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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

261 287 177 423 0 596 0 362 0

N.S.

1 1.10 0.68 1.62 0.00 2.28 0.00 1.39 0.00

time (sec)

N/A 1.857 3.275 1.047 0.000 0.317 0.000 1.593 0.000

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

216 232 161 377 0 557 0 276 0

N.S.

1 1.07 0.75 1.75 0.00 2.58 0.00 1.28 0.00

time (sec)

N/A 1.479 2.251 1.005 0.000 0.328 0.000 1.498 0.000

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

169 178 144 306 0 484 0 258 0

N.S.

1 1.05 0.85 1.81 0.00 2.86 0.00 1.53 0.00

time (sec)

N/A 1.139 1.086 0.970 0.000 0.293 0.000 1.396 0.000

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 132 131 335 0 475 0 170 0

N.S.

1 1.05 1.04 2.66 0.00 3.77 0.00 1.35 0.00

time (sec)

N/A 0.762 1.009 0.911 0.000 0.308 0.000 1.582 0.000

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 124 206 325 0 475 0 170 0

N.S.

1 0.98 1.63 2.58 0.00 3.77 0.00 1.35 0.00

time (sec)

N/A 0.493 1.056 0.690 0.000 0.289 0.000 1.957 0.000

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

164 176 299 376 0 670 0 0 0

N.S.

1 1.07 1.82 2.29 0.00 4.09 0.00 0.00 0.00

time (sec)

N/A 1.034 7.526 0.535 0.000 3.598 0.000 0.000 0.000

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

207 223 208 899 0 739 0 464 0

N.S.

1 1.08 1.00 4.34 0.00 3.57 0.00 2.24 0.00

time (sec)

N/A 1.450 3.537 2.102 0.000 4.616 0.000 2.264 0.000

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 139 101 159 266 164 0 299 251

N.S.

1 0.91 0.66 1.05 1.75 1.08 0.00 1.97 1.65

time (sec)

N/A 0.823 0.694 0.824 0.218 0.265 0.000 0.347 20.832

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 123 84 136 218 143 0 254 211

N.S.

1 0.97 0.66 1.07 1.72 1.13 0.00 2.00 1.66

time (sec)

N/A 0.828 0.415 0.638 0.211 0.268 0.000 0.319 21.156

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 94 63 106 155 114 0 205 165

N.S.

1 1.02 0.68 1.15 1.68 1.24 0.00 2.23 1.79

time (sec)

N/A 0.603 1.477 0.499 0.228 0.270 0.000 0.313 20.561

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 67 51 85 116 109 0 141 176

N.S.

1 1.06 0.81 1.35 1.84 1.73 0.00 2.24 2.79

time (sec)

N/A 0.265 1.084 0.385 0.213 0.291 0.000 0.316 18.119

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 71 74 92 92 0 134 159

N.S.

1 1.00 1.54 1.61 2.00 2.00 0.00 2.91 3.46

time (sec)

N/A 0.486 0.019 0.308 0.225 0.285 0.000 0.325 16.984

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 66 59 75 89 68 0 131 159

N.S.

1 1.06 0.95 1.21 1.44 1.10 0.00 2.11 2.56

time (sec)

N/A 0.539 0.092 0.224 0.212 0.271 0.000 0.308 17.372

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 84 64 61 98 62 0 171 100

N.S.

1 1.02 0.78 0.74 1.20 0.76 0.00 2.09 1.22

time (sec)

N/A 0.570 0.453 0.288 0.238 0.258 0.000 0.306 16.681

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 100 97 78 132 87 0 218 209

N.S.

1 0.98 0.95 0.76 1.29 0.85 0.00 2.14 2.05

time (sec)

N/A 0.694 0.254 0.384 0.209 0.267 0.000 0.315 19.295

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 129 94 93 166 108 0 263 248

N.S.

1 0.91 0.67 0.66 1.18 0.77 0.00 1.87 1.76

time (sec)

N/A 0.718 0.310 0.477 0.210 0.254 0.000 0.335 19.389

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

222 215 130 248 477 203 0 392 337

N.S.

1 0.97 0.59 1.12 2.15 0.91 0.00 1.77 1.52

time (sec)

N/A 1.334 7.122 0.865 0.269 0.262 0.000 0.382 19.828

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

190 193 114 200 360 180 0 341 286

N.S.

1 1.02 0.60 1.05 1.89 0.95 0.00 1.79 1.51

time (sec)

N/A 1.231 5.728 0.755 0.230 0.269 0.000 0.357 16.637

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 140 88 185 309 157 0 290 245

N.S.

1 0.95 0.60 1.26 2.10 1.07 0.00 1.97 1.67

time (sec)

N/A 0.854 3.731 0.648 0.225 0.282 0.000 0.355 19.283

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 128 75 139 210 150 0 250 421

N.S.

1 1.07 0.62 1.16 1.75 1.25 0.00 2.08 3.51

time (sec)

N/A 0.705 2.702 0.518 0.270 0.271 0.000 0.353 17.043

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 127 129 155 192 143 0 204 244

N.S.

1 1.05 1.07 1.28 1.59 1.18 0.00 1.69 2.02

time (sec)

N/A 0.759 2.172 0.457 0.226 0.274 0.000 0.349 16.984

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 129 329 124 151 130 0 198 232

N.S.

1 1.01 2.57 0.97 1.18 1.02 0.00 1.55 1.81

time (sec)

N/A 0.707 4.909 0.340 0.231 0.273 0.000 0.336 16.910

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 142 121 97 160 108 0 235 223

N.S.

1 1.06 0.90 0.72 1.19 0.81 0.00 1.75 1.66

time (sec)

N/A 0.717 0.855 0.323 0.241 0.279 0.000 0.345 16.363

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 142 114 84 190 99 0 248 174

N.S.

1 0.95 0.77 0.56 1.28 0.66 0.00 1.66 1.17

time (sec)

N/A 0.852 0.470 0.358 0.240 0.253 0.000 0.326 16.176

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

187 193 132 101 236 122 0 299 289

N.S.

1 1.03 0.71 0.54 1.26 0.65 0.00 1.60 1.55

time (sec)

N/A 1.097 0.393 0.466 0.250 0.263 0.000 0.335 18.990

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

213 206 170 126 296 145 0 350 333

N.S.

1 0.97 0.80 0.59 1.39 0.68 0.00 1.64 1.56

time (sec)

N/A 1.145 0.569 0.525 0.230 0.282 0.000 0.359 18.677

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

274 269 150 280 649 226 0 443 381

N.S.

1 0.98 0.55 1.02 2.37 0.82 0.00 1.62 1.39

time (sec)

N/A 1.719 5.983 1.032 0.247 0.274 0.000 0.406 20.609

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

216 208 134 251 559 203 0 392 337

N.S.

1 0.96 0.62 1.16 2.59 0.94 0.00 1.81 1.56

time (sec)

N/A 0.943 6.021 0.894 0.247 0.265 0.000 0.386 20.430

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

175 158 109 222 439 180 0 341 292

N.S.

1 0.90 0.62 1.27 2.51 1.03 0.00 1.95 1.67

time (sec)

N/A 0.637 5.761 0.796 0.236 0.271 0.000 0.395 20.232

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

162 173 94 206 352 173 0 301 611

N.S.

1 1.07 0.58 1.27 2.17 1.07 0.00 1.86 3.77

time (sec)

N/A 0.954 5.498 0.637 0.239 0.270 0.000 0.383 18.631

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 164 136 203 274 168 0 288 523

N.S.

1 1.05 0.87 1.30 1.76 1.08 0.00 1.85 3.35

time (sec)

N/A 0.988 5.202 0.593 0.229 0.285 0.000 0.368 17.924

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 164 406 186 237 165 0 280 329

N.S.

1 0.96 2.37 1.09 1.39 0.96 0.00 1.64 1.92

time (sec)

N/A 0.967 8.032 0.503 0.224 0.279 0.000 0.356 17.838

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 176 379 148 210 156 0 281 290

N.S.

1 1.04 2.24 0.88 1.24 0.92 0.00 1.66 1.72

time (sec)

N/A 1.020 5.178 0.468 0.246 0.270 0.000 0.358 17.627

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 194 147 114 240 131 0 286 243

N.S.

1 1.06 0.80 0.62 1.31 0.72 0.00 1.56 1.33

time (sec)

N/A 1.019 2.173 0.421 0.226 0.275 0.000 0.378 17.341

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 162 134 107 282 122 0 299 289

N.S.

1 0.91 0.75 0.60 1.58 0.68 0.00 1.67 1.61

time (sec)

N/A 0.720 1.348 0.421 0.237 0.257 0.000 0.360 19.349

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

235 243 170 126 354 145 0 350 333

N.S.

1 1.03 0.72 0.54 1.51 0.62 0.00 1.49 1.42

time (sec)

N/A 1.466 0.714 0.501 0.219 0.265 0.000 0.378 19.596

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

265 260 204 147 425 168 0 401 377

N.S.

1 0.98 0.77 0.55 1.60 0.63 0.00 1.51 1.42

time (sec)

N/A 1.546 0.943 0.620 0.253 0.271 0.000 0.381 19.240

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

252 234 154 280 731 226 0 443 381

N.S.

1 0.93 0.61 1.11 2.90 0.90 0.00 1.76 1.51

time (sec)

N/A 0.976 6.280 1.079 0.241 0.290 0.000 0.412 20.050

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

209 182 126 251 638 203 0 392 338

N.S.

1 0.87 0.60 1.20 3.05 0.97 0.00 1.88 1.62

time (sec)

N/A 0.664 5.966 0.901 0.232 0.284 0.000 0.413 20.029

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

195 214 113 258 482 196 0 352 996

N.S.

1 1.10 0.58 1.32 2.47 1.01 0.00 1.81 5.11

time (sec)

N/A 1.176 6.319 0.811 0.229 0.284 0.000 0.389 18.002

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

196 213 179 254 416 191 0 339 1346

N.S.

1 1.09 0.91 1.30 2.12 0.97 0.00 1.73 6.87

time (sec)

N/A 1.260 5.707 0.760 0.229 0.273 0.000 0.382 17.970

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

209 213 524 231 320 191 0 347 625

N.S.

1 1.02 2.51 1.11 1.53 0.91 0.00 1.66 2.99

time (sec)

N/A 1.273 9.823 0.666 0.250 0.283 0.000 0.379 18.278

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

217 222 1518 204 296 191 0 347 373

N.S.

1 1.02 7.00 0.94 1.36 0.88 0.00 1.60 1.72

time (sec)

N/A 1.330 12.399 0.647 0.228 0.280 0.000 0.393 17.756

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

217 233 423 167 290 179 0 332 1244

N.S.

1 1.07 1.95 0.77 1.34 0.82 0.00 1.53 5.73

time (sec)

N/A 1.370 10.029 0.561 0.242 0.282 0.000 0.383 17.686

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

225 244 182 139 332 154 0 337 1151

N.S.

1 1.08 0.81 0.62 1.48 0.68 0.00 1.50 5.12

time (sec)

N/A 1.333 3.826 0.511 0.225 0.272 0.000 0.394 17.130

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

213 186 147 128 400 145 0 350 334

N.S.

1 0.87 0.69 0.60 1.88 0.68 0.00 1.64 1.57

time (sec)

N/A 0.768 0.926 0.503 0.224 0.264 0.000 0.372 19.175

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

278 295 204 149 483 168 0 401 377

N.S.

1 1.06 0.73 0.54 1.74 0.60 0.00 1.44 1.36

time (sec)

N/A 1.857 0.624 0.612 0.272 0.270 0.000 0.383 18.759

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

303 307 237 168 579 191 0 452 421

N.S.

1 1.01 0.78 0.55 1.91 0.63 0.00 1.49 1.39

time (sec)

N/A 1.931 1.298 0.710 0.258 0.269 0.000 0.401 18.917

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 154 1099 217 611 216 0 285 203

N.S.

1 0.84 6.01 1.19 3.34 1.18 0.00 1.56 1.11

time (sec)

N/A 0.887 7.723 0.424 0.231 0.260 0.000 0.333 17.217

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 126 898 180 485 195 0 243 165

N.S.

1 0.85 6.07 1.22 3.28 1.32 0.00 1.64 1.11

time (sec)

N/A 0.735 7.671 0.350 0.248 0.273 0.000 0.340 16.785

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 110 392 134 356 174 0 173 124

N.S.

1 0.92 3.29 1.13 2.99 1.46 0.00 1.45 1.04

time (sec)

N/A 0.698 4.663 0.278 0.232 0.272 0.000 0.343 16.539

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 65 255 93 218 128 0 119 79

N.S.

1 1.03 4.05 1.48 3.46 2.03 0.00 1.89 1.25

time (sec)

N/A 0.546 2.271 0.206 0.226 0.255 0.000 0.325 16.550

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 54 163 60 146 91 0 92 113

N.S.

1 1.04 3.13 1.15 2.81 1.75 0.00 1.77 2.17

time (sec)

N/A 0.488 0.914 0.138 0.309 0.252 0.000 0.326 16.353

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 63 66 44 165 64 0 90 66

N.S.

1 1.02 1.06 0.71 2.66 1.03 0.00 1.45 1.06

time (sec)

N/A 0.454 0.425 0.178 0.307 0.271 0.000 0.308 16.021

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 98 213 67 273 90 0 137 111

N.S.

1 0.91 1.97 0.62 2.53 0.83 0.00 1.27 1.03

time (sec)

N/A 0.563 0.816 0.227 0.323 0.250 0.000 0.298 16.804

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 118 307 87 400 113 0 207 153

N.S.

1 0.85 2.21 0.63 2.88 0.81 0.00 1.49 1.10

time (sec)

N/A 0.594 2.184 0.259 0.323 0.255 0.000 0.310 17.937

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

174 142 393 108 525 132 0 249 189

N.S.

1 0.82 2.26 0.62 3.02 0.76 0.00 1.43 1.09

time (sec)

N/A 0.707 2.307 0.292 0.331 0.262 0.000 0.312 18.740

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

194 178 1069 219 567 271 0 303 218

N.S.

1 0.92 5.51 1.13 2.92 1.40 0.00 1.56 1.12

time (sec)

N/A 1.091 7.724 0.411 0.240 0.275 0.000 0.331 16.775

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 166 901 175 431 252 0 235 170

N.S.

1 0.98 5.33 1.04 2.55 1.49 0.00 1.39 1.01

time (sec)

N/A 1.028 8.003 0.342 0.307 0.276 0.000 0.350 16.132

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 120 312 134 287 198 0 181 122

N.S.

1 1.07 2.79 1.20 2.56 1.77 0.00 1.62 1.09

time (sec)

N/A 0.825 3.125 0.260 0.256 0.259 0.000 0.320 16.073

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 90 219 79 190 133 0 144 83

N.S.

1 1.11 2.70 0.98 2.35 1.64 0.00 1.78 1.02

time (sec)

N/A 0.591 2.308 0.172 0.237 0.290 0.000 0.323 15.894

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 78 175 53 164 100 0 116 113

N.S.

1 1.05 2.36 0.72 2.22 1.35 0.00 1.57 1.53

time (sec)

N/A 0.479 0.771 0.142 0.311 0.264 0.000 0.303 16.117

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 107 279 79 235 127 0 152 110

N.S.

1 1.07 2.79 0.79 2.35 1.27 0.00 1.52 1.10

time (sec)

N/A 0.713 1.543 0.220 0.313 0.266 0.000 0.313 15.903

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 152 377 100 352 153 0 198 159

N.S.

1 0.97 2.42 0.64 2.26 0.98 0.00 1.27 1.02

time (sec)

N/A 0.864 2.607 0.268 0.316 0.278 0.000 0.308 16.108

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 172 473 118 487 173 0 266 202

N.S.

1 0.93 2.56 0.64 2.63 0.94 0.00 1.44 1.09

time (sec)

N/A 0.927 3.029 0.291 0.324 0.265 0.000 0.312 15.926

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

216 219 1081 198 493 328 0 288 227

N.S.

1 1.01 5.00 0.92 2.28 1.52 0.00 1.33 1.05

time (sec)

N/A 1.437 7.771 0.405 0.243 0.274 0.000 0.348 16.043

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 177 839 154 350 263 0 234 176

N.S.

1 1.10 5.21 0.96 2.17 1.63 0.00 1.45 1.09

time (sec)

N/A 1.194 7.797 0.297 0.265 0.270 0.000 0.342 16.057

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 141 277 99 232 193 0 180 134

N.S.

1 1.07 2.10 0.75 1.76 1.46 0.00 1.36 1.02

time (sec)

N/A 0.938 3.747 0.188 0.243 0.270 0.000 0.339 15.966

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 112 156 64 179 102 0 115 73

N.S.

1 1.02 1.42 0.58 1.63 0.93 0.00 1.05 0.66

time (sec)

N/A 0.581 1.362 0.172 0.228 0.254 0.000 0.307 16.053

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 125 289 73 205 147 0 153 158

N.S.

1 1.09 2.51 0.63 1.78 1.28 0.00 1.33 1.37

time (sec)

N/A 0.697 2.024 0.155 0.316 0.274 0.000 0.321 16.337

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 157 419 100 295 182 0 206 164

N.S.

1 1.11 2.97 0.71 2.09 1.29 0.00 1.46 1.16

time (sec)

N/A 1.033 3.847 0.250 0.315 0.272 0.000 0.322 16.089

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

201 205 557 118 411 211 0 252 215

N.S.

1 1.02 2.77 0.59 2.04 1.05 0.00 1.25 1.07

time (sec)

N/A 1.216 4.170 0.305 0.319 0.259 0.000 0.340 16.236

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

237 229 655 139 547 229 0 320 259

N.S.

1 0.97 2.76 0.59 2.31 0.97 0.00 1.35 1.09

time (sec)

N/A 1.318 5.274 0.333 0.341 0.274 0.000 0.346 15.898

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

254 266 1322 216 556 400 0 339 296

N.S.

1 1.05 5.20 0.85 2.19 1.57 0.00 1.33 1.17

time (sec)

N/A 1.860 9.934 0.432 0.251 0.280 0.000 0.378 15.998

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

204 228 1208 175 411 328 0 285 250

N.S.

1 1.12 5.92 0.86 2.01 1.61 0.00 1.40 1.23

time (sec)

N/A 1.590 9.411 0.336 0.225 0.290 0.000 0.355 16.043

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

173 192 335 123 313 248 0 248 198

N.S.

1 1.11 1.94 0.71 1.81 1.43 0.00 1.43 1.14

time (sec)

N/A 1.268 3.678 0.222 0.232 0.268 0.000 0.361 15.846

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 159 200 90 259 135 0 171 99

N.S.

1 1.07 1.35 0.61 1.75 0.91 0.00 1.16 0.67

time (sec)

N/A 0.921 2.031 0.194 0.230 0.250 0.000 0.332 15.975

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 150 231 86 259 135 0 171 99

N.S.

1 0.97 1.50 0.56 1.68 0.88 0.00 1.11 0.64

time (sec)

N/A 0.744 2.154 0.195 0.221 0.249 0.000 0.339 15.931

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 168 405 97 286 192 0 220 229

N.S.

1 1.14 2.74 0.66 1.93 1.30 0.00 1.49 1.55

time (sec)

N/A 0.933 4.558 0.178 0.308 0.251 0.000 0.345 16.376

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

176 200 567 118 356 234 0 256 293

N.S.

1 1.14 3.22 0.67 2.02 1.33 0.00 1.45 1.66

time (sec)

N/A 1.336 7.042 0.291 0.320 0.261 0.000 0.341 17.557

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

239 251 345 138 474 267 0 302 285

N.S.

1 1.05 1.44 0.58 1.98 1.12 0.00 1.26 1.19

time (sec)

N/A 1.600 9.634 0.336 0.324 0.277 0.000 0.353 15.864

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

239 241 400 196 0 151 0 0 724

N.S.

1 1.01 1.67 0.82 0.00 0.63 0.00 0.00 3.03

time (sec)

N/A 1.358 7.925 1.098 0.000 0.263 0.000 0.000 27.236

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 200 150 163 0 131 0 0 600

N.S.

1 1.04 0.78 0.84 0.00 0.68 0.00 0.00 3.11

time (sec)

N/A 1.091 1.750 0.848 0.000 0.257 0.000 0.000 29.307

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 165 116 130 0 110 0 0 479

N.S.

1 1.12 0.79 0.88 0.00 0.75 0.00 0.00 3.26

time (sec)

N/A 0.920 1.688 0.917 0.000 0.255 0.000 0.000 21.753

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 115 87 89 0 89 0 0 246

N.S.

1 1.11 0.84 0.86 0.00 0.86 0.00 0.00 2.37

time (sec)

N/A 0.595 1.294 0.891 0.000 0.272 0.000 0.000 19.924

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 108 101 154 0 304 0 0 0

N.S.

1 1.08 1.01 1.54 0.00 3.04 0.00 0.00 0.00

time (sec)

N/A 0.589 1.739 1.011 0.000 0.321 0.000 0.000 0.000

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 109 94 305 939 272 0 0 0

N.S.

1 1.11 0.96 3.11 9.58 2.78 0.00 0.00 0.00

time (sec)

N/A 0.641 1.658 2.204 0.473 0.328 0.000 0.000 0.000

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 121 115 460 1996 320 0 0 0

N.S.

1 1.03 0.98 3.93 17.06 2.74 0.00 0.00 0.00

time (sec)

N/A 0.641 0.492 1.950 0.616 0.350 0.000 0.000 0.000

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 163 152 509 3770 364 0 0 0

N.S.

1 1.00 0.93 3.12 23.13 2.23 0.00 0.00 0.00

time (sec)

N/A 0.874 0.382 1.903 0.774 0.358 0.000 0.000 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

209 204 90 560 9618 404 0 0 0

N.S.

1 0.98 0.43 2.68 46.02 1.93 0.00 0.00 0.00

time (sec)

N/A 1.059 0.173 2.258 1.077 0.438 0.000 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

243 257 183 197 0 157 0 0 852

N.S.

1 1.06 0.75 0.81 0.00 0.65 0.00 0.00 3.51

time (sec)

N/A 1.560 2.440 1.019 0.000 0.260 0.000 0.000 28.851

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

187 201 150 164 0 135 0 0 709

N.S.

1 1.07 0.80 0.88 0.00 0.72 0.00 0.00 3.79

time (sec)

N/A 1.146 2.383 0.991 0.000 0.270 0.000 0.000 26.667

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 149 118 131 0 113 0 0 585

N.S.

1 1.03 0.82 0.91 0.00 0.78 0.00 0.00 4.06

time (sec)

N/A 0.757 2.059 0.937 0.000 0.266 0.000 0.000 22.446

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 155 132 218 0 364 0 0 0

N.S.

1 1.09 0.93 1.54 0.00 2.56 0.00 0.00 0.00

time (sec)

N/A 0.853 2.493 1.247 0.000 0.284 0.000 0.000 0.000

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 158 115 328 1801 366 0 0 0

N.S.

1 1.10 0.80 2.28 12.51 2.54 0.00 0.00 0.00

time (sec)

N/A 0.911 3.107 2.516 0.501 0.319 0.000 0.000 0.000

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 159 117 470 0 340 0 0 0

N.S.

1 1.01 0.75 2.99 0.00 2.17 0.00 0.00 0.00

time (sec)

N/A 0.961 5.248 2.596 0.000 0.372 0.000 0.000 0.000

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 175 143 510 0 378 0 0 0

N.S.

1 1.06 0.87 3.09 0.00 2.29 0.00 0.00 0.00

time (sec)

N/A 0.998 1.584 2.331 0.000 0.350 0.000 0.000 0.000

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

215 220 163 561 0 420 0 0 0

N.S.

1 1.02 0.76 2.61 0.00 1.95 0.00 0.00 0.00

time (sec)

N/A 1.293 1.753 2.122 0.000 0.440 0.000 0.000 0.000

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

263 261 182 612 0 462 0 0 0

N.S.

1 0.99 0.69 2.33 0.00 1.76 0.00 0.00 0.00

time (sec)

N/A 1.518 2.137 2.289 0.000 0.453 0.000 0.000 0.000

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

294 310 218 232 0 192 0 0 1201

N.S.

1 1.05 0.74 0.79 0.00 0.65 0.00 0.00 4.09

time (sec)

N/A 1.973 3.162 0.569 0.000 0.265 0.000 0.000 30.578

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