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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 0.192 0.891 0.073 0.717 0.000 8.407 0.000 0.096

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 0.193 4.786 0.102 0.703 0.000 16.239 1.566 0.095

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

120 137 100 144 0 99 85 0 0

N.S.

1 1.14 0.83 1.20 0.00 0.82 0.71 0.00 0.00

time (sec)

N/A 0.272 0.028 1.267 0.000 0.099 68.116 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 85 85 0 0

N.S.

1 1.10 0.53 1.11 0.00 0.69 0.69 0.00 0.00

time (sec)

N/A 0.318 0.023 0.636 0.000 0.094 11.194 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 66 119 0 68 85 0 0

N.S.

1 1.10 0.75 1.35 0.00 0.77 0.97 0.00 0.00

time (sec)

N/A 0.228 0.017 0.408 0.000 0.092 3.264 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 53 0 0 0

N.S.

1 1.06 0.51 1.10 0.00 0.60 0.00 0.00 0.00

time (sec)

N/A 0.274 0.016 0.274 0.000 0.094 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 40 85 0 49 0 0 0

N.S.

1 1.00 0.73 1.55 0.00 0.89 0.00 0.00 0.00

time (sec)

N/A 0.205 0.014 0.162 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 42 129 0 70 0 0 0

N.S.

1 1.06 0.34 1.03 0.00 0.56 0.00 0.00 0.00

time (sec)

N/A 0.306 0.017 0.296 0.000 0.087 0.000 0.000 0.000

Problem 209

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

109 113 90 0 0 0 0 0 0

N.S.

1 1.04 0.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.336 0.049 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 90 0 0 0 0 0 0

N.S.

1 1.04 0.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.338 0.043 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 90 0 0 0 0 0 0

N.S.

1 1.04 0.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.342 0.046 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 90 0 0 0 0 0 0

N.S.

1 1.02 0.84 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.328 0.039 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 87 0 0 0 0 0 0

N.S.

1 1.02 0.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.342 0.037 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 87 0 0 0 0 0 0

N.S.

1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.342 0.042 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 16 421 53 17 0 18

N.S.

1 1.00 1.11 0.89 23.39 2.94 0.94 0.00 1.00

time (sec)

N/A 0.353 58.945 0.098 3.550 0.260 78.696 0.000 0.129

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 16 398 44 17 0 18

N.S.

1 1.00 1.11 0.89 22.11 2.44 0.94 0.00 1.00

time (sec)

N/A 0.350 142.451 0.068 3.593 0.254 8.465 0.000 0.142

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 16 438 50 0 18 18

N.S.

1 1.00 1.11 0.89 24.33 2.78 0.00 1.00 1.00

time (sec)

N/A 0.339 71.710 0.021 3.579 0.243 0.000 0.571 0.140

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 16 469 50 0 18 18

N.S.

1 1.00 1.11 0.89 26.06 2.78 0.00 1.00 1.00

time (sec)

N/A 0.344 59.244 0.110 3.519 0.251 0.000 0.602 0.130

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 16 471 50 0 18 18

N.S.

1 1.00 1.11 0.89 26.17 2.78 0.00 1.00 1.00

time (sec)

N/A 0.355 41.968 0.131 3.587 0.255 0.000 0.631 0.133

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 1.852 0.079 0.422 0.242 4.158 0.306 0.092

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 0.176 1.604 0.077 0.445 0.229 0.486 0.305 0.093

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 0.179 0.960 0.080 0.469 0.238 1.425 0.290 0.094

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 0.794 0.085 0.506 0.234 3.485 0.289 0.093

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 16 182 34 17 18 18

N.S.

1 1.00 1.11 0.89 10.11 1.89 0.94 1.00 1.00

time (sec)

N/A 0.180 8.687 0.081 1.910 0.240 10.744 0.310 0.114

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 16 180 32 17 18 18

N.S.

1 1.00 1.11 0.89 10.00 1.78 0.94 1.00 1.00

time (sec)

N/A 0.176 8.426 0.083 1.901 0.229 1.992 0.311 0.119

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 16 195 39 19 18 18

N.S.

1 1.00 1.11 0.89 10.83 2.17 1.06 1.00 1.00

time (sec)

N/A 0.177 24.106 0.096 1.690 0.246 4.072 0.318 0.121

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 16 219 51 19 18 18

N.S.

1 1.00 1.11 0.89 12.17 2.83 1.06 1.00 1.00

time (sec)

N/A 0.179 16.641 0.089 1.971 0.231 11.473 0.295 0.114

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