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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

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 0.034 0.058 0.103 0.306 0.693 0.761 0.947 0.017

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

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 0.034 0.054 0.099 0.308 0.780 1.723 1.020 0.017

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

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 0.035 0.059 0.105 0.301 0.703 0.549 1.117 0.017

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

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 0.034 0.049 0.080 0.301 0.799 0.648 0.565 0.019

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

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 0.033 0.045 0.082 0.287 0.731 0.730 0.752 0.018

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

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 0.033 0.068 0.090 0.277 0.601 0.928 0.639 0.031

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

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 0.045 0.088 0.115 0.289 0.532 2.334 0.512 0.123

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

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 0.046 0.083 0.112 0.296 0.784 1.667 0.810 0.021

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

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 0.044 0.077 0.109 0.271 0.499 1.187 0.578 0.022

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

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 0.043 0.083 0.105 0.281 0.506 2.160 0.715 0.022

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

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 0.044 0.072 0.120 0.290 0.473 0.791 0.802 0.022

Problem 412

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

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 0.044 0.065 0.084 0.280 0.459 1.030 0.690 0.022

Problem 413

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

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 0.043 0.093 0.082 0.272 0.486 1.122 1.321 0.023

Problem 414

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

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 0.044 0.067 0.083 0.306 0.504 1.305 0.950 0.024

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

311 311 219 230 360 1334 561 436 1202

N.S.

1 1.00 0.70 0.74 1.16 4.29 1.80 1.40 3.86

time (sec)

N/A 0.220 0.236 0.128 0.516 0.627 93.270 1.068 0.232

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

290 290 187 192 263 1701 440 385 435

N.S.

1 1.00 0.64 0.66 0.91 5.87 1.52 1.33 1.50

time (sec)

N/A 0.183 0.207 0.107 0.499 0.652 226.342 0.785 0.178

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

288 288 187 194 324 1268 488 385 1175

N.S.

1 1.00 0.65 0.67 1.12 4.40 1.69 1.34 4.08

time (sec)

N/A 0.174 0.206 0.092 0.485 0.471 17.104 0.882 0.197

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

268 268 156 156 229 1629 87 361 390

N.S.

1 1.00 0.58 0.58 0.85 6.08 0.32 1.35 1.46

time (sec)

N/A 0.160 0.193 0.089 0.502 0.538 4.889 1.036 0.093

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

266 266 155 159 291 1245 423 360 1107

N.S.

1 1.00 0.58 0.60 1.09 4.68 1.59 1.35 4.16

time (sec)

N/A 0.153 0.180 0.095 0.503 0.519 4.694 1.238 0.204

Problem 420

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

260 260 154 153 223 1636 282 344 416

N.S.

1 1.00 0.59 0.59 0.86 6.29 1.08 1.32 1.60

time (sec)

N/A 0.186 0.191 0.099 0.525 0.531 12.516 0.881 0.189

Problem 421

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

260 260 155 155 286 1253 408 344 1201

N.S.

1 1.00 0.60 0.60 1.10 4.82 1.57 1.32 4.62

time (sec)

N/A 0.189 0.181 0.093 0.512 0.494 9.479 0.943 0.211

Problem 422

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

267 267 158 159 229 1648 299 353 417

N.S.

1 1.00 0.59 0.60 0.86 6.17 1.12 1.32 1.56

time (sec)

N/A 0.203 0.192 0.091 0.499 0.505 42.316 0.667 0.190

Problem 423

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

269 269 159 156 293 1252 449 354 1209

N.S.

1 1.00 0.59 0.58 1.09 4.65 1.67 1.32 4.49

time (sec)

N/A 0.193 0.194 0.098 0.505 0.481 68.541 0.737 0.238

Problem 424

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

288 288 192 186 263 1686 428 390 451

N.S.

1 1.00 0.67 0.65 0.91 5.85 1.49 1.35 1.57

time (sec)

N/A 0.215 0.227 0.100 0.499 0.538 184.599 0.628 0.203

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

375 375 255 240 377 1373 0 440 1367

N.S.

1 1.00 0.68 0.64 1.01 3.66 0.00 1.17 3.65

time (sec)

N/A 0.300 0.632 0.118 0.535 0.523 0.000 0.632 0.241

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

346 346 223 200 272 1733 0 413 160

N.S.

1 1.00 0.64 0.58 0.79 5.01 0.00 1.19 0.46

time (sec)

N/A 0.214 0.571 0.116 0.517 1.377 0.000 0.614 0.116

Problem 427

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

346 346 221 199 336 1334 1280 408 1238

N.S.

1 1.00 0.64 0.58 0.97 3.86 3.70 1.18 3.58

time (sec)

N/A 0.212 0.576 0.120 0.543 1.533 70.037 0.619 0.140

Problem 428

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

310 310 204 187 258 1723 173 388 137

N.S.

1 1.00 0.66 0.60 0.83 5.56 0.56 1.25 0.44

time (sec)

N/A 0.187 0.611 0.110 0.515 1.233 16.354 0.589 0.222

Problem 429

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

312 312 202 185 327 1341 1248 388 1267

N.S.

1 1.00 0.65 0.59 1.05 4.30 4.00 1.24 4.06

time (sec)

N/A 0.221 0.588 0.109 0.522 0.919 25.557 0.639 0.245

Problem 430

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

333 331 209 185 260 1739 976 389 138

N.S.

1 0.99 0.63 0.56 0.78 5.22 2.93 1.17 0.41

time (sec)

N/A 0.225 0.590 0.112 0.523 1.083 129.415 0.626 0.216

Problem 431

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

332 329 208 188 326 1340 1418 384 1340

N.S.

1 0.99 0.63 0.57 0.98 4.04 4.27 1.16 4.04

time (sec)

N/A 0.217 0.608 0.115 0.517 1.655 118.601 0.618 0.314

Problem 432

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

363 360 227 200 275 1737 0 401 152

N.S.

1 0.99 0.63 0.55 0.76 4.79 0.00 1.10 0.42

time (sec)

N/A 0.255 0.608 0.134 0.521 2.320 0.000 0.608 0.120

Problem 433

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

440 440 256 234 389 1427 0 451 1426

N.S.

1 1.00 0.58 0.53 0.88 3.24 0.00 1.02 3.24

time (sec)

N/A 0.257 0.735 0.154 0.524 2.121 0.000 0.597 0.254

Problem 434

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

401 401 235 220 306 1813 0 427 197

N.S.

1 1.00 0.59 0.55 0.76 4.52 0.00 1.06 0.49

time (sec)

N/A 0.231 0.767 0.148 0.498 1.196 0.000 0.615 0.219

Problem 435

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

402 402 232 216 374 1420 2302 426 1236

N.S.

1 1.00 0.58 0.54 0.93 3.53 5.73 1.06 3.07

time (sec)

N/A 0.221 0.822 0.128 0.510 1.184 160.525 0.562 0.247

Problem 436

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

364 364 224 213 297 1811 325 416 184

N.S.

1 1.00 0.62 0.59 0.82 4.98 0.89 1.14 0.51

time (sec)

N/A 0.193 0.686 0.091 0.517 1.202 58.560 0.554 0.220

Problem 437

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

364 364 225 213 366 1416 2258 416 1419

N.S.

1 1.00 0.62 0.59 1.01 3.89 6.20 1.14 3.90

time (sec)

N/A 0.207 0.652 0.092 0.527 0.873 144.213 0.594 0.327

Problem 438

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

399 396 238 216 307 1819 0 427 192

N.S.

1 0.99 0.60 0.54 0.77 4.56 0.00 1.07 0.48

time (sec)

N/A 0.262 0.781 0.144 0.499 0.770 0.000 0.619 0.216

Problem 439

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

402 398 241 220 377 1433 0 426 1508

N.S.

1 0.99 0.60 0.55 0.94 3.56 0.00 1.06 3.75

time (sec)

N/A 0.261 0.768 0.151 0.516 1.181 0.000 1.408 0.347

Problem 440

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

439 435 261 235 324 1832 0 444 208

N.S.

1 0.99 0.59 0.54 0.74 4.17 0.00 1.01 0.47

time (sec)

N/A 0.305 0.828 0.170 0.519 1.136 0.000 2.634 0.126

Problem 441

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

328 328 230 259 331 2528 743 531 634

N.S.

1 1.00 0.70 0.79 1.01 7.71 2.27 1.62 1.93

time (sec)

N/A 0.200 0.251 0.090 0.513 0.821 87.959 2.073 0.213

Problem 442

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

326 326 231 268 437 1898 736 531 1564

N.S.

1 1.00 0.71 0.82 1.34 5.82 2.26 1.63 4.80

time (sec)

N/A 0.193 0.249 0.092 0.547 0.633 37.783 1.214 0.216

Problem 443

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

306 306 188 208 282 2441 649 490 574

N.S.

1 1.00 0.61 0.68 0.92 7.98 2.12 1.60 1.88

time (sec)

N/A 0.175 0.225 0.095 0.539 0.646 18.282 1.610 0.086

Problem 444

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

304 304 188 214 390 1862 649 490 1460

N.S.

1 1.00 0.62 0.70 1.28 6.12 2.13 1.61 4.80

time (sec)

N/A 0.174 0.232 0.095 0.515 0.579 13.444 1.305 0.208

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

284 284 178 186 261 2442 435 462 580

N.S.

1 1.00 0.63 0.65 0.92 8.60 1.53 1.63 2.04

time (sec)

N/A 0.192 0.236 0.096 0.516 0.597 32.073 1.299 0.096

Problem 446

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

284 284 178 186 368 1866 604 461 1561

N.S.

1 1.00 0.63 0.65 1.30 6.57 2.13 1.62 5.50

time (sec)

N/A 0.179 0.240 0.092 0.536 0.552 21.604 2.188 0.123

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

283 283 177 188 259 2451 432 455 583

N.S.

1 1.00 0.63 0.66 0.92 8.66 1.53 1.61 2.06

time (sec)

N/A 0.191 0.228 0.097 0.503 0.586 59.728 1.414 0.200

Problem 448

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

283 283 177 188 368 1861 607 455 1564

N.S.

1 1.00 0.63 0.66 1.30 6.58 2.14 1.61 5.53

time (sec)

N/A 0.177 0.227 0.096 0.514 0.551 66.493 1.613 0.133

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

303 303 193 208 281 2459 469 483 591

N.S.

1 1.00 0.64 0.69 0.93 8.12 1.55 1.59 1.95

time (sec)

N/A 0.201 0.243 0.093 0.530 0.655 179.308 1.596 0.209

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

305 305 194 205 389 1866 0 483 1580

N.S.

1 1.00 0.64 0.67 1.28 6.12 0.00 1.58 5.18

time (sec)

N/A 0.183 0.247 0.094 0.494 0.757 0.000 1.107 0.287

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

325 325 238 249 330 2512 0 536 639

N.S.

1 1.00 0.73 0.77 1.02 7.73 0.00 1.65 1.97

time (sec)

N/A 0.212 0.258 0.096 0.523 0.876 0.000 2.344 0.215

Problem 452

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

409 409 301 327 499 2014 0 600 1850

N.S.

1 1.00 0.74 0.80 1.22 4.92 0.00 1.47 4.52

time (sec)

N/A 0.313 0.572 0.146 0.501 0.792 0.000 0.945 0.162

Problem 453

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

374 374 257 266 337 2542 0 552 681

N.S.

1 1.00 0.69 0.71 0.90 6.80 0.00 1.48 1.82

time (sec)

N/A 0.286 0.525 0.133 0.530 0.648 0.000 1.539 0.219

Problem 454

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

386 386 256 269 445 1961 1833 552 1691

N.S.

1 1.00 0.66 0.70 1.15 5.08 4.75 1.43 4.38

time (sec)

N/A 0.359 0.536 0.122 0.552 0.542 158.912 1.552 0.235

Problem 455

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

376 376 227 235 309 2531 173 516 616

N.S.

1 1.00 0.60 0.62 0.82 6.73 0.46 1.37 1.64

time (sec)

N/A 0.288 0.466 0.114 0.517 0.577 40.664 1.098 0.118

Problem 456

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

340 340 227 231 412 1944 1775 511 1636

N.S.

1 1.00 0.67 0.68 1.21 5.72 5.22 1.50 4.81

time (sec)

N/A 0.258 0.469 0.109 0.503 0.545 56.920 1.703 0.135

Problem 457

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

368 368 229 225 304 2547 1443 504 657

N.S.

1 1.00 0.62 0.61 0.83 6.92 3.92 1.37 1.79

time (sec)

N/A 0.294 0.483 0.146 0.505 0.562 202.380 1.815 0.225

Problem 458

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

367 367 229 225 415 1967 2008 501 1759

N.S.

1 1.00 0.62 0.61 1.13 5.36 5.47 1.37 4.79

time (sec)

N/A 0.286 0.493 0.125 0.501 0.506 116.771 0.952 0.248

Problem 459

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

376 376 236 232 315 2549 0 505 656

N.S.

1 1.00 0.63 0.62 0.84 6.78 0.00 1.34 1.74

time (sec)

N/A 0.292 0.562 0.125 0.552 0.576 0.000 1.339 0.136

Problem 460

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

376 376 236 236 424 1955 0 509 1746

N.S.

1 1.00 0.63 0.63 1.13 5.20 0.00 1.35 4.64

time (sec)

N/A 0.285 0.552 0.119 0.551 0.513 0.000 1.018 0.332

Problem 461

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

478 478 249 249 390 1422 0 476 2500

N.S.

1 1.00 0.52 0.52 0.82 2.97 0.00 1.00 5.23

time (sec)

N/A 0.381 0.505 0.110 0.542 1.810 0.000 1.771 1.080

Problem 462

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

476 476 247 245 384 1388 0 476 2500

N.S.

1 1.00 0.52 0.51 0.81 2.92 0.00 1.00 5.25

time (sec)

N/A 0.329 0.460 0.112 0.570 0.687 0.000 1.637 0.864

Problem 463

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

463 463 219 234 369 1385 0 457 2609

N.S.

1 1.00 0.47 0.51 0.80 2.99 0.00 0.99 5.63

time (sec)

N/A 0.244 0.386 0.095 0.501 0.551 0.000 1.116 0.677

Problem 464

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

463 463 219 226 367 1249 0 441 2500

N.S.

1 1.00 0.47 0.49 0.79 2.70 0.00 0.95 5.40

time (sec)

N/A 0.244 0.347 0.089 0.500 0.497 0.000 1.443 0.766

Problem 465

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

463 463 219 226 369 1285 0 481 2500

N.S.

1 1.00 0.47 0.49 0.80 2.78 0.00 1.04 5.40

time (sec)

N/A 0.251 0.406 0.091 0.518 0.510 0.000 1.582 0.638

Problem 466

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

463 463 219 234 371 1365 0 441 2500

N.S.

1 1.00 0.47 0.51 0.80 2.95 0.00 0.95 5.40

time (sec)

N/A 0.239 0.403 0.109 0.502 0.753 0.000 1.456 0.878

Problem 467

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

476 476 247 245 390 1421 0 492 2500

N.S.

1 1.00 0.52 0.51 0.82 2.99 0.00 1.03 5.25

time (sec)

N/A 0.367 0.525 0.113 0.521 0.892 0.000 2.367 0.897

Problem 468

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

478 478 249 249 396 1431 0 476 2500

N.S.

1 1.00 0.52 0.52 0.83 2.99 0.00 1.00 5.23

time (sec)

N/A 0.325 0.530 0.113 0.527 3.533 0.000 3.395 1.312

Problem 469

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

498 498 285 269 411 1484 0 487 2500

N.S.

1 1.00 0.57 0.54 0.83 2.98 0.00 0.98 5.02

time (sec)

N/A 0.456 0.607 0.127 0.563 10.086 0.000 1.376 1.400

Problem 470

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

570 570 301 286 494 3393 0 718 2500

N.S.

1 1.00 0.53 0.50 0.87 5.95 0.00 1.26 4.39

time (sec)

N/A 0.551 1.086 0.121 0.561 69.522 0.000 2.175 1.620

Problem 471

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

536 536 307 273 450 3524 0 681 2500

N.S.

1 1.00 0.57 0.51 0.84 6.57 0.00 1.27 4.66

time (sec)

N/A 0.408 0.894 0.091 0.525 39.888 0.000 1.593 1.343

Problem 472

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

532 532 304 271 468 3224 0 669 2500

N.S.

1 1.00 0.57 0.51 0.88 6.06 0.00 1.26 4.70

time (sec)

N/A 0.355 0.856 0.097 0.529 10.401 0.000 1.321 1.288

Problem 473

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

528 528 269 264 436 3393 0 683 2500

N.S.

1 1.00 0.51 0.50 0.83 6.43 0.00 1.29 4.73

time (sec)

N/A 0.390 0.795 0.093 0.507 12.185 0.000 2.101 1.268

Problem 474

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

528 528 268 263 461 3171 0 655 2500

N.S.

1 1.00 0.51 0.50 0.87 6.01 0.00 1.24 4.73

time (sec)

N/A 0.313 0.788 0.085 0.520 4.532 0.000 1.418 1.259

Problem 475

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

536 536 273 270 450 3457 0 701 2500

N.S.

1 1.00 0.51 0.50 0.84 6.45 0.00 1.31 4.66

time (sec)

N/A 0.408 1.006 0.092 0.540 12.243 0.000 1.601 1.234

Problem 476

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

536 536 273 273 489 3310 0 673 2500

N.S.

1 1.00 0.51 0.51 0.91 6.18 0.00 1.26 4.66

time (sec)

N/A 0.362 1.009 0.092 0.563 12.906 0.000 1.777 1.418

Problem 477

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

570 570 332 286 494 3630 0 725 2500

N.S.

1 1.00 0.58 0.50 0.87 6.37 0.00 1.27 4.39

time (sec)

N/A 0.516 1.166 0.128 0.538 24.132 0.000 1.785 2.336

Problem 478

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

570 570 334 286 539 3439 0 718 2500

N.S.

1 1.00 0.59 0.50 0.95 6.03 0.00 1.26 4.39

time (sec)

N/A 0.550 1.208 0.135 0.516 71.491 0.000 1.641 3.829

Problem 479

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

618 618 378 306 551 3728 0 715 2500

N.S.

1 1.00 0.61 0.50 0.89 6.03 0.00 1.16 4.05

time (sec)

N/A 0.651 1.276 0.138 0.523 100.565 0.000 1.805 3.003

Problem 480

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

631 631 328 330 653 5496 0 944 2500

N.S.

1 1.00 0.52 0.52 1.03 8.71 0.00 1.50 3.96

time (sec)

N/A 0.546 1.607 0.091 0.542 100.799 0.000 2.294 2.318

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

628 628 329 330 583 0 0 963 2500

N.S.

1 1.00 0.52 0.53 0.93 0.00 0.00 1.53 3.98

time (sec)

N/A 0.522 1.166 0.089 0.519 0.000 0.000 1.363 2.296

Problem 482

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

627 627 327 327 654 5450 0 946 2500

N.S.

1 1.00 0.52 0.52 1.04 8.69 0.00 1.51 3.99

time (sec)

N/A 0.484 1.180 0.092 0.513 88.785 0.000 1.811 2.346

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

633 633 361 336 594 0 0 968 2500

N.S.

1 1.00 0.57 0.53 0.94 0.00 0.00 1.53 3.95

time (sec)

N/A 0.553 1.378 0.086 0.521 0.000 0.000 1.048 2.372

Problem 484

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

633 633 362 336 675 5548 0 960 2500

N.S.

1 1.00 0.57 0.53 1.07 8.76 0.00 1.52 3.95

time (sec)

N/A 0.572 1.408 0.086 0.522 257.054 0.000 2.852 2.333

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

681 681 410 348 668 0 0 987 2500

N.S.

1 1.00 0.60 0.51 0.98 0.00 0.00 1.45 3.67

time (sec)

N/A 0.677 1.152 0.185 0.538 0.000 0.000 1.989 6.014

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

681 681 410 348 755 0 0 995 2500

N.S.

1 1.00 0.60 0.51 1.11 0.00 0.00 1.46 3.67

time (sec)

N/A 0.624 1.615 0.187 0.535 0.000 0.000 1.735 5.865

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

743 743 462 368 756 0 0 1000 2500

N.S.

1 1.00 0.62 0.50 1.02 0.00 0.00 1.35 3.36

time (sec)

N/A 0.826 1.175 0.227 0.609 0.000 0.000 2.921 7.028

Problem 488

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

624 624 344 302 617 5375 0 912 2500

N.S.

1 1.00 0.55 0.48 0.99 8.61 0.00 1.46 4.01

time (sec)

N/A 0.489 1.306 0.111 0.538 32.217 0.000 1.921 2.169

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

609 609 340 302 567 5814 0 952 2500

N.S.

1 1.00 0.56 0.50 0.93 9.55 0.00 1.56 4.11

time (sec)

N/A 0.520 1.606 0.118 0.511 63.140 0.000 1.107 2.114

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

601 601 338 300 620 5474 0 904 2500

N.S.

1 1.00 0.56 0.50 1.03 9.11 0.00 1.50 4.16

time (sec)

N/A 0.451 1.732 0.114 0.510 83.045 0.000 2.561 2.072

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

624 624 357 317 610 6028 0 973 2500

N.S.

1 1.00 0.57 0.51 0.98 9.66 0.00 1.56 4.01

time (sec)

N/A 0.574 1.423 0.115 0.544 84.733 0.000 1.638 2.454

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

628 628 361 312 678 0 0 977 2500

N.S.

1 1.00 0.57 0.50 1.08 0.00 0.00 1.56 3.98

time (sec)

N/A 0.581 1.672 0.111 0.525 0.000 0.000 1.100 2.333

Problem 493

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

676 676 421 323 694 6207 0 1035 2500

N.S.

1 1.00 0.62 0.48 1.03 9.18 0.00 1.53 3.70

time (sec)

N/A 0.712 1.196 0.191 0.561 270.749 0.000 1.297 5.959

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

676 676 425 323 761 0 0 1012 2500

N.S.

1 1.00 0.63 0.48 1.13 0.00 0.00 1.50 3.70

time (sec)

N/A 0.644 1.278 0.189 0.531 0.000 0.000 1.515 5.609

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

731 731 460 343 774 0 0 1015 2500

N.S.

1 1.00 0.63 0.47 1.06 0.00 0.00 1.39 3.42

time (sec)

N/A 0.857 1.332 0.204 0.580 0.000 0.000 2.163 6.625

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

718 718 383 364 855 0 0 1193 2500

N.S.

1 1.00 0.53 0.51 1.19 0.00 0.00 1.66 3.48

time (sec)

N/A 0.676 1.775 0.175 0.580 0.000 0.000 1.617 3.340

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

703 703 396 368 791 0 0 1238 2500

N.S.

1 1.00 0.56 0.52 1.13 0.00 0.00 1.76 3.56

time (sec)

N/A 0.677 2.593 0.179 0.514 0.000 0.000 1.969 3.633

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

703 703 392 364 889 0 0 1217 2500

N.S.

1 1.00 0.56 0.52 1.26 0.00 0.00 1.73 3.56

time (sec)

N/A 0.684 2.803 0.179 0.555 0.000 0.000 1.876 3.537

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

739 739 451 381 845 0 0 1233 2500

N.S.

1 1.00 0.61 0.52 1.14 0.00 0.00 1.67 3.38

time (sec)

N/A 0.757 2.045 0.181 0.535 0.000 0.000 2.353 4.253

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

739 739 450 375 951 0 0 1253 2500

N.S.

1 1.00 0.61 0.51 1.29 0.00 0.00 1.70 3.38

time (sec)

N/A 0.674 3.197 0.187 0.544 0.000 0.000 2.588 8.100

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