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2.2.2 Integrals 101 to 142

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 B A C B F(-1) F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

268 268 1120 263 1481 474 0 0 -1

N.S.

1 1.00 4.18 0.98 5.53 1.77 0.00 0.00 -0.00

time (sec)

N/A 0.460 6.684 0.767 0.323 2.183 0.000 0.000 0.000

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

430 430 3835 430 4349 873 0 0 -1

N.S.

1 1.00 8.92 1.00 10.11 2.03 0.00 0.00 -0.00

time (sec)

N/A 0.754 7.236 1.341 0.364 2.853 0.000 0.000 0.000

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

213 213 324 217 1012 384 0 0 -1

N.S.

1 1.00 1.52 1.02 4.75 1.80 0.00 0.00 -0.00

time (sec)

N/A 0.563 1.950 0.908 0.302 3.308 0.000 0.000 0.000

Problem 104

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

36 36 26 35 25 28 114 33 25

N.S.

1 1.00 0.72 0.97 0.69 0.78 3.17 0.92 0.69

time (sec)

N/A 0.010 0.061 0.077 0.285 2.177 0.238 0.424 0.093

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 109 86 100 193 0 127 -1

N.S.

1 1.00 0.95 0.75 0.87 1.68 0.00 1.10 -0.01

time (sec)

N/A 0.074 0.179 0.142 0.286 2.346 0.000 0.417 0.000

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

144 144 135 117 131 229 0 147 -1

N.S.

1 1.00 0.94 0.81 0.91 1.59 0.00 1.02 -0.01

time (sec)

N/A 0.138 0.250 0.142 0.280 3.244 0.000 0.422 0.000

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 82 54 52 46 0 0 -1

N.S.

1 1.00 1.06 0.70 0.68 0.60 0.00 0.00 -0.01

time (sec)

N/A 0.045 0.088 0.000 0.266 2.254 0.000 0.000 0.000

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 107 60 133 70 0 0 -1

N.S.

1 1.00 1.29 0.72 1.60 0.84 0.00 0.00 -0.01

time (sec)

N/A 0.057 0.218 0.107 0.291 2.628 0.000 0.000 0.000

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

151 151 166 127 474 164 0 0 -1

N.S.

1 1.00 1.10 0.84 3.14 1.09 0.00 0.00 -0.01

time (sec)

N/A 0.126 0.617 0.159 0.284 2.620 0.000 0.000 0.000

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 133 114 147 265 0 300 -1

N.S.

1 1.00 0.94 0.80 1.04 1.87 0.00 2.11 -0.01

time (sec)

N/A 0.135 0.251 0.168 0.273 2.069 0.000 0.455 0.000

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

157 157 158 139 186 270 0 521 -1

N.S.

1 1.00 1.01 0.89 1.18 1.72 0.00 3.32 -0.01

time (sec)

N/A 0.132 1.129 0.381 0.491 2.298 0.000 0.458 0.000

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

298 298 267 235 302 525 0 595 -1

N.S.

1 1.00 0.90 0.79 1.01 1.76 0.00 2.00 -0.00

time (sec)

N/A 0.230 0.956 0.601 0.490 2.897 0.000 0.492 0.000

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 163 150 189 321 0 378 -1

N.S.

1 1.00 1.01 0.93 1.17 1.98 0.00 2.33 -0.01

time (sec)

N/A 0.203 0.404 0.188 0.285 2.400 0.000 0.461 0.000

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

179 179 245 175 240 334 0 599 -1

N.S.

1 1.00 1.37 0.98 1.34 1.87 0.00 3.35 -0.01

time (sec)

N/A 0.225 1.157 0.398 0.485 3.043 0.000 0.476 0.000

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

340 340 322 307 374 645 0 751 -1

N.S.

1 1.00 0.95 0.90 1.10 1.90 0.00 2.21 -0.00

time (sec)

N/A 0.409 1.635 0.808 0.513 1.992 0.000 0.560 0.000

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 116 121 204 142 0 0 -1

N.S.

1 1.00 0.79 0.82 1.39 0.97 0.00 0.00 -0.01

time (sec)

N/A 0.139 0.161 0.162 0.288 1.853 0.000 0.000 0.000

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 131 145 236 159 0 0 -1

N.S.

1 1.00 0.77 0.85 1.38 0.93 0.00 0.00 -0.01

time (sec)

N/A 0.146 0.272 0.225 0.312 2.132 0.000 0.000 0.000

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

293 293 218 242 406 280 0 0 -1

N.S.

1 1.00 0.74 0.83 1.39 0.96 0.00 0.00 -0.00

time (sec)

N/A 0.235 0.445 0.565 0.293 3.313 0.000 0.000 0.000

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 170 82 205 109 0 0 -1

N.S.

1 1.00 1.65 0.80 1.99 1.06 0.00 0.00 -0.01

time (sec)

N/A 0.113 0.514 0.155 0.280 2.239 0.000 0.000 0.000

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 189 107 315 167 0 0 -1

N.S.

1 1.00 1.35 0.76 2.25 1.19 0.00 0.00 -0.01

time (sec)

N/A 0.147 0.893 0.263 0.275 2.269 0.000 0.000 0.000

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

205 205 389 162 667 311 0 0 -1

N.S.

1 1.00 1.90 0.79 3.25 1.52 0.00 0.00 -0.00

time (sec)

N/A 0.204 2.363 0.562 0.298 2.020 0.000 0.000 0.000

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

183 183 217 167 749 301 0 0 -1

N.S.

1 1.00 1.19 0.91 4.09 1.64 0.00 0.00 -0.01

time (sec)

N/A 0.224 0.961 0.189 0.291 1.773 0.000 0.000 0.000

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C B F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

211 211 252 191 851 361 0 0 -1

N.S.

1 1.00 1.19 0.91 4.03 1.71 0.00 0.00 -0.00

time (sec)

N/A 0.282 2.436 0.349 0.292 2.328 0.000 0.000 0.000

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

369 369 2997 334 2140 707 0 0 -1

N.S.

1 1.00 8.12 0.91 5.80 1.92 0.00 0.00 -0.00

time (sec)

N/A 0.425 7.012 0.809 0.333 2.593 0.000 0.000 0.000

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

172 172 151 168 362 178 0 0 -1

N.S.

1 1.00 0.88 0.98 2.10 1.03 0.00 0.00 -0.01

time (sec)

N/A 0.206 0.317 0.176 0.296 2.425 0.000 0.000 0.000

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

231 231 204 217 399 226 0 0 -1

N.S.

1 1.00 0.88 0.94 1.73 0.98 0.00 0.00 -0.00

time (sec)

N/A 0.258 0.598 0.276 0.298 2.394 0.000 0.000 0.000

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

346 346 386 334 696 348 0 0 -1

N.S.

1 1.00 1.12 0.97 2.01 1.01 0.00 0.00 -0.00

time (sec)

N/A 0.315 0.969 0.617 0.313 2.660 0.000 0.000 0.000

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

189 189 231 178 648 311 0 0 -1

N.S.

1 1.00 1.22 0.94 3.43 1.65 0.00 0.00 -0.01

time (sec)

N/A 0.240 1.042 0.154 0.285 2.705 0.000 0.000 0.000

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C B F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

245 245 301 227 997 402 0 0 -1

N.S.

1 1.00 1.23 0.93 4.07 1.64 0.00 0.00 -0.00

time (sec)

N/A 0.298 3.300 0.276 0.311 2.720 0.000 0.000 0.000

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

378 378 3285 354 2456 725 0 0 -1

N.S.

1 1.00 8.69 0.94 6.50 1.92 0.00 0.00 -0.00

time (sec)

N/A 0.368 6.999 0.731 0.335 2.951 0.000 0.000 0.000

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

208 208 348 214 1006 381 0 0 -1

N.S.

1 1.00 1.67 1.03 4.84 1.83 0.00 0.00 -0.00

time (sec)

N/A 0.334 2.208 0.230 0.304 3.130 0.000 0.000 0.000

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

268 268 1118 263 1481 474 0 0 -1

N.S.

1 1.00 4.17 0.98 5.53 1.77 0.00 0.00 -0.00

time (sec)

N/A 0.414 6.698 0.365 0.321 2.696 0.000 0.000 0.000

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

422 422 3829 426 4354 867 0 0 -1

N.S.

1 1.00 9.07 1.01 10.32 2.05 0.00 0.00 -0.00

time (sec)

N/A 0.709 6.825 1.128 0.361 3.582 0.000 0.000 0.000

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

209 209 325 215 1013 386 0 0 -1

N.S.

1 1.00 1.56 1.03 4.85 1.85 0.00 0.00 -0.00

time (sec)

N/A 0.402 1.278 0.198 0.312 3.580 0.000 0.000 0.000

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A C C B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

245 245 180 271 576 257 8277 1738 248

N.S.

1 1.00 0.73 1.11 2.35 1.05 33.78 7.09 1.01

time (sec)

N/A 0.248 0.784 0.565 0.299 2.892 23.712 0.463 3.420

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A C C B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 99 83 97 221 84 920 923 84

N.S.

1 1.00 0.84 0.98 2.23 0.85 9.29 9.32 0.85

time (sec)

N/A 0.110 0.226 0.124 0.286 2.648 2.492 0.451 2.590

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 128 0 0 0 0 0 -1

N.S.

1 1.00 1.60 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.046 1.056 0.105 0.000 0.000 0.000 0.000 0.000

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

184 184 240 0 0 0 0 0 -1

N.S.

1 1.00 1.30 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.067 1.821 0.786 0.000 0.000 0.000 0.000 0.000

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A C C B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

245 245 228 274 573 243 8277 1736 247

N.S.

1 1.00 0.93 1.12 2.34 0.99 33.78 7.09 1.01

time (sec)

N/A 0.232 0.391 0.431 0.304 2.389 23.622 0.503 3.311

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A C C B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 82 96 219 81 920 920 83

N.S.

1 1.00 0.84 0.98 2.23 0.83 9.39 9.39 0.85

time (sec)

N/A 0.110 0.133 0.167 0.292 1.682 2.502 0.444 2.557

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

79 79 80 0 0 0 0 0 -1

N.S.

1 1.00 1.01 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.042 0.037 0.082 0.000 0.000 0.000 0.000 0.000

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

169 169 145 0 0 0 0 0 -1

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.068 0.278 0.233 0.000 0.000 0.000 0.000 0.000

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