

1 0.93 0.66 0.54 0.83 4.65 0.00 1.25 0.44

time (sec)

N/A 0.511 0.666 2.759 0.289 0.290 0.000 0.295 5.090

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

312 288 202 166 327 1220 1248 388 1267

N.S.

1 0.92 0.65 0.53 1.05 3.91 4.00 1.24 4.06

time (sec)

N/A 0.520 0.666 2.752 0.299 0.279 24.801 0.282 5.790

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

333 308 209 167 260 1449 0 389 138

N.S.

1 0.92 0.63 0.50 0.78 4.35 0.00 1.17 0.41

time (sec)

N/A 0.541 0.704 2.797 0.324 0.269 0.000 0.284 5.256

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

332 312 208 169 326 1219 1418 384 1340

N.S.

1 0.94 0.63 0.51 0.98 3.67 4.27 1.16 4.04

time (sec)

N/A 0.547 0.743 2.756 0.395 0.291 112.772 0.293 5.391

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

363 329 227 179 275 1453 0 401 152

N.S.

1 0.91 0.63 0.49 0.76 4.00 0.00 1.10 0.42

time (sec)

N/A 0.573 0.799 2.749 0.390 0.278 0.000 0.291 5.386

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

440 362 256 230 389 1307 0 451 1426

N.S.

1 0.82 0.58 0.52 0.88 2.97 0.00 1.02 3.24

time (sec)

N/A 0.592 0.835 2.852 0.319 0.280 0.000 0.291 5.636

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

401 344 235 220 306 1539 0 427 197

N.S.

1 0.86 0.59 0.55 0.76 3.84 0.00 1.06 0.49

time (sec)

N/A 0.567 0.847 2.836 0.354 0.305 0.000 0.313 5.364

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

402 343 232 216 374 1310 2302 426 1236

N.S.

1 0.85 0.58 0.54 0.93 3.26 5.73 1.06 3.07

time (sec)

N/A 0.556 0.844 2.766 0.320 0.283 155.054 0.316 0.295

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

364 326 209 213 297 1532 0 416 184

N.S.

1 0.90 0.57 0.59 0.82 4.21 0.00 1.14 0.51

time (sec)

N/A 0.548 0.678 2.720 0.348 0.311 0.000 0.290 5.233

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

364 326 208 213 366 1305 2258 416 1419

N.S.

1 0.90 0.57 0.59 1.01 3.59 6.20 1.14 3.90

time (sec)

N/A 0.546 0.704 2.714 0.304 0.289 140.604 0.310 5.431

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

399 339 238 216 307 1540 0 427 192

N.S.

1 0.85 0.60 0.54 0.77 3.86 0.00 1.07 0.48

time (sec)

N/A 0.570 0.778 2.725 0.289 0.279 0.000 0.286 5.303

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

402 344 241 220 377 1322 0 426 1508

N.S.

1 0.86 0.60 0.55 0.94 3.29 0.00 1.06 3.75

time (sec)

N/A 0.566 0.745 2.716 0.298 0.274 0.000 0.302 5.493

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

439 361 261 233 324 1557 0 444 208

N.S.

1 0.82 0.59 0.53 0.74 3.55 0.00 1.01 0.47

time (sec)

N/A 0.596 0.778 2.708 0.303 0.289 0.000 0.321 0.244

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

328 328 230 259 331 2070 743 531 634

N.S.

1 1.00 0.70 0.79 1.01 6.31 2.27 1.62 1.93

time (sec)

N/A 0.535 0.257 2.965 0.291 0.300 83.476 0.306 5.318

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

326 326 231 260 437 1695 736 531 1564

N.S.

1 1.00 0.71 0.80 1.34 5.20 2.26 1.63 4.80

time (sec)

N/A 0.520 0.237 2.698 0.289 0.280 36.667 0.290 0.232

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

306 306 188 206 282 1992 649 490 574

N.S.

1 1.00 0.61 0.67 0.92 6.51 2.12 1.60 1.88

time (sec)

N/A 0.473 0.221 2.758 0.289 0.277 17.089 0.300 0.178

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

304 304 188 209 390 1653 649 490 1460

N.S.

1 1.00 0.62 0.69 1.28 5.44 2.13 1.61 4.80

time (sec)

N/A 0.476 0.229 2.759 0.290 0.275 12.912 0.288 5.233

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

284 291 178 186 261 1993 510 462 580

N.S.

1 1.02 0.63 0.65 0.92 7.02 1.80 1.63 2.04

time (sec)

N/A 0.433 0.236 2.854 0.309 0.293 42.374 0.306 5.072

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

284 290 178 186 368 1665 604 461 1561

N.S.

1 1.02 0.63 0.65 1.30 5.86 2.13 1.62 5.50

time (sec)

N/A 0.420 0.226 2.772 0.293 0.270 20.416 0.317 0.238

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

283 289 177 188 259 2000 507 455 583

N.S.

1 1.02 0.63 0.66 0.92 7.07 1.79 1.61 2.06

time (sec)

N/A 0.435 0.222 2.841 0.310 0.288 78.014 0.295 5.149

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

283 289 177 188 368 1656 607 455 1564

N.S.

1 1.02 0.63 0.66 1.30 5.85 2.14 1.61 5.53

time (sec)

N/A 0.420 0.224 2.831 0.282 0.278 63.788 0.295 0.260

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

303 310 193 208 281 2013 0 483 591

N.S.

1 1.02 0.64 0.69 0.93 6.64 0.00 1.59 1.95

time (sec)

N/A 0.457 0.245 2.771 0.299 0.284 0.000 0.307 5.101

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

305 312 194 205 389 1665 0 483 1580

N.S.

1 1.02 0.64 0.67 1.28 5.46 0.00 1.58 5.18

time (sec)

N/A 0.445 0.244 2.764 0.313 0.304 0.000 0.291 5.373

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

325 331 238 249 330 2059 0 536 639

N.S.

1 1.02 0.73 0.77 1.02 6.34 0.00 1.65 1.97

time (sec)

N/A 0.482 0.253 2.748 0.320 0.302 0.000 0.300 5.164

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

409 416 301 284 499 1822 0 600 1850

N.S.

1 1.02 0.74 0.69 1.22 4.45 0.00 1.47 4.52

time (sec)

N/A 0.579 0.553 2.882 0.336 0.284 0.000 0.294 0.300

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

374 384 257 230 337 2104 0 552 681

N.S.

1 1.03 0.69 0.61 0.90 5.63 0.00 1.48 1.82

time (sec)

N/A 0.543 0.523 3.015 0.301 0.293 0.000 0.300 5.237

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

386 376 256 230 445 1764 1833 552 1691

N.S.

1 0.97 0.66 0.60 1.15 4.57 4.75 1.43 4.38

time (sec)

N/A 0.695 0.502 2.779 0.311 0.281 152.056 0.298 5.427

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

376 383 227 198 309 2091 0 516 616

N.S.

1 1.02 0.60 0.53 0.82 5.56 0.00 1.37 1.64

time (sec)

N/A 0.552 0.462 2.781 0.324 0.298 0.000 0.309 5.390

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

340 341 227 195 412 1752 1775 511 1636

N.S.

1 1.00 0.67 0.57 1.21 5.15 5.22 1.50 4.81

time (sec)

N/A 0.522 0.444 2.768 0.309 0.294 54.736 0.295 0.297

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

368 373 229 200 304 2104 0 504 657

N.S.

1 1.01 0.62 0.54 0.83 5.72 0.00 1.37 1.79

time (sec)

N/A 0.579 0.485 2.787 0.329 0.494 0.000 0.295 0.248

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

367 372 229 201 415 1778 2008 501 1759

N.S.

1 1.01 0.62 0.55 1.13 4.84 5.47 1.37 4.79

time (sec)

N/A 0.553 0.478 2.780 0.311 0.389 113.349 0.293 5.486

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

376 380 236 197 315 2110 0 505 656

N.S.

1 1.01 0.63 0.52 0.84 5.61 0.00 1.34 1.74

time (sec)

N/A 0.582 0.553 2.704 0.317 0.289 0.000 0.300 0.264

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

376 383 236 201 424 1761 0 509 1746

N.S.

1 1.02 0.63 0.53 1.13 4.68 0.00 1.35 4.64

time (sec)

N/A 0.569 0.536 2.779 0.344 0.265 0.000 0.319 5.945

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

478 507 249 249 390 1472 0 476 7892

N.S.

1 1.06 0.52 0.52 0.82 3.08 0.00 1.00 16.51

time (sec)

N/A 0.665 0.488 2.870 0.309 1.350 0.000 0.359 7.353

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

476 479 247 245 384 1214 0 476 6428

N.S.

1 1.01 0.52 0.51 0.81 2.55 0.00 1.00 13.50

time (sec)

N/A 0.715 0.445 2.831 0.312 0.397 0.000 0.337 6.854

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

463 452 219 234 369 1443 0 457 2609

N.S.

1 0.98 0.47 0.51 0.80 3.12 0.00 0.99 5.63

time (sec)

N/A 0.651 0.362 2.824 0.301 0.335 0.000 0.327 6.271

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

463 452 219 226 367 1083 0 441 5963

N.S.

1 0.98 0.47 0.49 0.79 2.34 0.00 0.95 12.88

time (sec)

N/A 0.647 0.329 2.779 0.295 0.279 0.000 0.327 6.425

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

463 452 219 226 369 1347 0 481 6701

N.S.

1 0.98 0.47 0.49 0.80 2.91 0.00 1.04 14.47

time (sec)

N/A 0.661 0.370 2.746 0.292 0.303 0.000 0.326 5.961

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

463 452 219 234 371 1187 0 441 8785

N.S.

1 0.98 0.47 0.51 0.80 2.56 0.00 0.95 18.97

time (sec)

N/A 0.640 0.385 2.725 0.299 0.385 0.000 0.311 6.750

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

476 505 247 245 390 1481 0 492 6038

N.S.

1 1.06 0.52 0.51 0.82 3.11 0.00 1.03 12.68

time (sec)

N/A 0.650 0.493 2.774 0.300 0.491 0.000 0.333 6.791

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

478 482 249 249 396 1275 0 476 7540

N.S.

1 1.01 0.52 0.52 0.83 2.67 0.00 1.00 15.77

time (sec)

N/A 0.724 0.539 2.734 0.284 2.941 0.000 0.334 7.557

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

498 552 285 269 411 1548 0 487 4643

N.S.

1 1.11 0.57 0.54 0.83 3.11 0.00 0.98 9.32

time (sec)

N/A 0.724 0.611 2.788 0.294 4.898 0.000 0.336 7.334

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

570 549 301 286 494 3074 0 718 22978

N.S.

1 0.96 0.53 0.50 0.87 5.39 0.00 1.26 40.31

time (sec)

N/A 0.884 1.059 3.214 0.304 28.102 0.000 0.378 8.004

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

536 555 307 273 450 3551 0 681 19871

N.S.

1 1.04 0.57 0.51 0.84 6.62 0.00 1.27 37.07

time (sec)

N/A 0.694 0.849 3.230 0.285 5.675 0.000 0.407 7.752

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

532 513 304 271 468 2891 0 669 21485

N.S.

1 0.96 0.57 0.51 0.88 5.43 0.00 1.26 40.39

time (sec)

N/A 0.741 0.785 3.147 0.282 3.988 0.000 0.366 7.806

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

528 540 269 264 436 3417 0 683 18673

N.S.

1 1.02 0.51 0.50 0.83 6.47 0.00 1.29 35.37

time (sec)

N/A 0.687 0.748 3.126 0.300 1.852 0.000 0.377 7.567

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

528 504 268 263 461 2823 0 655 20689

N.S.

1 0.95 0.51 0.50 0.87 5.35 0.00 1.24 39.18

time (sec)

N/A 0.713 0.730 2.740 0.285 2.265 0.000 0.358 7.727

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

536 555 273 270 450 3495 0 701 19453

N.S.

1 1.04 0.51 0.50 0.84 6.52 0.00 1.31 36.29

time (sec)

N/A 0.678 0.934 2.844 0.287 3.035 0.000 0.413 7.469

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

536 515 273 273 489 2973 0 673 21987

N.S.

1 0.96 0.51 0.51 0.91 5.55 0.00 1.26 41.02

time (sec)

N/A 0.737 0.967 2.732 0.293 10.972 0.000 0.381 7.631

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

570 598 332 286 494 3677 0 725 21370

N.S.

1 1.05 0.58 0.50 0.87 6.45 0.00 1.27 37.49

time (sec)

N/A 0.776 1.106 2.801 0.290 12.263 0.000 0.397 9.226

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

570 553 334 286 539 3136 0 718 27743

N.S.

1 0.97 0.59 0.50 0.95 5.50 0.00 1.26 48.67

time (sec)

N/A 0.880 1.101 2.774 0.288 56.621 0.000 0.387 12.034

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

618 647 378 306 551 3783 0 715 17850

N.S.

1 1.05 0.61 0.50 0.89 6.12 0.00 1.16 28.88

time (sec)

N/A 0.903 1.233 2.897 0.294 42.384 0.000 0.437 10.516

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

631 579 328 330 653 5040 0 944 35251

N.S.

1 0.92 0.52 0.52 1.03 7.99 0.00 1.50 55.87

time (sec)

N/A 0.869 1.520 4.195 0.287 52.494 0.000 0.450 9.558

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

628 664 329 330 583 5969 0 963 31866

N.S.

1 1.06 0.52 0.53 0.93 9.50 0.00 1.53 50.74

time (sec)

N/A 0.834 1.099 4.203 0.301 33.452 0.000 0.479 9.307

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

627 579 327 327 654 5005 0 946 36160

N.S.

1 0.92 0.52 0.52 1.04 7.98 0.00 1.51 57.67

time (sec)

N/A 0.853 1.089 2.756 0.295 60.046 0.000 0.465 9.204

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

633 680 361 336 594 5966 0 968 32735

N.S.

1 1.07 0.57 0.53 0.94 9.42 0.00 1.53 51.71

time (sec)

N/A 0.828 1.268 2.750 0.284 43.262 0.000 0.450 9.124

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

633 590 362 336 675 5099 0 960 36997

N.S.

1 0.93 0.57 0.53 1.07 8.06 0.00 1.52 58.45

time (sec)

N/A 0.903 1.248 2.738 0.282 150.895 0.000 0.436 9.341

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

681 723 410 348 668 6173 0 987 33717

N.S.

1 1.06 0.60 0.51 0.98 9.06 0.00 1.45 49.51

time (sec)

N/A 0.948 1.016 2.804 0.299 117.228 0.000 0.474 18.452

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

681 634 410 348 755 0 0 995 44524

N.S.

1 0.93 0.60 0.51 1.11 0.00 0.00 1.46 65.38

time (sec)

N/A 1.035 0.968 2.821 0.286 0.000 0.000 0.459 17.267

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

743 792 462 368 756 6328 0 1000 36917

N.S.

1 1.07 0.62 0.50 1.02 8.52 0.00 1.35 49.69

time (sec)

N/A 1.136 1.029 2.781 0.305 296.875 0.000 0.462 20.153

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

624 575 344 302 617 4935 0 912 34921

N.S.

1 0.92 0.55 0.48 0.99 7.91 0.00 1.46 55.96

time (sec)

N/A 0.887 1.201 4.260 0.310 18.378 0.000 0.480 10.067

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

609 638 340 302 567 5884 0 952 30956

N.S.

1 1.05 0.56 0.50 0.93 9.66 0.00 1.56 50.83

time (sec)

N/A 0.777 1.524 4.132 0.299 14.891 0.000 0.463 9.847

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

601 559 338 300 620 5025 0 904 34586

N.S.

1 0.93 0.56 0.50 1.03 8.36 0.00 1.50 57.55

time (sec)

N/A 0.825 1.588 2.734 0.290 45.924 0.000 0.452 9.733

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

624 661 357 317 610 6126 0 973 32506

N.S.

1 1.06 0.57 0.51 0.98 9.82 0.00 1.56 52.09

time (sec)

N/A 0.844 1.288 2.758 0.300 37.794 0.000 0.488 10.545

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

628 585 361 312 678 5247 0 977 37332

N.S.

1 0.93 0.57 0.50 1.08 8.36 0.00 1.56 59.45

time (sec)

N/A 0.903 1.443 2.763 0.321 147.850 0.000 0.449 10.272

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

676 720 421 323 694 6313 0 1035 33548

N.S.

1 1.07 0.62 0.48 1.03 9.34 0.00 1.53 49.63

time (sec)

N/A 0.971 1.039 2.814 0.305 109.662 0.000 0.457 18.726

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

676 630 425 323 761 0 0 1012 44436

N.S.

1 0.93 0.63 0.48 1.13 0.00 0.00 1.50 65.73

time (sec)

N/A 1.039 0.997 2.817 0.303 0.000 0.000 0.478 15.913

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

731 774 460 343 774 6413 0 1015 36571

N.S.

1 1.06 0.63 0.47 1.06 8.77 0.00 1.39 50.03

time (sec)

N/A 1.125 1.196 2.823 0.295 286.132 0.000 0.527 18.428

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

718 648 383 364 855 0 0 1193 48950

N.S.

1 0.90 0.53 0.51 1.19 0.00 0.00 1.66 68.18

time (sec)

N/A 1.001 1.445 6.990 0.312 0.000 0.000 0.553 12.526

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

703 748 396 368 791 8884 0 1238 44169

N.S.

1 1.06 0.56 0.52 1.13 12.64 0.00 1.76 62.83

time (sec)

N/A 0.962 2.285 6.999 0.307 122.747 0.000 0.559 12.797

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

703 641 392 364 889 0 0 1217 50125

N.S.

1 0.91 0.56 0.52 1.26 0.00 0.00 1.73 71.30

time (sec)

N/A 0.992 2.199 2.772 0.305 0.000 0.000 0.553 12.526

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

739 796 451 381 845 9098 0 1233 45858

N.S.

1 1.08 0.61 0.52 1.14 12.31 0.00 1.67 62.05

time (sec)

N/A 1.052 1.709 2.747 0.329 246.757 0.000 0.574 14.695

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

739 681 450 375 951 0 0 1253 150312

N.S.

1 0.92 0.61 0.51 1.29 0.00 0.00 1.70 203.40

time (sec)

N/A 1.093 1.690 2.873 0.315 0.000 0.000 0.540 23.401

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