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2.2.5 Integrals 401 to 494

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 C A C F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

349 354 347 100 332 91191 0 345 670

N.S.

1 1.01 0.99 0.29 0.95 261.29 0.00 0.99 1.92

time (sec)

N/A 0.553 0.251 0.849 0.271 12.487 0.000 0.278 0.261

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

322 328 321 90 318 90963 318 325 391

N.S.

1 1.02 1.00 0.28 0.99 282.49 0.99 1.01 1.21

time (sec)

N/A 0.517 0.219 0.819 0.268 2.742 3.727 0.304 9.255

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

241 246 224 66 238 43065 155 238 282

N.S.

1 1.02 0.93 0.27 0.99 178.69 0.64 0.99 1.17

time (sec)

N/A 0.405 0.137 0.866 0.272 1.356 0.610 0.300 0.157

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

202 225 183 46 189 183 39 194 58

N.S.

1 1.11 0.91 0.23 0.94 0.91 0.19 0.96 0.29

time (sec)

N/A 0.397 0.074 0.762 0.272 0.259 0.139 0.276 0.051

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

855 855 558 430 601 0 0 795 1591

N.S.

1 1.00 0.65 0.50 0.70 0.00 0.00 0.93 1.86

time (sec)

N/A 1.234 0.261 0.938 0.280 0.000 0.000 0.459 9.659

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1141 1141 807 534 961 0 0 1145 2246

N.S.

1 1.00 0.71 0.47 0.84 0.00 0.00 1.00 1.97

time (sec)

N/A 1.978 0.486 1.005 0.283 0.000 0.000 6.610 10.589

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1384 1384 996 680 1394 0 0 1557 3256

N.S.

1 1.00 0.72 0.49 1.01 0.00 0.00 1.12 2.35

time (sec)

N/A 2.357 0.732 1.044 0.317 0.000 0.000 0.387 10.849

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

394 408 388 141 392 95566 413 392 721

N.S.

1 1.04 0.98 0.36 0.99 242.55 1.05 0.99 1.83

time (sec)

N/A 0.652 0.249 0.810 0.282 13.227 131.883 0.319 0.275

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

360 374 358 126 364 91420 374 358 676

N.S.

1 1.04 0.99 0.35 1.01 253.94 1.04 0.99 1.88

time (sec)

N/A 0.607 0.225 0.838 0.275 7.152 14.652 0.282 0.268

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

266 280 249 86 269 43180 192 256 315

N.S.

1 1.05 0.94 0.32 1.01 162.33 0.72 0.96 1.18

time (sec)

N/A 0.478 0.135 0.841 0.291 2.106 1.193 0.280 0.175

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

219 250 200 57 212 255 63 204 80

N.S.

1 1.14 0.91 0.26 0.97 1.16 0.29 0.93 0.37

time (sec)

N/A 0.432 0.058 0.802 0.267 0.316 0.248 0.274 0.053

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1352 1352 835 677 1015 0 0 1311 2720

N.S.

1 1.00 0.62 0.50 0.75 0.00 0.00 0.97 2.01

time (sec)

N/A 1.844 0.448 1.019 0.310 0.000 0.000 0.345 10.551

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1830 1830 1115 829 1564 0 0 1809 3572

N.S.

1 1.00 0.61 0.45 0.85 0.00 0.00 0.99 1.95

time (sec)

N/A 3.134 0.804 1.100 0.338 0.000 0.000 46.908 11.176

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

2204 2204 1338 1008 2198 0 0 2200 6280

N.S.

1 1.00 0.61 0.46 1.00 0.00 0.00 1.00 2.85

time (sec)

N/A 3.507 1.474 1.210 0.336 0.000 0.000 0.436 12.674

Problem 415

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

32 33 33 29 28 28 34 28 30

N.S.

1 1.03 1.03 0.91 0.88 0.88 1.06 0.88 0.94

time (sec)

N/A 0.182 0.007 1.277 0.280 0.319 0.051 0.277 0.025

Problem 416

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

32 33 33 29 28 28 34 28 30

N.S.

1 1.03 1.03 0.91 0.88 0.88 1.06 0.88 0.94

time (sec)

N/A 0.212 0.005 0.743 0.276 0.274 0.057 0.287 0.020

Problem 417

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

32 36 31 27 26 26 36 26 30

N.S.

1 1.12 0.97 0.84 0.81 0.81 1.12 0.81 0.94

time (sec)

N/A 0.182 0.008 1.253 0.296 0.297 0.052 0.274 9.175

Problem 418

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

32 36 31 27 26 26 36 26 30

N.S.

1 1.12 0.97 0.84 0.81 0.81 1.12 0.81 0.94

time (sec)

N/A 0.215 0.004 0.868 0.273 0.268 0.056 0.336 0.020

Problem 419

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

45 45 42 29 35 45 39 44 34

N.S.

1 1.00 0.93 0.64 0.78 1.00 0.87 0.98 0.76

time (sec)

N/A 0.209 0.015 0.887 0.282 0.307 0.048 0.280 0.084

Problem 420

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

45 45 42 29 35 45 39 44 34

N.S.

1 1.00 0.93 0.64 0.78 1.00 0.87 0.98 0.76

time (sec)

N/A 0.214 0.004 0.031 0.271 0.335 0.055 0.284 0.026

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

6 6 23 7 17 17 15 15 6

N.S.

1 1.00 3.83 1.17 2.83 2.83 2.50 2.50 1.00

time (sec)

N/A 0.127 0.003 0.770 0.175 0.334 0.046 0.297 9.091

Problem 422

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

21 21 23 14 17 17 15 19 6

N.S.

1 1.00 1.10 0.67 0.81 0.81 0.71 0.90 0.29

time (sec)

N/A 0.150 0.002 0.798 0.179 0.347 0.043 0.303 0.083

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 11 10 9 24 22 9 9

N.S.

1 1.00 0.85 0.77 0.69 1.85 1.69 0.69 0.69

time (sec)

N/A 0.133 0.002 0.797 0.188 0.258 0.044 0.267 9.355

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 81 11 13 57 24 22 57 9

N.S.

1 6.23 0.85 1.00 4.38 1.85 1.69 4.38 0.69

time (sec)

N/A 0.184 0.004 0.941 0.186 0.252 0.137 0.275 0.015

Problem 425

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

69 83 78 67 66 66 85 68 94

N.S.

1 1.20 1.13 0.97 0.96 0.96 1.23 0.99 1.36

time (sec)

N/A 0.255 0.012 0.826 0.261 0.259 0.126 0.296 0.057

Problem 426

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

69 81 78 63 66 66 85 68 94

N.S.

1 1.17 1.13 0.91 0.96 0.96 1.23 0.99 1.36

time (sec)

N/A 0.275 0.004 0.058 0.257 0.264 0.129 0.287 0.021

Problem 427

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

24 24 31 21 20 20 20 21 20

N.S.

1 1.00 1.29 0.88 0.83 0.83 0.83 0.88 0.83

time (sec)

N/A 0.181 0.005 0.783 0.179 0.268 0.031 0.275 0.022

Problem 428

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

26 26 25 21 20 20 19 21 20

N.S.

1 1.00 0.96 0.81 0.77 0.77 0.73 0.81 0.77

time (sec)

N/A 0.174 0.004 0.786 0.184 0.270 0.029 0.290 0.019

Problem 429

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

17 24 22 16 15 18 15 15 17

N.S.

1 1.41 1.29 0.94 0.88 1.06 0.88 0.88 1.00

time (sec)

N/A 0.137 0.000 0.014 0.183 0.235 0.018 0.266 0.014

Problem 430

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

24 24 22 16 20 18 15 20 17

N.S.

1 1.00 0.92 0.67 0.83 0.75 0.62 0.83 0.71

time (sec)

N/A 0.147 0.001 0.020 0.178 0.222 0.019 0.279 0.012

Problem 431

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

22 22 24 23 22 25 20 23 28

N.S.

1 1.00 1.09 1.05 1.00 1.14 0.91 1.05 1.27

time (sec)

N/A 0.166 0.005 0.773 0.273 0.262 0.064 0.295 0.025

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

17 17 27 16 15 15 15 18 15

N.S.

1 1.00 1.59 0.94 0.88 0.88 0.88 1.06 0.88

time (sec)

N/A 0.161 0.004 0.806 0.193 0.250 0.059 0.294 9.175

Problem 433

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

19 25 19 14 13 13 12 16 13

N.S.

1 1.32 1.00 0.74 0.68 0.68 0.63 0.84 0.68

time (sec)

N/A 0.182 0.005 0.806 0.192 0.253 0.040 0.284 0.045

Problem 434

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

12 12 17 11 10 10 8 13 10

N.S.

1 1.00 1.42 0.92 0.83 0.83 0.67 1.08 0.83

time (sec)

N/A 0.146 0.006 0.814 0.182 0.255 0.036 0.274 0.028

Problem 435

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

10 10 11 11 10 10 8 11 10

N.S.

1 1.00 1.10 1.10 1.00 1.00 0.80 1.10 1.00

time (sec)

N/A 0.151 0.006 0.791 0.188 0.257 0.063 0.280 0.033

Problem 436

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

17 17 17 16 15 15 15 18 15

N.S.

1 1.00 1.00 0.94 0.88 0.88 0.88 1.06 0.88

time (sec)

N/A 0.174 0.005 0.810 0.194 0.251 0.058 0.279 9.603

Problem 437

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

23 23 23 18 17 17 17 18 21

N.S.

1 1.00 1.00 0.78 0.74 0.74 0.74 0.78 0.91

time (sec)

N/A 0.173 0.005 0.798 0.261 0.256 0.061 0.269 9.448

Problem 438

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

15 15 15 14 13 13 10 13 13

N.S.

1 1.00 1.00 0.93 0.87 0.87 0.67 0.87 0.87

time (sec)

N/A 0.147 0.004 0.031 0.186 0.236 0.038 0.271 0.025

Problem 439

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

21 21 21 18 17 17 20 20 17

N.S.

1 1.00 1.00 0.86 0.81 0.81 0.95 0.95 0.81

time (sec)

N/A 0.178 0.006 0.043 0.181 0.240 0.062 0.271 9.553

Problem 440

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

10 10 9 11 9 9 7 9 10

N.S.

1 1.00 0.90 1.10 0.90 0.90 0.70 0.90 1.00

time (sec)

N/A 0.159 0.005 0.033 0.179 0.238 0.032 0.276 0.026

Problem 441

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

25 25 25 18 17 17 20 20 17

N.S.

1 1.00 1.00 0.72 0.68 0.68 0.80 0.80 0.68

time (sec)

N/A 0.179 0.006 0.041 0.184 0.235 0.062 0.290 0.070

Problem 442

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

14 14 14 15 14 14 12 14 14

N.S.

1 1.00 1.00 1.07 1.00 1.00 0.86 1.00 1.00

time (sec)

N/A 0.171 0.004 0.806 0.264 0.229 0.047 0.299 0.019

Problem 443

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

13 13 14 13 11 16 17 11 20

N.S.

1 1.00 1.08 1.00 0.85 1.23 1.31 0.85 1.54

time (sec)

N/A 0.147 0.006 0.829 0.185 0.230 0.055 0.280 9.884

Problem 444

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

26 26 25 26 26 25 20 27 25

N.S.

1 1.00 0.96 1.00 1.00 0.96 0.77 1.04 0.96

time (sec)

N/A 0.196 0.006 0.812 0.184 0.252 0.082 0.275 9.334

Problem 445

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

6 6 4 5 4 4 3 5 4

N.S.

1 1.00 0.67 0.83 0.67 0.67 0.50 0.83 0.67

time (sec)

N/A 0.141 0.001 0.023 0.191 0.247 0.020 0.310 0.010

Problem 446

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

20 24 20 19 20 25 19 27 18

N.S.

1 1.20 1.00 0.95 1.00 1.25 0.95 1.35 0.90

time (sec)

N/A 0.161 0.005 0.810 0.197 0.271 0.045 0.289 0.022

Problem 447

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 43 40 28 27 27 31 28 44

N.S.

1 1.13 1.05 0.74 0.71 0.71 0.82 0.74 1.16

time (sec)

N/A 0.167 0.008 0.770 0.280 0.252 0.060 0.292 0.095

Problem 448

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

17 17 18 16 15 15 14 16 15

N.S.

1 1.00 1.06 0.94 0.88 0.88 0.82 0.94 0.88

time (sec)

N/A 0.151 0.003 0.808 0.190 0.234 0.029 0.263 0.018

Problem 449

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

31 36 36 22 21 21 22 22 25

N.S.

1 1.16 1.16 0.71 0.68 0.68 0.71 0.71 0.81

time (sec)

N/A 0.155 0.005 0.835 0.277 0.252 0.066 0.297 9.316

Problem 450

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

19 25 19 14 17 15 17 17 13

N.S.

1 1.32 1.00 0.74 0.89 0.79 0.89 0.89 0.68

time (sec)

N/A 0.167 0.006 0.835 0.192 0.244 0.050 0.291 0.061

Problem 451

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

11 11 9 9 9 9 8 11 9

N.S.

1 1.00 0.82 0.82 0.82 0.82 0.73 1.00 0.82

time (sec)

N/A 0.143 0.003 0.796 0.203 0.252 0.035 0.303 9.010

Problem 452

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

18 18 18 13 12 12 14 12 12

N.S.

1 1.00 1.00 0.72 0.67 0.67 0.78 0.67 0.67

time (sec)

N/A 0.162 0.005 0.078 0.281 0.260 0.070 0.293 8.844

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 44 39 46 83 46 52 45

N.S.

1 1.00 0.96 0.85 1.00 1.80 1.00 1.13 0.98

time (sec)

N/A 0.181 0.012 0.779 0.195 0.257 0.094 0.274 8.875

Problem 454

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

12 12 10 9 8 8 7 9 8

N.S.

1 1.00 0.83 0.75 0.67 0.67 0.58 0.75 0.67

time (sec)

N/A 0.131 0.002 0.793 0.190 0.237 0.032 0.304 9.268

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 27 23 23 34 20 25 17

N.S.

1 1.00 1.29 1.10 1.10 1.62 0.95 1.19 0.81

time (sec)

N/A 0.140 0.006 0.812 0.196 0.268 0.049 0.309 0.017

Problem 456

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

19 19 19 16 15 21 12 15 17

N.S.

1 1.00 1.00 0.84 0.79 1.11 0.63 0.79 0.89

time (sec)

N/A 0.135 0.006 0.839 0.285 0.256 0.052 0.268 0.016

Problem 457

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

10 10 10 7 8 8 7 9 6

N.S.

1 1.00 1.00 0.70 0.80 0.80 0.70 0.90 0.60

time (sec)

N/A 0.123 0.002 0.795 0.189 0.248 0.018 0.294 0.041

Problem 458

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

10 10 10 11 10 10 20 10 10

N.S.

1 1.00 1.00 1.10 1.00 1.00 2.00 1.00 1.00

time (sec)

N/A 0.132 0.002 0.842 0.282 0.239 0.052 0.287 0.023

Problem 459

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

24 24 24 16 15 67 53 15 16

N.S.

1 1.00 1.00 0.67 0.62 2.79 2.21 0.62 0.67

time (sec)

N/A 0.137 0.003 0.802 0.268 0.265 0.060 0.284 8.861

Problem 460

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

19 19 19 17 16 16 26 16 16

N.S.

1 1.00 1.00 0.89 0.84 0.84 1.37 0.84 0.84

time (sec)

N/A 0.145 0.004 1.238 0.275 0.241 0.049 0.275 8.792

Problem 461

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

22 22 22 17 16 16 17 16 17

N.S.

1 1.00 1.00 0.77 0.73 0.73 0.77 0.73 0.77

time (sec)

N/A 0.152 0.001 0.823 0.188 0.232 0.016 0.281 0.019

Problem 462

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

22 22 22 17 16 16 15 16 17

N.S.

1 1.00 1.00 0.77 0.73 0.73 0.68 0.73 0.77

time (sec)

N/A 0.154 0.001 0.806 0.187 0.239 0.016 0.292 0.017

Problem 463

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

16 16 16 15 14 15 10 14 15

N.S.

1 1.00 1.00 0.94 0.88 0.94 0.62 0.88 0.94

time (sec)

N/A 0.165 0.001 0.025 0.200 0.252 0.026 0.262 0.015

Problem 464

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

37 40 37 31 30 30 39 30 30

N.S.

1 1.08 1.00 0.84 0.81 0.81 1.05 0.81 0.81

time (sec)

N/A 0.182 0.008 1.357 0.273 0.263 0.053 0.275 0.026

Problem 465

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

14 14 14 13 12 12 10 12 13

N.S.

1 1.00 1.00 0.93 0.86 0.86 0.71 0.86 0.93

time (sec)

N/A 0.154 0.000 0.790 0.196 0.240 0.017 0.272 0.013

Problem 466

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

11 11 11 7 9 9 7 9 6

N.S.

1 1.00 1.00 0.64 0.82 0.82 0.64 0.82 0.55

time (sec)

N/A 0.134 0.000 0.773 0.186 0.243 0.018 0.271 0.010

Problem 467

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

25 28 25 20 19 19 20 20 25

N.S.

1 1.12 1.00 0.80 0.76 0.76 0.80 0.80 1.00

time (sec)

N/A 0.159 0.007 0.807 0.280 0.263 0.067 0.286 9.095

Problem 468

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

25 26 25 20 19 19 19 20 25

N.S.

1 1.04 1.00 0.80 0.76 0.76 0.76 0.80 1.00

time (sec)

N/A 0.155 0.004 0.795 0.271 0.282 0.061 0.316 0.025

Problem 469

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

25 26 25 20 19 19 19 20 25

N.S.

1 1.04 1.00 0.80 0.76 0.76 0.76 0.80 1.00

time (sec)

N/A 0.154 0.005 0.811 0.276 0.248 0.055 0.287 8.869

Problem 470

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

9 7 7 8 7 12 5 8 7

N.S.

1 0.78 0.78 0.89 0.78 1.33 0.56 0.89 0.78

time (sec)

N/A 0.146 0.003 0.793 0.214 0.245 0.032 0.300 0.012

Problem 471

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

22 22 22 17 16 16 20 16 16

N.S.

1 1.00 1.00 0.77 0.73 0.73 0.91 0.73 0.73

time (sec)

N/A 0.151 0.010 0.072 0.279 0.244 0.071 0.291 0.033

Problem 472

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

37 40 37 31 30 30 44 30 30

N.S.

1 1.08 1.00 0.84 0.81 0.81 1.19 0.81 0.81

time (sec)

N/A 0.180 0.011 1.368 0.284 0.235 0.058 0.287 0.027

Problem 473

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

15 15 15 14 15 19 14 16 13

N.S.

1 1.00 1.00 0.93 1.00 1.27 0.93 1.07 0.87

time (sec)

N/A 0.163 0.002 0.031 0.204 0.241 0.037 0.276 8.823

Problem 474

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

15 15 15 14 13 15 10 14 13

N.S.

1 1.00 1.00 0.93 0.87 1.00 0.67 0.93 0.87

time (sec)

N/A 0.161 0.001 0.028 0.191 0.235 0.030 0.269 0.013

Problem 475

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

11 19 11 12 13 11 8 13 11

N.S.

1 1.73 1.00 1.09 1.18 1.00 0.73 1.18 1.00

time (sec)

N/A 0.161 0.003 0.838 0.197 0.250 0.040 0.270 0.033

Problem 476

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

22 27 19 18 17 17 17 17 17

N.S.

1 1.23 0.86 0.82 0.77 0.77 0.77 0.77 0.77

time (sec)

N/A 0.156 0.001 0.062 0.190 0.231 0.020 0.283 0.017

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 10 19 19 19 9 9

N.S.

1 1.00 1.00 0.91 1.73 1.73 1.73 0.82 0.82

time (sec)

N/A 0.128 0.001 0.800 0.185 0.234 0.018 0.261 0.081

Problem 478

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

13 13 16 12 13 13 12 14 11

N.S.

1 1.00 1.23 0.92 1.00 1.00 0.92 1.08 0.85

time (sec)

N/A 0.150 0.003 0.811 0.202 0.259 0.029 0.297 0.020

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

16 16 16 15 14 18 14 16 12

N.S.

1 1.00 1.00 0.94 0.88 1.12 0.88 1.00 0.75

time (sec)

N/A 0.156 0.003 0.827 0.192 0.267 0.043 0.282 0.021

Problem 480

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

27 31 26 24 25 39 24 27 23

N.S.

1 1.15 0.96 0.89 0.93 1.44 0.89 1.00 0.85

time (sec)

N/A 0.183 0.012 0.042 0.195 0.252 0.048 0.284 8.809

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

17 17 18 16 15 15 12 16 15

N.S.

1 1.00 1.06 0.94 0.88 0.88 0.71 0.94 0.88

time (sec)

N/A 0.151 0.003 0.816 0.186 0.276 0.029 0.267 0.015

Problem 482

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

18 18 18 17 16 20 15 17 16

N.S.

1 1.00 1.00 0.94 0.89 1.11 0.83 0.94 0.89

time (sec)

N/A 0.168 0.001 0.032 0.188 0.249 0.029 0.264 0.015

Problem 483

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

18 18 18 15 14 14 14 14 13

N.S.

1 1.00 1.00 0.83 0.78 0.78 0.78 0.78 0.72

time (sec)

N/A 0.153 0.001 0.049 0.266 0.257 0.018 0.291 0.013

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 23 22 34 46 31 25 23

N.S.

1 1.00 1.00 0.96 1.48 2.00 1.35 1.09 1.00

time (sec)

N/A 0.181 0.007 0.789 0.192 0.275 0.048 0.277 0.019

Problem 485

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

16 16 12 13 12 15 10 32 12

N.S.

1 1.00 0.75 0.81 0.75 0.94 0.62 2.00 0.75

time (sec)

N/A 0.139 0.007 0.851 0.270 0.288 0.052 0.271 9.022

Problem 486

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

29 29 30 26 25 25 24 26 25

N.S.

1 1.00 1.03 0.90 0.86 0.86 0.83 0.90 0.86

time (sec)

N/A 0.184 0.007 0.804 0.192 0.249 0.030 0.281 0.015

Problem 487

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

16 16 16 13 12 12 10 12 13

N.S.

1 1.00 1.00 0.81 0.75 0.75 0.62 0.75 0.81

time (sec)

N/A 0.160 0.000 0.793 0.197 0.243 0.020 0.279 0.012

Problem 488

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

17 17 17 13 17 25 14 12 17

N.S.

1 1.00 1.00 0.76 1.00 1.47 0.82 0.71 1.00

time (sec)

N/A 0.163 0.010 0.859 0.279 0.251 0.065 0.280 0.018

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 50 47 43 0 190 151 46 42

N.S.

1 1.06 1.00 0.91 0.00 4.04 3.21 0.98 0.89

time (sec)

N/A 0.200 0.019 1.286 0.000 0.272 0.163 0.280 0.055

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 60 61 61 0 240 294 60 82

N.S.

1 1.05 1.07 1.07 0.00 4.21 5.16 1.05 1.44

time (sec)

N/A 0.214 0.018 1.307 0.000 0.264 0.184 0.274 0.037

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 190 39 36 0 53 24 147 101

N.S.

1 1.01 0.21 0.19 0.00 0.28 0.13 0.78 0.54

time (sec)

N/A 0.415 0.032 0.108 0.000 0.288 0.304 0.653 0.057

Problem 492

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

60 64 27 28 65 65 60 30 27

N.S.

1 1.07 0.45 0.47 1.08 1.08 1.00 0.50 0.45

time (sec)

N/A 0.433 0.010 0.054 0.195 0.278 0.090 0.290 8.996

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B B B B B

verified

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

size

27 0 27 28 65 65 60 197 27

N.S.

1 0.00 1.00 1.04 2.41 2.41 2.22 7.30 1.00

time (sec)

N/A 0.000 0.006 0.110 0.232 0.273 0.149 0.285 0.025

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B B B B B

verified

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

size

27 0 27 28 65 65 60 111 27

N.S.

1 0.00 1.00 1.04 2.41 2.41 2.22 4.11 1.00

time (sec)

N/A 0.000 0.005 0.089 0.192 0.267 0.112 0.309 0.023

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