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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 A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 143 104 225 153 170 0 63 120

N.S.

1 1.04 0.75 1.63 1.11 1.23 0.00 0.46 0.87

time (sec)

N/A 0.623 0.088 0.178 0.203 0.251 0.000 0.324 0.090

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 158 112 265 169 204 0 0 137

N.S.

1 0.96 0.68 1.61 1.02 1.24 0.00 0.00 0.83

time (sec)

N/A 0.762 0.097 0.180 0.221 0.252 0.000 0.000 4.232

Problem 403

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

204 213 120 305 185 240 0 63 153

N.S.

1 1.04 0.59 1.50 0.91 1.18 0.00 0.31 0.75

time (sec)

N/A 0.955 0.110 0.171 0.193 0.252 0.000 0.352 3.934

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 51 51 48 59 67 63 123 51

N.S.

1 0.80 0.80 0.75 0.92 1.05 0.98 1.92 0.80

time (sec)

N/A 0.422 0.083 0.755 0.186 0.250 0.214 0.265 3.883

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 28 28 27 31 36 31 59 27

N.S.

1 0.93 0.93 0.90 1.03 1.20 1.03 1.97 0.90

time (sec)

N/A 0.402 0.060 0.701 0.193 0.231 0.096 0.265 0.053

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 35 38 30 34 43 37 98 31

N.S.

1 0.92 1.00 0.79 0.89 1.13 0.97 2.58 0.82

time (sec)

N/A 0.405 0.057 0.673 0.199 0.243 0.110 0.258 3.882

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 23 23 24 27 32 26 94 25

N.S.

1 0.85 0.85 0.89 1.00 1.19 0.96 3.48 0.93

time (sec)

N/A 0.393 0.049 0.613 0.193 0.256 0.086 0.271 3.856

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 22 22 22 24 23 17 55 24

N.S.

1 0.88 0.88 0.88 0.96 0.92 0.68 2.20 0.96

time (sec)

N/A 0.364 0.041 0.604 0.209 0.252 0.154 0.262 0.074

Problem 409

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

53 51 51 43 49 64 41 74 48

N.S.

1 0.96 0.96 0.81 0.92 1.21 0.77 1.40 0.91

time (sec)

N/A 0.413 0.039 0.575 0.201 0.242 0.153 0.262 0.064

Problem 410

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

71 66 63 56 75 100 73 94 71

N.S.

1 0.93 0.89 0.79 1.06 1.41 1.03 1.32 1.00

time (sec)

N/A 0.449 0.072 0.587 0.181 0.248 0.195 0.272 3.860

Problem 411

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

89 82 71 67 93 126 94 109 90

N.S.

1 0.92 0.80 0.75 1.04 1.42 1.06 1.22 1.01

time (sec)

N/A 0.468 0.087 0.595 0.197 0.240 0.305 0.266 3.793

Problem 412

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

105 94 79 78 113 154 114 124 109

N.S.

1 0.90 0.75 0.74 1.08 1.47 1.09 1.18 1.04

time (sec)

N/A 0.484 0.100 0.592 0.195 0.244 0.425 0.272 3.859

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 142 175 157 223 156 0 265 185

N.S.

1 1.05 1.30 1.16 1.65 1.16 0.00 1.96 1.37

time (sec)

N/A 0.698 0.176 0.169 0.291 0.260 0.000 0.294 0.131

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

106 107 167 149 201 143 0 232 163

N.S.

1 1.01 1.58 1.41 1.90 1.35 0.00 2.19 1.54

time (sec)

N/A 0.550 0.147 0.157 0.283 0.256 0.000 0.280 3.862

Problem 415

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

77 80 55 134 126 113 0 130 90

N.S.

1 1.04 0.71 1.74 1.64 1.47 0.00 1.69 1.17

time (sec)

N/A 0.423 0.220 0.152 0.275 0.260 0.000 0.275 0.083

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 55 73 136 114 88 0 85 82

N.S.

1 1.12 1.49 2.78 2.33 1.80 0.00 1.73 1.67

time (sec)

N/A 0.297 0.126 0.131 0.276 0.246 0.000 0.281 0.074

Problem 417

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

19 19 19 28 44 27 0 24 39

N.S.

1 1.00 1.00 1.47 2.32 1.42 0.00 1.26 2.05

time (sec)

N/A 0.226 0.107 0.187 0.200 0.244 0.000 0.262 0.055

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 74 69 144 120 97 0 0 62

N.S.

1 1.01 0.95 1.97 1.64 1.33 0.00 0.00 0.85

time (sec)

N/A 0.323 0.044 0.219 0.182 0.256 0.000 0.000 3.814

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 100 94 185 137 134 0 0 105

N.S.

1 0.95 0.90 1.76 1.30 1.28 0.00 0.00 1.00

time (sec)

N/A 0.458 0.076 0.230 0.193 0.258 0.000 0.000 3.865

Problem 420

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

138 129 104 225 153 170 0 59 121

N.S.

1 0.93 0.75 1.63 1.11 1.23 0.00 0.43 0.88

time (sec)

N/A 0.600 0.088 0.244 0.199 0.244 0.000 0.294 3.867

Problem 421

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 54 54 51 60 71 56 62 61

N.S.

1 0.83 0.83 0.78 0.92 1.09 0.86 0.95 0.94

time (sec)

N/A 0.424 0.085 0.651 0.187 0.274 0.301 0.275 0.102

Problem 422

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

54 44 46 43 51 62 42 53 51

N.S.

1 0.81 0.85 0.80 0.94 1.15 0.78 0.98 0.94

time (sec)

N/A 0.423 0.074 0.618 0.186 0.249 0.240 0.280 0.085

Problem 423

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 34 34 31 40 43 31 42 40

N.S.

1 0.85 0.85 0.78 1.00 1.08 0.78 1.05 1.00

time (sec)

N/A 0.413 0.061 0.579 0.190 0.239 0.210 0.281 4.252

Problem 424

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 19 23 20 23 22 17 25 23

N.S.

1 0.83 1.00 0.87 1.00 0.96 0.74 1.09 1.00

time (sec)

N/A 0.354 0.038 0.553 0.184 0.248 0.126 0.271 0.075

Problem 425

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

20 22 22 20 20 19 17 21 19

N.S.

1 1.10 1.10 1.00 1.00 0.95 0.85 1.05 0.95

time (sec)

N/A 0.379 0.023 0.498 0.180 0.243 0.093 0.276 3.801

Problem 426

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

18 23 18 28 34 27 34 36 17

N.S.

1 1.28 1.00 1.56 1.89 1.50 1.89 2.00 0.94

time (sec)

N/A 0.391 0.046 0.519 0.190 0.242 0.129 0.285 0.073

Problem 427

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

57 55 57 48 53 59 56 51 52

N.S.

1 0.96 1.00 0.84 0.93 1.04 0.98 0.89 0.91

time (sec)

N/A 0.449 0.075 0.506 0.186 0.242 0.241 0.265 0.096

Problem 428

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

75 72 72 60 69 93 73 57 68

N.S.

1 0.96 0.96 0.80 0.92 1.24 0.97 0.76 0.91

time (sec)

N/A 0.456 0.095 0.520 0.187 0.242 0.292 0.265 3.879

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 173 567 191 246 157 0 0 211

N.S.

1 1.05 3.46 1.16 1.50 0.96 0.00 0.00 1.29

time (sec)

N/A 0.855 1.328 0.182 0.279 0.258 0.000 0.000 0.144

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 138 663 181 225 146 0 0 190

N.S.

1 1.02 4.91 1.34 1.67 1.08 0.00 0.00 1.41

time (sec)

N/A 0.689 0.513 0.171 0.276 0.272 0.000 0.000 3.914

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 111 424 169 149 120 0 0 117

N.S.

1 1.06 4.04 1.61 1.42 1.14 0.00 0.00 1.11

time (sec)

N/A 0.551 0.404 0.176 0.269 0.276 0.000 0.000 0.110

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 87 234 371 135 92 0 0 107

N.S.

1 1.16 3.12 4.95 1.80 1.23 0.00 0.00 1.43

time (sec)

N/A 0.422 0.541 0.138 0.277 0.263 0.000 0.000 0.099

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 70 61 137 120 69 0 0 87

N.S.

1 0.97 0.85 1.90 1.67 0.96 0.00 0.00 1.21

time (sec)

N/A 0.327 0.146 0.150 0.180 0.257 0.000 0.000 0.062

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 68 69 138 125 67 0 0 90

N.S.

1 0.92 0.93 1.86 1.69 0.91 0.00 0.00 1.22

time (sec)

N/A 0.307 0.045 0.252 0.185 0.258 0.000 0.000 3.840

Problem 435

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

45 45 33 41 92 42 0 42 41

N.S.

1 1.00 0.73 0.91 2.04 0.93 0.00 0.93 0.91

time (sec)

N/A 0.234 0.027 0.203 0.199 0.247 0.000 0.266 0.077

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 105 94 218 160 134 0 0 128

N.S.

1 0.95 0.85 1.96 1.44 1.21 0.00 0.00 1.15

time (sec)

N/A 0.356 0.078 0.243 0.192 0.247 0.000 0.000 3.894

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 132 104 259 176 170 0 0 144

N.S.

1 0.96 0.75 1.88 1.28 1.23 0.00 0.00 1.04

time (sec)

N/A 0.600 0.095 0.242 0.195 0.259 0.000 0.000 0.096

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

235 183 109 166 0 437 0 0 0

N.S.

1 0.78 0.46 0.71 0.00 1.86 0.00 0.00 0.00

time (sec)

N/A 0.395 0.126 0.092 0.000 0.295 0.000 0.000 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

196 150 101 149 0 415 0 0 0

N.S.

1 0.77 0.52 0.76 0.00 2.12 0.00 0.00 0.00

time (sec)

N/A 0.373 0.089 0.082 0.000 0.273 0.000 0.000 0.000

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 115 89 132 0 381 0 0 0

N.S.

1 0.73 0.57 0.84 0.00 2.43 0.00 0.00 0.00

time (sec)

N/A 0.336 0.078 0.083 0.000 0.293 0.000 0.000 0.000

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 122 70 105 0 313 0 0 0

N.S.

1 1.04 0.60 0.90 0.00 2.68 0.00 0.00 0.00

time (sec)

N/A 0.398 0.058 0.084 0.000 0.276 0.000 0.000 0.000

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 82 66 87 0 295 0 0 0

N.S.

1 1.05 0.85 1.12 0.00 3.78 0.00 0.00 0.00

time (sec)

N/A 0.325 0.047 0.084 0.000 0.283 0.000 0.000 0.000

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 103 95 151 0 517 0 0 0

N.S.

1 0.68 0.62 0.99 0.00 3.40 0.00 0.00 0.00

time (sec)

N/A 0.340 0.073 0.264 0.000 0.326 0.000 0.000 0.000

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

215 137 122 259 0 594 0 0 0

N.S.

1 0.64 0.57 1.20 0.00 2.76 0.00 0.00 0.00

time (sec)

N/A 0.377 0.103 0.281 0.000 0.327 0.000 0.000 0.000

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

277 175 135 328 0 668 0 0 0

N.S.

1 0.63 0.49 1.18 0.00 2.41 0.00 0.00 0.00

time (sec)

N/A 0.405 0.136 0.300 0.000 0.326 0.000 0.000 0.000

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 146 91 155 0 234 2222 0 0

N.S.

1 1.02 0.64 1.08 0.00 1.64 15.54 0.00 0.00

time (sec)

N/A 0.465 0.160 0.546 0.000 0.257 22.535 0.000 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 124 83 144 0 212 740 0 0

N.S.

1 1.05 0.70 1.22 0.00 1.80 6.27 0.00 0.00

time (sec)

N/A 0.459 0.128 0.549 0.000 0.258 7.542 0.000 0.000

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 103 75 108 0 182 144 0 0

N.S.

1 1.08 0.79 1.14 0.00 1.92 1.52 0.00 0.00

time (sec)

N/A 0.433 0.088 0.559 0.000 0.257 16.411 0.000 0.000

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 80 55 103 0 137 173 0 0

N.S.

1 1.14 0.79 1.47 0.00 1.96 2.47 0.00 0.00

time (sec)

N/A 0.422 0.066 0.541 0.000 0.267 25.431 0.000 0.000

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 58 50 98 0 124 0 96 0

N.S.

1 1.16 1.00 1.96 0.00 2.48 0.00 1.92 0.00

time (sec)

N/A 0.393 0.037 0.526 0.000 0.257 0.000 0.294 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 83 43 150 0 176 0 170 0

N.S.

1 1.19 0.61 2.14 0.00 2.51 0.00 2.43 0.00

time (sec)

N/A 0.413 0.035 0.538 0.000 0.258 0.000 0.351 0.000

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 110 55 201 0 238 0 245 0

N.S.

1 1.16 0.58 2.12 0.00 2.51 0.00 2.58 0.00

time (sec)

N/A 0.436 0.038 0.544 0.000 0.278 0.000 0.410 0.000

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 137 58 247 0 294 0 316 0

N.S.

1 1.16 0.49 2.09 0.00 2.49 0.00 2.68 0.00

time (sec)

N/A 0.455 0.037 0.537 0.000 0.261 0.000 0.476 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 164 46 291 0 346 0 391 0

N.S.

1 1.13 0.32 2.01 0.00 2.39 0.00 2.70 0.00

time (sec)

N/A 0.488 0.049 0.540 0.000 0.276 0.000 0.629 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

268 168 109 178 0 437 0 0 0

N.S.

1 0.63 0.41 0.66 0.00 1.63 0.00 0.00 0.00

time (sec)

N/A 0.401 0.113 0.084 0.000 0.285 0.000 0.000 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

237 132 101 161 0 415 0 0 0

N.S.

1 0.56 0.43 0.68 0.00 1.75 0.00 0.00 0.00

time (sec)

N/A 0.355 0.090 0.086 0.000 0.280 0.000 0.000 0.000

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 162 89 144 0 381 0 0 0

N.S.

1 1.04 0.57 0.92 0.00 2.44 0.00 0.00 0.00

time (sec)

N/A 0.439 0.072 0.079 0.000 0.286 0.000 0.000 0.000

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 123 66 118 0 315 0 0 0

N.S.

1 1.04 0.56 1.00 0.00 2.67 0.00 0.00 0.00

time (sec)

N/A 0.387 0.049 0.073 0.000 0.289 0.000 0.000 0.000

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 104 95 160 0 512 0 0 0

N.S.

1 0.68 0.62 1.05 0.00 3.37 0.00 0.00 0.00

time (sec)

N/A 0.348 0.058 0.237 0.000 0.315 0.000 0.000 0.000

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

215 135 115 259 0 581 0 0 0

N.S.

1 0.63 0.53 1.20 0.00 2.70 0.00 0.00 0.00

time (sec)

N/A 0.369 0.115 0.277 0.000 0.337 0.000 0.000 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

275 172 135 326 0 668 0 0 0

N.S.

1 0.63 0.49 1.19 0.00 2.43 0.00 0.00 0.00

time (sec)

N/A 0.415 0.141 0.276 0.000 0.335 0.000 0.000 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

335 210 143 376 0 736 0 0 0

N.S.

1 0.63 0.43 1.12 0.00 2.20 0.00 0.00 0.00

time (sec)

N/A 0.453 0.168 0.282 0.000 0.327 0.000 0.000 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

221 148 101 161 0 415 0 0 0

N.S.

1 0.67 0.46 0.73 0.00 1.88 0.00 0.00 0.00

time (sec)

N/A 0.369 0.110 0.154 0.000 0.283 0.000 0.000 0.000

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 113 89 144 0 381 0 0 0

N.S.

1 0.70 0.55 0.89 0.00 2.37 0.00 0.00 0.00

time (sec)

N/A 0.347 0.074 0.161 0.000 0.284 0.000 0.000 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 93 70 118 0 315 0 0 0

N.S.

1 0.66 0.50 0.84 0.00 2.25 0.00 0.00 0.00

time (sec)

N/A 0.330 0.056 0.151 0.000 0.283 0.000 0.000 0.000

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 87 65 101 0 297 0 0 0

N.S.

1 1.10 0.82 1.28 0.00 3.76 0.00 0.00 0.00

time (sec)

N/A 0.325 0.041 0.138 0.000 0.281 0.000 0.000 0.000

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 84 65 102 0 299 0 0 0

N.S.

1 1.08 0.83 1.31 0.00 3.83 0.00 0.00 0.00

time (sec)

N/A 0.337 0.047 0.142 0.000 0.281 0.000 0.000 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 112 91 162 0 522 0 0 0

N.S.

1 0.74 0.60 1.07 0.00 3.46 0.00 0.00 0.00

time (sec)

N/A 0.340 0.077 0.312 0.000 0.328 0.000 0.000 0.000

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

219 140 123 264 0 596 0 0 0

N.S.

1 0.64 0.56 1.21 0.00 2.72 0.00 0.00 0.00

time (sec)

N/A 0.373 0.109 0.303 0.000 0.316 0.000 0.000 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

277 175 135 316 0 668 0 0 0

N.S.

1 0.63 0.49 1.14 0.00 2.41 0.00 0.00 0.00

time (sec)

N/A 0.408 0.148 0.334 0.000 0.325 0.000 0.000 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 172 125 223 0 323 0 0 0

N.S.

1 1.06 0.77 1.37 0.00 1.98 0.00 0.00 0.00

time (sec)

N/A 0.539 0.272 0.539 0.000 0.263 0.000 0.000 0.000

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 150 116 213 0 285 0 0 0

N.S.

1 1.09 0.84 1.54 0.00 2.07 0.00 0.00 0.00

time (sec)

N/A 0.510 0.117 0.517 0.000 0.269 0.000 0.000 0.000

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 128 95 193 0 235 0 0 0

N.S.

1 1.13 0.84 1.71 0.00 2.08 0.00 0.00 0.00

time (sec)

N/A 0.502 0.090 0.505 0.000 0.256 0.000 0.000 0.000

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 108 92 168 0 219 0 0 0

N.S.

1 1.17 1.00 1.83 0.00 2.38 0.00 0.00 0.00

time (sec)

N/A 0.457 0.057 0.501 0.000 0.267 0.000 0.000 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 105 95 136 0 234 0 0 0

N.S.

1 1.11 1.00 1.43 0.00 2.46 0.00 0.00 0.00

time (sec)

N/A 0.459 0.056 0.500 0.000 0.263 0.000 0.000 0.000

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 116 94 136 0 231 0 0 0

N.S.

1 1.23 1.00 1.45 0.00 2.46 0.00 0.00 0.00

time (sec)

N/A 0.458 0.061 0.536 0.000 0.270 0.000 0.000 0.000

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 132 70 227 0 287 0 0 0

N.S.

1 1.14 0.60 1.96 0.00 2.47 0.00 0.00 0.00

time (sec)

N/A 0.491 0.060 0.496 0.000 0.268 0.000 0.000 0.000

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 162 79 271 0 359 0 0 0

N.S.

1 1.10 0.54 1.84 0.00 2.44 0.00 0.00 0.00

time (sec)

N/A 0.528 0.073 0.517 0.000 0.266 0.000 0.000 0.000

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

172 192 82 315 0 431 0 0 0

N.S.

1 1.12 0.48 1.83 0.00 2.51 0.00 0.00 0.00

time (sec)

N/A 0.541 0.072 0.487 0.000 0.281 0.000 0.000 0.000

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

335 204 140 229 0 437 0 0 0

N.S.

1 0.61 0.42 0.68 0.00 1.30 0.00 0.00 0.00

time (sec)

N/A 0.418 0.129 0.165 0.000 0.304 0.000 0.000 0.000

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

277 177 132 212 0 415 0 0 0

N.S.

1 0.64 0.48 0.77 0.00 1.50 0.00 0.00 0.00

time (sec)

N/A 0.399 0.124 0.158 0.000 0.290 0.000 0.000 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

219 144 124 195 0 381 0 0 0

N.S.

1 0.66 0.57 0.89 0.00 1.74 0.00 0.00 0.00

time (sec)

N/A 0.370 0.110 0.161 0.000 0.288 0.000 0.000 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

158 109 71 169 0 315 0 0 0

N.S.

1 0.69 0.45 1.07 0.00 1.99 0.00 0.00 0.00

time (sec)

N/A 0.337 0.052 0.148 0.000 0.291 0.000 0.000 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 92 67 146 0 299 0 0 0

N.S.

1 0.66 0.48 1.04 0.00 2.14 0.00 0.00 0.00

time (sec)

N/A 0.325 0.056 0.147 0.000 0.283 0.000 0.000 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 125 69 149 0 303 0 0 0

N.S.

1 1.06 0.58 1.26 0.00 2.57 0.00 0.00 0.00

time (sec)

N/A 0.386 0.050 0.143 0.000 0.304 0.000 0.000 0.000

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 121 64 149 0 311 0 0 0

N.S.

1 1.03 0.55 1.27 0.00 2.66 0.00 0.00 0.00

time (sec)

N/A 0.388 0.051 0.139 0.000 0.282 0.000 0.000 0.000

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

199 121 90 258 0 524 0 0 0

N.S.

1 0.61 0.45 1.30 0.00 2.63 0.00 0.00 0.00

time (sec)

N/A 0.369 0.070 0.319 0.000 0.316 0.000 0.000 0.000

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

267 160 121 290 0 594 0 0 0

N.S.

1 0.60 0.45 1.09 0.00 2.22 0.00 0.00 0.00

time (sec)

N/A 0.387 0.091 0.330 0.000 0.321 0.000 0.000 0.000

Problem 489

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

60 60 60 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.482 0.036 0.000 0.000 0.000 0.000 0.000 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 174 147 121 0 337 0 0 0

N.S.

1 1.06 0.90 0.74 0.00 2.05 0.00 0.00 0.00

time (sec)

N/A 0.518 0.919 0.066 0.000 0.293 0.000 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 129 148 102 0 317 0 0 0

N.S.

1 1.04 1.19 0.82 0.00 2.56 0.00 0.00 0.00

time (sec)

N/A 0.423 1.428 0.066 0.000 0.285 0.000 0.000 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 82 66 87 0 295 0 0 0

N.S.

1 1.05 0.85 1.12 0.00 3.78 0.00 0.00 0.00

time (sec)

N/A 0.320 0.044 0.055 0.000 0.279 0.000 0.000 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 78 132 88 0 275 0 0 0

N.S.

1 1.03 1.74 1.16 0.00 3.62 0.00 0.00 0.00

time (sec)

N/A 0.393 0.599 0.069 0.000 0.274 0.000 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 45 41 0 58 0 0 47

N.S.

1 1.00 1.22 1.11 0.00 1.57 0.00 0.00 1.27

time (sec)

N/A 0.316 0.197 0.048 0.000 0.253 0.000 0.000 4.438

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 58 47 0 68 0 0 53

N.S.

1 1.00 0.75 0.61 0.00 0.88 0.00 0.00 0.69

time (sec)

N/A 0.368 0.243 0.047 0.000 0.252 0.000 0.000 4.046

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 122 66 55 0 77 0 0 100

N.S.

1 1.04 0.56 0.47 0.00 0.66 0.00 0.00 0.85

time (sec)

N/A 0.422 0.236 0.048 0.000 0.254 0.000 0.000 4.119

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 175 74 63 0 84 0 0 108

N.S.

1 1.10 0.47 0.40 0.00 0.53 0.00 0.00 0.68

time (sec)

N/A 0.637 0.286 0.049 0.000 0.260 0.000 0.000 4.153

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 157 50 127 0 179 0 142 0

N.S.

1 1.21 0.38 0.98 0.00 1.38 0.00 1.09 0.00

time (sec)

N/A 0.721 0.045 0.497 0.000 0.263 0.000 0.291 0.000

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 124 50 119 0 163 0 127 0

N.S.

1 1.18 0.48 1.13 0.00 1.55 0.00 1.21 0.00

time (sec)

N/A 0.691 0.042 0.495 0.000 0.255 0.000 0.300 0.000

Problem 500

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

80 91 77 111 0 147 0 112 0

N.S.

1 1.14 0.96 1.39 0.00 1.84 0.00 1.40 0.00

time (sec)

N/A 0.548 0.082 0.493 0.000 0.264 0.000 0.292 0.000

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