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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 B F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 171 215 336 0 0 0 0 0

N.S.

1 1.00 1.26 1.96 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.824 0.826 0.167 0.000 0.000 0.000 0.000 0.000

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

221 316 266 313 0 0 0 0 0

N.S.

1 1.43 1.20 1.42 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.446 1.949 0.250 0.000 0.000 0.000 0.000 0.000

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

24 24 26 22 24 43 26 24 24

N.S.

1 1.00 1.08 0.92 1.00 1.79 1.08 1.00 1.00

time (sec)

N/A 0.276 0.504 0.251 0.547 0.248 91.684 0.330 4.317

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

220 220 249 0 0 0 0 0 0

N.S.

1 1.00 1.13 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.359 0.355 0.000 0.000 0.000 0.000 0.000 0.000

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

246 234 541 0 0 0 0 0 0

N.S.

1 0.95 2.20 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.337 0.679 0.000 0.000 0.000 0.000 0.000 0.000

Problem 406

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

94 93 45 56 88 91 0 0 0

N.S.

1 0.99 0.48 0.60 0.94 0.97 0.00 0.00 0.00

time (sec)

N/A 0.380 0.049 0.164 0.216 0.256 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 F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 90 45 56 86 87 0 0 0

N.S.

1 1.02 0.51 0.64 0.98 0.99 0.00 0.00 0.00

time (sec)

N/A 0.336 0.040 0.245 0.203 0.261 0.000 0.000 0.000

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 220 230 305 0 0 0 0 0

N.S.

1 1.19 1.24 1.65 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.439 0.295 0.223 0.000 0.000 0.000 0.000 0.000

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

187 201 270 488 0 0 0 0 0

N.S.

1 1.07 1.44 2.61 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.415 1.409 0.187 0.000 0.000 0.000 0.000 0.000

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

360 488 377 482 0 0 0 0 0

N.S.

1 1.36 1.05 1.34 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 4.136 6.318 0.241 0.000 0.000 0.000 0.000 0.000

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

24 24 26 22 24 43 24 24 24

N.S.

1 1.00 1.08 0.92 1.00 1.79 1.00 1.00 1.00

time (sec)

N/A 0.279 0.459 0.241 0.280 0.253 65.829 0.329 4.153

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

24 24 26 22 24 43 24 24 24

N.S.

1 1.00 1.08 0.92 1.00 1.79 1.00 1.00 1.00

time (sec)

N/A 0.276 2.713 0.051 0.278 0.259 2.745 0.324 3.848

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 9 10 0 0 0 0 0

N.S.

1 1.00 1.00 1.11 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.298 0.096 0.170 0.000 0.000 0.000 0.000 0.000

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 9 10 0 0 0 0 0

N.S.

1 1.00 1.00 1.11 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.262 0.045 0.239 0.000 0.000 0.000 0.000 0.000

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 24 26 22 24 40 24 0 24

N.S.

1 1.00 1.08 0.92 1.00 1.67 1.00 0.00 1.00

time (sec)

N/A 0.274 1.591 0.065 0.282 0.251 5.277 0.000 3.707

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

24 24 26 22 24 43 26 24 24

N.S.

1 1.00 1.08 0.92 1.00 1.79 1.08 1.00 1.00

time (sec)

N/A 0.273 0.559 0.238 0.291 0.246 123.759 0.339 4.261

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

24 24 26 22 24 43 26 24 24

N.S.

1 1.00 1.08 0.92 1.00 1.79 1.08 1.00 1.00

time (sec)

N/A 0.807 3.107 0.060 0.287 0.248 3.756 0.339 4.233

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 34 65 0 0 0 0 0

N.S.

1 1.00 0.94 1.81 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.413 0.072 0.194 0.000 0.000 0.000 0.000 0.000

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 32 62 0 0 0 0 0

N.S.

1 1.00 0.91 1.77 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.408 0.105 0.255 0.000 0.000 0.000 0.000 0.000

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 24 26 22 24 40 26 0 24

N.S.

1 1.00 1.08 0.92 1.00 1.67 1.08 0.00 1.00

time (sec)

N/A 1.110 6.214 0.067 0.285 0.242 6.618 0.000 3.934

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 24 26 22 24 43 0 24 24

N.S.

1 1.00 1.08 0.92 1.00 1.79 0.00 1.00 1.00

time (sec)

N/A 0.271 0.730 0.254 0.292 0.253 0.000 0.356 4.363

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

24 24 26 22 24 43 26 24 24

N.S.

1 1.00 1.08 0.92 1.00 1.79 1.08 1.00 1.00

time (sec)

N/A 0.996 5.779 0.074 0.290 0.240 5.270 0.347 3.986

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 71 43 87 0 0 0 0 0

N.S.

1 1.04 0.63 1.28 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.563 0.132 0.207 0.000 0.000 0.000 0.000 0.000

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 69 44 86 0 0 0 0 0

N.S.

1 1.06 0.68 1.32 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.535 0.075 0.246 0.000 0.000 0.000 0.000 0.000

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 24 26 22 24 40 26 0 24

N.S.

1 1.00 1.08 0.92 1.00 1.67 1.08 0.00 1.00

time (sec)

N/A 1.363 12.171 0.082 0.302 0.249 9.197 0.000 3.911

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

243 331 178 195 0 0 0 0 0

N.S.

1 1.36 0.73 0.80 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.936 0.521 0.191 0.000 0.000 0.000 0.000 0.000

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 210 79 120 128 91 0 0 0

N.S.

1 1.54 0.58 0.88 0.94 0.67 0.00 0.00 0.00

time (sec)

N/A 0.651 0.048 0.212 0.285 0.268 0.000 0.000 0.000

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

194 226 160 175 0 0 0 0 0

N.S.

1 1.16 0.82 0.90 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.600 0.377 0.234 0.000 0.000 0.000 0.000 0.000

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 64 49 99 50 72 0 0 0

N.S.

1 1.08 0.83 1.68 0.85 1.22 0.00 0.00 0.00

time (sec)

N/A 0.236 0.046 0.189 0.272 0.312 0.000 0.000 0.000

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 144 117 152 0 0 0 0 0

N.S.

1 1.01 0.82 1.06 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.331 0.221 0.248 0.000 0.000 0.000 0.000 0.000

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 100 91 111 0 0 0 0 0

N.S.

1 1.00 0.91 1.11 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.388 0.127 0.176 0.000 0.000 0.000 0.000 0.000

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 142 133 186 0 0 0 0 0

N.S.

1 1.09 1.02 1.43 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.570 0.367 0.256 0.000 0.000 0.000 0.000 0.000

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 130 126 139 0 0 0 0 0

N.S.

1 0.96 0.93 1.02 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.534 0.537 0.171 0.000 0.000 0.000 0.000 0.000

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 79 96 90 75 0 0 0

N.S.

1 1.00 1.13 1.37 1.29 1.07 0.00 0.00 0.00

time (sec)

N/A 0.268 0.051 0.255 0.273 0.284 0.000 0.000 0.000

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

191 295 222 164 0 0 0 0 0

N.S.

1 1.54 1.16 0.86 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.885 1.206 0.191 0.000 0.000 0.000 0.000 0.000

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 331 104 116 204 93 0 0 0

N.S.

1 2.21 0.69 0.77 1.36 0.62 0.00 0.00 0.00

time (sec)

N/A 1.086 0.086 0.270 0.290 0.279 0.000 0.000 0.000

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

243 437 307 183 0 0 0 0 0

N.S.

1 1.80 1.26 0.75 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.279 2.491 0.181 0.000 0.000 0.000 0.000 0.000

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

336 892 268 0 0 0 0 0 0

N.S.

1 2.65 0.80 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 7.123 1.122 0.000 0.000 0.000 0.000 0.000 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

281 926 175 211 0 0 0 0 0

N.S.

1 3.30 0.62 0.75 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 4.184 0.502 0.180 0.000 0.000 0.000 0.000 0.000

Problem 440

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

254 475 228 0 0 0 0 0 0

N.S.

1 1.87 0.90 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 4.260 0.897 0.000 0.000 0.000 0.000 0.000 0.000

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

175 179 135 175 0 0 0 0 0

N.S.

1 1.02 0.77 1.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.477 0.327 0.200 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(-2) F(-1)

verified

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

size

158 150 187 0 0 0 0 0 0

N.S.

1 0.95 1.18 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.673 0.569 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(-2) F(-1)

verified

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

size

174 212 203 0 0 0 0 0 0

N.S.

1 1.22 1.17 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.257 0.250 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(-2) F(-1)

verified

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

size

197 193 223 0 0 0 0 0 0

N.S.

1 0.98 1.13 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.434 0.582 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 C A A F F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 157 188 229 0 0 0 0 0

N.S.

1 1.04 1.25 1.52 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.166 0.935 0.184 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 F F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 163 177 171 0 0 0 0 0

N.S.

1 0.96 1.05 1.01 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.709 1.384 0.250 0.000 0.000 0.000 0.000 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

292 791 272 215 0 0 0 0 0

N.S.

1 2.71 0.93 0.74 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.869 1.049 0.186 0.000 0.000 0.000 0.000 0.000

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

186 566 79 140 163 106 0 0 0

N.S.

1 3.04 0.42 0.75 0.88 0.57 0.00 0.00 0.00

time (sec)

N/A 1.998 0.064 0.254 0.286 0.266 0.000 0.000 0.000

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

243 562 224 195 0 0 0 0 0

N.S.

1 2.31 0.92 0.80 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.816 0.735 0.183 0.000 0.000 0.000 0.000 0.000

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 88 61 120 67 90 0 0 0

N.S.

1 1.09 0.75 1.48 0.83 1.11 0.00 0.00 0.00

time (sec)

N/A 0.263 0.046 0.251 0.283 0.252 0.000 0.000 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 193 176 173 0 0 0 0 0

N.S.

1 1.02 0.93 0.92 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.458 0.489 0.234 0.000 0.000 0.000 0.000 0.000

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 169 143 130 0 0 0 0 0

N.S.

1 1.17 0.99 0.90 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.736 0.214 0.217 0.000 0.000 0.000 0.000 0.000

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 291 181 203 0 0 0 0 0

N.S.

1 1.63 1.01 1.13 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.173 0.576 0.243 0.000 0.000 0.000 0.000 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

168 235 158 143 0 0 0 0 0

N.S.

1 1.40 0.94 0.85 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.065 0.765 0.172 0.000 0.000 0.000 0.000 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 217 240 218 0 0 0 0 0

N.S.

1 1.15 1.27 1.15 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.007 1.125 0.244 0.000 0.000 0.000 0.000 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

191 430 282 162 0 0 0 0 0

N.S.

1 2.25 1.48 0.85 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.660 2.615 0.188 0.000 0.000 0.000 0.000 0.000

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 99 104 116 126 93 0 0 0

N.S.

1 1.05 1.11 1.23 1.34 0.99 0.00 0.00 0.00

time (sec)

N/A 0.294 0.061 0.258 0.274 0.264 0.000 0.000 0.000

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

243 737 474 184 0 0 0 0 0

N.S.

1 3.03 1.95 0.76 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.559 4.733 0.240 0.000 0.000 0.000 0.000 0.000

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

233 242 224 193 0 0 0 0 0

N.S.

1 1.04 0.96 0.83 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.587 0.902 0.543 0.000 0.000 0.000 0.000 0.000

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 193 176 173 0 0 0 0 0

N.S.

1 1.02 0.93 0.92 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.442 0.037 0.000 0.000 0.000 0.000 0.000 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 144 117 152 0 0 0 0 0

N.S.

1 1.01 0.82 1.06 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.318 0.039 0.000 0.000 0.000 0.000 0.000 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 89 49 59 74 73 0 90 0

N.S.

1 1.00 0.55 0.66 0.83 0.82 0.00 1.01 0.00

time (sec)

N/A 0.305 0.039 0.343 0.192 0.255 0.000 0.324 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 138 65 79 108 99 0 114 0

N.S.

1 1.04 0.49 0.59 0.81 0.74 0.00 0.86 0.00

time (sec)

N/A 0.437 0.047 0.347 0.208 0.251 0.000 0.319 0.000

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

177 187 81 99 140 121 0 138 0

N.S.

1 1.06 0.46 0.56 0.79 0.68 0.00 0.78 0.00

time (sec)

N/A 0.570 0.052 0.340 0.195 0.262 0.000 0.320 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

291 228 206 345 0 0 0 0 0

N.S.

1 0.78 0.71 1.19 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.598 0.644 0.256 0.000 0.000 0.000 0.000 0.000

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

235 176 119 319 0 0 0 0 0

N.S.

1 0.75 0.51 1.36 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.456 0.305 0.184 0.000 0.000 0.000 0.000 0.000

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

182 125 109 290 0 0 0 0 0

N.S.

1 0.69 0.60 1.59 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.327 0.144 0.247 0.000 0.000 0.000 0.000 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 43 74 90 54 0 70 0

N.S.

1 1.00 0.90 1.54 1.88 1.12 0.00 1.46 0.00

time (sec)

N/A 0.224 0.056 0.173 0.294 0.248 0.000 0.329 0.000

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 108 64 160 90 84 0 111 0

N.S.

1 1.03 0.61 1.52 0.86 0.80 0.00 1.06 0.00

time (sec)

N/A 0.359 0.072 0.254 0.202 0.252 0.000 0.341 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 168 80 250 132 112 0 149 0

N.S.

1 1.07 0.51 1.59 0.84 0.71 0.00 0.95 0.00

time (sec)

N/A 0.501 0.080 0.262 0.208 0.255 0.000 0.341 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

158 150 187 0 0 0 0 0 0

N.S.

1 0.95 1.18 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.687 0.066 0.000 0.000 0.000 0.000 0.000 0.000

Problem 472

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

139 161 70 84 304 105 0 0 0

N.S.

1 1.16 0.50 0.60 2.19 0.76 0.00 0.00 0.00

time (sec)

N/A 0.415 0.056 0.191 0.348 0.257 0.000 0.000 0.000

Problem 473

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

208 283 94 118 514 139 0 0 0

N.S.

1 1.36 0.45 0.57 2.47 0.67 0.00 0.00 0.00

time (sec)

N/A 0.658 0.064 0.256 0.390 0.260 0.000 0.000 0.000

Problem 474

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

277 429 120 152 751 169 0 0 0

N.S.

1 1.55 0.43 0.55 2.71 0.61 0.00 0.00 0.00

time (sec)

N/A 0.970 0.081 0.174 0.392 0.253 0.000 0.000 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

302 291 569 0 0 0 0 0 0

N.S.

1 0.96 1.88 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.138 2.481 0.000 0.000 0.000 0.000 0.000 0.000

Problem 476

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

191 240 87 105 0 134 0 0 0

N.S.

1 1.26 0.46 0.55 0.00 0.70 0.00 0.00 0.00

time (sec)

N/A 0.859 0.070 0.179 0.000 0.250 0.000 0.000 0.000

Problem 477

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

289 439 119 153 0 176 0 0 0

N.S.

1 1.52 0.41 0.53 0.00 0.61 0.00 0.00 0.00

time (sec)

N/A 1.846 0.078 0.255 0.000 0.280 0.000 0.000 0.000

Problem 478

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

385 687 151 201 0 214 0 0 0

N.S.

1 1.78 0.39 0.52 0.00 0.56 0.00 0.00 0.00

time (sec)

N/A 3.500 0.099 0.178 0.000 0.275 0.000 0.000 0.000

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

21 21 23 19 21 21 20 21 21

N.S.

1 1.00 1.10 0.90 1.00 1.00 0.95 1.00 1.00

time (sec)

N/A 0.211 1.291 0.055 0.249 0.254 0.485 0.298 3.932

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

21 21 23 19 21 33 22 21 21

N.S.

1 1.00 1.10 0.90 1.00 1.57 1.05 1.00 1.00

time (sec)

N/A 0.210 0.361 0.058 0.253 0.247 0.698 0.323 4.173

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 9 10 0 0 0 0 0

N.S.

1 1.00 1.00 1.11 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.258 0.035 0.000 0.000 0.000 0.000 0.000 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 25 24 21 0 0 0 0 0

N.S.

1 0.93 0.89 0.78 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.318 0.057 0.247 0.000 0.000 0.000 0.000 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 36 31 30 0 0 0 0 0

N.S.

1 0.88 0.76 0.73 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.335 0.064 0.244 0.000 0.000 0.000 0.000 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 47 42 39 0 0 0 0 0

N.S.

1 0.85 0.76 0.71 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.340 0.069 0.180 0.000 0.000 0.000 0.000 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

21 21 23 19 21 21 22 21 21

N.S.

1 1.00 1.10 0.90 1.00 1.00 1.05 1.00 1.00

time (sec)

N/A 0.205 1.456 0.054 0.242 0.237 0.743 0.319 3.902

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

21 21 23 19 21 33 24 21 21

N.S.

1 1.00 1.10 0.90 1.00 1.57 1.14 1.00 1.00

time (sec)

N/A 0.205 1.063 0.035 0.253 0.240 1.009 0.308 4.050

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 32 62 0 0 0 0 0

N.S.

1 1.00 0.91 1.77 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.401 0.097 0.000 0.000 0.000 0.000 0.000 0.000

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 52 46 120 0 0 0 0 0

N.S.

1 1.00 0.88 2.31 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.450 0.109 0.300 0.000 0.000 0.000 0.000 0.000

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 63 56 176 0 0 0 0 0

N.S.

1 0.95 0.85 2.67 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.476 0.129 0.234 0.000 0.000 0.000 0.000 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 74 64 232 0 0 0 0 0

N.S.

1 0.92 0.80 2.90 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.493 0.155 0.313 0.000 0.000 0.000 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

21 21 23 19 21 21 22 21 21

N.S.

1 1.00 1.10 0.90 1.00 1.00 1.05 1.00 1.00

time (sec)

N/A 0.203 1.607 0.053 0.254 0.259 1.053 0.318 4.142

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

21 21 23 19 21 33 24 21 21

N.S.

1 1.00 1.10 0.90 1.00 1.57 1.14 1.00 1.00

time (sec)

N/A 0.205 1.032 0.035 0.251 0.235 1.385 0.316 4.197

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 69 44 86 0 0 0 0 0

N.S.

1 1.06 0.68 1.32 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.534 0.070 0.000 0.000 0.000 0.000 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 111 56 180 0 0 0 0 0

N.S.

1 1.41 0.71 2.28 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.256 0.169 0.316 0.000 0.000 0.000 0.000 0.000

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 133 79 272 0 0 0 0 0

N.S.

1 1.43 0.85 2.92 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.293 0.209 0.355 0.000 0.000 0.000 0.000 0.000

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 155 99 364 0 0 0 0 0

N.S.

1 1.45 0.93 3.40 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.318 0.196 0.332 0.000 0.000 0.000 0.000 0.000

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

122 122 193 1435 0 0 0 0 0

N.S.

1 1.00 1.58 11.76 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.554 0.689 2.240 0.000 0.000 0.000 0.000 0.000

Problem 498

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

245 247 213 245 276 248 372 1471 288

N.S.

1 1.01 0.87 1.00 1.13 1.01 1.52 6.00 1.18

time (sec)

N/A 0.665 0.061 0.544 0.190 0.258 0.708 0.348 4.286

Problem 499

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

169 171 150 167 198 178 245 930 190

N.S.

1 1.01 0.89 0.99 1.17 1.05 1.45 5.50 1.12

time (sec)

N/A 0.541 0.046 0.265 0.181 0.251 0.528 0.320 4.491

Problem 500

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

110 112 98 105 131 119 155 527 118

N.S.

1 1.02 0.89 0.95 1.19 1.08 1.41 4.79 1.07

time (sec)

N/A 0.366 0.035 0.245 0.180 0.243 0.393 0.302 4.129

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