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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 C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 15 19 13 23 37 0 25 11

N.S.

1 1.36 1.73 1.18 2.09 3.36 0.00 2.27 1.00

time (sec)

N/A 0.167 0.003 0.147 0.203 0.247 0.000 0.266 0.070

Problem 402

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

10 10 12 16 35 18 15 18 20

N.S.

1 1.00 1.20 1.60 3.50 1.80 1.50 1.80 2.00

time (sec)

N/A 0.196 0.277 0.184 0.278 0.247 3.293 0.257 2.182

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

10 10 12 16 46 18 17 18 20

N.S.

1 1.00 1.20 1.60 4.60 1.80 1.70 1.80 2.00

time (sec)

N/A 0.192 0.717 0.242 0.251 0.251 3.826 0.267 2.245

Problem 404

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

16 16 18 18 20 20 0 20 22

N.S.

1 1.00 1.12 1.12 1.25 1.25 0.00 1.25 1.38

time (sec)

N/A 0.391 17.231 0.253 0.395 0.244 0.000 0.270 2.210

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 225 175 246 206 511 0 0 0

N.S.

1 1.36 1.06 1.49 1.25 3.10 0.00 0.00 0.00

time (sec)

N/A 1.086 0.166 0.602 0.266 0.267 0.000 0.000 0.000

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 151 125 196 152 391 0 0 0

N.S.

1 1.31 1.09 1.70 1.32 3.40 0.00 0.00 0.00

time (sec)

N/A 0.780 0.113 0.625 0.264 0.256 0.000 0.000 0.000

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 88 73 139 94 255 0 0 0

N.S.

1 1.33 1.11 2.11 1.42 3.86 0.00 0.00 0.00

time (sec)

N/A 0.441 0.054 0.629 0.256 0.253 0.000 0.000 0.000

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 21 42 21 59 113 0 44 53

N.S.

1 0.91 1.83 0.91 2.57 4.91 0.00 1.91 2.30

time (sec)

N/A 0.191 0.008 0.372 0.196 0.266 0.000 0.270 2.228

Problem 409

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

16 16 18 18 20 20 17 20 22

N.S.

1 1.00 1.12 1.12 1.25 1.25 1.06 1.25 1.38

time (sec)

N/A 0.447 8.899 0.353 0.400 0.252 9.383 0.432 2.230

Problem 410

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

16 16 18 18 20 20 19 20 22

N.S.

1 1.00 1.12 1.12 1.25 1.25 1.19 1.25 1.38

time (sec)

N/A 0.545 24.615 0.381 0.400 0.250 10.631 0.440 2.236

Problem 411

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

18 18 20 18 20 20 0 20 22

N.S.

1 1.00 1.11 1.00 1.11 1.11 0.00 1.11 1.22

time (sec)

N/A 0.518 16.830 0.277 0.422 0.255 0.000 0.286 2.380

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

180 246 236 272 225 876 0 0 0

N.S.

1 1.37 1.31 1.51 1.25 4.87 0.00 0.00 0.00

time (sec)

N/A 1.252 0.457 1.139 0.281 0.259 0.000 0.000 0.000

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 172 178 222 171 697 0 0 0

N.S.

1 1.37 1.41 1.76 1.36 5.53 0.00 0.00 0.00

time (sec)

N/A 0.930 0.249 1.142 0.273 0.271 0.000 0.000 0.000

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 120 72 162 113 488 0 0 0

N.S.

1 1.36 0.82 1.84 1.28 5.55 0.00 0.00 0.00

time (sec)

N/A 0.617 0.302 1.018 0.266 0.266 0.000 0.000 0.000

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 28 25 23 70 203 0 63 49

N.S.

1 1.04 0.93 0.85 2.59 7.52 0.00 2.33 1.81

time (sec)

N/A 0.208 0.009 0.772 0.199 0.258 0.000 0.275 0.065

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

18 18 20 18 57 20 17 20 22

N.S.

1 1.00 1.11 1.00 3.17 1.11 0.94 1.11 1.22

time (sec)

N/A 0.560 7.144 0.396 0.323 0.263 21.801 0.281 2.285

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

18 18 20 18 72 20 19 20 22

N.S.

1 1.00 1.11 1.00 4.00 1.11 1.06 1.11 1.22

time (sec)

N/A 0.651 7.397 0.435 0.330 0.240 26.594 0.279 2.296

Problem 418

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

33 33 33 48 0 336 0 101 48

N.S.

1 1.00 1.00 1.45 0.00 10.18 0.00 3.06 1.45

time (sec)

N/A 0.354 0.038 0.327 0.000 0.272 0.000 0.266 0.130

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 98 64 87 0 617 0 0 0

N.S.

1 1.34 0.88 1.19 0.00 8.45 0.00 0.00 0.00

time (sec)

N/A 0.657 0.093 0.334 0.000 0.264 0.000 0.000 0.000

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 125 85 117 0 875 0 0 0

N.S.

1 1.23 0.83 1.15 0.00 8.58 0.00 0.00 0.00

time (sec)

N/A 0.802 0.098 0.361 0.000 0.279 0.000 0.000 0.000

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 141 56 82 146 916 0 0 0

N.S.

1 2.24 0.89 1.30 2.32 14.54 0.00 0.00 0.00

time (sec)

N/A 1.075 0.066 0.428 0.237 0.273 0.000 0.000 0.000

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

96 0 135 127 174 1512 0 0 0

N.S.

1 0.00 1.41 1.32 1.81 15.75 0.00 0.00 0.00

time (sec)

N/A 0.000 0.190 0.451 0.240 0.285 0.000 0.000 0.000

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

158 0 191 184 238 2067 0 0 0

N.S.

1 0.00 1.21 1.16 1.51 13.08 0.00 0.00 0.00

time (sec)

N/A 0.000 0.638 0.449 0.249 0.270 0.000 0.000 0.000

Problem 424

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

16 16 18 18 20 20 0 20 20

N.S.

1 1.00 1.12 1.12 1.25 1.25 0.00 1.25 1.25

time (sec)

N/A 0.462 15.271 0.117 0.337 0.249 0.000 0.274 2.291

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 117 109 174 121 551 0 0 0

N.S.

1 1.26 1.17 1.87 1.30 5.92 0.00 0.00 0.00

time (sec)

N/A 0.519 0.200 0.441 0.266 0.268 0.000 0.000 0.000

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 73 69 134 83 367 0 0 0

N.S.

1 1.24 1.17 2.27 1.41 6.22 0.00 0.00 0.00

time (sec)

N/A 0.355 0.199 0.407 0.262 0.251 0.000 0.000 0.000

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 114 54 64 169 0 93 53

N.S.

1 1.00 4.56 2.16 2.56 6.76 0.00 3.72 2.12

time (sec)

N/A 0.237 0.038 0.369 0.248 0.249 0.000 0.276 0.131

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 12 25 56 0 25 13

N.S.

1 1.00 1.00 1.09 2.27 5.09 0.00 2.27 1.18

time (sec)

N/A 0.182 0.003 0.155 0.189 0.253 0.000 0.265 2.273

Problem 429

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

16 16 18 18 79 20 17 20 20

N.S.

1 1.00 1.12 1.12 4.94 1.25 1.06 1.25 1.25

time (sec)

N/A 0.296 22.777 0.231 0.288 0.258 9.118 0.472 2.287

Problem 430

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

16 16 18 18 79 20 19 20 20

N.S.

1 1.00 1.12 1.12 4.94 1.25 1.19 1.25 1.25

time (sec)

N/A 0.341 32.498 0.232 0.293 0.286 11.472 0.748 2.404

Problem 431

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

12 12 14 20 145 22 0 22 22

N.S.

1 1.00 1.17 1.67 12.08 1.83 0.00 1.83 1.83

time (sec)

N/A 0.219 7.611 0.248 0.724 0.260 0.000 0.281 2.328

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 131 222 198 146 632 0 0 0

N.S.

1 1.51 2.55 2.28 1.68 7.26 0.00 0.00 0.00

time (sec)

N/A 0.635 0.606 0.990 0.267 0.269 0.000 0.000 0.000

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 96 117 156 108 453 0 0 0

N.S.

1 1.48 1.80 2.40 1.66 6.97 0.00 0.00 0.00

time (sec)

N/A 0.475 0.953 0.991 0.273 0.260 0.000 0.000 0.000

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 35 46 54 115 189 0 98 45

N.S.

1 1.13 1.48 1.74 3.71 6.10 0.00 3.16 1.45

time (sec)

N/A 0.260 0.088 0.862 0.236 0.257 0.000 0.272 2.720

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 27 18 25 33 0 24 20

N.S.

1 1.00 2.08 1.38 1.92 2.54 0.00 1.85 1.54

time (sec)

N/A 0.179 0.002 0.231 0.196 0.273 0.000 0.268 0.079

Problem 436

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

12 12 14 20 69 22 19 22 22

N.S.

1 1.00 1.17 1.67 5.75 1.83 1.58 1.83 1.83

time (sec)

N/A 0.208 0.126 0.330 0.310 0.260 21.531 0.280 2.362

Problem 437

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

12 12 14 20 91 22 20 22 22

N.S.

1 1.00 1.17 1.67 7.58 1.83 1.67 1.83 1.83

time (sec)

N/A 0.212 0.729 0.307 0.310 0.252 25.975 0.263 2.330

Problem 438

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

18 18 20 20 22 22 0 22 22

N.S.

1 1.00 1.11 1.11 1.22 1.22 0.00 1.22 1.22

time (sec)

N/A 0.513 26.427 0.255 0.435 0.258 0.000 0.275 2.377

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 184 219 241 216 1055 0 0 0

N.S.

1 1.29 1.53 1.69 1.51 7.38 0.00 0.00 0.00

time (sec)

N/A 1.100 0.317 0.612 0.279 0.275 0.000 0.000 0.000

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 121 152 185 157 731 0 0 0

N.S.

1 1.27 1.60 1.95 1.65 7.69 0.00 0.00 0.00

time (sec)

N/A 0.768 0.221 0.594 0.281 0.270 0.000 0.000 0.000

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 79 89 109 367 0 144 95

N.S.

1 1.00 1.68 1.89 2.32 7.81 0.00 3.06 2.02

time (sec)

N/A 0.438 0.321 0.563 0.272 0.260 0.000 0.301 0.100

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 28 22 33 56 31 0 45 22

N.S.

1 1.27 1.00 1.50 2.55 1.41 0.00 2.05 1.00

time (sec)

N/A 0.213 0.005 0.330 0.191 0.252 0.000 0.266 2.315

Problem 443

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

18 18 20 20 94 22 19 22 22

N.S.

1 1.00 1.11 1.11 5.22 1.22 1.06 1.22 1.22

time (sec)

N/A 0.534 18.292 0.308 0.332 0.261 52.124 0.750 2.391

Problem 444

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

18 18 20 20 102 22 20 22 22

N.S.

1 1.00 1.11 1.11 5.67 1.22 1.11 1.22 1.22

time (sec)

N/A 0.644 14.331 0.312 0.333 0.248 70.250 1.628 2.397

Problem 445

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

18 18 20 18 20 20 0 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.11 0.00 1.11 1.11

time (sec)

N/A 0.532 35.339 0.104 0.367 0.256 0.000 0.281 2.478

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 114 118 177 130 979 0 0 0

N.S.

1 1.37 1.42 2.13 1.57 11.80 0.00 0.00 0.00

time (sec)

N/A 0.575 1.103 0.535 0.264 0.270 0.000 0.000 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 52 55 72 107 383 0 139 101

N.S.

1 1.24 1.31 1.71 2.55 9.12 0.00 3.31 2.40

time (sec)

N/A 0.354 0.095 0.424 0.268 0.259 0.000 0.275 2.318

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 30 43 130 107 0 184 36

N.S.

1 1.00 1.00 1.43 4.33 3.57 0.00 6.13 1.20

time (sec)

N/A 0.246 0.178 0.381 0.208 0.250 0.000 0.270 2.367

Problem 449

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

15 15 15 14 25 86 0 27 13

N.S.

1 1.00 1.00 0.93 1.67 5.73 0.00 1.80 0.87

time (sec)

N/A 0.191 0.003 0.170 0.185 0.250 0.000 0.268 2.380

Problem 450

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

18 18 20 18 128 20 17 20 20

N.S.

1 1.00 1.11 1.00 7.11 1.11 0.94 1.11 1.11

time (sec)

N/A 0.320 15.930 0.213 0.306 0.258 21.179 0.273 2.455

Problem 451

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

18 18 20 18 127 20 19 20 20

N.S.

1 1.00 1.11 1.00 7.06 1.11 1.06 1.11 1.11

time (sec)

N/A 0.383 19.038 0.201 0.307 0.246 27.851 0.265 2.428

Problem 452

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

18 18 20 20 22 22 0 22 22

N.S.

1 1.00 1.11 1.11 1.22 1.22 0.00 1.22 1.22

time (sec)

N/A 0.301 164.808 0.201 0.406 0.258 0.000 0.275 2.387

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

201 398 280 340 262 1802 0 0 0

N.S.

1 1.98 1.39 1.69 1.30 8.97 0.00 0.00 0.00

time (sec)

N/A 1.712 3.309 1.093 0.282 0.284 0.000 0.000 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 256 222 210 197 1311 0 0 0

N.S.

1 2.08 1.80 1.71 1.60 10.66 0.00 0.00 0.00

time (sec)

N/A 1.272 1.835 1.052 0.289 0.279 0.000 0.000 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 153 116 156 124 842 0 0 0

N.S.

1 1.87 1.41 1.90 1.51 10.27 0.00 0.00 0.00

time (sec)

N/A 0.697 0.864 1.042 0.277 0.264 0.000 0.000 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 42 75 45 84 387 0 84 87

N.S.

1 1.24 2.21 1.32 2.47 11.38 0.00 2.47 2.56

time (sec)

N/A 0.260 0.008 0.779 0.200 0.253 0.000 0.266 2.333

Problem 457

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

18 18 20 20 157 22 19 22 22

N.S.

1 1.00 1.11 1.11 8.72 1.22 1.06 1.22 1.22

time (sec)

N/A 0.289 47.096 0.348 0.325 0.263 51.835 1.706 2.358

Problem 458

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

18 18 20 20 159 22 20 22 22

N.S.

1 1.00 1.11 1.11 8.83 1.22 1.11 1.22 1.22

time (sec)

N/A 0.298 47.665 0.373 0.326 0.253 61.924 2.492 2.398

Problem 459

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

12 12 14 20 173 22 0 22 22

N.S.

1 1.00 1.17 1.67 14.42 1.83 0.00 1.83 1.83

time (sec)

N/A 0.208 89.980 0.243 0.771 0.264 0.000 0.358 2.482

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 266 422 375 302 1985 0 0 0

N.S.

1 1.49 2.36 2.09 1.69 11.09 0.00 0.00 0.00

time (sec)

N/A 1.439 2.144 0.527 0.252 0.292 0.000 0.000 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 168 314 246 226 1467 0 0 0

N.S.

1 1.47 2.75 2.16 1.98 12.87 0.00 0.00 0.00

time (sec)

N/A 0.906 2.090 0.525 0.280 0.284 0.000 0.000 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 112 131 164 149 975 0 0 0

N.S.

1 1.37 1.60 2.00 1.82 11.89 0.00 0.00 0.00

time (sec)

N/A 0.520 0.937 0.518 0.265 0.279 0.000 0.000 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 40 34 23 79 346 0 66 25

N.S.

1 1.48 1.26 0.85 2.93 12.81 0.00 2.44 0.93

time (sec)

N/A 0.244 0.043 0.315 0.196 0.262 0.000 0.307 2.335

Problem 464

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

12 12 14 20 144 22 19 22 22

N.S.

1 1.00 1.17 1.67 12.00 1.83 1.58 1.83 1.83

time (sec)

N/A 0.209 0.262 0.332 0.310 0.260 118.960 0.284 2.560

Problem 465

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

12 12 14 20 175 22 20 22 22

N.S.

1 1.00 1.17 1.67 14.58 1.83 1.67 1.83 1.83

time (sec)

N/A 0.210 0.210 0.339 0.317 0.277 159.591 0.274 2.565

Problem 466

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

16 16 18 16 18 18 17 18 22

N.S.

1 1.00 1.12 1.00 1.12 1.12 1.06 1.12 1.38

time (sec)

N/A 0.395 8.760 0.100 0.314 0.251 0.342 0.265 2.389

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 184 150 241 203 448 0 0 0

N.S.

1 1.24 1.01 1.63 1.37 3.03 0.00 0.00 0.00

time (sec)

N/A 0.698 0.255 0.844 0.208 0.259 0.000 0.000 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 124 108 186 148 351 0 0 0

N.S.

1 1.28 1.11 1.92 1.53 3.62 0.00 0.00 0.00

time (sec)

N/A 0.495 0.194 0.674 0.189 0.263 0.000 0.000 0.000

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 68 67 125 87 224 0 0 0

N.S.

1 1.17 1.16 2.16 1.50 3.86 0.00 0.00 0.00

time (sec)

N/A 0.338 0.164 0.529 0.197 0.275 0.000 0.000 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 15 31 12 50 60 0 41 30

N.S.

1 1.36 2.82 1.09 4.55 5.45 0.00 3.73 2.73

time (sec)

N/A 0.182 0.005 0.356 0.269 0.267 0.000 0.257 0.069

Problem 471

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

16 16 18 16 18 18 15 18 22

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.94 1.12 1.38

time (sec)

N/A 0.246 13.677 0.201 0.314 0.256 0.537 0.298 2.318

Problem 472

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

16 16 18 16 18 18 17 18 22

N.S.

1 1.00 1.12 1.00 1.12 1.12 1.06 1.12 1.38

time (sec)

N/A 0.243 13.794 0.199 0.312 0.265 0.385 0.359 2.303

Problem 473

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

18 18 20 18 20 20 19 20 22

N.S.

1 1.00 1.11 1.00 1.11 1.11 1.06 1.11 1.22

time (sec)

N/A 0.485 102.848 0.114 0.302 0.263 0.382 0.264 2.398

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

226 262 263 0 0 1280 0 0 0

N.S.

1 1.16 1.16 0.00 0.00 5.66 0.00 0.00 0.00

time (sec)

N/A 0.609 0.267 0.000 0.000 0.303 0.000 0.000 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

146 179 181 0 0 937 0 0 0

N.S.

1 1.23 1.24 0.00 0.00 6.42 0.00 0.00 0.00

time (sec)

N/A 0.479 0.175 0.000 0.000 0.278 0.000 0.000 0.000

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 78 95 90 401 0 0 0

N.S.

1 1.00 1.16 1.42 1.34 5.99 0.00 0.00 0.00

time (sec)

N/A 0.312 0.284 1.309 0.291 0.253 0.000 0.000 0.000

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 20 42 23 61 155 0 64 52

N.S.

1 0.87 1.83 1.00 2.65 6.74 0.00 2.78 2.26

time (sec)

N/A 0.200 0.006 0.822 0.189 0.254 0.000 0.277 0.067

Problem 478

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

18 18 20 18 99 20 17 20 22

N.S.

1 1.00 1.11 1.00 5.50 1.11 0.94 1.11 1.22

time (sec)

N/A 0.366 35.641 0.194 0.320 0.259 0.752 0.968 2.295

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

18 18 20 18 111 20 19 20 22

N.S.

1 1.00 1.11 1.00 6.17 1.11 1.06 1.11 1.22

time (sec)

N/A 0.365 22.311 0.196 0.341 0.268 0.525 1.229 2.354

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

18 18 20 18 20 20 19 20 22

N.S.

1 1.00 1.11 1.00 1.11 1.11 1.06 1.11 1.22

time (sec)

N/A 0.543 80.004 0.116 0.313 0.252 0.367 0.276 2.311

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

240 260 524 359 329 3409 0 0 0

N.S.

1 1.08 2.18 1.50 1.37 14.20 0.00 0.00 0.00

time (sec)

N/A 0.706 6.395 7.581 0.211 0.312 0.000 0.000 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 148 380 256 229 2523 0 0 0

N.S.

1 1.00 2.57 1.73 1.55 17.05 0.00 0.00 0.00

time (sec)

N/A 0.485 2.611 5.470 0.213 0.291 0.000 0.000 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 95 87 166 142 1543 0 0 0

N.S.

1 1.00 0.92 1.75 1.49 16.24 0.00 0.00 0.00

time (sec)

N/A 0.329 0.379 3.822 0.231 0.288 0.000 0.000 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 28 36 23 88 371 0 93 78

N.S.

1 1.04 1.33 0.85 3.26 13.74 0.00 3.44 2.89

time (sec)

N/A 0.214 0.012 2.610 0.269 0.257 0.000 0.268 0.077

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

18 18 20 18 147 20 17 20 22

N.S.

1 1.00 1.11 1.00 8.17 1.11 0.94 1.11 1.22

time (sec)

N/A 0.397 47.503 0.204 0.329 0.255 0.731 0.456 2.436

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

18 18 20 18 155 20 19 20 22

N.S.

1 1.00 1.11 1.00 8.61 1.11 1.06 1.11 1.22

time (sec)

N/A 0.423 26.474 0.251 0.335 0.285 0.515 0.543 2.334

Problem 487

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

18 18 20 18 20 20 19 20 22

N.S.

1 1.00 1.11 1.00 1.11 1.11 1.06 1.11 1.22

time (sec)

N/A 0.545 45.165 0.098 0.322 0.258 0.343 0.278 2.351

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

237 274 334 0 0 1309 0 0 0

N.S.

1 1.16 1.41 0.00 0.00 5.52 0.00 0.00 0.00

time (sec)

N/A 0.625 1.886 0.000 0.000 0.308 0.000 0.000 0.000

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

157 191 252 0 0 966 0 0 0

N.S.

1 1.22 1.61 0.00 0.00 6.15 0.00 0.00 0.00

time (sec)

N/A 0.489 1.033 0.000 0.000 0.277 0.000 0.000 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 79 184 179 0 567 0 0 0

N.S.

1 1.00 2.33 2.27 0.00 7.18 0.00 0.00 0.00

time (sec)

N/A 0.315 0.493 0.994 0.000 0.285 0.000 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C C A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 29 29 25 43 103 0 54 48

N.S.

1 1.21 1.21 1.04 1.79 4.29 0.00 2.25 2.00

time (sec)

N/A 0.198 0.003 0.615 0.280 0.252 0.000 0.263 2.265

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

18 18 20 18 106 20 17 20 22

N.S.

1 1.00 1.11 1.00 5.89 1.11 0.94 1.11 1.22

time (sec)

N/A 0.362 31.244 0.223 0.350 0.267 0.565 0.835 2.377

Problem 493

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

18 18 20 18 114 20 19 0 22

N.S.

1 1.00 1.11 1.00 6.33 1.11 1.06 0.00 1.22

time (sec)

N/A 0.386 24.083 0.256 0.350 0.254 0.403 0.000 2.439

Problem 494

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

20 20 22 20 22 22 20 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.10 1.00 1.10 1.10

time (sec)

N/A 0.655 5.218 0.140 0.334 0.264 0.386 0.272 2.454

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 135 307 263 180 1924 0 0 0

N.S.

1 1.59 3.61 3.09 2.12 22.64 0.00 0.00 0.00

time (sec)

N/A 0.721 1.477 6.984 0.208 0.286 0.000 0.000 0.000

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 96 216 199 118 1327 0 0 0

N.S.

1 1.50 3.38 3.11 1.84 20.73 0.00 0.00 0.00

time (sec)

N/A 0.537 0.906 4.993 0.209 0.286 0.000 0.000 0.000

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 41 26 62 87 292 0 72 43

N.S.

1 1.37 0.87 2.07 2.90 9.73 0.00 2.40 1.43

time (sec)

N/A 0.324 0.163 3.527 0.203 0.265 0.000 0.268 0.080

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 28 13 32 18 81 0 18 18

N.S.

1 1.22 0.57 1.39 0.78 3.52 0.00 0.78 0.78

time (sec)

N/A 0.214 0.003 2.729 0.194 0.271 0.000 0.288 2.455

Problem 499

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

20 20 22 20 101 22 19 22 22

N.S.

1 1.00 1.10 1.00 5.05 1.10 0.95 1.10 1.10

time (sec)

N/A 0.273 24.151 0.246 0.322 0.251 0.566 0.270 2.323

Problem 500

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

20 20 22 20 105 22 20 22 22

N.S.

1 1.00 1.10 1.00 5.25 1.10 1.00 1.10 1.10

time (sec)

N/A 0.279 18.241 0.241 0.321 0.267 0.390 0.264 2.312

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