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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 B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 104 438 153 170 0 63 120

N.S.

1 1.00 0.75 3.17 1.11 1.23 0.00 0.46 0.87

time (sec)

N/A 0.271 0.051 0.118 0.260 0.343 0.000 0.434 0.091

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

165 165 112 530 169 204 0 0 137

N.S.

1 1.00 0.68 3.21 1.02 1.24 0.00 0.00 0.83

time (sec)

N/A 0.345 0.058 0.122 0.259 0.334 0.000 0.000 0.110

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

204 204 120 622 185 240 0 63 153

N.S.

1 1.00 0.59 3.05 0.91 1.18 0.00 0.31 0.75

time (sec)

N/A 0.440 0.064 0.122 0.272 0.336 0.000 0.486 1.245

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 66 48 59 67 63 123 51

N.S.

1 1.00 1.03 0.75 0.92 1.05 0.98 1.92 0.80

time (sec)

N/A 0.092 0.056 0.250 0.298 0.329 0.143 0.408 0.064

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 30 27 31 36 31 59 27

N.S.

1 1.00 1.00 0.90 1.03 1.20 1.03 1.97 0.90

time (sec)

N/A 0.083 0.044 0.210 0.256 0.327 0.068 0.404 0.047

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 40 30 34 43 37 98 31

N.S.

1 1.00 1.05 0.79 0.89 1.13 0.97 2.58 0.82

time (sec)

N/A 0.087 0.042 0.194 0.262 0.382 0.085 0.434 1.184

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 29 24 27 32 26 94 25

N.S.

1 1.00 1.07 0.89 1.00 1.19 0.96 3.48 0.93

time (sec)

N/A 0.081 0.038 0.162 0.296 0.335 0.049 0.403 1.181

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 25 22 24 23 17 55 24

N.S.

1 1.00 1.00 0.88 0.96 0.92 0.68 2.20 0.96

time (sec)

N/A 0.054 0.022 0.154 0.275 0.349 0.121 0.395 0.069

Problem 409

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

53 53 51 47 49 64 41 74 48

N.S.

1 1.00 0.96 0.89 0.92 1.21 0.77 1.40 0.91

time (sec)

N/A 0.089 0.024 0.132 0.266 0.333 0.135 0.388 0.062

Problem 410

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

71 71 63 61 75 100 73 94 71

N.S.

1 1.00 0.89 0.86 1.06 1.41 1.03 1.32 1.00

time (sec)

N/A 0.108 0.050 0.135 0.267 0.335 0.192 0.407 0.075

Problem 411

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

89 89 71 73 93 126 94 109 90

N.S.

1 1.00 0.80 0.82 1.04 1.42 1.06 1.22 1.01

time (sec)

N/A 0.117 0.052 0.135 0.263 0.396 0.257 0.401 1.225

Problem 412

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

105 105 79 85 113 154 114 124 109

N.S.

1 1.00 0.75 0.81 1.08 1.47 1.09 1.18 1.04

time (sec)

N/A 0.129 0.058 0.129 0.278 0.326 0.311 0.399 1.252

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F B B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

135 135 175 290 223 156 0 265 185

N.S.

1 1.00 1.30 2.15 1.65 1.16 0.00 1.96 1.37

time (sec)

N/A 0.302 0.098 0.108 0.466 0.356 0.000 0.428 0.121

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F B B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

106 106 167 266 201 143 0 232 163

N.S.

1 1.00 1.58 2.51 1.90 1.35 0.00 2.19 1.54

time (sec)

N/A 0.224 0.083 0.102 0.461 0.361 0.000 0.420 1.255

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

77 77 55 227 126 113 0 130 90

N.S.

1 1.00 0.71 2.95 1.64 1.47 0.00 1.69 1.17

time (sec)

N/A 0.163 0.131 0.099 0.458 0.334 0.000 0.412 1.224

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F A B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

49 49 73 136 114 88 0 85 82

N.S.

1 1.00 1.49 2.78 2.33 1.80 0.00 1.73 1.67

time (sec)

N/A 0.100 0.072 0.081 0.469 0.345 0.000 0.418 0.071

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD 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 0.028 0.032 0.112 0.262 0.327 0.000 0.412 0.053

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 69 255 120 97 0 0 62

N.S.

1 1.00 0.95 3.49 1.64 1.33 0.00 0.00 0.85

time (sec)

N/A 0.079 0.025 0.148 0.253 0.337 0.000 0.000 1.227

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

105 105 94 344 137 134 0 0 105

N.S.

1 1.00 0.90 3.28 1.30 1.28 0.00 0.00 1.00

time (sec)

N/A 0.199 0.044 0.140 0.261 0.347 0.000 0.000 1.246

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 104 436 153 170 0 59 121

N.S.

1 1.00 0.75 3.16 1.11 1.23 0.00 0.43 0.88

time (sec)

N/A 0.266 0.055 0.144 0.256 0.341 0.000 0.449 1.238

Problem 421

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

65 65 67 51 60 71 56 62 61

N.S.

1 1.00 1.03 0.78 0.92 1.09 0.86 0.95 0.94

time (sec)

N/A 0.098 0.058 0.177 0.260 0.357 0.232 0.407 0.095

Problem 422

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

54 54 56 43 51 62 42 53 51

N.S.

1 1.00 1.04 0.80 0.94 1.15 0.78 0.98 0.94

time (sec)

N/A 0.093 0.044 0.155 0.260 0.353 0.188 0.401 0.078

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

40 40 42 31 40 43 31 42 40

N.S.

1 1.00 1.05 0.78 1.00 1.08 0.78 1.05 1.00

time (sec)

N/A 0.089 0.040 0.130 0.261 0.369 0.143 0.397 1.223

Problem 424

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

23 23 23 20 23 22 17 25 23

N.S.

1 1.00 1.00 0.87 1.00 0.96 0.74 1.09 1.00

time (sec)

N/A 0.057 0.020 0.112 0.249 0.356 0.106 0.408 0.064

Problem 425

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

20 20 22 23 20 19 17 21 19

N.S.

1 1.00 1.10 1.15 1.00 0.95 0.85 1.05 0.95

time (sec)

N/A 0.077 0.013 0.092 0.261 0.343 0.039 0.405 1.201

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

18 18 39 36 34 27 34 36 17

N.S.

1 1.00 2.17 2.00 1.89 1.50 1.89 2.00 0.94

time (sec)

N/A 0.092 0.047 0.092 0.252 0.351 0.074 0.409 1.238

Problem 427

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

57 57 56 48 53 59 56 51 52

N.S.

1 1.00 0.98 0.84 0.93 1.04 0.98 0.89 0.91

time (sec)

N/A 0.104 0.049 0.095 0.261 0.333 0.168 0.404 0.090

Problem 428

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

75 75 73 60 69 93 73 57 68

N.S.

1 1.00 0.97 0.80 0.92 1.24 0.97 0.76 0.91

time (sec)

N/A 0.111 0.060 0.098 0.257 0.326 0.220 0.408 0.096

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B A A F F B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

164 164 567 672 246 157 0 0 211

N.S.

1 1.00 3.46 4.10 1.50 0.96 0.00 0.00 1.29

time (sec)

N/A 0.371 0.725 0.121 0.483 0.336 0.000 0.000 0.137

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B A A F F B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

135 135 663 450 225 146 0 0 190

N.S.

1 1.00 4.91 3.33 1.67 1.08 0.00 0.00 1.41

time (sec)

N/A 0.295 0.294 0.115 0.482 0.355 0.000 0.000 1.273

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B A A F F B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

105 105 424 600 149 120 0 0 117

N.S.

1 1.00 4.04 5.71 1.42 1.14 0.00 0.00 1.11

time (sec)

N/A 0.222 0.261 0.115 0.478 0.346 0.000 0.000 0.102

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B A A F F B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

75 75 234 376 135 92 0 0 107

N.S.

1 1.00 3.12 5.01 1.80 1.23 0.00 0.00 1.43

time (sec)

N/A 0.155 0.321 0.085 0.486 0.349 0.000 0.000 0.093

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

72 72 61 250 120 69 0 0 87

N.S.

1 1.00 0.85 3.47 1.67 0.96 0.00 0.00 1.21

time (sec)

N/A 0.120 0.056 0.100 0.260 0.345 0.000 0.000 0.056

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 69 250 125 67 0 0 90

N.S.

1 1.00 0.93 3.38 1.69 0.91 0.00 0.00 1.22

time (sec)

N/A 0.071 0.026 0.095 0.249 0.353 0.000 0.000 1.188

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 33 50 92 42 0 42 41

N.S.

1 1.00 0.73 1.11 2.04 0.93 0.00 0.93 0.91

time (sec)

N/A 0.035 0.016 0.137 0.271 0.351 0.000 0.400 0.069

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 94 523 160 134 0 0 128

N.S.

1 1.00 0.85 4.71 1.44 1.21 0.00 0.00 1.15

time (sec)

N/A 0.103 0.046 0.149 0.262 0.334 0.000 0.000 1.235

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 104 615 176 170 0 0 144

N.S.

1 1.00 0.75 4.46 1.28 1.23 0.00 0.00 1.04

time (sec)

N/A 0.268 0.057 0.157 0.270 0.343 0.000 0.000 0.087

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

235 279 109 166 0 437 0 0 -1

N.S.

1 1.19 0.46 0.71 0.00 1.86 0.00 0.00 -0.00

time (sec)

N/A 0.117 0.078 0.082 0.000 0.384 0.000 0.000 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

196 221 101 149 0 415 0 0 -1

N.S.

1 1.13 0.52 0.76 0.00 2.12 0.00 0.00 -0.01

time (sec)

N/A 0.101 0.054 0.056 0.000 0.382 0.000 0.000 0.000

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

157 189 89 132 0 381 0 0 -1

N.S.

1 1.20 0.57 0.84 0.00 2.43 0.00 0.00 -0.01

time (sec)

N/A 0.092 0.046 0.056 0.000 0.392 0.000 0.000 0.000

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 70 106 0 313 0 0 -1

N.S.

1 1.00 0.60 0.91 0.00 2.68 0.00 0.00 -0.01

time (sec)

N/A 0.146 0.035 0.050 0.000 0.399 0.000 0.000 0.000

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

78 78 66 87 0 295 0 0 -1

N.S.

1 1.00 0.85 1.12 0.00 3.78 0.00 0.00 -0.01

time (sec)

N/A 0.108 0.030 0.044 0.000 0.410 0.000 0.000 0.000

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 93 151 0 517 0 0 -1

N.S.

1 1.00 0.61 0.99 0.00 3.40 0.00 0.00 -0.01

time (sec)

N/A 0.090 0.045 0.142 0.000 0.426 0.000 0.000 0.000

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

215 215 122 259 0 594 0 0 -1

N.S.

1 1.00 0.57 1.20 0.00 2.76 0.00 0.00 -0.00

time (sec)

N/A 0.103 0.064 0.158 0.000 0.442 0.000 0.000 0.000

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

277 277 135 366 0 668 0 0 -1

N.S.

1 1.00 0.49 1.32 0.00 2.41 0.00 0.00 -0.00

time (sec)

N/A 0.119 0.080 0.161 0.000 0.447 0.000 0.000 0.000

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

143 143 91 163 0 234 0 0 -1

N.S.

1 1.00 0.64 1.14 0.00 1.64 0.00 0.00 -0.01

time (sec)

N/A 0.168 0.102 0.119 0.000 0.388 0.000 0.000 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 83 144 0 212 731 0 -1

N.S.

1 1.00 0.70 1.22 0.00 1.80 6.19 0.00 -0.01

time (sec)

N/A 0.155 0.079 0.106 0.000 0.359 8.100 0.000 0.000

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 75 108 0 182 0 0 -1

N.S.

1 1.00 0.79 1.14 0.00 1.92 0.00 0.00 -0.01

time (sec)

N/A 0.142 0.045 0.104 0.000 0.349 0.000 0.000 0.000

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 55 103 0 137 0 0 -1

N.S.

1 1.00 0.79 1.47 0.00 1.96 0.00 0.00 -0.01

time (sec)

N/A 0.123 0.034 0.099 0.000 0.352 0.000 0.000 0.000

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 50 120 0 124 0 96 -1

N.S.

1 1.00 1.00 2.40 0.00 2.48 0.00 1.92 -0.02

time (sec)

N/A 0.109 0.022 0.138 0.000 0.351 0.000 0.427 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 43 194 0 176 0 167 -1

N.S.

1 1.00 0.61 2.77 0.00 2.51 0.00 2.39 -0.01

time (sec)

N/A 0.120 0.023 0.146 0.000 0.329 0.000 0.475 0.000

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 55 260 0 238 0 243 -1

N.S.

1 1.00 0.58 2.74 0.00 2.51 0.00 2.56 -0.01

time (sec)

N/A 0.141 0.022 0.159 0.000 0.340 0.000 0.517 0.000

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 58 328 0 294 0 316 -1

N.S.

1 1.00 0.49 2.78 0.00 2.49 0.00 2.68 -0.01

time (sec)

N/A 0.148 0.023 0.168 0.000 0.342 0.000 0.571 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 46 396 0 346 0 389 -1

N.S.

1 1.00 0.32 2.73 0.00 2.39 0.00 2.68 -0.01

time (sec)

N/A 0.163 0.029 0.179 0.000 0.360 0.000 0.681 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

268 268 109 178 0 437 0 0 -1

N.S.

1 1.00 0.41 0.66 0.00 1.63 0.00 0.00 -0.00

time (sec)

N/A 0.113 0.065 0.058 0.000 0.382 0.000 0.000 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

237 237 101 161 0 415 0 0 -1

N.S.

1 1.00 0.43 0.68 0.00 1.75 0.00 0.00 -0.00

time (sec)

N/A 0.102 0.057 0.053 0.000 0.372 0.000 0.000 0.000

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

156 156 89 144 0 381 0 0 -1

N.S.

1 1.00 0.57 0.92 0.00 2.44 0.00 0.00 -0.01

time (sec)

N/A 0.185 0.045 0.051 0.000 0.383 0.000 0.000 0.000

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 66 118 0 315 0 0 -1

N.S.

1 1.00 0.56 1.00 0.00 2.67 0.00 0.00 -0.01

time (sec)

N/A 0.148 0.031 0.048 0.000 0.395 0.000 0.000 0.000

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 93 160 0 512 0 0 -1

N.S.

1 1.00 0.61 1.05 0.00 3.37 0.00 0.00 -0.01

time (sec)

N/A 0.097 0.041 0.147 0.000 0.441 0.000 0.000 0.000

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

215 215 115 259 0 581 0 0 -1

N.S.

1 1.00 0.53 1.20 0.00 2.70 0.00 0.00 -0.00

time (sec)

N/A 0.107 0.062 0.152 0.000 0.435 0.000 0.000 0.000

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

275 275 135 373 0 668 0 0 -1

N.S.

1 1.00 0.49 1.36 0.00 2.43 0.00 0.00 -0.00

time (sec)

N/A 0.126 0.080 0.158 0.000 0.423 0.000 0.000 0.000

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

335 335 143 480 0 736 0 0 -1

N.S.

1 1.00 0.43 1.43 0.00 2.20 0.00 0.00 -0.00

time (sec)

N/A 0.139 0.098 0.158 0.000 0.457 0.000 0.000 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

221 221 101 161 0 415 0 0 -1

N.S.

1 1.00 0.46 0.73 0.00 1.88 0.00 0.00 -0.00

time (sec)

N/A 0.101 0.068 0.105 0.000 0.365 0.000 0.000 0.000

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 89 144 0 381 0 0 -1

N.S.

1 1.00 0.55 0.89 0.00 2.37 0.00 0.00 -0.01

time (sec)

N/A 0.089 0.045 0.105 0.000 0.366 0.000 0.000 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 70 118 0 315 0 0 -1

N.S.

1 1.00 0.50 0.84 0.00 2.25 0.00 0.00 -0.01

time (sec)

N/A 0.087 0.035 0.095 0.000 0.383 0.000 0.000 0.000

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

79 79 65 101 0 297 0 0 -1

N.S.

1 1.00 0.82 1.28 0.00 3.76 0.00 0.00 -0.01

time (sec)

N/A 0.105 0.027 0.094 0.000 0.381 0.000 0.000 0.000

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 66 102 0 299 0 0 -1

N.S.

1 1.00 0.85 1.31 0.00 3.83 0.00 0.00 -0.01

time (sec)

N/A 0.112 0.029 0.099 0.000 0.459 0.000 0.000 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

151 151 91 162 0 522 0 0 -1

N.S.

1 1.00 0.60 1.07 0.00 3.46 0.00 0.00 -0.01

time (sec)

N/A 0.103 0.044 0.180 0.000 0.399 0.000 0.000 0.000

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

219 219 123 264 0 596 0 0 -1

N.S.

1 1.00 0.56 1.21 0.00 2.72 0.00 0.00 -0.00

time (sec)

N/A 0.113 0.067 0.182 0.000 0.419 0.000 0.000 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

277 277 135 371 0 668 0 0 -1

N.S.

1 1.00 0.49 1.34 0.00 2.41 0.00 0.00 -0.00

time (sec)

N/A 0.122 0.088 0.200 0.000 0.430 0.000 0.000 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

163 163 125 281 0 323 0 0 -1

N.S.

1 1.00 0.77 1.72 0.00 1.98 0.00 0.00 -0.01

time (sec)

N/A 0.198 0.171 0.202 0.000 0.340 0.000 0.000 0.000

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 116 257 0 285 0 0 -1

N.S.

1 1.00 0.84 1.86 0.00 2.07 0.00 0.00 -0.01

time (sec)

N/A 0.179 0.068 0.208 0.000 0.354 0.000 0.000 0.000

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 113 95 229 0 235 0 0 -1

N.S.

1 1.00 0.84 2.03 0.00 2.08 0.00 0.00 -0.01

time (sec)

N/A 0.159 0.056 0.193 0.000 0.339 0.000 0.000 0.000

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

92 92 92 190 0 219 0 0 -1

N.S.

1 1.00 1.00 2.07 0.00 2.38 0.00 0.00 -0.01

time (sec)

N/A 0.141 0.034 0.190 0.000 0.379 0.000 0.000 0.000

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 95 136 0 234 0 0 -1

N.S.

1 1.00 1.00 1.43 0.00 2.46 0.00 0.00 -0.01

time (sec)

N/A 0.137 0.033 0.184 0.000 0.369 0.000 0.000 0.000

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 94 136 0 231 0 0 -1

N.S.

1 1.00 1.00 1.45 0.00 2.46 0.00 0.00 -0.01

time (sec)

N/A 0.147 0.035 0.230 0.000 0.380 0.000 0.000 0.000

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 70 368 0 287 0 0 -1

N.S.

1 1.00 0.60 3.17 0.00 2.47 0.00 0.00 -0.01

time (sec)

N/A 0.163 0.037 0.242 0.000 0.362 0.000 0.000 0.000

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 79 497 0 359 0 0 -1

N.S.

1 1.00 0.54 3.38 0.00 2.44 0.00 0.00 -0.01

time (sec)

N/A 0.184 0.068 0.237 0.000 0.356 0.000 0.000 0.000

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

172 172 82 626 0 431 0 0 -1

N.S.

1 1.00 0.48 3.64 0.00 2.51 0.00 0.00 -0.01

time (sec)

N/A 0.203 0.045 0.248 0.000 0.409 0.000 0.000 0.000

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

335 335 140 229 0 437 0 0 -1

N.S.

1 1.00 0.42 0.68 0.00 1.30 0.00 0.00 -0.00

time (sec)

N/A 0.132 0.076 0.117 0.000 0.409 0.000 0.000 0.000

Problem 481

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

277 277 132 212 0 415 0 0 -1

N.S.

1 1.00 0.48 0.77 0.00 1.50 0.00 0.00 -0.00

time (sec)

N/A 0.120 0.074 0.109 0.000 0.383 0.000 0.000 0.000

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

219 219 124 195 0 381 0 0 -1

N.S.

1 1.00 0.57 0.89 0.00 1.74 0.00 0.00 -0.00

time (sec)

N/A 0.103 0.069 0.107 0.000 0.398 0.000 0.000 0.000

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

158 158 71 169 0 315 0 0 -1

N.S.

1 1.00 0.45 1.07 0.00 1.99 0.00 0.00 -0.01

time (sec)

N/A 0.098 0.031 0.103 0.000 0.373 0.000 0.000 0.000

Problem 484

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 67 146 0 299 0 0 -1

N.S.

1 1.00 0.48 1.04 0.00 2.14 0.00 0.00 -0.01

time (sec)

N/A 0.086 0.034 0.094 0.000 0.378 0.000 0.000 0.000

Problem 485

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 69 149 0 303 0 0 -1

N.S.

1 1.00 0.58 1.26 0.00 2.57 0.00 0.00 -0.01

time (sec)

N/A 0.150 0.029 0.095 0.000 0.382 0.000 0.000 0.000

Problem 486

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 64 149 0 311 0 0 -1

N.S.

1 1.00 0.55 1.27 0.00 2.66 0.00 0.00 -0.01

time (sec)

N/A 0.149 0.031 0.095 0.000 0.361 0.000 0.000 0.000

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

199 199 90 264 0 524 0 0 -1

N.S.

1 1.00 0.45 1.33 0.00 2.63 0.00 0.00 -0.01

time (sec)

N/A 0.116 0.044 0.186 0.000 0.471 0.000 0.000 0.000

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

267 267 121 290 0 594 0 0 -1

N.S.

1 1.00 0.45 1.09 0.00 2.22 0.00 0.00 -0.00

time (sec)

N/A 0.123 0.051 0.194 0.000 0.404 0.000 0.000 0.000

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 60 0 0 0 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.157 0.022 0.020 0.000 0.000 0.000 0.000 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

164 164 147 121 0 337 0 0 -1

N.S.

1 1.00 0.90 0.74 0.00 2.05 0.00 0.00 -0.01

time (sec)

N/A 0.230 0.270 0.048 0.000 0.425 0.000 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

124 124 148 102 0 317 0 0 -1

N.S.

1 1.00 1.19 0.82 0.00 2.56 0.00 0.00 -0.01

time (sec)

N/A 0.161 0.159 0.045 0.000 0.410 0.000 0.000 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

78 78 66 87 0 295 0 0 -1

N.S.

1 1.00 0.85 1.12 0.00 3.78 0.00 0.00 -0.01

time (sec)

N/A 0.101 0.032 0.039 0.000 0.387 0.000 0.000 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

76 76 132 88 0 275 0 0 -1

N.S.

1 1.00 1.74 1.16 0.00 3.62 0.00 0.00 -0.01

time (sec)

N/A 0.152 0.163 0.045 0.000 0.432 0.000 0.000 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F F B

verified

N/A Yes Yes TBD 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 0.105 0.064 0.032 0.000 0.355 0.000 0.000 1.367

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD 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 0.129 0.061 0.032 0.000 0.359 0.000 0.000 1.394

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 66 55 0 77 0 0 100

N.S.

1 1.00 0.56 0.47 0.00 0.66 0.00 0.00 0.85

time (sec)

N/A 0.164 0.063 0.033 0.000 0.337 0.000 0.000 1.415

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 74 63 0 84 0 0 108

N.S.

1 1.00 0.47 0.40 0.00 0.53 0.00 0.00 0.68

time (sec)

N/A 0.200 0.071 0.037 0.000 0.375 0.000 0.000 1.441

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

130 130 50 172 0 179 0 142 -1

N.S.

1 1.00 0.38 1.32 0.00 1.38 0.00 1.09 -0.01

time (sec)

N/A 0.263 0.027 0.138 0.000 0.359 0.000 0.440 0.000

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

105 105 50 155 0 163 0 127 -1

N.S.

1 1.00 0.48 1.48 0.00 1.55 0.00 1.21 -0.01

time (sec)

N/A 0.253 0.025 0.135 0.000 0.370 0.000 0.439 0.000

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 77 139 0 147 0 112 -1

N.S.

1 1.00 0.96 1.74 0.00 1.84 0.00 1.40 -0.01

time (sec)

N/A 0.164 0.046 0.134 0.000 0.452 0.000 0.423 0.000

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