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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 F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 39 41 20 49 0 0 0

N.S.

1 1.00 1.08 1.14 0.56 1.36 0.00 0.00 0.00

time (sec)

N/A 0.354 0.075 1.437 0.373 0.261 0.000 0.000 0.000

Problem 402

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

57 57 74 135 241 180 0 0 0

N.S.

1 1.00 1.30 2.37 4.23 3.16 0.00 0.00 0.00

time (sec)

N/A 0.368 0.123 2.219 0.393 0.277 0.000 0.000 0.000

Problem 403

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

92 93 95 173 662 325 0 0 0

N.S.

1 1.01 1.03 1.88 7.20 3.53 0.00 0.00 0.00

time (sec)

N/A 0.510 0.173 2.472 0.420 0.300 0.000 0.000 0.000

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 136 128 205 1264 355 0 0 0

N.S.

1 1.00 0.94 1.51 9.29 2.61 0.00 0.00 0.00

time (sec)

N/A 0.676 0.283 2.161 0.414 0.291 0.000 0.000 0.000

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 187 72 73 303 84 0 0 0

N.S.

1 1.16 0.45 0.45 1.88 0.52 0.00 0.00 0.00

time (sec)

N/A 0.900 0.233 1.582 0.393 0.297 0.000 0.000 0.000

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 142 60 61 210 72 0 0 0

N.S.

1 1.22 0.52 0.53 1.81 0.62 0.00 0.00 0.00

time (sec)

N/A 0.675 0.160 1.738 0.364 0.255 0.000 0.000 0.000

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 100 50 51 38 61 0 0 0

N.S.

1 1.27 0.63 0.65 0.48 0.77 0.00 0.00 0.00

time (sec)

N/A 0.511 0.125 1.700 0.404 0.269 0.000 0.000 0.000

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 97 81 157 274 298 0 0 0

N.S.

1 1.01 0.84 1.64 2.85 3.10 0.00 0.00 0.00

time (sec)

N/A 0.510 0.113 2.104 0.393 0.296 0.000 0.000 0.000

Problem 409

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

95 96 92 174 1143 337 0 0 0

N.S.

1 1.01 0.97 1.83 12.03 3.55 0.00 0.00 0.00

time (sec)

N/A 0.532 0.242 2.213 0.404 0.282 0.000 0.000 0.000

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 139 107 206 2244 369 0 0 0

N.S.

1 0.99 0.76 1.47 16.03 2.64 0.00 0.00 0.00

time (sec)

N/A 0.678 0.371 2.112 0.479 0.293 0.000 0.000 0.000

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

180 182 117 236 2361 391 0 0 0

N.S.

1 1.01 0.65 1.31 13.12 2.17 0.00 0.00 0.00

time (sec)

N/A 0.871 0.436 2.391 0.472 0.298 0.000 0.000 0.000

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

201 233 90 85 422 105 0 0 0

N.S.

1 1.16 0.45 0.42 2.10 0.52 0.00 0.00 0.00

time (sec)

N/A 1.106 0.184 1.230 0.390 0.262 0.000 0.000 0.000

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 186 74 75 323 92 0 0 0

N.S.

1 1.19 0.47 0.48 2.07 0.59 0.00 0.00 0.00

time (sec)

N/A 0.847 0.201 0.982 0.387 0.257 0.000 0.000 0.000

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 144 64 65 60 79 0 0 0

N.S.

1 1.21 0.54 0.55 0.50 0.66 0.00 0.00 0.00

time (sec)

N/A 0.689 0.183 1.033 0.373 0.270 0.000 0.000 0.000

Problem 415

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

138 143 93 306 593 339 0 0 0

N.S.

1 1.04 0.67 2.22 4.30 2.46 0.00 0.00 0.00

time (sec)

N/A 0.732 0.162 2.108 0.401 0.283 0.000 0.000 0.000

Problem 416

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

132 140 90 322 11494 373 0 0 0

N.S.

1 1.06 0.68 2.44 87.08 2.83 0.00 0.00 0.00

time (sec)

N/A 0.736 0.229 2.160 0.488 0.283 0.000 0.000 0.000

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 143 95 208 2826 385 0 0 0

N.S.

1 1.02 0.68 1.49 20.19 2.75 0.00 0.00 0.00

time (sec)

N/A 0.750 0.455 2.328 3.080 0.283 0.000 0.000 0.000

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

180 185 115 238 3469 411 0 0 0

N.S.

1 1.03 0.64 1.32 19.27 2.28 0.00 0.00 0.00

time (sec)

N/A 0.934 0.506 2.109 0.552 0.291 0.000 0.000 0.000

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

220 228 125 268 3860 437 0 0 0

N.S.

1 1.04 0.57 1.22 17.55 1.99 0.00 0.00 0.00

time (sec)

N/A 1.157 0.623 2.272 0.623 0.309 0.000 0.000 0.000

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 208 136 194 357 324 0 0 0

N.S.

1 1.10 0.72 1.03 1.89 1.71 0.00 0.00 0.00

time (sec)

N/A 1.000 0.227 1.653 0.371 0.290 0.000 0.000 0.000

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 160 116 178 282 300 0 0 0

N.S.

1 1.06 0.77 1.18 1.87 1.99 0.00 0.00 0.00

time (sec)

N/A 0.766 0.148 1.871 0.395 0.281 0.000 0.000 0.000

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 114 100 100 104 281 0 0 0

N.S.

1 1.01 0.88 0.88 0.92 2.49 0.00 0.00 0.00

time (sec)

N/A 0.523 0.071 1.431 0.347 0.283 0.000 0.000 0.000

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 76 95 92 90 160 0 0 0

N.S.

1 1.36 1.70 1.64 1.61 2.86 0.00 0.00 0.00

time (sec)

N/A 0.378 0.056 1.868 0.351 0.268 0.000 0.000 0.000

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 116 109 181 476 342 0 0 0

N.S.

1 0.86 0.81 1.34 3.53 2.53 0.00 0.00 0.00

time (sec)

N/A 0.658 0.068 2.129 0.394 0.303 0.000 0.000 0.000

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

168 158 145 222 876 520 0 0 0

N.S.

1 0.94 0.86 1.32 5.21 3.10 0.00 0.00 0.00

time (sec)

N/A 0.910 0.161 2.473 0.409 0.295 0.000 0.000 0.000

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

211 205 178 257 1646 550 0 0 0

N.S.

1 0.97 0.84 1.22 7.80 2.61 0.00 0.00 0.00

time (sec)

N/A 1.188 0.287 2.490 0.429 0.303 0.000 0.000 0.000

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

237 256 152 273 0 400 0 0 0

N.S.

1 1.08 0.64 1.15 0.00 1.69 0.00 0.00 0.00

time (sec)

N/A 1.359 0.708 1.815 0.000 0.304 0.000 0.000 0.000

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

197 208 133 257 33960 380 0 0 0

N.S.

1 1.06 0.68 1.30 172.39 1.93 0.00 0.00 0.00

time (sec)

N/A 1.062 0.488 1.602 0.786 0.279 0.000 0.000 0.000

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 160 138 201 7176 360 0 0 0

N.S.

1 1.02 0.88 1.28 45.71 2.29 0.00 0.00 0.00

time (sec)

N/A 0.781 0.673 1.809 0.433 0.287 0.000 0.000 0.000

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 118 131 164 1031 340 0 0 0

N.S.

1 1.01 1.12 1.40 8.81 2.91 0.00 0.00 0.00

time (sec)

N/A 0.531 0.318 1.795 0.373 0.283 0.000 0.000 0.000

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 118 248 164 15721 338 0 0 0

N.S.

1 1.01 2.12 1.40 134.37 2.89 0.00 0.00 0.00

time (sec)

N/A 0.537 0.648 1.700 0.864 0.275 0.000 0.000 0.000

Problem 432

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 No TBD TBD TBD TBD TBD

size

174 161 248 361 2122 550 0 0 0

N.S.

1 0.93 1.43 2.07 12.20 3.16 0.00 0.00 0.00

time (sec)

N/A 0.909 0.572 2.300 0.427 0.292 0.000 0.000 0.000

Problem 433

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

214 203 272 404 4934 614 0 0 0

N.S.

1 0.95 1.27 1.89 23.06 2.87 0.00 0.00 0.00

time (sec)

N/A 1.194 0.468 2.477 0.607 0.302 0.000 0.000 0.000

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

237 256 144 361 148823 448 0 0 0

N.S.

1 1.08 0.61 1.52 627.95 1.89 0.00 0.00 0.00

time (sec)

N/A 1.328 0.785 1.685 2.706 0.268 0.000 0.000 0.000

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

197 208 141 223 258456 428 0 0 0

N.S.

1 1.06 0.72 1.13 1311.96 2.17 0.00 0.00 0.00

time (sec)

N/A 1.048 0.702 1.654 2.749 0.267 0.000 0.000 0.000

Problem 436

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

157 164 168 277 3049 408 0 0 0

N.S.

1 1.04 1.07 1.76 19.42 2.60 0.00 0.00 0.00

time (sec)

N/A 0.768 0.927 1.558 0.642 0.270 0.000 0.000 0.000

Problem 437

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

157 163 224 304 2875 408 0 0 0

N.S.

1 1.04 1.43 1.94 18.31 2.60 0.00 0.00 0.00

time (sec)

N/A 0.708 2.682 1.584 0.578 0.277 0.000 0.000 0.000

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 163 328 304 84332 408 0 0 0

N.S.

1 1.04 2.09 1.94 537.15 2.60 0.00 0.00 0.00

time (sec)

N/A 0.706 0.856 1.655 14.835 0.268 0.000 0.000 0.000

Problem 439

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 No TBD TBD TBD TBD TBD

size

214 207 328 410 4988 638 0 0 0

N.S.

1 0.97 1.53 1.92 23.31 2.98 0.00 0.00 0.00

time (sec)

N/A 1.193 1.031 2.464 0.615 0.286 0.000 0.000 0.000

Problem 440

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 No TBD TBD TBD TBD TBD

size

254 251 360 669 9048 702 0 0 0

N.S.

1 0.99 1.42 2.63 35.62 2.76 0.00 0.00 0.00

time (sec)

N/A 1.527 1.188 2.509 2.557 0.320 0.000 0.000 0.000

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

244 278 155 0 0 0 0 0 0

N.S.

1 1.14 0.64 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.247 0.965 0.000 0.000 0.000 0.000 0.000 0.000

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

179 203 125 0 0 0 0 0 0

N.S.

1 1.13 0.70 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.981 0.391 0.000 0.000 0.000 0.000 0.000 0.000

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

132 137 105 0 0 0 0 0 0

N.S.

1 1.04 0.80 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.442 0.117 0.000 0.000 0.000 0.000 0.000 0.000

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

178 207 165 0 0 0 0 0 0

N.S.

1 1.16 0.93 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.855 0.588 0.000 0.000 0.000 0.000 0.000 0.000

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

215 245 223 0 0 0 0 0 0

N.S.

1 1.14 1.04 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.144 0.882 0.000 0.000 0.000 0.000 0.000 0.000

Problem 446

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

85 90 59 73 95 99 0 164 152

N.S.

1 1.06 0.69 0.86 1.12 1.16 0.00 1.93 1.79

time (sec)

N/A 0.478 0.185 1.100 0.206 0.277 0.000 0.300 17.067

Problem 447

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 64 60 60 70 88 0 122 109

N.S.

1 1.02 0.95 0.95 1.11 1.40 0.00 1.94 1.73

time (sec)

N/A 0.391 0.112 0.961 0.214 0.281 0.000 0.321 15.392

Problem 448

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

47 48 47 47 58 74 0 107 85

N.S.

1 1.02 1.00 1.00 1.23 1.57 0.00 2.28 1.81

time (sec)

N/A 0.361 0.011 0.745 0.216 0.274 0.000 0.305 14.160

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 24 30 29 60 37 63 47

N.S.

1 1.00 1.00 1.25 1.21 2.50 1.54 2.62 1.96

time (sec)

N/A 0.279 0.011 0.542 0.205 0.269 2.187 0.299 13.666

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 24 23 36 41 49 57

N.S.

1 1.00 1.00 1.50 1.44 2.25 2.56 3.06 3.56

time (sec)

N/A 0.149 0.002 0.157 0.204 0.279 0.818 0.277 14.546

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 26 16 20 17 17 39 17

N.S.

1 1.00 1.73 1.07 1.33 1.13 1.13 2.60 1.13

time (sec)

N/A 0.227 0.008 0.392 0.197 0.243 0.779 0.282 14.227

Problem 452

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

38 39 35 32 34 29 0 82 31

N.S.

1 1.03 0.92 0.84 0.89 0.76 0.00 2.16 0.82

time (sec)

N/A 0.283 0.050 0.491 0.207 0.264 0.000 0.298 13.575

Problem 453

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

54 55 57 44 46 42 0 98 55

N.S.

1 1.02 1.06 0.81 0.85 0.78 0.00 1.81 1.02

time (sec)

N/A 0.323 0.055 0.693 0.201 0.273 0.000 0.283 13.433

Problem 454

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

76 81 73 57 57 53 0 140 75

N.S.

1 1.07 0.96 0.75 0.75 0.70 0.00 1.84 0.99

time (sec)

N/A 0.383 0.095 0.890 0.203 0.263 0.000 0.288 14.016

Problem 455

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

92 93 89 69 69 64 0 154 113

N.S.

1 1.01 0.97 0.75 0.75 0.70 0.00 1.67 1.23

time (sec)

N/A 0.386 0.100 0.834 0.214 0.263 0.000 0.305 17.837

Problem 456

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

135 128 90 110 132 136 0 272 221

N.S.

1 0.95 0.67 0.81 0.98 1.01 0.00 2.01 1.64

time (sec)

N/A 0.728 0.429 1.400 0.200 0.288 0.000 0.309 17.075

Problem 457

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

110 102 82 111 144 133 0 258 184

N.S.

1 0.93 0.75 1.01 1.31 1.21 0.00 2.35 1.67

time (sec)

N/A 0.564 0.204 1.205 0.208 0.295 0.000 0.334 16.183

Problem 458

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

80 87 71 74 84 100 0 178 141

N.S.

1 1.09 0.89 0.92 1.05 1.25 0.00 2.22 1.76

time (sec)

N/A 0.550 0.158 1.224 0.203 0.278 0.000 0.307 15.110

Problem 459

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

59 59 45 69 80 93 0 129 99

N.S.

1 1.00 0.76 1.17 1.36 1.58 0.00 2.19 1.68

time (sec)

N/A 0.416 0.090 0.805 0.217 0.265 0.000 0.306 13.503

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 32 41 40 74 0 77 181

N.S.

1 1.00 0.97 1.24 1.21 2.24 0.00 2.33 5.48

time (sec)

N/A 0.294 0.071 0.668 0.193 0.262 0.000 0.315 13.496

Problem 461

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

33 33 46 43 51 52 0 78 73

N.S.

1 1.00 1.39 1.30 1.55 1.58 0.00 2.36 2.21

time (sec)

N/A 0.335 0.011 0.414 0.200 0.283 0.000 0.294 13.440

Problem 462

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

50 50 46 43 47 40 0 96 42

N.S.

1 1.00 0.92 0.86 0.94 0.80 0.00 1.92 0.84

time (sec)

N/A 0.345 0.171 0.389 0.201 0.252 0.000 0.285 13.484

Problem 463

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

58 66 59 61 60 52 0 153 72

N.S.

1 1.14 1.02 1.05 1.03 0.90 0.00 2.64 1.24

time (sec)

N/A 0.454 0.289 0.639 0.198 0.248 0.000 0.299 13.444

Problem 464

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

101 93 86 75 82 77 0 224 93

N.S.

1 0.92 0.85 0.74 0.81 0.76 0.00 2.22 0.92

time (sec)

N/A 0.458 0.174 0.880 0.210 0.255 0.000 0.305 13.563

Problem 465

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

111 113 85 95 94 86 0 247 117

N.S.

1 1.02 0.77 0.86 0.85 0.77 0.00 2.23 1.05

time (sec)

N/A 0.602 0.139 1.172 0.207 0.266 0.000 0.311 13.457

Problem 466

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

189 201 120 148 181 170 0 367 258

N.S.

1 1.06 0.63 0.78 0.96 0.90 0.00 1.94 1.37

time (sec)

N/A 1.176 0.651 1.893 0.206 0.279 0.000 0.354 17.165

Problem 467

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

130 141 90 125 158 140 0 330 226

N.S.

1 1.08 0.69 0.96 1.22 1.08 0.00 2.54 1.74

time (sec)

N/A 0.870 0.324 1.234 0.209 0.291 0.000 0.336 17.079

Problem 468

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

99 105 70 96 106 126 0 205 157

N.S.

1 1.06 0.71 0.97 1.07 1.27 0.00 2.07 1.59

time (sec)

N/A 0.652 0.182 1.142 0.202 0.285 0.000 0.325 16.326

Problem 469

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

73 74 55 82 93 112 0 145 136

N.S.

1 1.01 0.75 1.12 1.27 1.53 0.00 1.99 1.86

time (sec)

N/A 0.261 0.121 0.883 0.196 0.278 0.000 0.294 14.009

Problem 470

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

67 67 88 57 66 94 0 131 97

N.S.

1 1.00 1.31 0.85 0.99 1.40 0.00 1.96 1.45

time (sec)

N/A 0.535 0.856 0.791 0.217 0.276 0.000 0.330 13.911

Problem 471

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

79 80 105 73 76 72 0 137 123

N.S.

1 1.01 1.33 0.92 0.96 0.91 0.00 1.73 1.56

time (sec)

N/A 0.559 0.356 0.542 0.202 0.272 0.000 0.324 13.585

Problem 472

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

100 102 80 67 73 66 0 170 77

N.S.

1 1.02 0.80 0.67 0.73 0.66 0.00 1.70 0.77

time (sec)

N/A 0.590 0.227 0.671 0.198 0.250 0.000 0.330 13.538

Problem 473

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

123 117 100 90 95 84 0 297 250

N.S.

1 0.95 0.81 0.73 0.77 0.68 0.00 2.41 2.03

time (sec)

N/A 0.726 0.371 0.853 0.201 0.258 0.000 0.319 16.569

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

160 144 130 113 119 110 0 332 287

N.S.

1 0.90 0.81 0.71 0.74 0.69 0.00 2.08 1.79

time (sec)

N/A 0.746 0.479 1.080 0.213 0.276 0.000 0.317 16.280

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 164 159 135 145 132 0 431 350

N.S.

1 0.89 0.86 0.73 0.78 0.71 0.00 2.33 1.89

time (sec)

N/A 0.961 0.504 1.528 0.198 0.277 0.000 0.322 15.667

Problem 476

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

244 258 154 209 275 217 0 592 370

N.S.

1 1.06 0.63 0.86 1.13 0.89 0.00 2.43 1.52

time (sec)

N/A 1.551 0.676 4.206 0.217 0.277 0.000 0.352 18.305

Problem 477

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

179 195 125 162 195 182 0 461 304

N.S.

1 1.09 0.70 0.91 1.09 1.02 0.00 2.58 1.70

time (sec)

N/A 1.180 0.541 3.673 0.212 0.281 0.000 0.334 18.148

Problem 478

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

146 157 101 147 180 163 0 360 245

N.S.

1 1.08 0.69 1.01 1.23 1.12 0.00 2.47 1.68

time (sec)

N/A 0.950 0.363 1.458 0.203 0.266 0.000 0.337 17.169

Problem 479

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

107 114 77 109 121 138 0 221 185

N.S.

1 1.07 0.72 1.02 1.13 1.29 0.00 2.07 1.73

time (sec)

N/A 0.425 0.232 1.234 0.212 0.273 0.000 0.329 13.757

Problem 480

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

104 103 280 96 115 130 0 179 152

N.S.

1 0.99 2.69 0.92 1.11 1.25 0.00 1.72 1.46

time (sec)

N/A 0.795 1.227 0.996 0.196 0.290 0.000 0.330 13.796

Problem 481

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

108 108 119 87 90 116 0 170 150

N.S.

1 1.00 1.10 0.81 0.83 1.07 0.00 1.57 1.39

time (sec)

N/A 0.811 0.977 0.901 0.216 0.296 0.000 0.339 14.202

Problem 482

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

115 116 128 98 102 98 0 212 158

N.S.

1 1.01 1.11 0.85 0.89 0.85 0.00 1.84 1.37

time (sec)

N/A 0.838 0.402 0.765 0.203 0.282 0.000 0.331 13.145

Problem 483

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

145 153 104 101 109 96 0 318 123

N.S.

1 1.06 0.72 0.70 0.75 0.66 0.00 2.19 0.85

time (sec)

N/A 0.905 0.365 0.902 0.205 0.265 0.000 0.313 12.873

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

173 164 133 125 133 121 0 425 330

N.S.

1 0.95 0.77 0.72 0.77 0.70 0.00 2.46 1.91

time (sec)

N/A 1.084 0.661 1.274 0.206 0.258 0.000 0.326 15.809

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

213 194 156 153 170 150 0 550 214

N.S.

1 0.91 0.73 0.72 0.80 0.70 0.00 2.58 1.00

time (sec)

N/A 1.122 0.745 1.258 0.216 0.288 0.000 0.337 13.078

Problem 486

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

158 170 114 160 198 183 0 380 274

N.S.

1 1.08 0.72 1.01 1.25 1.16 0.00 2.41 1.73

time (sec)

N/A 0.665 0.428 1.662 0.195 0.289 0.000 0.312 13.952

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 174 258 252 0 557 0 286 1021

N.S.

1 1.11 1.64 1.61 0.00 3.55 0.00 1.82 6.50

time (sec)

N/A 1.283 2.045 0.707 0.000 0.387 0.000 0.331 15.234

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 129 238 192 0 485 0 211 1002

N.S.

1 1.08 2.00 1.61 0.00 4.08 0.00 1.77 8.42

time (sec)

N/A 0.873 0.994 0.582 0.000 0.390 0.000 0.331 14.124

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 88 115 123 0 392 0 152 119

N.S.

1 1.04 1.35 1.45 0.00 4.61 0.00 1.79 1.40

time (sec)

N/A 0.577 0.502 0.427 0.000 0.314 0.000 0.344 14.045

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 102 83 0 290 0 120 186

N.S.

1 1.00 1.50 1.22 0.00 4.26 0.00 1.76 2.74

time (sec)

N/A 0.445 0.182 0.419 0.000 0.319 0.000 0.319 13.885

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 48 44 0 185 0 77 40

N.S.

1 1.00 0.98 0.90 0.00 3.78 0.00 1.57 0.82

time (sec)

N/A 0.283 0.031 0.337 0.000 0.256 0.000 0.305 14.056

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 60 65 0 230 0 218 186

N.S.

1 1.00 1.02 1.10 0.00 3.90 0.00 3.69 3.15

time (sec)

N/A 0.274 0.117 0.296 0.000 0.284 0.000 0.309 14.234

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 79 72 97 0 277 0 126 395

N.S.

1 1.04 0.95 1.28 0.00 3.64 0.00 1.66 5.20

time (sec)

N/A 0.387 0.312 0.615 0.000 0.284 0.000 0.306 13.776

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 121 97 138 0 334 0 178 592

N.S.

1 1.10 0.88 1.25 0.00 3.04 0.00 1.62 5.38

time (sec)

N/A 0.790 0.335 0.691 0.000 0.316 0.000 0.325 14.290

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 165 122 179 0 401 0 249 654

N.S.

1 1.11 0.82 1.21 0.00 2.71 0.00 1.68 4.42

time (sec)

N/A 1.117 0.397 0.712 0.000 0.305 0.000 0.311 14.666

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 218 153 256 0 482 0 393 2678

N.S.

1 1.13 0.79 1.33 0.00 2.50 0.00 2.04 13.88

time (sec)

N/A 1.589 0.599 0.905 0.000 0.317 0.000 0.316 16.374

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

222 234 285 277 0 909 0 299 3685

N.S.

1 1.05 1.28 1.25 0.00 4.09 0.00 1.35 16.60

time (sec)

N/A 1.561 5.177 0.952 0.000 0.725 0.000 0.348 19.940

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 183 162 209 0 760 0 331 3159

N.S.

1 1.12 0.99 1.27 0.00 4.63 0.00 2.02 19.26

time (sec)

N/A 1.089 0.987 0.668 0.000 0.475 0.000 0.313 19.211

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 142 146 166 0 596 0 203 2848

N.S.

1 1.21 1.25 1.42 0.00 5.09 0.00 1.74 24.34

time (sec)

N/A 0.747 0.473 0.521 0.000 0.514 0.000 0.318 19.067

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 96 83 118 0 329 0 150 92

N.S.

1 1.13 0.98 1.39 0.00 3.87 0.00 1.76 1.08

time (sec)

N/A 0.449 0.192 0.352 0.000 0.304 0.000 0.314 14.331

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