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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 F F F F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 62 0 0 0 0 0 -1

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.060 0.048 0.216 0.000 0.000 0.000 0.000 0.000

Problem 402

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

92 92 43 110 100 48 56 72 63

N.S.

1 1.00 0.47 1.20 1.09 0.52 0.61 0.78 0.68

time (sec)

N/A 0.065 0.033 0.344 0.295 0.346 0.137 4.447 0.473

Problem 403

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

102 102 58 169 161 63 75 104 92

N.S.

1 1.00 0.57 1.66 1.58 0.62 0.74 1.02 0.90

time (sec)

N/A 0.075 0.049 0.372 0.281 0.353 0.162 4.991 0.496

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

160 160 132 0 609 1438 609 1802 380

N.S.

1 1.00 0.82 0.00 3.81 8.99 3.81 11.26 2.38

time (sec)

N/A 0.141 0.048 0.042 0.324 0.379 3.129 6.317 0.576

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 100 0 343 655 360 822 242

N.S.

1 1.00 0.83 0.00 2.83 5.41 2.98 6.79 2.00

time (sec)

N/A 0.106 0.011 0.046 0.298 0.387 1.352 4.125 0.409

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 69 0 159 238 178 303 111

N.S.

1 1.00 0.88 0.00 2.04 3.05 2.28 3.88 1.42

time (sec)

N/A 0.069 0.008 0.034 0.301 0.360 0.636 6.757 0.280

Problem 407

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

34 34 34 42 48 52 53 64 41

N.S.

1 1.00 1.00 1.24 1.41 1.53 1.56 1.88 1.21

time (sec)

N/A 0.022 0.007 0.071 0.279 0.337 0.222 1.800 0.213

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 83 0 0 66 0 79 -1

N.S.

1 1.00 1.00 0.00 0.00 0.80 0.00 0.95 -0.01

time (sec)

N/A 0.095 0.074 0.047 0.000 0.369 0.000 6.396 0.000

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 163 0 0 175 0 593 -1

N.S.

1 1.00 1.33 0.00 0.00 1.42 0.00 4.82 -0.01

time (sec)

N/A 0.119 0.080 0.032 0.000 0.356 0.000 4.747 0.000

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

169 169 189 0 0 455 0 3481 -1

N.S.

1 1.00 1.12 0.00 0.00 2.69 0.00 20.60 -0.01

time (sec)

N/A 0.159 0.127 0.047 0.000 0.369 0.000 6.207 0.000

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

219 219 190 0 0 0 0 0 -1

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.265 0.223 0.057 0.000 0.000 0.000 0.000 0.000

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

176 176 160 0 0 0 0 0 -1

N.S.

1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.198 0.045 0.035 0.000 0.000 0.000 0.000 0.000

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 134 0 0 0 0 0 -1

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.159 0.044 0.035 0.000 0.000 0.000 0.000 0.000

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 104 0 0 0 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.139 0.017 0.030 0.000 0.000 0.000 0.000 0.000

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 181 0 0 0 0 0 -1

N.S.

1 1.00 1.23 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.178 0.155 0.033 0.000 0.000 0.000 0.000 0.000

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

194 194 211 0 0 0 0 0 -1

N.S.

1 1.00 1.09 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.230 0.208 0.035 0.000 0.000 0.000 0.000 0.000

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

237 237 272 0 0 0 0 0 -1

N.S.

1 1.00 1.15 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.282 0.292 0.030 0.000 0.000 0.000 0.000 0.000

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 131 0 0 81 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.62 0.00 0.00 -0.01

time (sec)

N/A 0.110 0.140 0.057 0.000 0.090 0.000 0.000 0.000

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

109 109 109 0 72 0 0 0 -1

N.S.

1 1.00 1.00 0.00 0.66 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.107 0.102 0.088 0.051 0.000 0.000 0.000 0.000

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

158 158 233 0 309 419 457 1047 370

N.S.

1 1.00 1.47 0.00 1.96 2.65 2.89 6.63 2.34

time (sec)

N/A 0.122 0.181 0.173 0.321 0.354 2.956 6.281 0.421

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

128 128 157 0 207 275 286 585 225

N.S.

1 1.00 1.23 0.00 1.62 2.15 2.23 4.57 1.76

time (sec)

N/A 0.095 0.114 0.185 0.289 0.361 1.356 3.483 0.347

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 113 0 117 150 156 259 113

N.S.

1 1.00 1.15 0.00 1.19 1.53 1.59 2.64 1.15

time (sec)

N/A 0.061 0.046 0.050 0.287 0.350 0.614 4.942 0.294

Problem 423

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

34 34 34 42 48 52 53 64 41

N.S.

1 1.00 1.00 1.24 1.41 1.53 1.56 1.88 1.21

time (sec)

N/A 0.022 0.008 0.079 0.282 0.355 0.215 4.994 0.218

Problem 424

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

68 68 67 0 0 0 0 0 -1

N.S.

1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.083 0.011 0.211 0.000 0.000 0.000 0.000 0.000

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 97 0 94 119 0 129 89

N.S.

1 1.00 1.21 0.00 1.18 1.49 0.00 1.61 1.11

time (sec)

N/A 0.056 0.058 0.224 0.290 0.401 0.000 6.058 2.044

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 187 0 176 315 0 359 180

N.S.

1 1.00 1.57 0.00 1.48 2.65 0.00 3.02 1.51

time (sec)

N/A 0.098 0.092 0.213 0.299 0.389 0.000 3.184 2.259

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

149 149 297 0 307 563 5673 643 293

N.S.

1 1.00 1.99 0.00 2.06 3.78 38.07 4.32 1.97

time (sec)

N/A 0.124 0.098 0.201 0.301 0.400 72.229 6.189 2.477

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

409 409 634 0 914 1892 1421 3938 1154

N.S.

1 1.00 1.55 0.00 2.23 4.63 3.47 9.63 2.82

time (sec)

N/A 0.707 0.472 0.216 0.313 0.390 6.698 2.685 0.915

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

323 323 422 0 624 1215 894 2241 652

N.S.

1 1.00 1.31 0.00 1.93 3.76 2.77 6.94 2.02

time (sec)

N/A 0.571 0.334 0.208 0.297 0.389 3.097 3.877 0.692

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

211 211 164 0 365 646 466 1014 302

N.S.

1 1.00 0.78 0.00 1.73 3.06 2.21 4.81 1.43

time (sec)

N/A 0.280 0.069 0.048 0.289 0.375 1.411 4.942 0.464

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 69 0 159 238 178 303 111

N.S.

1 1.00 0.88 0.00 2.04 3.05 2.28 3.88 1.42

time (sec)

N/A 0.065 0.014 0.034 0.280 0.345 0.556 5.898 0.301

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 324 0 0 0 0 0 -1

N.S.

1 1.00 2.63 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.186 0.079 0.177 0.000 0.000 0.000 0.000 0.000

Problem 433

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

144 144 200 0 0 0 0 0 -1

N.S.

1 1.00 1.39 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.144 0.127 0.209 0.000 0.000 0.000 0.000 0.000

Problem 434

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

222 222 316 0 0 0 0 0 -1

N.S.

1 1.00 1.42 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.486 0.262 0.183 0.000 0.000 0.000 0.000 0.000

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

492 492 858 0 1286 3392 1846 5481 1400

N.S.

1 1.00 1.74 0.00 2.61 6.89 3.75 11.14 2.85

time (sec)

N/A 0.647 0.722 0.227 0.338 0.476 6.666 4.649 1.264

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

306 306 231 0 770 1776 991 2717 651

N.S.

1 1.00 0.75 0.00 2.52 5.80 3.24 8.88 2.13

time (sec)

N/A 0.378 0.111 0.079 0.315 0.427 3.171 5.696 0.831

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 100 0 343 655 360 822 242

N.S.

1 1.00 0.83 0.00 2.83 5.41 2.98 6.79 2.00

time (sec)

N/A 0.106 0.019 0.053 0.280 0.369 1.192 3.579 0.426

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 646 0 0 0 0 0 -1

N.S.

1 1.00 3.65 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.295 0.140 0.183 0.000 0.000 0.000 0.000 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

209 209 444 0 0 0 0 0 -1

N.S.

1 1.00 2.12 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.258 0.316 0.192 0.000 0.000 0.000 0.000 0.000

Problem 440

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

376 376 660 0 0 0 0 0 -1

N.S.

1 1.00 1.76 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.856 0.519 0.199 0.000 0.000 0.000 0.000 0.000

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

160 160 132 0 609 1438 609 1802 380

N.S.

1 1.00 0.82 0.00 3.81 8.99 3.81 11.26 2.38

time (sec)

N/A 0.143 0.040 0.039 0.306 0.372 2.668 5.021 0.561

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

231 231 1095 0 0 0 0 0 -1

N.S.

1 1.00 4.74 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.365 0.228 0.208 0.000 0.000 0.000 0.000 0.000

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

274 274 1301 0 0 0 0 0 -1

N.S.

1 1.00 4.75 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.352 0.324 0.241 0.000 0.000 0.000 0.000 0.000

Problem 444

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

29 29 29 41 43 44 48 58 36

N.S.

1 1.00 1.00 1.41 1.48 1.52 1.66 2.00 1.24

time (sec)

N/A 0.019 0.008 0.071 0.274 0.348 0.215 4.055 0.073

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

279 279 252 0 0 244 0 524 -1

N.S.

1 1.00 0.90 0.00 0.00 0.87 0.00 1.88 -0.00

time (sec)

N/A 0.531 0.478 0.187 0.000 0.390 0.000 5.187 0.000

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

179 179 164 0 0 142 0 252 -1

N.S.

1 1.00 0.92 0.00 0.00 0.79 0.00 1.41 -0.01

time (sec)

N/A 0.297 0.164 0.042 0.000 0.419 0.000 3.302 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 83 0 0 66 0 79 -1

N.S.

1 1.00 1.00 0.00 0.00 0.80 0.00 0.95 -0.01

time (sec)

N/A 0.088 0.043 0.042 0.000 0.342 0.000 5.169 0.000

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

31 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.048 0.155 0.164 0.000 0.000 0.000 0.000 0.000

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

31 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.042 0.445 0.168 0.000 0.000 0.000 0.000 0.000

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

326 326 1310 0 0 595 0 4046 -1

N.S.

1 1.00 4.02 0.00 0.00 1.83 0.00 12.41 -0.00

time (sec)

N/A 0.921 0.548 0.173 0.000 0.359 0.000 4.918 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

224 224 269 0 0 342 0 1968 -1

N.S.

1 1.00 1.20 0.00 0.00 1.53 0.00 8.79 -0.00

time (sec)

N/A 0.449 0.280 0.044 0.000 0.349 0.000 4.990 0.000

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 163 0 0 175 0 593 -1

N.S.

1 1.00 1.33 0.00 0.00 1.42 0.00 4.82 -0.01

time (sec)

N/A 0.115 0.082 0.035 0.000 0.375 0.000 4.281 0.000

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

31 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.043 0.738 0.216 0.000 0.000 0.000 0.000 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

31 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.042 9.225 0.170 0.000 0.000 0.000 0.000 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

432 432 438 0 0 1803 0 6028 -1

N.S.

1 1.00 1.01 0.00 0.00 4.17 0.00 13.95 -0.00

time (sec)

N/A 1.488 1.453 0.163 0.000 0.395 0.000 3.747 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

322 322 322 0 0 988 0 11533 -1

N.S.

1 1.00 1.00 0.00 0.00 3.07 0.00 35.82 -0.00

time (sec)

N/A 0.651 0.458 0.036 0.000 0.374 0.000 5.021 0.000

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

169 169 189 0 0 455 0 3481 -1

N.S.

1 1.00 1.12 0.00 0.00 2.69 0.00 20.60 -0.01

time (sec)

N/A 0.152 0.139 0.041 0.000 0.353 0.000 5.909 0.000

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

31 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.044 0.764 0.202 0.000 0.000 0.000 0.000 0.000

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

31 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.041 24.834 0.201 0.000 0.000 0.000 0.000 0.000

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

488 488 458 0 0 0 0 0 -1

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.150 0.453 0.177 0.000 0.000 0.000 0.000 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

311 311 298 0 0 0 0 0 -1

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.612 0.263 0.032 0.000 0.000 0.000 0.000 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 134 0 0 0 0 0 -1

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.164 0.046 0.036 0.000 0.000 0.000 0.000 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.066 2.770 0.175 0.000 0.000 0.000 0.000 0.000

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.099 0.255 0.209 0.000 0.000 0.000 0.000 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

625 625 545 0 0 0 0 0 -1

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.363 0.898 0.136 0.000 0.000 0.000 0.000 0.000

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

396 396 348 0 0 0 0 0 -1

N.S.

1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.761 0.374 0.044 0.000 0.000 0.000 0.000 0.000

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

176 176 160 0 0 0 0 0 -1

N.S.

1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.193 0.142 0.042 0.000 0.000 0.000 0.000 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.081 1.123 0.214 0.000 0.000 0.000 0.000 0.000

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.108 1.418 0.209 0.000 0.000 0.000 0.000 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

355 355 315 0 0 0 0 0 -1

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.927 0.239 0.193 0.000 0.000 0.000 0.000 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

229 229 208 0 0 0 0 0 -1

N.S.

1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.492 0.129 0.048 0.000 0.000 0.000 0.000 0.000

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 104 0 0 0 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.130 0.017 0.044 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 A A F(-2) A A A

verified

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

size

33 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.072 0.080 0.205 0.000 0.000 0.000 0.000 0.000

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

404 404 1821 0 0 0 0 0 -1

N.S.

1 1.00 4.51 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.635 2.761 0.175 0.000 0.000 0.000 0.000 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

275 275 435 0 0 0 0 0 -1

N.S.

1 1.00 1.58 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.727 0.876 0.031 0.000 0.000 0.000 0.000 0.000

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 181 0 0 0 0 0 -1

N.S.

1 1.00 1.23 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.174 0.121 0.042 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 A A F(-2) A A A

verified

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

size

33 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.080 0.319 0.174 0.000 0.000 0.000 0.000 0.000

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

514 514 1471 0 0 0 0 0 -1

N.S.

1 1.00 2.86 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 2.588 3.105 0.186 0.000 0.000 0.000 0.000 0.000

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

380 380 491 0 0 0 0 0 -1

N.S.

1 1.00 1.29 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.052 1.517 0.033 0.000 0.000 0.000 0.000 0.000

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

194 194 211 0 0 0 0 0 -1

N.S.

1 1.00 1.09 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.221 0.235 0.038 0.000 0.000 0.000 0.000 0.000

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.077 0.565 0.184 0.000 0.000 0.000 0.000 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 163 0 0 647 484 0 -1

N.S.

1 1.00 0.95 0.00 0.00 3.78 2.83 0.00 -0.01

time (sec)

N/A 0.196 0.393 0.186 0.000 0.419 58.762 0.000 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 124 0 0 366 144 0 -1

N.S.

1 1.00 0.89 0.00 0.00 2.63 1.04 0.00 -0.01

time (sec)

N/A 0.132 0.233 0.215 0.000 0.419 3.047 0.000 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 89 147 0 210 347 128 -1

N.S.

1 1.00 0.86 1.43 0.00 2.04 3.37 1.24 -0.01

time (sec)

N/A 0.100 0.200 0.774 0.000 0.384 17.095 3.036 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 84 0 0 250 90 99 -1

N.S.

1 1.00 0.98 0.00 0.00 2.91 1.05 1.15 -0.01

time (sec)

N/A 0.090 0.183 0.192 0.000 0.415 10.767 6.277 0.000

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 124 0 0 491 122 209 -1

N.S.

1 1.00 1.03 0.00 0.00 4.09 1.02 1.74 -0.01

time (sec)

N/A 0.116 0.322 0.198 0.000 0.434 95.070 2.732 0.000

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 135 0 0 883 0 378 -1

N.S.

1 1.00 0.89 0.00 0.00 5.81 0.00 2.49 -0.01

time (sec)

N/A 0.148 0.532 0.215 0.000 0.426 0.000 5.711 0.000

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

184 184 160 0 0 1380 0 0 -1

N.S.

1 1.00 0.87 0.00 0.00 7.50 0.00 0.00 -0.01

time (sec)

N/A 0.195 0.565 0.211 0.000 0.447 0.000 0.000 0.000

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F(-2) F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

635 635 1168 0 0 0 0 0 -1

N.S.

1 1.00 1.84 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 2.916 6.625 0.162 0.000 0.000 0.000 0.000 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

547 547 365 0 0 0 0 0 -1

N.S.

1 1.00 0.67 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 2.080 1.213 0.219 0.000 0.000 0.000 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

447 447 646 0 0 0 0 0 -1

N.S.

1 1.00 1.45 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.524 1.253 0.186 0.000 0.000 0.000 0.000 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

330 330 356 0 0 0 0 0 -1

N.S.

1 1.00 1.08 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.134 2.613 0.225 0.000 0.000 0.000 0.000 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

449 449 657 0 0 0 0 0 -1

N.S.

1 1.00 1.46 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.600 4.850 0.208 0.000 0.000 0.000 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

537 537 726 0 0 0 0 0 -1

N.S.

1 1.00 1.35 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 2.105 6.816 0.185 0.000 0.000 0.000 0.000 0.000

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F(-2) F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

625 625 1249 0 0 0 0 0 -1

N.S.

1 1.00 2.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 2.684 8.704 0.156 0.000 0.000 0.000 0.000 0.000

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.053 0.764 0.216 0.000 0.000 0.000 0.000 0.000

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.049 0.689 0.202 0.000 0.000 0.000 0.000 0.000

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

33 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.050 0.928 0.187 0.000 0.000 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 A A A

verified

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

size

33 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.056 1.002 0.234 0.000 0.000 0.000 0.000 0.000

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

35 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.202 0.750 0.189 0.000 0.000 0.000 0.000 0.000

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