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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 B A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 63 31 30 74 37 0 0 35

N.S.

1 1.91 0.94 0.91 2.24 1.12 0.00 0.00 1.06

time (sec)

N/A 0.224 0.028 0.070 0.197 0.246 0.000 0.000 4.926

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 0 33 32 0 56 0 0 43

N.S.

1 0.00 1.00 0.97 0.00 1.70 0.00 0.00 1.30

time (sec)

N/A 0.000 0.743 3.860 0.000 14.343 0.000 0.000 5.684

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 54 14 47 50 27 0 12

N.S.

1 1.00 1.64 0.42 1.42 1.52 0.82 0.00 0.36

time (sec)

N/A 0.152 0.004 2.648 0.276 0.242 0.421 0.000 4.877

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 0 61 61 0 28 0 0 0

N.S.

1 0.00 1.85 1.85 0.00 0.85 0.00 0.00 0.00

time (sec)

N/A 0.000 8.165 6.924 0.000 0.279 0.000 0.000 0.000

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 50 31 0 31 0 36 27

N.S.

1 1.00 1.52 0.94 0.00 0.94 0.00 1.09 0.82

time (sec)

N/A 0.174 0.125 3.442 0.000 0.276 0.000 0.279 5.519

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A C F B F A B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

33 70 61 33 0 95 0 43 31

N.S.

1 2.12 1.85 1.00 0.00 2.88 0.00 1.30 0.94

time (sec)

N/A 0.187 0.143 2.138 0.000 1.689 0.000 0.275 5.049

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 489 33 0 0 0 0 0 0

N.S.

1 14.82 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.855 0.127 0.000 0.000 0.000 0.000 0.000 0.000

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 37 33 30 0 31 0 66 0

N.S.

1 1.12 1.00 0.91 0.00 0.94 0.00 2.00 0.00

time (sec)

N/A 0.222 0.074 3.385 0.000 0.299 0.000 0.281 0.000

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 37 33 30 0 29 0 66 0

N.S.

1 1.12 1.00 0.91 0.00 0.88 0.00 2.00 0.00

time (sec)

N/A 0.216 0.071 3.438 0.000 0.282 0.000 0.293 0.000

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 83 33 26 0 29 0 37 57

N.S.

1 2.52 1.00 0.79 0.00 0.88 0.00 1.12 1.73

time (sec)

N/A 0.246 0.053 0.861 0.000 0.248 0.000 0.275 4.978

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 32 33 25 49 67 53 27 0

N.S.

1 0.97 1.00 0.76 1.48 2.03 1.61 0.82 0.00

time (sec)

N/A 0.157 0.244 1.146 0.271 0.261 0.545 0.288 0.000

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 75 33 25 37 29 260 0 49

N.S.

1 2.27 1.00 0.76 1.12 0.88 7.88 0.00 1.48

time (sec)

N/A 0.209 0.110 0.904 0.207 0.250 1.994 0.000 5.233

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 0 33 60 0 71 0 0 75

N.S.

1 0.00 1.00 1.82 0.00 2.15 0.00 0.00 2.27

time (sec)

N/A 0.000 10.860 1.885 0.000 0.276 0.000 0.000 8.209

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 49 33 30 39 29 60 39 29

N.S.

1 1.48 1.00 0.91 1.18 0.88 1.82 1.18 0.88

time (sec)

N/A 0.277 0.194 1.375 0.330 0.255 1.343 0.317 5.270

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 19 19 16 15 28 56 15 15

N.S.

1 0.58 0.58 0.48 0.45 0.85 1.70 0.45 0.45

time (sec)

N/A 0.401 0.011 1.354 0.201 0.241 0.702 0.287 5.415

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 56 56 25 0 68 0 0 179

N.S.

1 1.65 1.65 0.74 0.00 2.00 0.00 0.00 5.26

time (sec)

N/A 0.354 0.195 2.704 0.000 0.264 0.000 0.000 5.295

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 56 56 25 0 68 0 0 227

N.S.

1 1.65 1.65 0.74 0.00 2.00 0.00 0.00 6.68

time (sec)

N/A 0.399 0.247 3.440 0.000 0.268 0.000 0.000 0.086

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 55 34 24 0 66 0 0 0

N.S.

1 1.62 1.00 0.71 0.00 1.94 0.00 0.00 0.00

time (sec)

N/A 0.306 0.646 1.408 0.000 0.265 0.000 0.000 0.000

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 54 34 26 0 68 0 0 0

N.S.

1 1.59 1.00 0.76 0.00 2.00 0.00 0.00 0.00

time (sec)

N/A 0.315 0.627 1.388 0.000 0.269 0.000 0.000 0.000

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 62 34 32 0 73 0 0 0

N.S.

1 1.82 1.00 0.94 0.00 2.15 0.00 0.00 0.00

time (sec)

N/A 0.341 0.394 2.376 0.000 0.286 0.000 0.000 0.000

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 0 34 32 0 38 0 0 0

N.S.

1 0.00 1.00 0.94 0.00 1.12 0.00 0.00 0.00

time (sec)

N/A 0.000 0.103 1.764 0.000 0.275 0.000 0.000 0.000

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 0 34 61 0 40 0 0 0

N.S.

1 0.00 1.00 1.79 0.00 1.18 0.00 0.00 0.00

time (sec)

N/A 0.000 0.099 4.733 0.000 0.274 0.000 0.000 0.000

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 0 34 59 0 38 0 0 0

N.S.

1 0.00 1.00 1.74 0.00 1.12 0.00 0.00 0.00

time (sec)

N/A 0.000 0.116 1.829 0.000 0.269 0.000 0.000 0.000

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 0 34 61 0 40 0 0 0

N.S.

1 0.00 1.00 1.79 0.00 1.18 0.00 0.00 0.00

time (sec)

N/A 0.000 0.101 4.815 0.000 0.253 0.000 0.000 0.000

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 0 34 53 0 58 0 0 0

N.S.

1 0.00 1.00 1.56 0.00 1.71 0.00 0.00 0.00

time (sec)

N/A 0.000 5.407 1.810 0.000 0.270 0.000 0.000 0.000

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

35 43 35 42 45 83 41 0 0

N.S.

1 1.23 1.00 1.20 1.29 2.37 1.17 0.00 0.00

time (sec)

N/A 0.169 0.156 0.856 0.279 0.498 0.491 0.000 0.000

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A F A A A B

verified

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

size

35 0 35 52 0 51 56 60 31

N.S.

1 0.00 1.00 1.49 0.00 1.46 1.60 1.71 0.89

time (sec)

N/A 0.000 0.040 2.779 0.000 0.239 4.440 0.354 5.824

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 36 35 30 0 106 85 66 29

N.S.

1 1.03 1.00 0.86 0.00 3.03 2.43 1.89 0.83

time (sec)

N/A 0.158 0.092 1.501 0.000 0.255 0.349 0.284 5.336

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 57 35 27 37 31 68 37 31

N.S.

1 1.63 1.00 0.77 1.06 0.89 1.94 1.06 0.89

time (sec)

N/A 0.173 0.018 0.854 0.190 0.247 0.207 0.263 5.300

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A C F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 289 58 63 0 73 0 0 175

N.S.

1 8.26 1.66 1.80 0.00 2.09 0.00 0.00 5.00

time (sec)

N/A 1.022 1.607 4.807 0.000 0.262 0.000 0.000 5.233

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A F F B

verified

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

size

35 0 35 31 31 33 0 0 33

N.S.

1 0.00 1.00 0.89 0.89 0.94 0.00 0.00 0.94

time (sec)

N/A 0.000 0.203 6.684 0.244 0.247 0.000 0.000 0.318

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 25 37 20 45 38 19 38 19

N.S.

1 0.71 1.06 0.57 1.29 1.09 0.54 1.09 0.54

time (sec)

N/A 0.160 0.049 0.924 0.281 0.233 0.652 0.271 5.457

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 85 28 25 0 30 0 28 31

N.S.

1 2.43 0.80 0.71 0.00 0.86 0.00 0.80 0.89

time (sec)

N/A 0.319 10.020 1.085 0.000 0.242 0.000 0.295 5.399

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 60 31 0 37 0 35 0

N.S.

1 1.00 1.71 0.89 0.00 1.06 0.00 1.00 0.00

time (sec)

N/A 0.177 0.130 3.807 0.000 0.257 0.000 0.287 0.000

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 83 35 30 36 31 0 37 57

N.S.

1 2.37 1.00 0.86 1.03 0.89 0.00 1.06 1.63

time (sec)

N/A 0.223 1.398 0.919 0.284 0.234 0.000 0.280 5.512

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 37 35 36 0 33 0 71 0

N.S.

1 1.06 1.00 1.03 0.00 0.94 0.00 2.03 0.00

time (sec)

N/A 0.215 0.083 2.033 0.000 0.265 0.000 0.296 0.000

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 91 33 30 0 31 0 59 65

N.S.

1 2.60 0.94 0.86 0.00 0.89 0.00 1.69 1.86

time (sec)

N/A 0.250 0.044 0.915 0.000 0.236 0.000 0.288 5.471

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 39 37 34 0 33 0 67 0

N.S.

1 1.11 1.06 0.97 0.00 0.94 0.00 1.91 0.00

time (sec)

N/A 0.218 0.072 2.976 0.000 0.272 0.000 0.291 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

35 0 35 0 0 0 0 0 0

N.S.

1 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 0.798 0.000 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 A B A C A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 39 32 28 58 29 61 48 0

N.S.

1 1.11 0.91 0.80 1.66 0.83 1.74 1.37 0.00

time (sec)

N/A 0.165 0.121 1.151 0.193 0.248 0.994 0.309 0.000

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 33 35 28 45 34 76 46 0

N.S.

1 0.94 1.00 0.80 1.29 0.97 2.17 1.31 0.00

time (sec)

N/A 0.161 0.104 1.164 0.189 0.253 0.708 0.281 0.000

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 39 35 28 58 29 61 30 0

N.S.

1 1.11 1.00 0.80 1.66 0.83 1.74 0.86 0.00

time (sec)

N/A 0.153 0.096 1.197 0.198 0.259 0.807 0.268 0.000

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 29 35 20 58 29 19 42 0

N.S.

1 0.83 1.00 0.57 1.66 0.83 0.54 1.20 0.00

time (sec)

N/A 0.150 0.114 1.109 0.218 0.247 0.971 0.296 0.000

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 23 35 20 45 34 34 38 0

N.S.

1 0.66 1.00 0.57 1.29 0.97 0.97 1.09 0.00

time (sec)

N/A 0.157 0.117 1.102 0.185 0.256 0.637 0.267 0.000

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 107 28 25 0 30 0 28 31

N.S.

1 3.06 0.80 0.71 0.00 0.86 0.00 0.80 0.89

time (sec)

N/A 0.350 10.047 1.049 0.000 0.265 0.000 0.276 5.697

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 60 27 0 35 0 43 0

N.S.

1 1.00 1.71 0.77 0.00 1.00 0.00 1.23 0.00

time (sec)

N/A 0.176 0.144 1.235 0.000 0.294 0.000 0.306 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

35 0 35 60 0 0 0 0 0

N.S.

1 0.00 1.00 1.71 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 3.572 1.973 0.000 0.000 0.000 0.000 0.000

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 41 35 62 0 28 42 0 0

N.S.

1 1.17 1.00 1.77 0.00 0.80 1.20 0.00 0.00

time (sec)

N/A 0.176 0.042 0.102 0.000 0.247 0.178 0.000 0.000

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 47 36 45 44 44 37 44 30

N.S.

1 1.31 1.00 1.25 1.22 1.22 1.03 1.22 0.83

time (sec)

N/A 0.164 0.023 1.311 0.275 0.257 0.567 0.263 5.201

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 49 33 34 46 31 138 63 189

N.S.

1 1.36 0.92 0.94 1.28 0.86 3.83 1.75 5.25

time (sec)

N/A 0.162 0.038 2.364 0.280 0.253 1.771 0.281 4.908

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 59 59 25 0 159 0 0 51

N.S.

1 1.64 1.64 0.69 0.00 4.42 0.00 0.00 1.42

time (sec)

N/A 0.512 1.306 3.759 0.000 0.304 0.000 0.000 7.377

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

36 0 36 64 0 43 0 0 0

N.S.

1 0.00 1.00 1.78 0.00 1.19 0.00 0.00 0.00

time (sec)

N/A 0.000 0.097 4.019 0.000 0.287 0.000 0.000 0.000

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 49 33 40 46 31 124 63 35

N.S.

1 1.36 0.92 1.11 1.28 0.86 3.44 1.75 0.97

time (sec)

N/A 0.163 0.030 1.273 0.274 0.249 1.927 0.264 5.534

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

36 0 0 70 0 78 0 0 0

N.S.

1 0.00 0.00 1.94 0.00 2.17 0.00 0.00 0.00

time (sec)

N/A 0.000 0.000 1.314 0.000 0.296 0.000 0.000 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 83 29 32 0 81 0 0 0

N.S.

1 2.24 0.78 0.86 0.00 2.19 0.00 0.00 0.00

time (sec)

N/A 0.541 10.437 2.027 0.000 0.287 0.000 0.000 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 87 29 32 0 87 0 0 0

N.S.

1 2.35 0.78 0.86 0.00 2.35 0.00 0.00 0.00

time (sec)

N/A 0.538 10.319 1.995 0.000 0.281 0.000 0.000 0.000

Problem 457

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

37 37 37 30 0 30 0 0 0

N.S.

1 1.00 1.00 0.81 0.00 0.81 0.00 0.00 0.00

time (sec)

N/A 0.331 0.269 3.092 0.000 0.303 0.000 0.000 0.000

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 86 30 27 0 34 0 34 33

N.S.

1 2.32 0.81 0.73 0.00 0.92 0.00 0.92 0.89

time (sec)

N/A 0.319 10.019 1.045 0.000 0.253 0.000 0.284 5.054

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 53 36 0 35 0 42 29

N.S.

1 1.00 1.43 0.97 0.00 0.95 0.00 1.14 0.78

time (sec)

N/A 0.172 0.121 3.724 0.000 0.268 0.000 0.290 5.070

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 91 37 34 39 33 0 59 65

N.S.

1 2.46 1.00 0.92 1.05 0.89 0.00 1.59 1.76

time (sec)

N/A 0.228 1.336 0.869 0.201 0.245 0.000 0.270 4.994

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

37 29 37 32 0 31 0 67 0

N.S.

1 0.78 1.00 0.86 0.00 0.84 0.00 1.81 0.00

time (sec)

N/A 0.206 0.092 1.539 0.000 0.272 0.000 0.276 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

37 64 52 27 0 60 0 40 0

N.S.

1 1.73 1.41 0.73 0.00 1.62 0.00 1.08 0.00

time (sec)

N/A 0.258 0.157 1.832 0.000 0.242 0.000 0.282 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 31 41 26 43 33 36 0 25

N.S.

1 0.84 1.11 0.70 1.16 0.89 0.97 0.00 0.68

time (sec)

N/A 0.190 0.075 0.951 0.268 0.250 1.947 0.000 5.472

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 56 41 26 43 33 34 0 25

N.S.

1 1.51 1.11 0.70 1.16 0.89 0.92 0.00 0.68

time (sec)

N/A 0.186 0.067 0.954 0.276 0.256 3.634 0.000 4.987

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 33 41 26 43 33 36 0 25

N.S.

1 0.89 1.11 0.70 1.16 0.89 0.97 0.00 0.68

time (sec)

N/A 0.186 0.078 0.992 0.281 0.242 1.933 0.000 5.128

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 31 41 26 43 33 36 0 25

N.S.

1 0.84 1.11 0.70 1.16 0.89 0.97 0.00 0.68

time (sec)

N/A 0.183 0.077 0.947 0.274 0.256 3.604 0.000 4.987

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 31 41 26 43 33 36 0 25

N.S.

1 0.84 1.11 0.70 1.16 0.89 0.97 0.00 0.68

time (sec)

N/A 0.186 0.076 0.944 0.285 0.252 3.602 0.000 5.371

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 109 30 27 0 34 0 34 33

N.S.

1 2.95 0.81 0.73 0.00 0.92 0.00 0.92 0.89

time (sec)

N/A 0.344 10.059 1.014 0.000 0.251 0.000 0.285 4.903

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

37 0 37 0 0 0 0 0 0

N.S.

1 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 0.983 0.000 0.000 0.000 0.000 0.000 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 41 37 57 0 26 42 0 0

N.S.

1 1.11 1.00 1.54 0.00 0.70 1.14 0.00 0.00

time (sec)

N/A 0.175 0.036 0.046 0.000 0.259 0.108 0.000 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 74 31 28 0 250 0 0 532

N.S.

1 1.95 0.82 0.74 0.00 6.58 0.00 0.00 14.00

time (sec)

N/A 0.688 15.155 1.941 0.000 0.352 0.000 0.000 4.912

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 74 31 28 0 299 0 0 531

N.S.

1 1.95 0.82 0.74 0.00 7.87 0.00 0.00 13.97

time (sec)

N/A 0.720 15.178 1.954 0.000 0.472 0.000 0.000 4.944

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 36 63 37 0 37 0 0 0

N.S.

1 0.95 1.66 0.97 0.00 0.97 0.00 0.00 0.00

time (sec)

N/A 0.315 5.172 2.782 0.000 0.286 0.000 0.000 0.000

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 40 61 37 0 37 0 0 0

N.S.

1 1.05 1.61 0.97 0.00 0.97 0.00 0.00 0.00

time (sec)

N/A 0.309 4.981 4.211 0.000 0.290 0.000 0.000 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 297 21 20 0 36 0 0 28

N.S.

1 7.82 0.55 0.53 0.00 0.95 0.00 0.00 0.74

time (sec)

N/A 1.514 11.151 0.970 0.000 0.253 0.000 0.000 4.907

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 49 38 36 48 34 138 35 189

N.S.

1 1.29 1.00 0.95 1.26 0.89 3.63 0.92 4.97

time (sec)

N/A 0.168 0.041 2.184 0.282 0.259 2.084 0.267 4.874

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 50 38 34 64 52 65 50 189

N.S.

1 1.32 1.00 0.89 1.68 1.37 1.71 1.32 4.97

time (sec)

N/A 0.166 0.048 1.553 0.197 0.260 2.089 0.265 5.109

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 50 34 34 60 49 65 78 189

N.S.

1 1.32 0.89 0.89 1.58 1.29 1.71 2.05 4.97

time (sec)

N/A 0.162 0.049 1.533 0.192 0.253 1.698 0.261 0.072

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 49 38 36 60 34 46 35 189

N.S.

1 1.29 1.00 0.95 1.58 0.89 1.21 0.92 4.97

time (sec)

N/A 0.165 0.037 2.015 0.281 0.252 8.326 0.260 4.923

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A F B F F B

verified

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

size

38 0 38 34 0 99 0 0 56

N.S.

1 0.00 1.00 0.89 0.00 2.61 0.00 0.00 1.47

time (sec)

N/A 0.000 0.640 2.640 0.000 0.328 0.000 0.000 5.849

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 42 38 25 30 34 66 29 29

N.S.

1 1.11 1.00 0.66 0.79 0.89 1.74 0.76 0.76

time (sec)

N/A 0.177 0.024 0.866 0.195 0.252 0.191 0.278 5.343

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 33 28 25 34 34 178 0 50

N.S.

1 0.87 0.74 0.66 0.89 0.89 4.68 0.00 1.32

time (sec)

N/A 0.260 0.444 1.116 0.300 0.247 2.570 0.000 0.347

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 33 28 25 0 34 180 0 58

N.S.

1 0.87 0.74 0.66 0.00 0.89 4.74 0.00 1.53

time (sec)

N/A 0.244 0.439 1.175 0.000 0.238 3.324 0.000 5.225

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 33 28 25 0 34 187 0 58

N.S.

1 0.87 0.74 0.66 0.00 0.89 4.92 0.00 1.53

time (sec)

N/A 0.263 0.433 1.210 0.000 0.257 3.422 0.000 5.246

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 89 28 25 46 34 199 0 61

N.S.

1 2.34 0.74 0.66 1.21 0.89 5.24 0.00 1.61

time (sec)

N/A 0.474 1.885 1.010 0.318 0.262 3.177 0.000 5.422

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 95 28 25 50 34 184 0 52

N.S.

1 2.50 0.74 0.66 1.32 0.89 4.84 0.00 1.37

time (sec)

N/A 0.454 0.806 1.153 0.321 0.259 2.807 0.000 5.251

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 95 28 25 46 34 194 0 52

N.S.

1 2.50 0.74 0.66 1.21 0.89 5.11 0.00 1.37

time (sec)

N/A 0.450 0.799 1.154 0.330 0.256 2.909 0.000 5.270

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 89 28 23 50 34 192 0 61

N.S.

1 2.34 0.74 0.61 1.32 0.89 5.05 0.00 1.61

time (sec)

N/A 0.467 1.891 0.996 0.319 0.253 3.037 0.000 5.746

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 95 28 25 50 34 185 0 52

N.S.

1 2.50 0.74 0.66 1.32 0.89 4.87 0.00 1.37

time (sec)

N/A 0.452 0.883 1.026 0.323 0.274 2.869 0.000 5.278

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 49 38 41 48 34 124 35 35

N.S.

1 1.29 1.00 1.08 1.26 0.89 3.26 0.92 0.92

time (sec)

N/A 0.163 0.034 1.321 0.279 0.241 2.202 0.276 5.148

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 50 38 37 76 52 87 49 47

N.S.

1 1.32 1.00 0.97 2.00 1.37 2.29 1.29 1.24

time (sec)

N/A 0.174 0.045 1.317 0.290 0.245 33.633 0.262 5.551

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 50 34 35 60 49 58 77 49

N.S.

1 1.32 0.89 0.92 1.58 1.29 1.53 2.03 1.29

time (sec)

N/A 0.162 0.045 1.228 0.199 0.250 1.789 0.264 5.086

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 49 38 41 60 34 44 35 35

N.S.

1 1.29 1.00 1.08 1.58 0.89 1.16 0.92 0.92

time (sec)

N/A 0.168 0.038 1.451 0.298 0.248 24.100 0.259 5.032

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 51 28 25 55 34 148 0 56

N.S.

1 1.34 0.74 0.66 1.45 0.89 3.89 0.00 1.47

time (sec)

N/A 0.294 0.709 0.958 0.325 0.240 1.944 0.000 5.214

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 33 28 25 55 34 187 0 59

N.S.

1 0.87 0.74 0.66 1.45 0.89 4.92 0.00 1.55

time (sec)

N/A 0.279 2.224 1.020 0.317 0.260 3.243 0.000 5.461

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 33 28 25 46 34 177 0 59

N.S.

1 0.87 0.74 0.66 1.21 0.89 4.66 0.00 1.55

time (sec)

N/A 0.289 1.990 1.101 0.305 0.284 3.105 0.000 5.273

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

38 0 40 12 0 36 0 76 0

N.S.

1 0.00 1.05 0.32 0.00 0.95 0.00 2.00 0.00

time (sec)

N/A 0.000 0.079 0.615 0.000 0.276 0.000 0.278 0.000

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 40 38 30 0 29 36 29 29

N.S.

1 1.05 1.00 0.79 0.00 0.76 0.95 0.76 0.76

time (sec)

N/A 0.187 0.037 2.096 0.000 0.258 9.393 0.268 5.196

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 41 38 58 0 29 36 29 29

N.S.

1 1.08 1.00 1.53 0.00 0.76 0.95 0.76 0.76

time (sec)

N/A 0.190 0.038 5.300 0.000 0.246 10.646 0.257 5.548

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 46 39 56 0 77 68 0 48

N.S.

1 1.18 1.00 1.44 0.00 1.97 1.74 0.00 1.23

time (sec)

N/A 0.215 10.014 1.579 0.000 0.659 1.580 0.000 5.552

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