[prev] [prev-tail] [tail] [up]

2.2.2 Integrals 101 to 145

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 101

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

81 81 73 69 66 90 80 71 69

N.S.

1 1.00 0.90 0.85 0.81 1.11 0.99 0.88 0.85

time (sec)

N/A 0.086 0.021 0.031 0.509 0.374 0.067 3.724 0.051

Problem 102

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

74 74 66 64 59 85 73 66 65

N.S.

1 1.00 0.89 0.86 0.80 1.15 0.99 0.89 0.88

time (sec)

N/A 0.082 0.021 0.039 0.511 0.374 0.066 3.089 0.045

Problem 103

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 61 59 54 80 68 54 60

N.S.

1 1.00 0.94 0.91 0.83 1.23 1.05 0.83 0.92

time (sec)

N/A 0.069 0.018 0.028 0.507 0.367 0.066 3.311 0.919

Problem 104

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

58 58 58 54 49 70 60 49 69

N.S.

1 1.00 1.00 0.93 0.84 1.21 1.03 0.84 1.19

time (sec)

N/A 0.048 0.015 0.025 0.505 0.364 0.065 4.279 0.048

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 93 58 55 84 65 62 59

N.S.

1 1.00 1.41 0.88 0.83 1.27 0.98 0.94 0.89

time (sec)

N/A 0.072 0.045 0.030 0.493 0.373 0.072 5.420 0.907

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 97 63 66 105 76 66 68

N.S.

1 1.00 1.37 0.89 0.93 1.48 1.07 0.93 0.96

time (sec)

N/A 0.093 0.036 0.031 0.506 0.363 0.083 5.380 0.061

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 105 68 71 110 80 79 72

N.S.

1 1.00 1.31 0.85 0.89 1.38 1.00 0.99 0.90

time (sec)

N/A 0.093 0.042 0.032 0.508 0.363 0.087 4.299 0.060

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 110 73 76 115 85 84 78

N.S.

1 1.00 1.26 0.84 0.87 1.32 0.98 0.97 0.90

time (sec)

N/A 0.098 0.046 0.033 0.506 0.368 0.096 4.085 0.065

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

248 248 145 296 0 521 71 585 171

N.S.

1 1.00 0.58 1.19 0.00 2.10 0.29 2.36 0.69

time (sec)

N/A 0.231 0.112 0.091 0.000 0.383 0.331 3.745 0.106

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

237 237 132 288 0 483 1205 576 164

N.S.

1 1.00 0.56 1.22 0.00 2.04 5.08 2.43 0.69

time (sec)

N/A 0.194 0.098 0.044 0.000 0.374 0.731 3.013 0.943

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

232 232 129 285 0 510 60 573 162

N.S.

1 1.00 0.56 1.23 0.00 2.20 0.26 2.47 0.70

time (sec)

N/A 0.199 0.099 0.038 0.000 0.368 0.337 3.687 0.095

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

225 225 121 281 0 461 51 566 156

N.S.

1 1.00 0.54 1.25 0.00 2.05 0.23 2.52 0.69

time (sec)

N/A 0.194 0.102 0.037 0.000 0.372 0.330 5.358 0.958

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

224 224 115 277 0 461 1185 565 153

N.S.

1 1.00 0.51 1.24 0.00 2.06 5.29 2.52 0.68

time (sec)

N/A 0.142 0.172 0.038 0.000 0.373 0.721 4.033 0.127

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

229 229 126 283 0 478 1192 572 159

N.S.

1 1.00 0.55 1.24 0.00 2.09 5.21 2.50 0.69

time (sec)

N/A 0.195 0.116 0.043 0.000 0.407 0.748 3.778 0.136

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

238 238 131 288 0 530 60 579 165

N.S.

1 1.00 0.55 1.21 0.00 2.23 0.25 2.43 0.69

time (sec)

N/A 0.201 0.182 0.045 0.000 0.390 0.349 4.470 0.137

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

245 245 140 293 0 503 1202 584 171

N.S.

1 1.00 0.57 1.20 0.00 2.05 4.91 2.38 0.70

time (sec)

N/A 0.203 0.196 0.045 0.000 0.380 0.761 4.449 0.143

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

243 243 156 298 0 568 1204 588 184

N.S.

1 1.00 0.64 1.23 0.00 2.34 4.95 2.42 0.76

time (sec)

N/A 0.234 0.138 0.043 0.000 0.386 0.718 5.734 0.111

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

242 242 155 295 0 564 82 585 182

N.S.

1 1.00 0.64 1.22 0.00 2.33 0.34 2.42 0.75

time (sec)

N/A 0.207 0.128 0.040 0.000 0.380 0.364 4.572 0.942

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

235 235 138 291 0 553 71 580 176

N.S.

1 1.00 0.59 1.24 0.00 2.35 0.30 2.47 0.75

time (sec)

N/A 0.204 0.203 0.038 0.000 0.385 0.347 3.210 0.992

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

238 238 129 287 0 548 1198 577 173

N.S.

1 1.00 0.54 1.21 0.00 2.30 5.03 2.42 0.73

time (sec)

N/A 0.183 0.194 0.042 0.000 0.371 0.701 4.625 0.146

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

246 246 133 287 0 574 1200 577 174

N.S.

1 1.00 0.54 1.17 0.00 2.33 4.88 2.35 0.71

time (sec)

N/A 0.189 0.195 0.045 0.000 0.388 0.716 4.573 1.012

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

248 248 129 287 0 580 1195 577 173

N.S.

1 1.00 0.52 1.16 0.00 2.34 4.82 2.33 0.70

time (sec)

N/A 0.174 0.188 0.050 0.000 0.384 0.692 3.986 1.008

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

253 253 140 293 0 633 75 582 179

N.S.

1 1.00 0.55 1.16 0.00 2.50 0.30 2.30 0.71

time (sec)

N/A 0.231 0.240 0.046 0.000 0.399 0.361 4.183 0.993

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

262 262 139 298 0 652 80 589 185

N.S.

1 1.00 0.53 1.14 0.00 2.49 0.31 2.25 0.71

time (sec)

N/A 0.249 0.215 0.046 0.000 0.396 0.367 7.547 1.022

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

149 149 142 151 0 486 0 146 1834

N.S.

1 1.00 0.95 1.01 0.00 3.26 0.00 0.98 12.31

time (sec)

N/A 0.188 0.078 0.112 0.000 0.465 0.000 5.654 1.685

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

594 594 721 760 0 0 0 10761 2500

N.S.

1 1.00 1.21 1.28 0.00 0.00 0.00 18.12 4.21

time (sec)

N/A 11.263 1.640 0.097 0.000 0.000 0.000 7.928 4.731

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

471 471 575 584 0 23774 0 9170 2500

N.S.

1 1.00 1.22 1.24 0.00 50.48 0.00 19.47 5.31

time (sec)

N/A 4.354 1.192 0.083 0.000 176.559 0.000 7.382 4.218

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

449 449 512 543 0 19375 0 8913 2500

N.S.

1 1.00 1.14 1.21 0.00 43.15 0.00 19.85 5.57

time (sec)

N/A 1.957 1.023 0.078 0.000 141.882 0.000 6.922 5.821

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

460 460 529 550 0 23991 0 9176 2500

N.S.

1 1.00 1.15 1.20 0.00 52.15 0.00 19.95 5.43

time (sec)

N/A 1.814 1.512 0.145 0.000 128.532 0.000 9.077 7.761

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

542 542 612 629 0 0 0 10422 2500

N.S.

1 1.00 1.13 1.16 0.00 0.00 0.00 19.23 4.61

time (sec)

N/A 4.859 1.316 0.152 0.000 0.000 0.000 6.394 8.467

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 20 21 31 31 54 58 31

N.S.

1 1.00 1.00 1.05 1.55 1.55 2.70 2.90 1.55

time (sec)

N/A 0.029 0.382 0.034 0.324 0.403 174.572 5.214 1.098

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

210 278 149 145 271 138 367 225 287

N.S.

1 1.32 0.71 0.69 1.29 0.66 1.75 1.07 1.37

time (sec)

N/A 0.207 0.318 0.170 0.505 0.381 81.994 3.549 1.645

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 213 116 109 199 104 367 163 215

N.S.

1 1.34 0.73 0.69 1.25 0.65 2.31 1.03 1.35

time (sec)

N/A 0.128 0.238 0.168 0.488 0.391 56.862 4.544 1.494

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

109 149 80 73 127 71 350 103 143

N.S.

1 1.37 0.73 0.67 1.17 0.65 3.21 0.94 1.31

time (sec)

N/A 0.082 0.164 0.143 0.488 0.415 37.089 5.204 1.377

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 151 106 143 98 80 304 0 161

N.S.

1 1.62 1.14 1.54 1.05 0.86 3.27 0.00 1.73

time (sec)

N/A 0.108 0.219 0.158 0.501 0.393 45.402 0.000 2.949

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 155 85 163 117 98 0 0 422

N.S.

1 1.57 0.86 1.65 1.18 0.99 0.00 0.00 4.26

time (sec)

N/A 0.162 0.254 0.157 0.492 0.413 0.000 0.000 5.151

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 182 102 222 184 102 0 0 932

N.S.

1 1.44 0.81 1.76 1.46 0.81 0.00 0.00 7.40

time (sec)

N/A 0.187 0.263 0.157 0.489 0.381 0.000 0.000 10.816

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

212 248 141 306 256 137 0 0 1621

N.S.

1 1.17 0.67 1.44 1.21 0.65 0.00 0.00 7.65

time (sec)

N/A 0.251 0.398 0.182 0.504 0.391 0.000 0.000 20.051

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

216 245 134 273 178 134 0 176 1132

N.S.

1 1.13 0.62 1.26 0.82 0.62 0.00 0.81 5.24

time (sec)

N/A 0.136 0.285 0.150 0.481 0.363 0.000 5.198 23.121

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

128 179 98 191 107 100 0 116 651

N.S.

1 1.40 0.77 1.49 0.84 0.78 0.00 0.91 5.09

time (sec)

N/A 0.061 0.198 0.144 0.487 0.368 0.000 5.718 12.861

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 155 86 148 70 90 0 251 306

N.S.

1 1.52 0.84 1.45 0.69 0.88 0.00 2.46 3.00

time (sec)

N/A 0.079 0.177 0.156 0.493 0.364 0.000 5.663 7.002

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

157 157 81 146 81 90 257 555 138

N.S.

1 1.00 0.52 0.93 0.52 0.57 1.64 3.54 0.88

time (sec)

N/A 0.080 0.167 0.152 0.499 0.370 55.950 3.482 2.268

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

160 160 87 86 139 76 0 1103 146

N.S.

1 1.00 0.54 0.54 0.87 0.48 0.00 6.89 0.91

time (sec)

N/A 0.097 0.140 0.154 0.492 0.369 0.000 3.511 1.732

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

226 226 124 122 211 110 0 1517 218

N.S.

1 1.00 0.55 0.54 0.93 0.49 0.00 6.71 0.96

time (sec)

N/A 0.119 0.189 0.168 0.509 0.396 0.000 6.406 1.817

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

292 292 158 158 283 144 0 1931 290

N.S.

1 1.00 0.54 0.54 0.97 0.49 0.00 6.61 0.99

time (sec)

N/A 0.156 0.236 0.161 0.494 0.440 0.000 7.385 1.873

[prev] [prev-tail] [front] [up]