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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 136 216 180 180 252 0 226 554

N.S.

1 1.03 1.64 1.36 1.36 1.91 0.00 1.71 4.20

time (sec)

N/A 0.426 1.005 0.408 0.304 0.290 0.000 0.458 11.391

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

168 168 217 178 215 290 0 239 313

N.S.

1 1.00 1.29 1.06 1.28 1.73 0.00 1.42 1.86

time (sec)

N/A 0.480 0.808 0.406 0.341 0.289 0.000 0.417 10.706

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 150 363 135 206 247 0 261 387

N.S.

1 1.00 2.42 0.90 1.37 1.65 0.00 1.74 2.58

time (sec)

N/A 0.475 0.337 0.425 0.228 0.298 0.000 0.438 11.789

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

176 176 313 146 246 271 0 293 319

N.S.

1 1.00 1.78 0.83 1.40 1.54 0.00 1.66 1.81

time (sec)

N/A 0.543 10.051 0.501 0.236 0.290 0.000 0.588 10.449

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

194 194 313 157 268 304 0 325 357

N.S.

1 1.00 1.61 0.81 1.38 1.57 0.00 1.68 1.84

time (sec)

N/A 0.564 6.737 0.622 0.219 0.309 0.000 0.621 10.592

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

216 216 366 168 308 340 0 357 395

N.S.

1 1.00 1.69 0.78 1.43 1.57 0.00 1.65 1.83

time (sec)

N/A 0.586 7.516 0.702 0.233 0.285 0.000 0.625 10.738

Problem 407

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

187 201 116 122 186 124 746 174 572

N.S.

1 1.07 0.62 0.65 0.99 0.66 3.99 0.93 3.06

time (sec)

N/A 0.927 0.664 0.974 0.221 0.285 1.310 0.624 12.763

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 144 209 167 218 219 0 274 384

N.S.

1 1.03 1.49 1.19 1.56 1.56 0.00 1.96 2.74

time (sec)

N/A 0.428 4.757 0.458 0.521 0.293 0.000 0.940 9.566

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 128 86 89 380 80 2635 166 159

N.S.

1 0.95 0.64 0.66 2.81 0.59 19.52 1.23 1.18

time (sec)

N/A 0.612 0.696 0.338 0.310 0.274 31.756 0.312 12.270

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 118 377 78 339 70 2067 153 147

N.S.

1 1.01 3.22 0.67 2.90 0.60 17.67 1.31 1.26

time (sec)

N/A 0.597 3.612 0.321 0.317 0.261 19.658 0.352 12.161

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 88 258 56 278 60 1464 127 120

N.S.

1 0.97 2.84 0.62 3.05 0.66 16.09 1.40 1.32

time (sec)

N/A 0.503 1.626 0.220 0.306 0.270 11.424 0.314 13.566

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 75 219 45 257 50 1134 127 43

N.S.

1 1.03 3.00 0.62 3.52 0.68 15.53 1.74 0.59

time (sec)

N/A 0.418 1.120 0.181 0.316 0.291 6.419 0.296 9.612

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 55 60 46 156 57 0 88 136

N.S.

1 0.93 1.02 0.78 2.64 0.97 0.00 1.49 2.31

time (sec)

N/A 0.345 0.652 0.215 0.309 0.259 0.000 0.313 9.869

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 43 93 66 154 80 0 113 147

N.S.

1 0.88 1.90 1.35 3.14 1.63 0.00 2.31 3.00

time (sec)

N/A 0.370 1.035 0.257 0.313 0.271 0.000 0.341 10.039

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 59 102 72 138 104 0 103 159

N.S.

1 1.02 1.76 1.24 2.38 1.79 0.00 1.78 2.74

time (sec)

N/A 0.425 0.812 0.263 0.308 0.276 0.000 0.335 10.292

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 58 124 94 155 111 0 127 115

N.S.

1 1.00 2.14 1.62 2.67 1.91 0.00 2.19 1.98

time (sec)

N/A 0.400 0.342 0.222 0.219 0.290 0.000 0.339 9.745

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 83 125 98 154 132 0 129 119

N.S.

1 1.01 1.52 1.20 1.88 1.61 0.00 1.57 1.45

time (sec)

N/A 0.538 1.369 0.240 0.209 0.260 0.000 0.363 10.264

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 98 189 122 195 161 0 157 151

N.S.

1 0.98 1.89 1.22 1.95 1.61 0.00 1.57 1.51

time (sec)

N/A 0.592 1.159 0.295 0.221 0.259 0.000 0.325 9.559

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 124 229 168 274 188 0 216 339

N.S.

1 1.00 1.85 1.35 2.21 1.52 0.00 1.74 2.73

time (sec)

N/A 0.697 1.129 0.350 0.205 0.268 0.000 0.451 10.458

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 151 418 89 396 88 2895 166 160

N.S.

1 1.03 2.84 0.61 2.69 0.60 19.69 1.13 1.09

time (sec)

N/A 0.480 3.834 0.369 0.309 0.275 81.112 0.438 13.033

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 133 76 78 353 78 2271 153 146

N.S.

1 1.03 0.59 0.60 2.74 0.60 17.60 1.19 1.13

time (sec)

N/A 0.446 0.756 0.299 0.299 0.261 53.165 0.445 12.727

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 106 308 67 290 68 1608 127 89

N.S.

1 1.04 3.02 0.66 2.84 0.67 15.76 1.25 0.87

time (sec)

N/A 0.431 1.032 0.370 0.314 0.277 33.927 0.426 10.355

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 91 258 56 247 58 1153 114 79

N.S.

1 1.05 2.97 0.64 2.84 0.67 13.25 1.31 0.91

time (sec)

N/A 0.403 0.909 0.378 0.322 0.249 20.550 0.703 9.897

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 79 204 43 184 43 694 88 55

N.S.

1 1.13 2.91 0.61 2.63 0.61 9.91 1.26 0.79

time (sec)

N/A 0.399 0.489 0.283 0.310 0.250 12.021 0.312 9.756

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 40 46 32 82 45 0 52 97

N.S.

1 1.11 1.28 0.89 2.28 1.25 0.00 1.44 2.69

time (sec)

N/A 0.428 0.633 0.284 0.328 0.284 0.000 0.310 10.273

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 39 98 46 93 70 0 73 95

N.S.

1 1.11 2.80 1.31 2.66 2.00 0.00 2.09 2.71

time (sec)

N/A 0.369 1.237 0.299 0.323 0.264 0.000 0.338 10.020

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 58 86 68 115 93 0 98 84

N.S.

1 1.07 1.59 1.26 2.13 1.72 0.00 1.81 1.56

time (sec)

N/A 0.373 1.473 0.297 0.225 0.259 0.000 0.343 9.838

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 70 121 94 153 123 0 128 119

N.S.

1 1.06 1.83 1.42 2.32 1.86 0.00 1.94 1.80

time (sec)

N/A 0.353 1.081 0.395 0.216 0.295 0.000 0.333 10.059

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 100 116 122 195 149 0 157 151

N.S.

1 1.04 1.21 1.27 2.03 1.55 0.00 1.64 1.57

time (sec)

N/A 0.425 1.733 0.402 0.223 0.265 0.000 0.383 10.129

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 116 189 146 233 179 0 186 289

N.S.

1 1.04 1.69 1.30 2.08 1.60 0.00 1.66 2.58

time (sec)

N/A 0.445 1.398 0.442 0.329 0.268 0.000 0.371 10.432

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 142 229 168 275 204 0 215 339

N.S.

1 1.03 1.66 1.22 1.99 1.48 0.00 1.56 2.46

time (sec)

N/A 0.485 1.509 0.528 0.219 0.290 0.000 0.390 10.913

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 101 195 115 398 144 3578 145 146

N.S.

1 0.93 1.79 1.06 3.65 1.32 32.83 1.33 1.34

time (sec)

N/A 0.494 1.147 0.448 0.299 0.265 58.109 0.353 14.206

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 81 181 98 312 123 2264 106 121

N.S.

1 0.93 2.08 1.13 3.59 1.41 26.02 1.22 1.39

time (sec)

N/A 0.453 1.406 0.464 0.316 0.267 37.428 0.336 13.641

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 88 143 67 225 100 1244 91 94

N.S.

1 1.10 1.79 0.84 2.81 1.25 15.55 1.14 1.18

time (sec)

N/A 0.454 0.545 0.369 0.303 0.267 23.077 0.317 11.777

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 43 122 46 78 117 0 47 115

N.S.

1 0.96 2.71 1.02 1.73 2.60 0.00 1.04 2.56

time (sec)

N/A 0.389 0.763 0.352 0.319 0.270 0.000 0.321 9.625

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 52 156 59 116 165 0 90 87

N.S.

1 0.96 2.89 1.09 2.15 3.06 0.00 1.67 1.61

time (sec)

N/A 0.447 1.183 0.419 0.225 0.290 0.000 0.352 10.066

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 74 213 87 161 246 0 116 120

N.S.

1 0.95 2.73 1.12 2.06 3.15 0.00 1.49 1.54

time (sec)

N/A 0.466 4.415 0.436 0.229 0.270 0.000 0.347 9.565

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 90 251 113 199 302 0 146 153

N.S.

1 0.94 2.61 1.18 2.07 3.15 0.00 1.52 1.59

time (sec)

N/A 0.340 3.920 0.464 0.215 0.280 0.000 0.493 9.571

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 109 601 139 241 381 0 174 176

N.S.

1 0.93 5.14 1.19 2.06 3.26 0.00 1.49 1.50

time (sec)

N/A 0.525 6.886 0.570 0.220 0.284 0.000 0.534 10.135

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 58 143 87 269 195 901 86 157

N.S.

1 1.00 2.47 1.50 4.64 3.36 15.53 1.48 2.71

time (sec)

N/A 0.334 1.190 0.526 0.235 0.278 93.366 0.495 9.855

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 135 293 100 335 243 0 99 181

N.S.

1 1.52 3.29 1.12 3.76 2.73 0.00 1.11 2.03

time (sec)

N/A 0.653 3.156 0.633 0.228 0.260 0.000 0.620 10.487

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 161 195 113 401 291 0 112 205

N.S.

1 1.03 1.24 0.72 2.55 1.85 0.00 0.71 1.31

time (sec)

N/A 0.739 3.799 0.936 0.232 0.251 0.000 1.019 10.467

Problem 443

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

156 175 109 85 0 172 0 157 0

N.S.

1 1.12 0.70 0.54 0.00 1.10 0.00 1.01 0.00

time (sec)

N/A 0.902 2.340 0.149 0.000 0.274 0.000 0.313 0.000

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 133 99 75 0 151 0 128 0

N.S.

1 1.07 0.80 0.60 0.00 1.22 0.00 1.03 0.00

time (sec)

N/A 0.660 1.173 0.125 0.000 0.266 0.000 0.314 0.000

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 238 195 141 0 294 0 190 0

N.S.

1 1.50 1.23 0.89 0.00 1.85 0.00 1.19 0.00

time (sec)

N/A 1.589 0.931 0.123 0.000 0.285 0.000 0.357 0.000

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 195 258 162 0 320 0 208 0

N.S.

1 1.32 1.74 1.09 0.00 2.16 0.00 1.41 0.00

time (sec)

N/A 1.333 1.167 0.119 0.000 0.286 0.000 0.329 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 162 297 178 0 359 0 211 0

N.S.

1 1.04 1.90 1.14 0.00 2.30 0.00 1.35 0.00

time (sec)

N/A 1.041 1.059 0.135 0.000 0.282 0.000 0.327 0.000

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 175 309 170 0 380 0 211 0

N.S.

1 1.07 1.90 1.04 0.00 2.33 0.00 1.29 0.00

time (sec)

N/A 0.982 1.289 0.122 0.000 0.277 0.000 0.359 0.000

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

173 227 367 162 0 415 0 213 0

N.S.

1 1.31 2.12 0.94 0.00 2.40 0.00 1.23 0.00

time (sec)

N/A 1.273 2.283 0.125 0.000 0.278 0.000 0.334 0.000

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

209 294 403 180 0 461 0 242 0

N.S.

1 1.41 1.93 0.86 0.00 2.21 0.00 1.16 0.00

time (sec)

N/A 1.711 3.705 0.126 0.000 0.303 0.000 0.345 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

245 374 485 198 0 525 0 271 0

N.S.

1 1.53 1.98 0.81 0.00 2.14 0.00 1.11 0.00

time (sec)

N/A 2.314 5.812 0.130 0.000 0.293 0.000 0.358 0.000

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

281 456 191 216 0 567 0 300 0

N.S.

1 1.62 0.68 0.77 0.00 2.02 0.00 1.07 0.00

time (sec)

N/A 2.913 1.960 0.139 0.000 0.288 0.000 0.348 0.000

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 211 120 97 0 210 0 192 0

N.S.

1 1.12 0.64 0.52 0.00 1.12 0.00 1.02 0.00

time (sec)

N/A 1.067 6.128 0.122 0.000 0.289 0.000 0.388 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 169 110 87 0 189 0 162 0

N.S.

1 1.08 0.71 0.56 0.00 1.21 0.00 1.04 0.00

time (sec)

N/A 0.765 2.915 0.118 0.000 0.263 0.000 0.398 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

199 310 219 159 0 332 0 225 0

N.S.

1 1.56 1.10 0.80 0.00 1.67 0.00 1.13 0.00

time (sec)

N/A 2.258 5.759 0.125 0.000 0.285 0.000 0.460 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

178 264 283 180 0 360 0 243 0

N.S.

1 1.48 1.59 1.01 0.00 2.02 0.00 1.37 0.00

time (sec)

N/A 1.958 6.496 0.124 0.000 0.294 0.000 0.430 0.000

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

186 230 322 178 0 404 0 218 0

N.S.

1 1.24 1.73 0.96 0.00 2.17 0.00 1.17 0.00

time (sec)

N/A 1.563 6.140 0.121 0.000 0.302 0.000 0.765 0.000

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

197 208 334 196 0 424 0 246 0

N.S.

1 1.06 1.70 0.99 0.00 2.15 0.00 1.25 0.00

time (sec)

N/A 1.279 1.277 0.133 0.000 0.305 0.000 0.349 0.000

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

205 257 392 188 0 460 0 246 0

N.S.

1 1.25 1.91 0.92 0.00 2.24 0.00 1.20 0.00

time (sec)

N/A 1.780 2.639 0.133 0.000 0.299 0.000 0.344 0.000

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

215 300 404 180 0 488 0 248 0

N.S.

1 1.40 1.88 0.84 0.00 2.27 0.00 1.15 0.00

time (sec)

N/A 1.974 3.401 0.121 0.000 0.300 0.000 0.342 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

253 381 486 198 0 557 0 278 0

N.S.

1 1.51 1.92 0.78 0.00 2.20 0.00 1.10 0.00

time (sec)

N/A 2.556 3.921 0.122 0.000 0.329 0.000 0.346 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

291 463 522 216 0 600 0 308 0

N.S.

1 1.59 1.79 0.74 0.00 2.06 0.00 1.06 0.00

time (sec)

N/A 2.935 5.585 0.131 0.000 0.323 0.000 0.361 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

329 0 604 234 0 657 0 338 0

N.S.

1 0.00 1.84 0.71 0.00 2.00 0.00 1.03 0.00

time (sec)

N/A 0.000 6.667 0.128 0.000 0.347 0.000 0.361 0.000

Problem 464

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

124 172 143 74 0 155 0 103 0

N.S.

1 1.39 1.15 0.60 0.00 1.25 0.00 0.83 0.00

time (sec)

N/A 0.871 2.112 0.098 0.000 0.280 0.000 0.292 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 97 87 64 0 136 0 84 0

N.S.

1 1.05 0.95 0.70 0.00 1.48 0.00 0.91 0.00

time (sec)

N/A 0.483 1.016 0.095 0.000 0.285 0.000 0.292 0.000

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 268 169 123 0 279 0 151 0

N.S.

1 2.06 1.30 0.95 0.00 2.15 0.00 1.16 0.00

time (sec)

N/A 2.057 0.633 0.111 0.000 0.274 0.000 0.361 0.000

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 229 190 130 0 306 0 178 0

N.S.

1 1.92 1.60 1.09 0.00 2.57 0.00 1.50 0.00

time (sec)

N/A 1.560 0.925 0.111 0.000 0.283 0.000 0.337 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 231 296 150 0 346 0 0 0

N.S.

1 1.85 2.37 1.20 0.00 2.77 0.00 0.00 0.00

time (sec)

N/A 1.428 2.914 0.113 0.000 0.293 0.000 0.000 0.000

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 253 292 144 0 369 0 185 0

N.S.

1 1.87 2.16 1.07 0.00 2.73 0.00 1.37 0.00

time (sec)

N/A 1.480 0.754 0.127 0.000 0.305 0.000 0.476 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

170 335 374 162 0 426 0 190 0

N.S.

1 1.97 2.20 0.95 0.00 2.51 0.00 1.12 0.00

time (sec)

N/A 2.327 1.498 0.132 0.000 0.280 0.000 0.477 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

205 0 410 180 0 472 0 223 0

N.S.

1 0.00 2.00 0.88 0.00 2.30 0.00 1.09 0.00

time (sec)

N/A 0.000 1.810 0.134 0.000 0.270 0.000 0.432 0.000

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

205 414 102 77 0 161 0 103 0

N.S.

1 2.02 0.50 0.38 0.00 0.79 0.00 0.50 0.00

time (sec)

N/A 2.746 4.416 0.108 0.000 0.251 0.000 0.439 0.000

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 136 92 67 0 142 0 84 0

N.S.

1 1.48 1.00 0.73 0.00 1.54 0.00 0.91 0.00

time (sec)

N/A 0.752 4.391 0.108 0.000 0.290 0.000 0.294 0.000

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 82 57 0 121 0 65 0

N.S.

1 1.00 1.37 0.95 0.00 2.02 0.00 1.08 0.00

time (sec)

N/A 0.374 1.220 0.105 0.000 0.253 0.000 0.314 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 134 147 103 0 260 0 138 0

N.S.

1 1.37 1.50 1.05 0.00 2.65 0.00 1.41 0.00

time (sec)

N/A 0.822 0.687 0.122 0.000 0.271 0.000 0.329 0.000

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 141 220 127 0 291 0 165 0

N.S.

1 1.50 2.34 1.35 0.00 3.10 0.00 1.76 0.00

time (sec)

N/A 0.941 1.133 0.118 0.000 0.288 0.000 0.330 0.000

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 181 274 126 0 337 0 152 0

N.S.

1 1.71 2.58 1.19 0.00 3.18 0.00 1.43 0.00

time (sec)

N/A 1.200 1.675 0.126 0.000 0.278 0.000 0.318 0.000

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 262 294 144 0 383 0 168 0

N.S.

1 1.82 2.04 1.00 0.00 2.66 0.00 1.17 0.00

time (sec)

N/A 1.566 0.922 0.121 0.000 0.284 0.000 0.330 0.000

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

182 344 376 162 0 442 0 184 0

N.S.

1 1.89 2.07 0.89 0.00 2.43 0.00 1.01 0.00

time (sec)

N/A 2.257 1.581 0.135 0.000 0.300 0.000 0.330 0.000

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

220 426 412 180 0 492 0 200 0

N.S.

1 1.94 1.87 0.82 0.00 2.24 0.00 0.91 0.00

time (sec)

N/A 2.868 2.215 0.135 0.000 0.302 0.000 0.357 0.000

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

260 0 224 166 0 299 0 201 0

N.S.

1 0.00 0.86 0.64 0.00 1.15 0.00 0.77 0.00

time (sec)

N/A 0.000 1.353 0.159 0.000 0.279 0.000 0.351 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

222 0 225 166 0 280 0 201 0

N.S.

1 0.00 1.01 0.75 0.00 1.26 0.00 0.91 0.00

time (sec)

N/A 0.000 5.589 0.137 0.000 0.278 0.000 0.335 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 186 201 132 0 258 0 163 0

N.S.

1 1.10 1.19 0.78 0.00 1.53 0.00 0.96 0.00

time (sec)

N/A 0.949 4.021 0.127 0.000 0.270 0.000 0.466 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 143 177 130 0 239 0 163 0

N.S.

1 1.04 1.29 0.95 0.00 1.74 0.00 1.19 0.00

time (sec)

N/A 0.665 0.988 0.122 0.000 0.277 0.000 0.422 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 167 154 116 0 377 0 184 0

N.S.

1 1.48 1.36 1.03 0.00 3.34 0.00 1.63 0.00

time (sec)

N/A 0.999 0.759 0.146 0.000 0.318 0.000 0.426 0.000

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 212 170 132 0 421 0 205 0

N.S.

1 1.88 1.50 1.17 0.00 3.73 0.00 1.81 0.00

time (sec)

N/A 1.461 2.482 0.148 0.000 0.294 0.000 0.416 0.000

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 288 309 164 0 508 0 224 0

N.S.

1 1.88 2.02 1.07 0.00 3.32 0.00 1.46 0.00

time (sec)

N/A 2.029 2.819 0.135 0.000 0.312 0.000 0.426 0.000

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

191 376 332 182 0 564 0 240 0

N.S.

1 1.97 1.74 0.95 0.00 2.95 0.00 1.26 0.00

time (sec)

N/A 2.793 2.099 0.165 0.000 0.288 0.000 0.406 0.000

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

229 0 414 200 0 643 0 256 0

N.S.

1 0.00 1.81 0.87 0.00 2.81 0.00 1.12 0.00

time (sec)

N/A 0.000 4.343 0.168 0.000 0.325 0.000 0.355 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

200 200 164 0 0 0 0 0 0

N.S.

1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.457 0.227 0.000 0.000 0.000 0.000 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

129 129 141 0 0 0 0 0 0

N.S.

1 1.00 1.09 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.380 0.773 0.000 0.000 0.000 0.000 0.000 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

134 134 441 0 0 0 0 0 0

N.S.

1 1.00 3.29 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.423 11.838 0.000 0.000 0.000 0.000 0.000 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

173 174 312 0 0 0 0 0 0

N.S.

1 1.01 1.80 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.605 4.009 0.000 0.000 0.000 0.000 0.000 0.000

Problem 494

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

97 98 97 67 72 106 136 133 71

N.S.

1 1.01 1.00 0.69 0.74 1.09 1.40 1.37 0.73

time (sec)

N/A 0.282 0.374 0.563 0.230 0.277 1.809 0.437 9.266

Problem 495

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

97 98 87 67 72 95 136 118 71

N.S.

1 1.01 0.90 0.69 0.74 0.98 1.40 1.22 0.73

time (sec)

N/A 0.289 0.209 0.494 0.228 0.308 1.281 0.375 9.009

Problem 496

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

81 74 97 67 72 84 114 133 71

N.S.

1 0.91 1.20 0.83 0.89 1.04 1.41 1.64 0.88

time (sec)

N/A 0.418 0.211 0.383 0.228 0.269 0.912 0.385 0.067

Problem 497

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

81 74 87 67 72 73 114 118 71

N.S.

1 0.91 1.07 0.83 0.89 0.90 1.41 1.46 0.88

time (sec)

N/A 0.411 0.157 0.338 0.240 0.254 0.642 0.451 10.048

Problem 498

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

65 59 78 67 72 62 90 103 71

N.S.

1 0.91 1.20 1.03 1.11 0.95 1.38 1.58 1.09

time (sec)

N/A 0.345 0.094 0.257 0.216 0.265 0.441 0.427 9.297

Problem 499

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

86 89 86 65 69 74 0 70 126

N.S.

1 1.03 1.00 0.76 0.80 0.86 0.00 0.81 1.47

time (sec)

N/A 0.257 0.027 0.320 0.214 0.285 0.000 0.406 9.859

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 86 83 85 69 91 0 79 250

N.S.

1 1.04 1.00 1.02 0.83 1.10 0.00 0.95 3.01

time (sec)

N/A 0.273 0.025 0.234 0.213 0.287 0.000 0.424 10.863

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