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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 C F B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

172 172 174 73 0 327 63 152 250

N.S.

1 1.00 1.01 0.42 0.00 1.90 0.37 0.88 1.45

time (sec)

N/A 0.065 0.241 0.100 0.000 0.280 0.751 0.356 8.311

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

182 182 166 73 0 347 63 152 268

N.S.

1 1.00 0.91 0.40 0.00 1.91 0.35 0.84 1.47

time (sec)

N/A 0.086 0.211 0.104 0.000 0.280 0.753 0.358 8.533

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

173 173 189 79 0 324 73 159 257

N.S.

1 1.00 1.09 0.46 0.00 1.87 0.42 0.92 1.49

time (sec)

N/A 0.095 0.226 0.108 0.000 0.264 0.775 0.393 8.328

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 189 189 79 0 352 70 159 291

N.S.

1 1.00 1.00 0.42 0.00 1.86 0.37 0.84 1.54

time (sec)

N/A 0.115 0.242 0.117 0.000 0.282 0.803 0.348 8.385

Problem 405

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 15 17 16

N.S.

1 1.00 1.00 0.86 0.81 0.81 0.71 0.81 0.76

time (sec)

N/A 0.008 0.009 0.048 0.180 0.245 0.047 0.296 0.041

Problem 406

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 26 23 22 22 19 22 22

N.S.

1 1.00 1.00 0.88 0.85 0.85 0.73 0.85 0.85

time (sec)

N/A 0.013 0.010 0.042 0.179 0.248 0.061 0.306 8.318

Problem 407

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 37 37 31 30 30 37 30 32

N.S.

1 1.00 1.00 0.84 0.81 0.81 1.00 0.81 0.86

time (sec)

N/A 0.025 0.023 0.055 0.263 0.260 0.067 1.101 8.396

Problem 408

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 19 18 18 27 18 20

N.S.

1 1.00 1.00 0.83 0.78 0.78 1.17 0.78 0.87

time (sec)

N/A 0.015 0.012 0.036 0.271 0.271 0.056 1.101 8.422

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 197 31 36 32 41 33 34

N.S.

1 1.00 5.05 0.79 0.92 0.82 1.05 0.85 0.87

time (sec)

N/A 0.024 0.048 0.098 0.262 0.264 0.078 0.300 0.037

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 208 38 41 49 48 45 41

N.S.

1 1.00 4.33 0.79 0.85 1.02 1.00 0.94 0.85

time (sec)

N/A 0.033 0.047 0.089 0.267 0.287 0.091 0.288 8.305

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 197 31 0 32 41 33 34

N.S.

1 1.00 5.05 0.79 0.00 0.82 1.05 0.85 0.87

time (sec)

N/A 0.023 0.021 0.063 0.000 0.278 0.080 0.285 0.019

Problem 412

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

147 147 140 164 0 466 605 145 183

N.S.

1 1.00 0.95 1.12 0.00 3.17 4.12 0.99 1.24

time (sec)

N/A 0.090 0.122 0.155 0.000 0.290 0.735 0.277 0.095

Problem 413

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

118 118 112 128 0 383 498 113 151

N.S.

1 1.00 0.95 1.08 0.00 3.25 4.22 0.96 1.28

time (sec)

N/A 0.071 0.066 0.123 0.000 0.312 0.602 0.283 8.289

Problem 414

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

89 89 84 98 0 297 381 86 112

N.S.

1 1.00 0.94 1.10 0.00 3.34 4.28 0.97 1.26

time (sec)

N/A 0.058 0.073 0.077 0.000 0.285 0.467 0.307 8.318

Problem 415

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

70 70 73 75 0 235 306 67 172

N.S.

1 1.00 1.04 1.07 0.00 3.36 4.37 0.96 2.46

time (sec)

N/A 0.034 0.046 0.044 0.000 0.294 0.336 0.294 0.082

Problem 416

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

56 56 57 56 0 185 216 55 112

N.S.

1 1.00 1.02 1.00 0.00 3.30 3.86 0.98 2.00

time (sec)

N/A 0.023 0.023 0.037 0.000 0.292 0.165 0.309 8.390

Problem 417

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

36 36 38 35 0 120 124 34 46

N.S.

1 1.00 1.06 0.97 0.00 3.33 3.44 0.94 1.28

time (sec)

N/A 0.022 0.007 0.037 0.000 0.297 0.107 0.286 0.026

Problem 418

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

62 62 61 61 0 211 564 62 213

N.S.

1 1.00 0.98 0.98 0.00 3.40 9.10 1.00 3.44

time (sec)

N/A 0.035 0.052 0.069 0.000 0.291 4.462 0.324 0.273

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 81 77 81 0 269 0 79 339

N.S.

1 1.00 0.95 1.00 0.00 3.32 0.00 0.98 4.19

time (sec)

N/A 0.066 0.066 0.056 0.000 0.295 0.000 0.302 8.619

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 104 102 128 0 358 0 105 447

N.S.

1 1.00 0.98 1.23 0.00 3.44 0.00 1.01 4.30

time (sec)

N/A 0.101 0.096 0.121 0.000 0.315 0.000 0.310 8.586

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 137 131 157 0 445 0 136 524

N.S.

1 1.00 0.96 1.15 0.00 3.25 0.00 0.99 3.82

time (sec)

N/A 0.127 0.076 0.119 0.000 0.328 0.000 0.298 8.599

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

196 196 163 238 0 1029 1012 188 382

N.S.

1 1.00 0.83 1.21 0.00 5.25 5.16 0.96 1.95

time (sec)

N/A 0.141 0.183 0.174 0.000 0.292 1.347 0.330 8.686

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 150 132 198 0 837 842 161 261

N.S.

1 1.00 0.88 1.32 0.00 5.58 5.61 1.07 1.74

time (sec)

N/A 0.098 0.128 0.159 0.000 0.298 1.072 0.280 8.471

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 114 109 169 0 635 729 125 279

N.S.

1 1.00 0.96 1.48 0.00 5.57 6.39 1.10 2.45

time (sec)

N/A 0.066 0.100 0.106 0.000 0.316 0.758 0.297 8.523

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 71 81 97 0 387 280 88 135

N.S.

1 1.00 1.14 1.37 0.00 5.45 3.94 1.24 1.90

time (sec)

N/A 0.026 0.069 0.075 0.000 0.277 0.317 0.288 8.310

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 69 70 0 338 253 76 110

N.S.

1 1.00 1.05 1.06 0.00 5.12 3.83 1.15 1.67

time (sec)

N/A 0.021 0.052 0.068 0.000 0.296 0.294 0.293 0.058

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 70 68 0 341 265 76 119

N.S.

1 1.00 1.06 1.03 0.00 5.17 4.02 1.15 1.80

time (sec)

N/A 0.021 0.050 0.066 0.000 0.275 0.309 0.303 0.048

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 108 107 177 0 781 0 126 620

N.S.

1 1.00 0.99 1.64 0.00 7.23 0.00 1.17 5.74

time (sec)

N/A 0.096 0.122 0.132 0.000 0.343 0.000 0.297 8.703

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 148 131 205 0 975 0 171 775

N.S.

1 1.00 0.89 1.39 0.00 6.59 0.00 1.16 5.24

time (sec)

N/A 0.124 0.177 0.089 0.000 0.401 0.000 0.308 8.847

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

202 202 175 255 0 1226 0 229 914

N.S.

1 1.00 0.87 1.26 0.00 6.07 0.00 1.13 4.52

time (sec)

N/A 0.169 0.259 0.184 0.000 0.458 0.000 0.314 9.119

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

238 238 260 401 0 1926 1714 282 705

N.S.

1 1.00 1.09 1.68 0.00 8.09 7.20 1.18 2.96

time (sec)

N/A 0.212 0.238 0.200 0.000 0.294 3.038 0.330 8.593

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

190 190 221 357 0 1603 1510 245 620

N.S.

1 1.00 1.16 1.88 0.00 8.44 7.95 1.29 3.26

time (sec)

N/A 0.187 0.197 0.154 0.000 0.287 1.868 0.295 8.820

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 111 174 260 0 953 547 202 343

N.S.

1 1.00 1.57 2.34 0.00 8.59 4.93 1.82 3.09

time (sec)

N/A 0.047 0.118 0.099 0.000 0.292 0.822 0.308 0.114

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 107 126 223 0 872 513 163 271

N.S.

1 1.00 1.18 2.08 0.00 8.15 4.79 1.52 2.53

time (sec)

N/A 0.039 0.138 0.096 0.000 0.286 0.663 0.286 8.205

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 115 131 210 0 887 570 154 313

N.S.

1 1.00 1.14 1.83 0.00 7.71 4.96 1.34 2.72

time (sec)

N/A 0.046 0.092 0.106 0.000 0.280 0.755 0.287 8.410

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 103 102 118 0 788 481 135 253

N.S.

1 1.00 0.99 1.15 0.00 7.65 4.67 1.31 2.46

time (sec)

N/A 0.028 0.064 0.092 0.000 0.286 0.604 0.289 8.392

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 101 97 116 0 785 474 136 285

N.S.

1 0.98 0.94 1.13 0.00 7.62 4.60 1.32 2.77

time (sec)

N/A 0.028 0.069 0.093 0.000 0.263 0.697 0.297 8.492

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 185 178 352 0 1985 0 239 1089

N.S.

1 1.00 0.96 1.90 0.00 10.73 0.00 1.29 5.89

time (sec)

N/A 0.148 0.233 0.185 0.000 0.524 0.000 0.293 8.990

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

239 239 221 404 0 2280 0 309 1255

N.S.

1 1.00 0.92 1.69 0.00 9.54 0.00 1.29 5.25

time (sec)

N/A 0.192 0.259 0.133 0.000 0.674 0.000 0.298 9.079

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

40 40 40 27 30 30 34 32 26

N.S.

1 1.00 1.00 0.68 0.75 0.75 0.85 0.80 0.65

time (sec)

N/A 0.015 0.006 0.034 0.183 0.249 0.060 0.295 0.025

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

33 33 33 22 25 25 27 27 21

N.S.

1 1.00 1.00 0.67 0.76 0.76 0.82 0.82 0.64

time (sec)

N/A 0.013 0.004 0.033 0.184 0.231 0.059 0.307 8.287

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

26 26 26 17 20 20 20 22 16

N.S.

1 1.00 1.00 0.65 0.77 0.77 0.77 0.85 0.62

time (sec)

N/A 0.009 0.004 0.031 0.182 0.245 0.060 0.279 0.042

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

21 21 21 14 17 17 17 19 13

N.S.

1 1.00 1.00 0.67 0.81 0.81 0.81 0.90 0.62

time (sec)

N/A 0.008 0.004 0.027 0.186 0.248 0.066 0.282 0.036

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

23 23 21 14 17 17 15 19 8

N.S.

1 1.00 0.91 0.61 0.74 0.74 0.65 0.83 0.35

time (sec)

N/A 0.009 0.003 0.031 0.185 0.248 0.046 0.307 8.486

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

27 27 27 18 21 21 24 24 17

N.S.

1 1.00 1.00 0.67 0.78 0.78 0.89 0.89 0.63

time (sec)

N/A 0.011 0.014 0.042 0.226 0.298 0.066 0.289 0.056

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

34 34 34 27 26 30 31 29 22

N.S.

1 1.00 1.00 0.79 0.76 0.88 0.91 0.85 0.65

time (sec)

N/A 0.021 0.004 0.048 0.196 0.254 0.072 0.275 0.025

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

41 41 41 31 31 39 36 34 26

N.S.

1 1.00 1.00 0.76 0.76 0.95 0.88 0.83 0.63

time (sec)

N/A 0.023 0.005 0.047 0.189 0.261 0.075 0.323 8.552

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

48 48 48 36 36 44 41 39 32

N.S.

1 1.00 1.00 0.75 0.75 0.92 0.85 0.81 0.67

time (sec)

N/A 0.030 0.006 0.050 0.181 0.275 0.087 0.310 0.027

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

204 204 208 249 0 959 0 0 0

N.S.

1 1.00 1.02 1.22 0.00 4.70 0.00 0.00 0.00

time (sec)

N/A 0.154 1.375 0.147 0.000 0.426 0.000 0.000 0.000

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 145 158 179 0 709 0 0 0

N.S.

1 1.00 1.09 1.23 0.00 4.89 0.00 0.00 0.00

time (sec)

N/A 0.091 0.584 0.067 0.000 0.323 0.000 0.000 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 105 131 121 0 590 0 0 100

N.S.

1 1.00 1.25 1.15 0.00 5.62 0.00 0.00 0.95

time (sec)

N/A 0.055 0.194 0.038 0.000 0.320 0.000 0.000 8.525

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 89 88 0 171 0 0 53

N.S.

1 1.00 1.33 1.31 0.00 2.55 0.00 0.00 0.79

time (sec)

N/A 0.027 0.153 0.048 0.000 0.275 0.000 0.000 8.578

Problem 453

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

133 133 140 197 0 465 0 231 0

N.S.

1 1.00 1.05 1.48 0.00 3.50 0.00 1.74 0.00

time (sec)

N/A 0.068 0.461 0.083 0.000 0.310 0.000 0.410 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

220 220 246 376 0 1081 0 499 0

N.S.

1 1.00 1.12 1.71 0.00 4.91 0.00 2.27 0.00

time (sec)

N/A 0.134 1.199 0.151 0.000 0.407 0.000 0.374 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 32 40 8 8 0 29 134

N.S.

1 1.00 0.44 0.55 0.11 0.11 0.00 0.40 1.84

time (sec)

N/A 0.025 1.016 0.069 0.192 0.251 0.000 0.318 8.388

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 179 202 57 0 1059 129 2109 3026

N.S.

1 1.00 1.13 0.32 0.00 5.92 0.72 11.78 16.91

time (sec)

N/A 0.175 0.110 0.048 0.000 0.277 1.233 0.786 8.733

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

631 631 70 59 0 2882 196 0 2280

N.S.

1 1.00 0.11 0.09 0.00 4.57 0.31 0.00 3.61

time (sec)

N/A 0.749 0.041 0.059 0.000 0.388 54.067 0.000 10.265

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

376 376 70 59 0 4001 0 0 10382

N.S.

1 1.00 0.19 0.16 0.00 10.64 0.00 0.00 27.61

time (sec)

N/A 0.373 0.040 0.047 0.000 0.456 0.000 0.000 9.601

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 106 105 84 0 0 0 0 0

N.S.

1 1.00 0.99 0.79 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.060 0.204 0.032 0.000 0.000 0.000 0.000 0.000

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 40 55 50 54 53 51 49 44

N.S.

1 1.00 1.38 1.25 1.35 1.32 1.28 1.22 1.10

time (sec)

N/A 0.014 0.030 0.079 0.188 0.285 0.162 0.282 0.027

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 75 50 41 23 0 124 45 0

N.S.

1 1.00 0.67 0.55 0.31 0.00 1.65 0.60 0.00

time (sec)

N/A 0.027 0.028 0.091 0.198 0.000 0.397 0.289 0.000

Problem 462

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

137 137 117 98 114 84 233 140 0

N.S.

1 1.00 0.85 0.72 0.83 0.61 1.70 1.02 0.00

time (sec)

N/A 0.054 0.057 0.075 0.190 0.262 5.616 0.309 0.000

Problem 463

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

137 137 93 76 114 61 204 102 0

N.S.

1 1.00 0.68 0.55 0.83 0.45 1.49 0.74 0.00

time (sec)

N/A 0.047 0.022 0.020 0.185 0.284 1.431 0.295 0.000

Problem 464

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

137 137 67 54 114 32 175 64 0

N.S.

1 1.00 0.49 0.39 0.83 0.23 1.28 0.47 0.00

time (sec)

N/A 0.040 0.018 0.023 0.199 0.258 0.616 0.292 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

88 88 43 42 114 10 146 26 71

N.S.

1 1.00 0.49 0.48 1.30 0.11 1.66 0.30 0.81

time (sec)

N/A 0.028 0.008 0.086 0.184 0.245 0.478 0.277 8.736

Problem 466

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

147 147 65 52 36 33 170 61 0

N.S.

1 1.00 0.44 0.35 0.24 0.22 1.16 0.41 0.00

time (sec)

N/A 0.048 0.023 0.041 0.183 0.262 0.432 0.319 0.000

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 130 72 81 55 113 0 64 0

N.S.

1 1.00 0.55 0.62 0.42 0.87 0.00 0.49 0.00

time (sec)

N/A 0.052 0.029 0.115 0.190 0.270 0.000 0.292 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 135 56 43 53 136 0 43 53

N.S.

1 1.00 0.41 0.32 0.39 1.01 0.00 0.32 0.39

time (sec)

N/A 0.050 0.055 0.263 0.188 0.278 0.000 0.314 9.067

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 137 56 43 53 209 0 43 53

N.S.

1 1.00 0.41 0.31 0.39 1.53 0.00 0.31 0.39

time (sec)

N/A 0.053 0.052 0.493 0.186 0.338 0.000 0.291 9.485

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 137 56 43 53 275 0 43 53

N.S.

1 1.00 0.41 0.31 0.39 2.01 0.00 0.31 0.39

time (sec)

N/A 0.053 0.055 0.779 0.185 0.410 0.000 0.289 9.598

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 137 56 43 53 343 0 43 53

N.S.

1 1.00 0.41 0.31 0.39 2.50 0.00 0.31 0.39

time (sec)

N/A 0.053 0.054 1.184 0.191 0.577 0.000 0.290 10.060

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

77 77 68 0 0 0 0 0 0

N.S.

1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.025 0.139 0.000 0.000 0.000 0.000 0.000 0.000

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A A F B B

verified

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

size

468 468 207 0 362 579 0 1564 777

N.S.

1 1.00 0.44 0.00 0.77 1.24 0.00 3.34 1.66

time (sec)

N/A 0.153 0.308 0.000 0.201 0.425 0.000 0.323 9.607

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A A F B B

verified

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

size

315 315 143 0 198 297 0 745 390

N.S.

1 1.00 0.45 0.00 0.63 0.94 0.00 2.37 1.24

time (sec)

N/A 0.094 0.240 0.000 0.199 0.330 0.000 0.317 8.760

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A A F A B

verified

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

size

142 142 83 0 77 110 0 229 138

N.S.

1 1.00 0.58 0.00 0.54 0.77 0.00 1.61 0.97

time (sec)

N/A 0.048 0.137 0.000 0.197 0.302 0.000 0.341 8.439

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

69 69 58 0 0 0 0 0 0

N.S.

1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.020 0.106 0.000 0.000 0.000 0.000 0.000 0.000

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

75 75 61 0 0 0 0 0 0

N.S.

1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.023 0.104 0.000 0.000 0.000 0.000 0.000 0.000

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C C F F A F F B

verified

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

size

146 162 101 0 0 82 0 0 69

N.S.

1 1.11 0.69 0.00 0.00 0.56 0.00 0.00 0.47

time (sec)

N/A 0.067 0.333 0.000 0.000 0.338 0.000 0.000 8.602

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

176 176 93 103 114 147 0 0 0

N.S.

1 1.00 0.53 0.59 0.65 0.84 0.00 0.00 0.00

time (sec)

N/A 0.066 0.093 0.256 0.198 1.994 0.000 0.000 0.000

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

268 268 121 163 119 0 0 105 0

N.S.

1 1.00 0.45 0.61 0.44 0.00 0.00 0.39 0.00

time (sec)

N/A 0.097 0.129 5.449 0.199 0.000 0.000 0.304 0.000

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 179 66 65 0 0 0 80 0

N.S.

1 1.00 0.37 0.36 0.00 0.00 0.00 0.45 0.00

time (sec)

N/A 0.062 0.046 0.170 0.000 0.000 0.000 0.443 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

391 391 125 113 79 0 0 173 0

N.S.

1 1.00 0.32 0.29 0.20 0.00 0.00 0.44 0.00

time (sec)

N/A 0.126 0.070 0.126 0.209 0.000 0.000 0.325 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

291 291 99 91 57 0 0 128 0

N.S.

1 1.00 0.34 0.31 0.20 0.00 0.00 0.44 0.00

time (sec)

N/A 0.093 0.060 0.036 0.193 0.000 0.000 0.331 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 189 75 69 30 0 0 79 0

N.S.

1 1.00 0.40 0.37 0.16 0.00 0.00 0.42 0.00

time (sec)

N/A 0.067 0.044 0.030 0.196 0.000 0.000 0.312 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 88 49 47 10 0 0 34 39

N.S.

1 1.00 0.56 0.53 0.11 0.00 0.00 0.39 0.44

time (sec)

N/A 0.039 0.024 0.023 0.196 0.000 0.000 0.306 8.479

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

190 190 86 78 44 0 0 77 0

N.S.

1 1.00 0.45 0.41 0.23 0.00 0.00 0.41 0.00

time (sec)

N/A 0.082 0.040 0.026 0.240 0.000 0.000 0.337 0.000

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

300 300 126 141 97 0 0 127 0

N.S.

1 1.00 0.42 0.47 0.32 0.00 0.00 0.42 0.00

time (sec)

N/A 0.130 0.097 0.038 0.227 0.000 0.000 0.312 0.000

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

410 410 152 199 139 0 0 147 0

N.S.

1 1.00 0.37 0.49 0.34 0.00 0.00 0.36 0.00

time (sec)

N/A 0.176 0.096 0.037 0.188 0.000 0.000 0.310 0.000

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

289 289 98 91 57 0 0 126 0

N.S.

1 1.00 0.34 0.31 0.20 0.00 0.00 0.44 0.00

time (sec)

N/A 0.096 0.057 0.153 0.181 0.000 0.000 0.310 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

291 291 101 91 52 0 0 125 0

N.S.

1 1.00 0.35 0.31 0.18 0.00 0.00 0.43 0.00

time (sec)

N/A 0.092 0.062 0.136 0.188 0.000 0.000 0.314 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

222 222 98 141 99 302 0 84 0

N.S.

1 1.00 0.44 0.64 0.45 1.36 0.00 0.38 0.00

time (sec)

N/A 0.088 0.088 1.248 0.187 0.390 0.000 0.314 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

391 391 124 117 79 0 0 172 0

N.S.

1 1.00 0.32 0.30 0.20 0.00 0.00 0.44 0.00

time (sec)

N/A 0.121 0.067 0.058 0.179 0.000 0.000 0.427 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 38 47 45 38 63 0 0

N.S.

1 1.00 0.83 1.02 0.98 0.83 1.37 0.00 0.00

time (sec)

N/A 0.026 0.051 0.663 0.178 0.271 22.442 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 27 31 32 24 48 0 0

N.S.

1 1.00 0.96 1.11 1.14 0.86 1.71 0.00 0.00

time (sec)

N/A 0.017 0.043 0.650 0.173 0.270 8.957 0.000 0.000

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 18 19 15 46 0 0

N.S.

1 1.00 1.00 1.20 1.27 1.00 3.07 0.00 0.00

time (sec)

N/A 0.009 0.024 0.627 0.174 0.258 1.745 0.000 0.000

Problem 496

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

23 23 25 26 27 22 54 25 20

N.S.

1 1.00 1.09 1.13 1.17 0.96 2.35 1.09 0.87

time (sec)

N/A 0.013 0.037 0.642 0.182 0.272 1.744 0.276 8.710

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 57 48 58 58 59 100 0 0

N.S.

1 1.00 0.84 1.02 1.02 1.04 1.75 0.00 0.00

time (sec)

N/A 0.029 0.078 0.625 0.180 0.287 29.315 0.000 0.000

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 63 75 71 72 0 0 0

N.S.

1 1.00 0.83 0.99 0.93 0.95 0.00 0.00 0.00

time (sec)

N/A 0.033 0.091 0.615 0.174 0.276 0.000 0.000 0.000

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 93 76 90 84 85 0 0 0

N.S.

1 1.00 0.82 0.97 0.90 0.91 0.00 0.00 0.00

time (sec)

N/A 0.036 0.103 0.628 0.179 0.264 0.000 0.000 0.000

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

236 236 34 54 0 270 0 203 0

N.S.

1 1.00 0.14 0.23 0.00 1.14 0.00 0.86 0.00

time (sec)

N/A 0.144 0.040 0.691 0.000 0.266 0.000 0.321 0.000

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