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2.2.4 Integrals 301 to 400

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 301

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

53 53 35 32 41 64 124 233 37

N.S.

1 1.00 0.66 0.60 0.77 1.21 2.34 4.40 0.70

time (sec)

N/A 0.161 0.024 0.094 0.210 0.220 0.530 0.299 0.052

Problem 302

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

34 34 24 21 26 52 102 182 25

N.S.

1 1.00 0.71 0.62 0.76 1.53 3.00 5.35 0.74

time (sec)

N/A 0.147 0.020 0.086 0.199 0.229 0.524 0.317 0.070

Problem 303

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 13 12 39 12 95 12

N.S.

1 1.00 1.00 0.81 0.75 2.44 0.75 5.94 0.75

time (sec)

N/A 0.121 0.003 0.059 0.211 0.217 0.022 0.291 0.026

Problem 304

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 67 56 47 64 114 97 56 52

N.S.

1 1.03 0.86 0.72 0.98 1.75 1.49 0.86 0.80

time (sec)

N/A 0.158 0.048 0.075 0.328 0.232 3.848 0.281 0.068

Problem 305

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

66 71 60 57 71 126 99 74 58

N.S.

1 1.08 0.91 0.86 1.08 1.91 1.50 1.12 0.88

time (sec)

N/A 0.163 0.071 0.104 0.287 0.231 3.331 0.305 0.191

Problem 306

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

78 77 63 55 101 133 126 80 64

N.S.

1 0.99 0.81 0.71 1.29 1.71 1.62 1.03 0.82

time (sec)

N/A 0.164 0.095 0.097 0.296 0.237 3.708 0.296 0.079

Problem 307

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 83 64 53 115 146 104 79 64

N.S.

1 1.02 0.79 0.65 1.42 1.80 1.28 0.98 0.79

time (sec)

N/A 0.164 0.129 0.093 0.300 0.238 3.512 0.286 0.084

Problem 308

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

103 107 78 67 144 167 155 99 79

N.S.

1 1.04 0.76 0.65 1.40 1.62 1.50 0.96 0.77

time (sec)

N/A 0.178 0.143 0.119 0.292 0.239 9.273 0.286 0.158

Problem 309

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

146 146 90 87 116 141 279 781 116

N.S.

1 1.00 0.62 0.60 0.79 0.97 1.91 5.35 0.79

time (sec)

N/A 0.237 0.045 0.143 0.207 0.218 2.489 0.291 0.100

Problem 310

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

127 127 79 76 101 130 257 709 101

N.S.

1 1.00 0.62 0.60 0.80 1.02 2.02 5.58 0.80

time (sec)

N/A 0.230 0.041 0.128 0.212 0.223 1.335 0.291 0.043

Problem 311

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

110 110 68 65 86 119 235 637 86

N.S.

1 1.00 0.62 0.59 0.78 1.08 2.14 5.79 0.78

time (sec)

N/A 0.215 0.033 0.121 0.217 0.222 1.805 0.292 0.052

Problem 312

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

91 91 57 54 71 108 212 565 71

N.S.

1 1.00 0.63 0.59 0.78 1.19 2.33 6.21 0.78

time (sec)

N/A 0.216 0.029 0.110 0.208 0.217 1.254 0.307 0.034

Problem 313

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

72 72 46 43 56 97 190 493 56

N.S.

1 1.00 0.64 0.60 0.78 1.35 2.64 6.85 0.78

time (sec)

N/A 0.194 0.027 0.104 0.232 0.220 1.345 0.303 0.073

Problem 314

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

53 53 35 32 41 86 168 421 36

N.S.

1 1.00 0.66 0.60 0.77 1.62 3.17 7.94 0.68

time (sec)

N/A 0.166 0.025 0.096 0.209 0.223 1.106 0.326 0.218

Problem 315

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

34 34 24 21 26 74 146 347 25

N.S.

1 1.00 0.71 0.62 0.76 2.18 4.29 10.21 0.74

time (sec)

N/A 0.153 0.021 0.089 0.217 0.234 0.976 0.317 0.069

Problem 316

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 13 12 61 12 229 12

N.S.

1 1.00 1.00 0.81 0.75 3.81 0.75 14.31 0.75

time (sec)

N/A 0.122 0.004 0.056 0.214 0.227 0.036 0.301 0.057

Problem 317

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 99 78 69 88 158 148 80 76

N.S.

1 1.02 0.80 0.71 0.91 1.63 1.53 0.82 0.78

time (sec)

N/A 0.184 0.046 0.079 0.300 0.230 15.929 0.303 0.047

Problem 318

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

98 103 82 81 97 172 150 104 84

N.S.

1 1.05 0.84 0.83 0.99 1.76 1.53 1.06 0.86

time (sec)

N/A 0.186 0.082 0.113 0.294 0.244 13.430 0.348 0.059

Problem 319

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

114 109 86 79 131 180 184 112 117

N.S.

1 0.96 0.75 0.69 1.15 1.58 1.61 0.98 1.03

time (sec)

N/A 0.189 0.110 0.122 0.306 0.237 13.368 0.312 0.062

Problem 320

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

114 115 85 78 145 178 184 112 131

N.S.

1 1.01 0.75 0.68 1.27 1.56 1.61 0.98 1.15

time (sec)

N/A 0.188 0.133 0.129 0.439 0.232 13.530 0.301 0.173

Problem 321

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

116 121 86 77 155 177 182 110 94

N.S.

1 1.04 0.74 0.66 1.34 1.53 1.57 0.95 0.81

time (sec)

N/A 0.195 0.153 0.119 0.370 0.229 13.017 0.316 0.087

Problem 322

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

119 127 86 75 169 190 158 109 94

N.S.

1 1.07 0.72 0.63 1.42 1.60 1.33 0.92 0.79

time (sec)

N/A 0.189 0.182 0.126 0.301 0.230 14.436 0.291 0.183

Problem 323

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

141 151 100 89 198 211 209 129 109

N.S.

1 1.07 0.71 0.63 1.40 1.50 1.48 0.91 0.77

time (sec)

N/A 0.207 0.204 0.147 0.294 0.231 63.648 0.308 0.214

Problem 324

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

163 179 111 100 229 233 0 144 124

N.S.

1 1.10 0.68 0.61 1.40 1.43 0.00 0.88 0.76

time (sec)

N/A 0.220 0.229 0.164 0.320 0.235 0.000 0.309 0.195

Problem 325

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

39 39 39 32 31 78 148 31 31

N.S.

1 1.00 1.00 0.82 0.79 2.00 3.79 0.79 0.79

time (sec)

N/A 0.151 0.022 0.232 0.284 0.227 1.404 0.286 0.116

Problem 326

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

42 42 42 40 34 98 117 41 34

N.S.

1 1.00 1.00 0.95 0.81 2.33 2.79 0.98 0.81

time (sec)

N/A 0.145 0.040 0.085 0.299 0.229 1.448 0.312 0.157

Problem 327

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 68 60 53 83 124 207 66 54

N.S.

1 0.96 0.85 0.75 1.17 1.75 2.92 0.93 0.76

time (sec)

N/A 0.163 0.085 0.087 0.287 0.234 3.045 0.315 0.126

Problem 328

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

55 58 48 40 43 93 187 43 43

N.S.

1 1.05 0.87 0.73 0.78 1.69 3.40 0.78 0.78

time (sec)

N/A 0.163 0.034 0.074 0.281 0.236 1.623 0.311 0.050

Problem 329

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

57 61 48 43 47 105 197 58 47

N.S.

1 1.07 0.84 0.75 0.82 1.84 3.46 1.02 0.82

time (sec)

N/A 0.162 0.051 0.087 0.292 0.235 2.266 0.311 0.059

Problem 330

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

68 66 56 52 80 129 189 66 52

N.S.

1 0.97 0.82 0.76 1.18 1.90 2.78 0.97 0.76

time (sec)

N/A 0.161 0.086 0.081 0.285 0.240 2.385 0.316 0.251

Problem 331

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 77 60 51 57 119 240 57 57

N.S.

1 1.05 0.82 0.70 0.78 1.63 3.29 0.78 0.78

time (sec)

N/A 0.166 0.051 0.076 0.306 0.237 3.422 0.320 0.052

Problem 332

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 80 64 55 63 131 245 75 63

N.S.

1 1.08 0.86 0.74 0.85 1.77 3.31 1.01 0.85

time (sec)

N/A 0.172 0.065 0.099 0.298 0.231 3.221 0.326 0.136

Problem 333

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

86 85 67 62 97 139 267 83 69

N.S.

1 0.99 0.78 0.72 1.13 1.62 3.10 0.97 0.80

time (sec)

N/A 0.176 0.090 0.103 0.289 0.232 3.625 0.331 0.132

Problem 334

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

89 89 57 54 71 53 3755 61 71

N.S.

1 1.00 0.64 0.61 0.80 0.60 42.19 0.69 0.80

time (sec)

N/A 0.188 0.026 0.073 0.200 0.220 3.373 0.311 0.028

Problem 335

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 68 46 43 56 42 1640 49 56

N.S.

1 1.00 0.68 0.63 0.82 0.62 24.12 0.72 0.82

time (sec)

N/A 0.175 0.024 0.068 0.192 0.216 2.003 0.303 0.075

Problem 336

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 0.165 0.005 0.064 0.196 0.219 1.455 0.293 0.046

Problem 337

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 0.157 0.002 0.060 0.206 0.215 0.883 0.304 0.036

Problem 338

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 0.124 0.001 0.056 0.196 0.216 0.018 0.295 0.022

Problem 339

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 23 23 18 32 56 24 21 17

N.S.

1 1.00 1.00 0.78 1.39 2.43 1.04 0.91 0.74

time (sec)

N/A 0.140 0.002 0.058 0.284 0.235 1.105 0.298 0.071

Problem 340

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

41 41 41 34 60 93 44 47 33

N.S.

1 1.00 1.00 0.83 1.46 2.27 1.07 1.15 0.80

time (sec)

N/A 0.154 0.008 0.075 0.294 0.235 2.031 0.327 0.277

Problem 341

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 69 56 45 92 123 102 69 51

N.S.

1 1.01 0.82 0.66 1.35 1.81 1.50 1.01 0.75

time (sec)

N/A 0.167 0.072 0.074 0.313 0.235 3.383 0.300 0.073

Problem 342

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

90 97 67 56 121 145 129 84 69

N.S.

1 1.08 0.74 0.62 1.34 1.61 1.43 0.93 0.77

time (sec)

N/A 0.178 0.080 0.085 0.298 0.235 10.858 0.299 0.063

Problem 343

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

85 85 57 54 71 63 3606 77 71

N.S.

1 1.00 0.67 0.64 0.84 0.74 42.42 0.91 0.84

time (sec)

N/A 0.186 0.026 0.082 0.207 0.215 4.048 0.298 0.033

Problem 344

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

66 66 45 42 56 51 1538 61 56

N.S.

1 1.00 0.68 0.64 0.85 0.77 23.30 0.92 0.85

time (sec)

N/A 0.175 0.023 0.075 0.211 0.224 2.294 0.299 0.054

Problem 345

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 0.175 0.021 0.070 0.200 0.220 1.456 0.309 0.046

Problem 346

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

30 30 21 20 26 29 37 29 19

N.S.

1 1.00 0.70 0.67 0.87 0.97 1.23 0.97 0.63

time (sec)

N/A 0.152 0.014 0.068 0.195 0.222 0.332 0.320 0.097

Problem 347

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 0.126 0.001 0.113 0.200 0.227 0.028 0.298 0.023

Problem 348

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

38 38 38 31 45 110 146 37 30

N.S.

1 1.00 1.00 0.82 1.18 2.89 3.84 0.97 0.79

time (sec)

N/A 0.156 0.032 0.079 0.285 0.220 1.324 0.304 0.050

Problem 349

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 64 49 50 76 151 73 64 60

N.S.

1 1.12 0.86 0.88 1.33 2.65 1.28 1.12 1.05

time (sec)

N/A 0.173 0.066 0.100 0.285 0.235 3.140 0.314 0.135

Problem 350

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

87 92 67 60 108 189 107 80 90

N.S.

1 1.06 0.77 0.69 1.24 2.17 1.23 0.92 1.03

time (sec)

N/A 0.178 0.097 0.105 0.289 0.237 5.549 0.294 0.069

Problem 351

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

87 87 57 54 71 74 3456 75 68

N.S.

1 1.00 0.66 0.62 0.82 0.85 39.72 0.86 0.78

time (sec)

N/A 0.196 0.030 0.094 0.207 0.221 3.343 0.307 0.056

Problem 352

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 68 47 39 56 62 163 59 47

N.S.

1 1.00 0.69 0.57 0.82 0.91 2.40 0.87 0.69

time (sec)

N/A 0.176 0.027 0.152 0.213 0.220 0.649 0.318 0.052

Problem 353

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 35 32 41 52 121 39 35

N.S.

1 1.00 0.71 0.65 0.84 1.06 2.47 0.80 0.71

time (sec)

N/A 0.155 0.024 0.082 0.210 0.219 0.638 0.298 0.095

Problem 354

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 24 21 26 41 80 20 20

N.S.

1 1.00 0.75 0.66 0.81 1.28 2.50 0.62 0.62

time (sec)

N/A 0.143 0.015 0.072 0.195 0.219 0.420 0.312 0.038

Problem 355

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 13 12 31 14 12 12

N.S.

1 1.00 1.00 0.81 0.75 1.94 0.88 0.75 0.75

time (sec)

N/A 0.116 0.002 0.064 0.198 0.219 0.023 0.305 0.023

Problem 356

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 59 49 43 53 177 697 45 42

N.S.

1 1.09 0.91 0.80 0.98 3.28 12.91 0.83 0.78

time (sec)

N/A 0.163 0.052 0.080 0.300 0.237 1.920 0.311 0.058

Problem 357

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

74 85 63 60 89 221 818 65 73

N.S.

1 1.15 0.85 0.81 1.20 2.99 11.05 0.88 0.99

time (sec)

N/A 0.171 0.082 0.118 0.290 0.234 4.225 0.318 0.124

Problem 358

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

106 113 78 70 123 255 464 93 105

N.S.

1 1.07 0.74 0.66 1.16 2.41 4.38 0.88 0.99

time (sec)

N/A 0.187 0.112 0.136 0.295 0.238 14.860 0.313 0.155

Problem 359

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

25 25 25 20 19 58 54 19 19

N.S.

1 1.00 1.00 0.80 0.76 2.32 2.16 0.76 0.76

time (sec)

N/A 0.130 0.018 0.064 0.286 0.227 0.933 0.303 0.061

Problem 360

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

44 44 44 39 46 97 121 43 36

N.S.

1 1.00 1.00 0.89 1.05 2.20 2.75 0.98 0.82

time (sec)

N/A 0.150 0.039 0.076 0.309 0.233 1.606 0.316 0.049

Problem 361

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 60 55 86 128 216 68 57

N.S.

1 1.00 0.81 0.74 1.16 1.73 2.92 0.92 0.77

time (sec)

N/A 0.164 0.064 0.080 0.285 0.228 3.528 0.294 0.059

Problem 362

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

42 42 42 35 34 124 437 34 34

N.S.

1 1.00 1.00 0.83 0.81 2.95 10.40 0.81 0.81

time (sec)

N/A 0.152 0.030 0.083 0.320 0.224 2.144 0.289 0.103

Problem 363

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

62 69 51 55 67 164 156 64 52

N.S.

1 1.11 0.82 0.89 1.08 2.65 2.52 1.03 0.84

time (sec)

N/A 0.168 0.063 0.108 0.302 0.233 2.416 0.282 0.211

Problem 364

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

95 99 71 71 104 198 226 81 101

N.S.

1 1.04 0.75 0.75 1.09 2.08 2.38 0.85 1.06

time (sec)

N/A 0.179 0.094 0.108 0.308 0.235 5.503 0.275 0.153

Problem 365

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

60 66 52 49 42 182 1950 42 48

N.S.

1 1.10 0.87 0.82 0.70 3.03 32.50 0.70 0.80

time (sec)

N/A 0.169 0.057 0.087 0.289 0.238 142.309 0.316 0.107

Problem 366

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

81 93 67 74 82 226 0 66 70

N.S.

1 1.15 0.83 0.91 1.01 2.79 0.00 0.81 0.86

time (sec)

N/A 0.178 0.086 0.124 0.294 0.235 0.000 0.279 0.125

Problem 367

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

116 123 82 89 121 260 1108 97 117

N.S.

1 1.06 0.71 0.77 1.04 2.24 9.55 0.84 1.01

time (sec)

N/A 0.192 0.121 0.139 0.293 0.241 17.583 0.287 0.085

Problem 368

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 13 12 11 14 87 0 11

N.S.

1 1.00 1.00 0.92 0.85 1.08 6.69 0.00 0.85

time (sec)

N/A 0.129 0.172 0.057 0.252 0.235 10.511 0.000 0.462

Problem 369

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

13 92 13 0 11 11 80 0 0

N.S.

1 7.08 1.00 0.00 0.85 0.85 6.15 0.00 0.00

time (sec)

N/A 0.200 0.004 0.000 0.263 0.231 2.786 0.000 0.000

Problem 370

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 23 23 18 32 56 24 21 17

N.S.

1 1.00 1.00 0.78 1.39 2.43 1.04 0.91 0.74

time (sec)

N/A 0.145 0.002 0.058 0.299 0.226 0.801 0.289 0.004

Problem 371

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

72 72 46 43 56 53 1742 117 56

N.S.

1 1.00 0.64 0.60 0.78 0.74 24.19 1.62 0.78

time (sec)

N/A 0.180 0.023 0.135 0.204 0.216 2.382 0.303 0.056

Problem 372

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

53 53 35 32 41 42 666 92 37

N.S.

1 1.00 0.66 0.60 0.77 0.79 12.57 1.74 0.70

time (sec)

N/A 0.172 0.020 0.117 0.207 0.220 1.329 0.299 0.047

Problem 373

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

34 34 34 21 26 30 202 67 25

N.S.

1 1.00 1.00 0.62 0.76 0.88 5.94 1.97 0.74

time (sec)

N/A 0.157 0.015 0.108 0.203 0.215 1.154 0.287 0.034

Problem 374

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

16 16 16 13 12 12 12 12 12

N.S.

1 1.00 1.00 0.81 0.75 0.75 0.75 0.75 0.75

time (sec)

N/A 0.127 0.002 0.063 0.198 0.214 0.026 0.304 0.038

Problem 375

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

91 90 113 87 86 91 180 87 107

N.S.

1 0.99 1.24 0.96 0.95 1.00 1.98 0.96 1.18

time (sec)

N/A 0.196 0.070 0.450 0.309 0.228 1.943 0.524 0.190

Problem 376

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

97 96 119 95 93 139 643 105 117

N.S.

1 0.99 1.23 0.98 0.96 1.43 6.63 1.08 1.21

time (sec)

N/A 0.198 0.145 0.128 0.292 0.229 2.037 0.527 0.083

Problem 377

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

127 124 129 118 139 187 2266 128 196

N.S.

1 0.98 1.02 0.93 1.09 1.47 17.84 1.01 1.54

time (sec)

N/A 0.214 0.202 0.198 0.306 0.234 3.420 0.535 0.414

Problem 378

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

72 72 46 43 56 53 1742 117 56

N.S.

1 1.00 0.64 0.60 0.78 0.74 24.19 1.62 0.78

time (sec)

N/A 0.184 0.023 0.123 0.205 0.231 2.910 0.317 0.049

Problem 379

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

53 53 35 32 41 42 666 92 37

N.S.

1 1.00 0.66 0.60 0.77 0.79 12.57 1.74 0.70

time (sec)

N/A 0.172 0.021 0.114 0.218 0.217 1.849 0.288 0.048

Problem 380

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

34 34 35 21 26 31 202 68 25

N.S.

1 1.00 1.03 0.62 0.76 0.91 5.94 2.00 0.74

time (sec)

N/A 0.161 0.016 0.108 0.214 0.219 0.824 0.290 0.031

Problem 381

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

16 16 16 13 12 12 12 12 12

N.S.

1 1.00 1.00 0.81 0.75 0.75 0.75 0.75 0.75

time (sec)

N/A 0.133 0.002 0.130 0.222 0.222 0.037 0.309 0.020

Problem 382

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

92 91 114 86 85 110 182 86 117

N.S.

1 0.99 1.24 0.93 0.92 1.20 1.98 0.93 1.27

time (sec)

N/A 0.200 0.056 0.079 0.299 0.230 1.742 0.531 0.125

Problem 383

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

94 95 120 91 93 252 643 106 127

N.S.

1 1.01 1.28 0.97 0.99 2.68 6.84 1.13 1.35

time (sec)

N/A 0.198 0.121 0.175 0.312 0.239 2.102 0.592 0.130

Problem 384

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

127 123 147 107 139 350 2266 129 194

N.S.

1 0.97 1.16 0.84 1.09 2.76 17.84 1.02 1.53

time (sec)

N/A 0.213 0.200 0.098 0.313 0.248 2.409 0.527 0.322

Problem 385

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

72 72 46 43 56 64 1844 193 56

N.S.

1 1.00 0.64 0.60 0.78 0.89 25.61 2.68 0.78

time (sec)

N/A 0.185 0.026 0.126 0.213 0.224 2.486 0.329 0.048

Problem 386

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

53 53 35 32 41 53 733 157 37

N.S.

1 1.00 0.66 0.60 0.77 1.00 13.83 2.96 0.70

time (sec)

N/A 0.171 0.023 0.118 0.200 0.229 1.343 0.289 0.044

Problem 387

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

34 34 24 21 26 41 80 118 25

N.S.

1 1.00 0.71 0.62 0.76 1.21 2.35 3.47 0.74

time (sec)

N/A 0.152 0.017 0.111 0.201 0.220 0.294 0.302 0.029

Problem 388

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 13 12 28 12 58 12

N.S.

1 1.00 1.00 0.81 0.75 1.75 0.75 3.62 0.75

time (sec)

N/A 0.127 0.002 0.061 0.210 0.220 0.016 0.313 0.021

Problem 389

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

105 106 122 90 96 98 209 97 123

N.S.

1 1.01 1.16 0.86 0.91 0.93 1.99 0.92 1.17

time (sec)

N/A 0.204 0.068 0.159 0.283 0.227 1.693 0.518 0.068

Problem 390

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

107 110 128 97 104 111 719 119 131

N.S.

1 1.03 1.20 0.91 0.97 1.04 6.72 1.11 1.22

time (sec)

N/A 0.212 0.162 0.139 0.292 0.232 2.032 0.508 0.079

Problem 391

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

124 118 136 110 136 162 2266 127 174

N.S.

1 0.95 1.10 0.89 1.10 1.31 18.27 1.02 1.40

time (sec)

N/A 0.213 0.223 0.130 0.303 0.240 1.912 0.516 0.139

Problem 392

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 72 46 43 56 42 1640 49 56

N.S.

1 1.00 0.64 0.60 0.78 0.58 22.78 0.68 0.78

time (sec)

N/A 0.183 0.023 0.123 0.213 0.222 1.784 0.288 0.049

Problem 393

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 53 35 32 41 31 600 37 37

N.S.

1 1.00 0.66 0.60 0.77 0.58 11.32 0.70 0.70

time (sec)

N/A 0.171 0.023 0.116 0.207 0.219 1.821 0.296 0.064

Problem 394

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

34 34 24 21 26 20 162 25 25

N.S.

1 1.00 0.71 0.62 0.76 0.59 4.76 0.74 0.74

time (sec)

N/A 0.158 0.014 0.065 0.206 0.228 0.757 0.309 0.047

Problem 395

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

16 16 16 13 12 12 12 12 12

N.S.

1 1.00 1.00 0.81 0.75 0.75 0.75 0.75 0.75

time (sec)

N/A 0.131 0.001 0.062 0.212 0.218 0.035 0.311 0.020

Problem 396

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

79 75 95 75 76 213 155 77 99

N.S.

1 0.95 1.20 0.95 0.96 2.70 1.96 0.97 1.25

time (sec)

N/A 0.187 0.045 0.077 0.298 0.231 1.785 0.515 0.099

Problem 397

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

100 101 120 95 106 306 831 109 130

N.S.

1 1.01 1.20 0.95 1.06 3.06 8.31 1.09 1.30

time (sec)

N/A 0.197 0.138 0.090 0.311 0.235 1.901 0.562 0.165

Problem 398

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

130 129 149 109 142 296 2730 130 182

N.S.

1 0.99 1.15 0.84 1.09 2.28 21.00 1.00 1.40

time (sec)

N/A 0.215 0.132 0.103 0.304 0.242 2.943 0.576 0.423

Problem 399

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

80 80 48 45 64 44 4974 57 64

N.S.

1 1.00 0.60 0.56 0.80 0.55 62.18 0.71 0.80

time (sec)

N/A 0.188 0.022 0.131 0.201 0.228 2.233 0.324 0.055

Problem 400

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

59 59 37 34 47 33 1326 43 43

N.S.

1 1.00 0.63 0.58 0.80 0.56 22.47 0.73 0.73

time (sec)

N/A 0.174 0.022 0.115 0.216 0.215 1.242 0.297 0.046

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