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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 C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 26 23 30 22 486 29 29

N.S.

1 1.00 0.68 0.61 0.79 0.58 12.79 0.76 0.76

time (sec)

N/A 0.160 0.014 0.067 0.201 0.219 0.791 0.306 0.031

Problem 402

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

18 18 18 15 14 14 12 14 14

N.S.

1 1.00 1.00 0.83 0.78 0.78 0.67 0.78 0.78

time (sec)

N/A 0.128 0.001 0.064 0.214 0.218 0.050 0.312 0.026

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 78 100 79 86 285 160 112 117

N.S.

1 0.95 1.22 0.96 1.05 3.48 1.95 1.37 1.43

time (sec)

N/A 0.178 0.062 0.436 0.296 0.235 1.626 0.583 0.107

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 105 128 103 116 328 838 144 133

N.S.

1 1.02 1.24 1.00 1.13 3.18 8.14 1.40 1.29

time (sec)

N/A 0.198 0.113 0.167 0.297 0.239 1.884 0.533 0.195

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 135 160 124 159 374 2744 167 216

N.S.

1 0.99 1.18 0.91 1.17 2.75 20.18 1.23 1.59

time (sec)

N/A 0.220 0.117 0.278 0.290 0.235 3.858 0.537 0.248

Problem 406

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

70 70 46 43 56 42 1640 49 56

N.S.

1 1.00 0.66 0.61 0.80 0.60 23.43 0.70 0.80

time (sec)

N/A 0.187 0.023 0.076 0.223 0.225 1.619 0.300 0.049

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

51 51 35 32 41 31 600 37 37

N.S.

1 1.00 0.69 0.63 0.80 0.61 11.76 0.73 0.73

time (sec)

N/A 0.167 0.021 0.070 0.219 0.228 1.062 0.313 0.042

Problem 408

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

32 32 23 21 26 19 162 23 25

N.S.

1 1.00 0.72 0.66 0.81 0.59 5.06 0.72 0.78

time (sec)

N/A 0.156 0.012 0.069 0.194 0.229 1.097 0.288 0.032

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

14 14 14 13 12 12 10 12 12

N.S.

1 1.00 1.00 0.93 0.86 0.86 0.71 0.86 0.86

time (sec)

N/A 0.131 0.001 0.064 0.212 0.216 0.036 0.287 0.018

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 76 93 75 77 115 150 78 95

N.S.

1 0.95 1.16 0.94 0.96 1.44 1.88 0.98 1.19

time (sec)

N/A 0.180 0.056 0.081 0.279 0.225 1.686 0.543 0.201

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 102 119 95 106 166 830 108 122

N.S.

1 1.04 1.21 0.97 1.08 1.69 8.47 1.10 1.24

time (sec)

N/A 0.196 0.123 0.119 0.286 0.224 2.637 0.531 0.145

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 130 149 122 142 162 2728 130 175

N.S.

1 1.00 1.15 0.94 1.09 1.25 20.98 1.00 1.35

time (sec)

N/A 0.211 0.127 0.131 0.290 0.234 3.099 0.496 0.181

Problem 413

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

70 70 46 43 56 52 1538 62 56

N.S.

1 1.00 0.66 0.61 0.80 0.74 21.97 0.89 0.80

time (sec)

N/A 0.179 0.024 0.088 0.201 0.220 2.224 0.311 0.077

Problem 414

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

49 49 34 31 41 40 534 46 35

N.S.

1 1.00 0.69 0.63 0.84 0.82 10.90 0.94 0.71

time (sec)

N/A 0.170 0.023 0.078 0.200 0.218 1.513 0.322 0.051

Problem 415

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

32 32 23 20 26 29 41 30 20

N.S.

1 1.00 0.72 0.62 0.81 0.91 1.28 0.94 0.62

time (sec)

N/A 0.155 0.015 0.075 0.203 0.218 0.350 0.451 0.037

Problem 416

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

14 14 14 13 12 20 12 12 12

N.S.

1 1.00 1.00 0.93 0.86 1.43 0.86 0.86 0.86

time (sec)

N/A 0.128 0.002 0.067 0.211 0.226 0.045 0.367 0.021

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 94 111 92 88 285 184 89 114

N.S.

1 1.01 1.19 0.99 0.95 3.06 1.98 0.96 1.23

time (sec)

N/A 0.197 0.089 0.100 0.291 0.234 2.041 0.731 0.163

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 120 123 108 122 407 857 120 173

N.S.

1 1.06 1.09 0.96 1.08 3.60 7.58 1.06 1.53

time (sec)

N/A 0.208 0.202 0.113 0.290 0.236 3.686 0.518 0.075

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 148 142 118 158 407 2793 140 221

N.S.

1 0.99 0.95 0.79 1.06 2.73 18.74 0.94 1.48

time (sec)

N/A 0.234 0.266 0.130 0.288 0.235 4.534 0.522 0.148

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 71 97 85 86 88 138 87 105

N.S.

1 1.00 1.37 1.20 1.21 1.24 1.94 1.23 1.48

time (sec)

N/A 0.192 0.051 0.395 0.301 0.223 1.338 0.292 0.113

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 101 89 90 92 136 91 108

N.S.

1 1.00 1.38 1.22 1.23 1.26 1.86 1.25 1.48

time (sec)

N/A 0.198 0.052 0.381 0.333 0.229 1.469 0.294 0.136

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 102 90 94 93 134 95 112

N.S.

1 1.00 1.38 1.22 1.27 1.26 1.81 1.28 1.51

time (sec)

N/A 0.190 0.055 0.400 0.315 0.230 1.303 0.326 0.119

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 106 94 98 97 139 99 115

N.S.

1 1.00 1.39 1.24 1.29 1.28 1.83 1.30 1.51

time (sec)

N/A 0.189 0.065 0.393 0.317 0.227 2.558 0.314 0.083

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 95 85 87 86 134 88 101

N.S.

1 1.00 1.32 1.18 1.21 1.19 1.86 1.22 1.40

time (sec)

N/A 0.187 0.043 0.096 0.319 0.231 1.295 0.302 0.153

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 99 89 91 90 136 92 104

N.S.

1 1.00 1.34 1.20 1.23 1.22 1.84 1.24 1.41

time (sec)

N/A 0.190 0.043 0.093 0.301 0.232 1.306 0.307 0.129

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 102 92 93 95 134 94 107

N.S.

1 1.00 1.38 1.24 1.26 1.28 1.81 1.27 1.45

time (sec)

N/A 0.185 0.042 0.091 0.312 0.228 2.282 0.326 0.174

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 106 96 97 99 133 98 110

N.S.

1 1.00 1.39 1.26 1.28 1.30 1.75 1.29 1.45

time (sec)

N/A 0.184 0.044 0.089 0.289 0.231 2.027 0.289 0.179

Problem 428

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

25 25 22 30 25 33 87 43 30

N.S.

1 1.00 0.88 1.20 1.00 1.32 3.48 1.72 1.20

time (sec)

N/A 0.159 0.022 0.021 0.209 0.224 0.357 0.292 0.362

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 17 14 13 18 19 13 13

N.S.

1 1.00 0.81 0.67 0.62 0.86 0.90 0.62 0.62

time (sec)

N/A 0.142 0.011 0.065 0.203 0.224 0.212 0.302 0.148

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 17 14 13 18 19 13 13

N.S.

1 1.00 0.81 0.67 0.62 0.86 0.90 0.62 0.62

time (sec)

N/A 0.145 0.010 0.063 0.203 0.218 0.183 0.314 0.030

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 17 14 13 16 19 13 13

N.S.

1 1.00 0.81 0.67 0.62 0.76 0.90 0.62 0.62

time (sec)

N/A 0.143 0.009 0.060 0.201 0.220 0.869 0.276 0.032

Problem 432

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

19 19 16 13 13 12 17 13 12

N.S.

1 1.00 0.84 0.68 0.68 0.63 0.89 0.68 0.63

time (sec)

N/A 0.142 0.010 0.023 0.206 0.221 0.070 0.294 0.031

Problem 433

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

17 17 13 12 13 12 15 13 11

N.S.

1 1.00 0.76 0.71 0.76 0.71 0.88 0.76 0.65

time (sec)

N/A 0.143 0.011 0.029 0.213 0.225 0.259 0.304 0.033

Problem 434

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

19 19 15 12 11 11 19 11 13

N.S.

1 1.00 0.79 0.63 0.58 0.58 1.00 0.58 0.68

time (sec)

N/A 0.145 0.012 0.032 0.213 0.228 0.262 0.289 0.109

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 38 51 43 85 299 117 93

N.S.

1 1.00 0.88 1.19 1.00 1.98 6.95 2.72 2.16

time (sec)

N/A 0.176 0.037 0.059 0.201 0.223 0.374 0.286 0.469

Problem 436

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

36 36 28 25 24 29 34 24 24

N.S.

1 1.00 0.78 0.69 0.67 0.81 0.94 0.67 0.67

time (sec)

N/A 0.157 0.014 0.079 0.208 0.225 0.317 0.288 0.113

Problem 437

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

36 36 28 25 24 29 34 24 24

N.S.

1 1.00 0.78 0.69 0.67 0.81 0.94 0.67 0.67

time (sec)

N/A 0.155 0.013 0.071 0.201 0.225 0.263 0.303 0.040

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 28 25 24 27 1851 24 24

N.S.

1 1.00 0.78 0.69 0.67 0.75 51.42 0.67 0.67

time (sec)

N/A 0.154 0.013 0.071 0.203 0.216 81.194 0.281 0.045

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 28 24 24 24 32 24 24

N.S.

1 1.00 0.82 0.71 0.71 0.71 0.94 0.71 0.71

time (sec)

N/A 0.153 0.013 0.053 0.216 0.215 0.105 0.288 0.040

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 28 25 24 23 31 24 24

N.S.

1 1.00 0.88 0.78 0.75 0.72 0.97 0.75 0.75

time (sec)

N/A 0.153 0.015 0.054 0.211 0.227 0.190 0.303 0.040

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 26 23 23 24 31 23 24

N.S.

1 1.00 0.81 0.72 0.72 0.75 0.97 0.72 0.75

time (sec)

N/A 0.154 0.016 0.057 0.222 0.224 0.231 0.282 0.035

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 61 54 72 61 157 663 224 167

N.S.

1 1.00 0.89 1.18 1.00 2.57 10.87 3.67 2.74

time (sec)

N/A 0.189 0.040 0.067 0.200 0.227 0.390 0.287 0.444

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 39 36 35 40 49 35 35

N.S.

1 1.00 0.76 0.71 0.69 0.78 0.96 0.69 0.69

time (sec)

N/A 0.162 0.016 0.087 0.202 0.219 0.373 0.290 0.048

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 39 36 35 40 49 35 35

N.S.

1 1.00 0.76 0.71 0.69 0.78 0.96 0.69 0.69

time (sec)

N/A 0.164 0.016 0.073 0.245 0.230 0.271 0.273 0.049

Problem 445

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

51 51 39 36 35 38 0 35 35

N.S.

1 1.00 0.76 0.71 0.69 0.75 0.00 0.69 0.69

time (sec)

N/A 0.165 0.015 0.074 0.205 0.219 0.000 0.282 0.048

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 39 35 35 35 46 35 35

N.S.

1 1.00 0.83 0.74 0.74 0.74 0.98 0.74 0.74

time (sec)

N/A 0.166 0.015 0.055 0.203 0.222 0.119 0.280 0.046

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 39 36 35 34 44 35 35

N.S.

1 1.00 0.87 0.80 0.78 0.76 0.98 0.78 0.78

time (sec)

N/A 0.173 0.017 0.056 0.205 0.222 0.214 0.294 0.049

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 38 34 34 34 46 34 35

N.S.

1 1.00 0.81 0.72 0.72 0.72 0.98 0.72 0.74

time (sec)

N/A 0.173 0.019 0.058 0.214 0.223 0.246 0.288 0.045

Problem 449

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

68 78 61 53 54 132 122 59 48

N.S.

1 1.15 0.90 0.78 0.79 1.94 1.79 0.87 0.71

time (sec)

N/A 0.184 0.048 0.084 0.277 0.230 2.462 0.281 0.075

Problem 450

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

53 59 49 42 42 103 107 45 37

N.S.

1 1.11 0.92 0.79 0.79 1.94 2.02 0.85 0.70

time (sec)

N/A 0.167 0.037 0.072 0.286 0.231 1.129 0.293 0.087

Problem 451

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

40 40 40 32 31 85 88 31 28

N.S.

1 1.00 1.00 0.80 0.78 2.12 2.20 0.78 0.70

time (sec)

N/A 0.152 0.022 0.072 0.297 0.225 0.316 0.314 0.066

Problem 452

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

29 29 29 19 18 68 73 18 19

N.S.

1 1.00 1.00 0.66 0.62 2.34 2.52 0.62 0.66

time (sec)

N/A 0.145 0.015 0.068 0.278 0.225 0.481 0.292 0.056

Problem 453

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

40 40 40 32 31 93 85 31 28

N.S.

1 1.00 1.00 0.80 0.78 2.32 2.12 0.78 0.70

time (sec)

N/A 0.151 0.026 0.075 0.299 0.226 0.948 0.302 0.053

Problem 454

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

53 59 48 40 41 118 107 41 38

N.S.

1 1.11 0.91 0.75 0.77 2.23 2.02 0.77 0.72

time (sec)

N/A 0.160 0.040 0.075 0.314 0.237 2.431 0.294 0.120

Problem 455

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

68 78 61 53 52 144 126 52 49

N.S.

1 1.15 0.90 0.78 0.76 2.12 1.85 0.76 0.72

time (sec)

N/A 0.174 0.049 0.076 0.333 0.227 9.822 0.295 0.120

Problem 456

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

70 84 68 56 63 161 389 65 58

N.S.

1 1.20 0.97 0.80 0.90 2.30 5.56 0.93 0.83

time (sec)

N/A 0.176 0.077 0.098 0.303 0.233 12.894 0.291 0.116

Problem 457

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

57 65 54 47 49 134 332 46 46

N.S.

1 1.14 0.95 0.82 0.86 2.35 5.82 0.81 0.81

time (sec)

N/A 0.155 0.067 0.083 0.294 0.241 3.558 0.295 0.126

Problem 458

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

46 46 46 37 37 115 269 36 34

N.S.

1 1.00 1.00 0.80 0.80 2.50 5.85 0.78 0.74

time (sec)

N/A 0.149 0.056 0.070 0.282 0.227 1.961 0.278 0.043

Problem 459

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

45 45 45 36 35 116 277 35 33

N.S.

1 1.00 1.00 0.80 0.78 2.58 6.16 0.78 0.73

time (sec)

N/A 0.148 0.050 0.068 0.287 0.224 3.189 0.298 0.096

Problem 460

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

56 64 54 47 51 147 384 49 48

N.S.

1 1.14 0.96 0.84 0.91 2.62 6.86 0.88 0.86

time (sec)

N/A 0.157 0.071 0.086 0.294 0.233 8.012 0.312 0.128

Problem 461

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

69 83 68 53 64 184 452 58 58

N.S.

1 1.20 0.99 0.77 0.93 2.67 6.55 0.84 0.84

time (sec)

N/A 0.173 0.073 0.088 0.285 0.239 20.423 0.302 0.151

Problem 462

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

95 111 81 66 86 227 762 77 81

N.S.

1 1.17 0.85 0.69 0.91 2.39 8.02 0.81 0.85

time (sec)

N/A 0.182 0.122 0.124 0.293 0.236 66.065 0.330 0.128

Problem 463

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

82 92 70 56 73 200 683 59 69

N.S.

1 1.12 0.85 0.68 0.89 2.44 8.33 0.72 0.84

time (sec)

N/A 0.169 0.112 0.112 0.290 0.230 28.379 0.313 0.155

Problem 464

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

70 73 59 50 61 185 605 47 58

N.S.

1 1.04 0.84 0.71 0.87 2.64 8.64 0.67 0.83

time (sec)

N/A 0.158 0.102 0.070 0.297 0.239 16.623 0.301 0.148

Problem 465

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

73 72 60 52 64 186 627 52 56

N.S.

1 0.99 0.82 0.71 0.88 2.55 8.59 0.71 0.77

time (sec)

N/A 0.163 0.104 0.070 0.387 0.238 8.307 0.304 0.143

Problem 466

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

70 72 59 59 60 186 632 47 57

N.S.

1 1.03 0.84 0.84 0.86 2.66 9.03 0.67 0.81

time (sec)

N/A 0.167 0.070 0.070 0.319 0.230 12.056 0.292 0.138

Problem 467

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

82 91 70 56 73 214 779 59 70

N.S.

1 1.11 0.85 0.68 0.89 2.61 9.50 0.72 0.85

time (sec)

N/A 0.179 0.102 0.094 0.300 0.237 28.040 0.312 0.178

Problem 468

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

95 110 81 64 86 250 869 71 80

N.S.

1 1.16 0.85 0.67 0.91 2.63 9.15 0.75 0.84

time (sec)

N/A 0.186 0.107 0.109 0.312 0.238 65.484 0.317 0.235

Problem 469

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

68 77 61 53 70 131 117 61 51

N.S.

1 1.13 0.90 0.78 1.03 1.93 1.72 0.90 0.75

time (sec)

N/A 0.173 0.049 0.082 0.301 0.231 2.432 0.295 0.167

Problem 470

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

53 59 49 41 58 103 102 47 37

N.S.

1 1.11 0.92 0.77 1.09 1.94 1.92 0.89 0.70

time (sec)

N/A 0.164 0.038 0.073 0.293 0.237 1.248 0.293 0.127

Problem 471

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

40 40 40 32 47 83 83 33 28

N.S.

1 1.00 1.00 0.80 1.18 2.08 2.08 0.82 0.70

time (sec)

N/A 0.152 0.032 0.078 0.311 0.231 0.471 0.301 0.148

Problem 472

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

29 29 29 19 34 67 68 20 19

N.S.

1 1.00 1.00 0.66 1.17 2.31 2.34 0.69 0.66

time (sec)

N/A 0.142 0.022 0.072 0.308 0.226 0.525 0.301 0.150

Problem 473

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

40 40 40 32 47 91 76 33 28

N.S.

1 1.00 1.00 0.80 1.18 2.28 1.90 0.82 0.70

time (sec)

N/A 0.155 0.034 0.077 0.279 0.228 1.343 0.298 0.061

Problem 474

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

53 59 48 40 55 113 99 41 37

N.S.

1 1.11 0.91 0.75 1.04 2.13 1.87 0.77 0.70

time (sec)

N/A 0.162 0.061 0.082 0.298 0.236 2.706 0.310 0.138

Problem 475

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

68 77 61 53 68 143 117 54 48

N.S.

1 1.13 0.90 0.78 1.00 2.10 1.72 0.79 0.71

time (sec)

N/A 0.175 0.062 0.080 0.296 0.238 7.932 0.293 0.152

Problem 476

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

70 83 70 57 81 167 354 69 61

N.S.

1 1.19 1.00 0.81 1.16 2.39 5.06 0.99 0.87

time (sec)

N/A 0.175 0.100 0.104 0.305 0.227 12.462 0.297 0.079

Problem 477

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

57 65 56 48 68 138 301 51 47

N.S.

1 1.14 0.98 0.84 1.19 2.42 5.28 0.89 0.82

time (sec)

N/A 0.162 0.073 0.091 0.304 0.233 5.086 0.303 0.138

Problem 478

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

47 47 49 38 56 123 243 40 35

N.S.

1 1.00 1.04 0.81 1.19 2.62 5.17 0.85 0.74

time (sec)

N/A 0.156 0.067 0.074 0.289 0.226 2.613 0.303 0.130

Problem 479

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

46 46 46 37 56 122 252 41 34

N.S.

1 1.00 1.00 0.80 1.22 2.65 5.48 0.89 0.74

time (sec)

N/A 0.154 0.060 0.075 0.284 0.227 3.180 0.315 0.065

Problem 480

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

57 65 55 48 69 151 354 52 49

N.S.

1 1.14 0.96 0.84 1.21 2.65 6.21 0.91 0.86

time (sec)

N/A 0.168 0.075 0.092 0.279 0.232 12.416 0.299 0.087

Problem 481

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

70 83 69 56 82 187 416 61 60

N.S.

1 1.19 0.99 0.80 1.17 2.67 5.94 0.87 0.86

time (sec)

N/A 0.177 0.092 0.094 0.291 0.238 22.124 0.295 0.162

Problem 482

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

97 111 82 67 103 227 695 81 83

N.S.

1 1.14 0.85 0.69 1.06 2.34 7.16 0.84 0.86

time (sec)

N/A 0.190 0.128 0.123 0.320 0.235 64.023 0.302 0.166

Problem 483

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

84 93 71 57 90 199 624 63 69

N.S.

1 1.11 0.85 0.68 1.07 2.37 7.43 0.75 0.82

time (sec)

N/A 0.186 0.123 0.118 0.317 0.233 22.943 0.297 0.077

Problem 484

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

72 75 60 51 78 186 552 51 58

N.S.

1 1.04 0.83 0.71 1.08 2.58 7.67 0.71 0.81

time (sec)

N/A 0.168 0.121 0.075 0.291 0.242 15.788 0.290 0.171

Problem 485

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

75 74 60 53 80 183 575 55 57

N.S.

1 0.99 0.80 0.71 1.07 2.44 7.67 0.73 0.76

time (sec)

N/A 0.165 0.102 0.076 0.308 0.233 10.405 0.304 0.190

Problem 486

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

72 74 60 61 77 185 580 51 58

N.S.

1 1.03 0.83 0.85 1.07 2.57 8.06 0.71 0.81

time (sec)

N/A 0.165 0.087 0.077 0.300 0.237 14.766 0.303 0.178

Problem 487

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

84 93 71 57 90 213 716 63 69

N.S.

1 1.11 0.85 0.68 1.07 2.54 8.52 0.75 0.82

time (sec)

N/A 0.177 0.114 0.099 0.322 0.240 24.368 0.295 0.180

Problem 488

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

97 111 82 66 103 249 799 73 80

N.S.

1 1.14 0.85 0.68 1.06 2.57 8.24 0.75 0.82

time (sec)

N/A 0.195 0.122 0.111 0.300 0.243 59.596 0.295 0.354

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 132 96 98 178 162 153 224 0

N.S.

1 1.08 0.79 0.80 1.46 1.33 1.25 1.84 0.00

time (sec)

N/A 0.199 0.321 0.090 0.298 0.241 29.003 152.739 0.000

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 102 85 87 146 141 122 182 0

N.S.

1 1.04 0.87 0.89 1.49 1.44 1.24 1.86 0.00

time (sec)

N/A 0.183 0.253 0.077 0.304 0.227 8.043 158.636 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 72 71 74 108 114 97 147 52

N.S.

1 0.97 0.96 1.00 1.46 1.54 1.31 1.99 0.70

time (sec)

N/A 0.170 0.179 0.076 0.294 0.233 2.676 153.614 0.177

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 47 62 70 93 42 68 41

N.S.

1 1.00 1.07 1.41 1.59 2.11 0.95 1.55 0.93

time (sec)

N/A 0.151 0.055 0.077 0.312 0.226 1.553 76.153 0.761

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 55 61 54 89 68 65 0

N.S.

1 1.00 1.22 1.36 1.20 1.98 1.51 1.44 0.00

time (sec)

N/A 0.155 0.077 0.076 0.293 0.239 1.026 79.155 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 16 15 15 41 33 21

N.S.

1 1.00 1.00 0.76 0.71 0.71 1.95 1.57 1.00

time (sec)

N/A 0.136 0.022 0.076 0.224 0.233 1.021 0.315 0.275

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

44 44 39 24 31 34 65 50 32

N.S.

1 1.00 0.89 0.55 0.70 0.77 1.48 1.14 0.73

time (sec)

N/A 0.145 0.074 0.077 0.214 0.231 3.460 0.336 0.348

Problem 496

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 74 51 35 46 45 347 66 43

N.S.

1 1.09 0.75 0.51 0.68 0.66 5.10 0.97 0.63

time (sec)

N/A 0.164 0.080 0.076 0.239 0.221 9.987 0.322 0.309

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 137 98 102 170 164 323 257 0

N.S.

1 1.08 0.77 0.80 1.34 1.29 2.54 2.02 0.00

time (sec)

N/A 0.205 0.319 0.091 0.300 0.235 30.401 157.006 0.000

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 106 87 91 135 142 260 207 0

N.S.

1 1.04 0.85 0.89 1.32 1.39 2.55 2.03 0.00

time (sec)

N/A 0.192 0.260 0.079 0.291 0.229 6.751 156.147 0.000

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 75 75 78 95 118 207 166 58

N.S.

1 0.97 0.97 1.01 1.23 1.53 2.69 2.16 0.75

time (sec)

N/A 0.171 0.202 0.076 0.280 0.236 4.627 156.001 0.096

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 57 66 52 94 119 74 43

N.S.

1 1.00 1.24 1.43 1.13 2.04 2.59 1.61 0.93

time (sec)

N/A 0.151 0.117 0.078 0.286 0.246 1.710 76.649 0.653

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