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2.2.5 Integrals 401 to 500

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 401

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 140 90 0 94 0 390 179

N.S.

1 1.00 0.95 0.61 0.00 0.64 0.00 2.65 1.22

time (sec)

N/A 0.101 0.482 0.035 0.000 0.355 0.000 3.674 2.954

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 101 66 0 70 0 206 129

N.S.

1 1.00 1.06 0.69 0.00 0.74 0.00 2.17 1.36

time (sec)

N/A 0.059 0.361 0.031 0.000 0.317 0.000 4.342 2.703

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 35 40 0 29 136 75 79

N.S.

1 1.00 0.74 0.85 0.00 0.62 2.89 1.60 1.68

time (sec)

N/A 0.033 0.214 0.008 0.000 0.324 0.478 4.388 2.706

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 160 73 0 318 0 1016 2500

N.S.

1 1.00 1.65 0.75 0.00 3.28 0.00 10.47 25.77

time (sec)

N/A 0.072 0.504 0.010 0.000 0.366 0.000 4.701 18.080

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 187 88 0 399 0 1190 2642

N.S.

1 1.00 1.82 0.85 0.00 3.87 0.00 11.55 25.65

time (sec)

N/A 0.080 0.809 0.014 0.000 0.361 0.000 9.226 18.884

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

228 228 187 604 0 196 0 797 1358

N.S.

1 1.00 0.82 2.65 0.00 0.86 0.00 3.50 5.96

time (sec)

N/A 0.262 0.524 0.020 0.000 0.330 0.000 3.948 81.167

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

165 165 131 431 0 149 0 445 1012

N.S.

1 1.00 0.79 2.61 0.00 0.90 0.00 2.70 6.13

time (sec)

N/A 0.151 0.354 0.016 0.000 0.342 0.000 3.556 37.521

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 114 81 377 0 103 388 189 110

N.S.

1 1.81 1.29 5.98 0.00 1.63 6.16 3.00 1.75

time (sec)

N/A 0.073 0.214 0.015 0.000 0.346 0.511 3.759 0.239

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

133 133 137 258 0 290 0 194 524

N.S.

1 1.00 1.03 1.94 0.00 2.18 0.00 1.46 3.94

time (sec)

N/A 0.161 0.274 0.015 0.000 0.353 0.000 4.352 11.141

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 128 274 0 367 0 311 2500

N.S.

1 1.00 0.91 1.94 0.00 2.60 0.00 2.21 17.73

time (sec)

N/A 0.158 0.516 0.017 0.000 0.376 0.000 5.043 28.822

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

375 375 138 294 0 208 0 1447 529

N.S.

1 1.00 0.37 0.78 0.00 0.55 0.00 3.86 1.41

time (sec)

N/A 0.277 0.776 0.053 0.000 0.329 0.000 5.581 3.303

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

261 261 93 222 0 159 942 866 385

N.S.

1 1.00 0.36 0.85 0.00 0.61 3.61 3.32 1.48

time (sec)

N/A 0.172 0.611 0.054 0.000 0.337 0.904 4.559 3.211

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A B A B F B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 151 55 146 0 106 384 427 252

N.S.

1 2.36 0.86 2.28 0.00 1.66 6.00 6.67 3.94

time (sec)

N/A 0.075 0.485 0.032 0.000 0.342 0.771 5.241 2.995

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

157 157 244 181 0 516 0 2652 2500

N.S.

1 1.00 1.55 1.15 0.00 3.29 0.00 16.89 15.92

time (sec)

N/A 0.162 0.957 0.010 0.000 0.351 0.000 5.519 27.722

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 223 112 252 0 675 0 2594 2500

N.S.

1 1.38 0.69 1.56 0.00 4.17 0.00 16.01 15.43

time (sec)

N/A 0.194 10.282 0.017 0.000 0.375 0.000 24.437 33.215

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 21 14 0 13 63 13 21

N.S.

1 1.00 1.00 0.67 0.00 0.62 3.00 0.62 1.00

time (sec)

N/A 0.004 0.065 0.015 0.000 0.323 0.202 4.663 2.968

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 21 14 0 13 63 13 21

N.S.

1 1.00 1.00 0.67 0.00 0.62 3.00 0.62 1.00

time (sec)

N/A 0.005 0.067 0.015 0.000 0.321 0.183 4.355 2.937

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

23 23 23 16 0 15 51 15 15

N.S.

1 1.00 1.00 0.70 0.00 0.65 2.22 0.65 0.65

time (sec)

N/A 0.016 0.108 0.007 0.000 0.326 0.190 6.275 2.838

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 44 33 31 32 0 77 45

N.S.

1 1.00 1.16 0.87 0.82 0.84 0.00 2.03 1.18

time (sec)

N/A 0.078 0.134 0.220 0.494 0.346 0.000 3.350 3.021

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 59 59 34 51 270 76 563

N.S.

1 1.00 1.23 1.23 0.71 1.06 5.62 1.58 11.73

time (sec)

N/A 0.069 0.122 0.219 0.492 0.341 159.229 4.090 14.086

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 25 24 15 23 144 51 33

N.S.

1 1.00 1.32 1.26 0.79 1.21 7.58 2.68 1.74

time (sec)

N/A 0.041 0.089 0.211 0.480 0.358 53.901 4.007 2.977

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 37 58 17 40 61 48 206

N.S.

1 1.00 1.95 3.05 0.89 2.11 3.21 2.53 10.84

time (sec)

N/A 0.016 0.085 0.207 0.492 0.404 16.248 4.816 7.725

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F F(-2) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

32 32 81 51 41 41 0 0 122

N.S.

1 1.00 2.53 1.59 1.28 1.28 0.00 0.00 3.81

time (sec)

N/A 0.062 0.179 0.211 0.489 0.321 0.000 0.000 4.098

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

26 26 39 50 24 44 0 149 120

N.S.

1 1.00 1.50 1.92 0.92 1.69 0.00 5.73 4.62

time (sec)

N/A 0.057 0.099 0.217 0.489 0.352 0.000 4.472 3.795

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F F(-2) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 43 58 54 44 0 0 189

N.S.

1 1.00 1.26 1.71 1.59 1.29 0.00 0.00 5.56

time (sec)

N/A 0.067 0.157 0.214 0.495 0.342 0.000 0.000 4.879

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 155 90 0 122 0 451 179

N.S.

1 1.00 1.05 0.61 0.00 0.83 0.00 3.07 1.22

time (sec)

N/A 0.086 1.092 0.037 0.000 0.339 0.000 3.962 2.920

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 113 66 0 92 0 255 129

N.S.

1 1.00 1.19 0.69 0.00 0.97 0.00 2.68 1.36

time (sec)

N/A 0.069 0.738 0.032 0.000 0.326 0.000 4.901 2.862

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 71 40 0 50 0 107 79

N.S.

1 1.00 1.51 0.85 0.00 1.06 0.00 2.28 1.68

time (sec)

N/A 0.039 0.492 0.008 0.000 0.329 0.000 5.185 2.906

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 263 73 0 158 0 1093 213

N.S.

1 1.00 2.71 0.75 0.00 1.63 0.00 11.27 2.20

time (sec)

N/A 0.063 1.399 0.009 0.000 0.351 0.000 4.708 4.330

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 81 88 0 182 0 1402 1637

N.S.

1 1.00 0.79 0.85 0.00 1.77 0.00 13.61 15.89

time (sec)

N/A 0.063 10.151 0.013 0.000 0.385 0.000 7.404 10.926

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 123 120 0 243 0 1895 1610

N.S.

1 1.00 0.72 0.70 0.00 1.42 0.00 11.08 9.42

time (sec)

N/A 0.079 10.138 0.013 0.000 0.350 0.000 15.752 11.847

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

195 195 213 517 0 479 0 511 1107

N.S.

1 1.00 1.09 2.65 0.00 2.46 0.00 2.62 5.68

time (sec)

N/A 0.252 1.177 0.020 0.000 0.355 0.000 4.668 18.151

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 161 385 0 372 0 272 129

N.S.

1 1.00 1.13 2.71 0.00 2.62 0.00 1.92 0.91

time (sec)

N/A 0.172 0.666 0.013 0.000 0.366 0.000 4.735 0.246

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 232 266 0 346 0 306 2500

N.S.

1 1.00 1.72 1.97 0.00 2.56 0.00 2.27 18.52

time (sec)

N/A 0.131 0.911 0.018 0.000 0.381 0.000 5.135 19.761

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 215 272 0 317 0 438 2500

N.S.

1 1.00 1.56 1.97 0.00 2.30 0.00 3.17 18.12

time (sec)

N/A 0.081 1.203 0.014 0.000 0.349 0.000 5.166 17.444

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 148 313 0 126 0 532 787

N.S.

1 1.00 1.20 2.54 0.00 1.02 0.00 4.33 6.40

time (sec)

N/A 0.140 1.847 0.016 0.000 0.362 0.000 7.315 12.320

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

174 174 164 457 0 182 0 802 1290

N.S.

1 1.00 0.94 2.63 0.00 1.05 0.00 4.61 7.41

time (sec)

N/A 0.156 10.274 0.017 0.000 0.332 0.000 6.365 18.735

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

277 277 114 246 0 225 0 932 429

N.S.

1 1.00 0.41 0.89 0.00 0.81 0.00 3.36 1.55

time (sec)

N/A 0.228 10.268 0.056 0.000 0.337 0.000 4.236 3.342

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

163 163 197 172 0 167 0 480 268

N.S.

1 1.00 1.21 1.06 0.00 1.02 0.00 2.94 1.64

time (sec)

N/A 0.157 1.063 0.032 0.000 0.342 0.000 6.789 3.360

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

155 155 127 148 0 321 0 2374 762

N.S.

1 1.00 0.82 0.95 0.00 2.07 0.00 15.32 4.92

time (sec)

N/A 0.140 10.216 0.010 0.000 0.362 0.000 5.704 7.023

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

157 223 143 237 0 260 0 2318 559

N.S.

1 1.42 0.91 1.51 0.00 1.66 0.00 14.76 3.56

time (sec)

N/A 0.150 10.152 0.014 0.000 0.362 0.000 23.327 7.488

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

164 275 146 300 0 297 0 2766 287

N.S.

1 1.68 0.89 1.83 0.00 1.81 0.00 16.87 1.75

time (sec)

N/A 0.126 10.158 0.016 0.000 0.358 0.000 55.114 5.743

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 45 63 23 44 65 54 209

N.S.

1 1.00 1.45 2.03 0.74 1.42 2.10 1.74 6.74

time (sec)

N/A 0.030 0.049 0.243 0.491 0.347 1.186 2.730 8.122

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 44 33 31 32 0 77 42

N.S.

1 1.00 1.16 0.87 0.82 0.84 0.00 2.03 1.11

time (sec)

N/A 0.238 0.013 0.264 0.481 0.332 0.000 3.176 3.065

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 60 59 34 51 270 76 381

N.S.

1 1.00 1.25 1.23 0.71 1.06 5.62 1.58 7.94

time (sec)

N/A 0.172 0.017 0.260 0.486 0.396 143.804 3.931 10.394

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 25 26 17 25 144 54 25

N.S.

1 1.00 1.19 1.24 0.81 1.19 6.86 2.57 1.19

time (sec)

N/A 0.078 0.005 0.254 0.492 0.348 54.637 3.038 3.061

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 38 59 20 41 63 49 205

N.S.

1 1.00 1.73 2.68 0.91 1.86 2.86 2.23 9.32

time (sec)

N/A 0.036 0.006 0.253 0.502 0.374 21.115 3.384 3.714

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F F(-2) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

32 32 81 51 41 41 0 0 122

N.S.

1 1.00 2.53 1.59 1.28 1.28 0.00 0.00 3.81

time (sec)

N/A 0.137 0.017 0.258 0.494 0.351 0.000 0.000 4.127

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

26 26 39 50 24 44 0 149 118

N.S.

1 1.00 1.50 1.92 0.92 1.69 0.00 5.73 4.54

time (sec)

N/A 0.144 0.006 0.260 0.481 0.387 0.000 4.203 3.787

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F F(-2) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 42 57 51 43 0 0 186

N.S.

1 1.00 1.27 1.73 1.55 1.30 0.00 0.00 5.64

time (sec)

N/A 0.151 0.010 0.255 0.484 0.345 0.000 0.000 4.777

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A F A F F(-2) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

28 28 81 48 0 36 0 0 93

N.S.

1 1.00 2.89 1.71 0.00 1.29 0.00 0.00 3.32

time (sec)

N/A 0.219 0.184 0.220 0.000 0.393 0.000 0.000 4.493

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 42 62 0 37 224 41 200

N.S.

1 1.00 1.27 1.88 0.00 1.12 6.79 1.24 6.06

time (sec)

N/A 0.100 0.089 0.227 0.000 0.354 16.551 3.725 10.853

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 86 0 0 0 0 0 -1

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.080 0.454 0.009 0.000 0.000 0.000 0.000 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

175 175 159 341 252 150 279 163 -1

N.S.

1 1.00 0.91 1.95 1.44 0.86 1.59 0.93 -0.01

time (sec)

N/A 0.093 0.781 0.214 0.282 0.359 5.474 3.635 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 118 124 95 110 116 103 210

N.S.

1 1.00 0.87 0.91 0.70 0.81 0.85 0.76 1.54

time (sec)

N/A 0.080 0.600 0.209 0.272 0.342 2.155 3.373 4.657

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 83 75 46 74 54 65 136

N.S.

1 1.00 1.22 1.10 0.68 1.09 0.79 0.96 2.00

time (sec)

N/A 0.032 0.097 0.243 0.282 0.349 1.171 3.306 3.888

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 337 1325 0 187 0 219 -1

N.S.

1 1.00 2.88 11.32 0.00 1.60 0.00 1.87 -0.01

time (sec)

N/A 0.073 0.902 0.029 0.000 0.353 0.000 5.204 0.000

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

151 151 378 4161 0 290 0 398 -1

N.S.

1 1.00 2.50 27.56 0.00 1.92 0.00 2.64 -0.01

time (sec)

N/A 0.079 1.447 0.041 0.000 0.376 0.000 4.250 0.000

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

193 193 464 9871 0 521 0 679 -1

N.S.

1 1.00 2.40 51.15 0.00 2.70 0.00 3.52 -0.01

time (sec)

N/A 0.092 1.907 0.063 0.000 0.408 0.000 4.980 0.000

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

225 225 212 0 0 408 0 0 -1

N.S.

1 1.00 0.94 0.00 0.00 1.81 0.00 0.00 -0.00

time (sec)

N/A 0.127 1.475 0.018 0.000 0.417 0.000 0.000 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

183 183 170 0 0 335 0 0 -1

N.S.

1 1.00 0.93 0.00 0.00 1.83 0.00 0.00 -0.01

time (sec)

N/A 0.112 1.281 0.011 0.000 0.406 0.000 0.000 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 142 0 0 299 0 0 -1

N.S.

1 1.00 0.97 0.00 0.00 2.03 0.00 0.00 -0.01

time (sec)

N/A 0.092 0.894 0.006 0.000 0.405 0.000 0.000 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 141 0 0 296 0 0 -1

N.S.

1 1.00 0.96 0.00 0.00 2.01 0.00 0.00 -0.01

time (sec)

N/A 0.083 0.868 0.010 0.000 0.416 0.000 0.000 0.000

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

158 158 169 0 0 490 0 0 -1

N.S.

1 1.00 1.07 0.00 0.00 3.10 0.00 0.00 -0.01

time (sec)

N/A 0.113 1.413 0.007 0.000 0.426 0.000 0.000 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

199 199 209 0 0 784 0 0 -1

N.S.

1 1.00 1.05 0.00 0.00 3.94 0.00 0.00 -0.01

time (sec)

N/A 0.130 1.434 0.008 0.000 0.452 0.000 0.000 0.000

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 41 0 0 26 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.63 0.00 0.00 -0.02

time (sec)

N/A 0.012 0.041 0.037 0.000 0.381 0.000 0.000 0.000

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 69 0 0 59 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.86 0.00 0.00 -0.01

time (sec)

N/A 0.043 0.527 0.012 0.000 0.379 0.000 0.000 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 35 60 0 34 415 0 -1

N.S.

1 1.00 0.78 1.33 0.00 0.76 9.22 0.00 -0.02

time (sec)

N/A 0.007 0.059 0.033 0.000 0.381 0.592 0.000 0.000

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A B F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 31 55 0 28 197 0 -1

N.S.

1 1.00 0.76 1.34 0.00 0.68 4.80 0.00 -0.02

time (sec)

N/A 0.005 0.060 0.025 0.000 0.376 0.578 0.000 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A B F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 31 64 0 30 197 0 -1

N.S.

1 1.00 0.76 1.56 0.00 0.73 4.80 0.00 -0.02

time (sec)

N/A 0.005 0.046 0.026 0.000 0.365 0.633 0.000 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 72 0 0 70 0 0 -1

N.S.

1 1.00 1.09 0.00 0.00 1.06 0.00 0.00 -0.02

time (sec)

N/A 0.023 3.958 0.010 0.000 0.414 0.000 0.000 0.000

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

166 166 134 0 0 0 0 0 -1

N.S.

1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.141 1.121 0.009 0.000 0.000 0.000 0.000 0.000

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F(-2) A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

303 303 490 809 0 326 0 373 -1

N.S.

1 1.00 1.62 2.67 0.00 1.08 0.00 1.23 -0.00

time (sec)

N/A 0.272 5.830 0.361 0.000 0.353 0.000 3.779 0.000

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

237 237 213 300 0 204 0 224 -1

N.S.

1 1.00 0.90 1.27 0.00 0.86 0.00 0.95 -0.00

time (sec)

N/A 0.172 10.297 0.301 0.000 0.346 0.000 3.647 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A F(-2) A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 478 173 0 117 0 111 -1

N.S.

1 1.00 4.05 1.47 0.00 0.99 0.00 0.94 -0.01

time (sec)

N/A 0.045 2.264 0.309 0.000 0.378 0.000 2.914 0.000

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

215 215 570 4918 0 362 0 523 -1

N.S.

1 1.00 2.65 22.87 0.00 1.68 0.00 2.43 -0.00

time (sec)

N/A 0.148 1.804 0.040 0.000 5.667 0.000 3.878 0.000

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

266 266 551 58069 0 803 0 1243 -1

N.S.

1 1.00 2.07 218.30 0.00 3.02 0.00 4.67 -0.00

time (sec)

N/A 0.163 3.771 0.099 0.000 3.037 0.000 4.272 0.000

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

330 330 300 295126 0 1942 0 3015 -1

N.S.

1 1.00 0.91 894.32 0.00 5.88 0.00 9.14 -0.00

time (sec)

N/A 0.205 10.554 0.145 0.000 26.982 0.000 11.771 0.000

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

370 370 985 0 0 858 0 0 -1

N.S.

1 1.00 2.66 0.00 0.00 2.32 0.00 0.00 -0.00

time (sec)

N/A 0.421 5.003 0.019 0.000 0.548 0.000 0.000 0.000

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

302 302 443 0 0 612 0 0 -1

N.S.

1 1.00 1.47 0.00 0.00 2.03 0.00 0.00 -0.00

time (sec)

N/A 0.301 2.841 0.013 0.000 0.496 0.000 0.000 0.000

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

233 233 327 0 0 600 0 0 -1

N.S.

1 1.00 1.40 0.00 0.00 2.58 0.00 0.00 -0.00

time (sec)

N/A 0.225 1.506 0.007 0.000 0.504 0.000 0.000 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

244 244 341 0 0 620 0 0 -1

N.S.

1 1.00 1.40 0.00 0.00 2.54 0.00 0.00 -0.00

time (sec)

N/A 0.218 1.580 0.010 0.000 0.519 0.000 0.000 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

269 269 395 0 0 1312 0 0 -1

N.S.

1 1.00 1.47 0.00 0.00 4.88 0.00 0.00 -0.00

time (sec)

N/A 0.281 2.574 0.009 0.000 0.650 0.000 0.000 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

335 335 557 0 0 2523 0 0 -1

N.S.

1 1.00 1.66 0.00 0.00 7.53 0.00 0.00 -0.00

time (sec)

N/A 0.372 3.640 0.010 0.000 1.492 0.000 0.000 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

164 164 138 216 0 158 0 0 -1

N.S.

1 1.00 0.84 1.32 0.00 0.96 0.00 0.00 -0.01

time (sec)

N/A 0.077 0.416 0.242 0.000 0.376 0.000 0.000 0.000

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A B F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 108 92 167 0 78 14884 0 -1

N.S.

1 1.00 0.85 1.55 0.00 0.72 137.81 0.00 -0.01

time (sec)

N/A 0.045 0.237 0.016 0.000 0.352 15.841 0.000 0.000

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A B F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

52 52 43 120 0 32 2147 0 -1

N.S.

1 1.00 0.83 2.31 0.00 0.62 41.29 0.00 -0.02

time (sec)

N/A 0.016 0.130 0.013 0.000 0.394 1.653 0.000 0.000

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 61 0 0 0 0 0 -1

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.047 0.155 0.026 0.000 0.000 0.000 0.000 0.000

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 61 0 0 0 0 0 -1

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.045 0.171 0.031 0.000 0.000 0.000 0.000 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

176 176 150 0 0 159 0 0 -1

N.S.

1 1.00 0.85 0.00 0.00 0.90 0.00 0.00 -0.01

time (sec)

N/A 0.073 0.450 0.037 0.000 0.376 0.000 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 100 0 0 79 0 0 -1

N.S.

1 1.00 0.86 0.00 0.00 0.68 0.00 0.00 -0.01

time (sec)

N/A 0.044 0.238 0.023 0.000 0.353 0.000 0.000 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 50 0 0 33 0 0 -1

N.S.

1 1.00 0.89 0.00 0.00 0.59 0.00 0.00 -0.02

time (sec)

N/A 0.016 0.145 0.024 0.000 0.357 0.000 0.000 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 65 0 0 0 0 0 -1

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.046 0.162 0.044 0.000 0.000 0.000 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 65 0 0 0 0 0 -1

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.045 0.167 0.043 0.000 0.000 0.000 0.000 0.000

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

187 187 157 0 0 201 0 0 -1

N.S.

1 1.00 0.84 0.00 0.00 1.07 0.00 0.00 -0.01

time (sec)

N/A 0.086 0.376 0.022 0.000 0.390 0.000 0.000 0.000

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 111 0 0 110 0 0 -1

N.S.

1 1.00 0.85 0.00 0.00 0.84 0.00 0.00 -0.01

time (sec)

N/A 0.066 0.222 0.023 0.000 0.358 0.000 0.000 0.000

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 65 0 0 48 0 0 -1

N.S.

1 1.00 0.87 0.00 0.00 0.64 0.00 0.00 -0.01

time (sec)

N/A 0.049 0.184 0.022 0.000 0.362 0.000 0.000 0.000

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

17 17 17 0 0 15 311 15 15

N.S.

1 1.00 1.00 0.00 0.00 0.88 18.29 0.88 0.88

time (sec)

N/A 0.036 0.023 0.023 0.000 0.352 1.538 3.346 3.000

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 61 0 0 0 0 0 -1

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.048 0.074 0.023 0.000 0.000 0.000 0.000 0.000

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 61 0 0 0 0 0 -1

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.049 0.088 0.026 0.000 0.000 0.000 0.000 0.000

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