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2.2.3 Integrals 201 to 227

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 201

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A F(-2) N/A F(-2) N/A

verified

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

size

16 16 18 14 16 0 15 0 16

N.S.

1 1.00 1.12 0.88 1.00 0.00 0.94 0.00 1.00

time (sec)

N/A 0.186 1.217 0.961 0.642 0.000 8.329 0.000 0.293

Problem 202

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A F(-2) N/A N/A N/A

verified

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

size

16 16 18 14 16 0 17 16 16

N.S.

1 1.00 1.12 0.88 1.00 0.00 1.06 1.00 1.00

time (sec)

N/A 0.188 7.736 1.179 0.655 0.000 15.375 1.559 0.263

Problem 203

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 137 158 144 0 100 85 0 0

N.S.

1 1.14 1.32 1.20 0.00 0.83 0.71 0.00 0.00

time (sec)

N/A 0.268 11.246 2.131 0.000 0.103 77.054 0.000 0.000

Problem 204

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 136 66 138 0 84 85 0 0

N.S.

1 1.10 0.53 1.11 0.00 0.68 0.69 0.00 0.00

time (sec)

N/A 0.310 10.086 1.576 0.000 0.100 12.547 0.000 0.000

Problem 205

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 97 113 119 0 69 85 0 0

N.S.

1 1.10 1.28 1.35 0.00 0.78 0.97 0.00 0.00

time (sec)

N/A 0.228 0.160 1.292 0.000 0.102 3.842 0.000 0.000

Problem 206

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 94 45 98 0 52 0 0 0

N.S.

1 1.06 0.51 1.10 0.00 0.58 0.00 0.00 0.00

time (sec)

N/A 0.269 0.038 1.207 0.000 0.095 0.000 0.000 0.000

Problem 207

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 55 93 85 0 50 0 0 0

N.S.

1 1.00 1.69 1.55 0.00 0.91 0.00 0.00 0.00

time (sec)

N/A 0.199 0.134 1.109 0.000 0.085 0.000 0.000 0.000

Problem 208

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 133 68 129 0 73 0 0 0

N.S.

1 1.06 0.54 1.03 0.00 0.58 0.00 0.00 0.00

time (sec)

N/A 0.300 0.081 1.266 0.000 0.090 0.000 0.000 0.000

Problem 209

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

109 113 234 0 0 0 0 0 0

N.S.

1 1.04 2.15 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.338 10.982 0.000 0.000 0.000 0.000 0.000 0.000

Problem 210

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F(-2) F(-1)

verified

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

size

109 113 176 0 0 0 0 0 0

N.S.

1 1.04 1.61 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.335 3.373 0.000 0.000 0.000 0.000 0.000 0.000

Problem 211

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F(-2) F(-1)

verified

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

size

109 113 202 0 0 0 0 0 0

N.S.

1 1.04 1.85 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.339 0.453 0.000 0.000 0.000 0.000 0.000 0.000

Problem 212

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F(-2) F F(-1)

verified

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

size

107 109 142 0 0 0 0 0 0

N.S.

1 1.02 1.33 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.327 0.993 0.000 0.000 0.000 0.000 0.000 0.000

Problem 213

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F(-2) F F(-1)

verified

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

size

105 107 129 0 0 0 0 0 0

N.S.

1 1.02 1.23 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.333 0.398 0.000 0.000 0.000 0.000 0.000 0.000

Problem 214

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F(-2) F F(-1)

verified

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

size

109 109 198 0 0 0 0 0 0

N.S.

1 1.00 1.82 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.339 0.650 0.000 0.000 0.000 0.000 0.000 0.000

Problem 215

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A F(-2) N/A

verified

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

size

18 18 20 16 441 53 17 0 18

N.S.

1 1.00 1.11 0.89 24.50 2.94 0.94 0.00 1.00

time (sec)

N/A 0.359 45.481 0.819 3.500 0.251 80.913 0.000 0.317

Problem 216

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A F(-2) N/A

verified

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

size

18 18 20 16 418 44 17 0 18

N.S.

1 1.00 1.11 0.89 23.22 2.44 0.94 0.00 1.00

time (sec)

N/A 0.355 141.232 1.385 3.425 0.250 8.492 0.000 0.339

Problem 217

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A F(-2) N/A N/A

verified

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

size

18 18 20 16 458 50 0 18 18

N.S.

1 1.00 1.11 0.89 25.44 2.78 0.00 1.00 1.00

time (sec)

N/A 0.343 73.008 0.312 3.395 0.254 0.000 0.682 0.320

Problem 218

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A F(-2) N/A N/A

verified

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

size

18 18 20 16 489 50 0 18 18

N.S.

1 1.00 1.11 0.89 27.17 2.78 0.00 1.00 1.00

time (sec)

N/A 0.343 51.877 2.240 3.414 0.255 0.000 0.800 0.324

Problem 219

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A F(-2) N/A N/A

verified

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

size

18 18 20 16 491 50 0 18 18

N.S.

1 1.00 1.11 0.89 27.28 2.78 0.00 1.00 1.00

time (sec)

N/A 0.351 37.277 1.589 3.472 0.246 0.000 0.757 0.309

Problem 220

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 18 20 15 18 18

N.S.

1 1.00 1.11 0.89 1.00 1.11 0.83 1.00 1.00

time (sec)

N/A 0.182 2.899 0.441 0.403 0.231 4.130 0.283 0.255

Problem 221

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 18 18 15 18 18

N.S.

1 1.00 1.11 0.89 1.00 1.00 0.83 1.00 1.00

time (sec)

N/A 0.177 2.519 0.959 0.413 0.243 0.511 0.287 0.283

Problem 222

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 18 23 17 18 18

N.S.

1 1.00 1.11 0.89 1.00 1.28 0.94 1.00 1.00

time (sec)

N/A 0.177 1.473 0.967 0.445 0.234 1.451 0.282 0.267

Problem 223

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 18 31 17 18 18

N.S.

1 1.00 1.11 0.89 1.00 1.72 0.94 1.00 1.00

time (sec)

N/A 0.179 1.400 0.938 0.497 0.234 3.529 0.284 0.281

Problem 224

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 181 34 17 18 18

N.S.

1 1.00 1.11 0.89 10.06 1.89 0.94 1.00 1.00

time (sec)

N/A 0.179 16.110 0.526 1.853 0.236 10.481 0.337 0.286

Problem 225

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 181 32 17 18 18

N.S.

1 1.00 1.11 0.89 10.06 1.78 0.94 1.00 1.00

time (sec)

N/A 0.175 16.350 0.967 1.875 0.237 2.066 0.321 0.285

Problem 226

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 196 39 19 18 18

N.S.

1 1.00 1.11 0.89 10.89 2.17 1.06 1.00 1.00

time (sec)

N/A 0.173 40.224 0.984 1.683 0.243 4.302 0.303 0.299

Problem 227

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 218 51 19 18 18

N.S.

1 1.00 1.11 0.89 12.11 2.83 1.06 1.00 1.00

time (sec)

N/A 0.181 22.856 0.980 1.934 0.235 11.732 0.299 0.322

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