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

2.2.3 Integrals 201 to 243

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 201

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

133 133 178 314 234 201 972 0 341

N.S.

1 1.00 1.34 2.36 1.76 1.51 7.31 0.00 2.56

time (sec)

N/A 0.196 0.079 0.117 0.261 0.378 9.711 0.000 2.707

Problem 202

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

374 374 418 1431 1972 0 0 0 -1

N.S.

1 1.00 1.12 3.83 5.27 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.091 0.834 19.473 0.854 0.000 0.000 0.000 0.000

Problem 203

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

304 304 351 1341 1579 0 0 0 -1

N.S.

1 1.00 1.15 4.41 5.19 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.731 0.578 7.973 0.770 0.000 0.000 0.000 0.000

Problem 204

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

234 234 285 1250 1184 0 0 0 -1

N.S.

1 1.00 1.22 5.34 5.06 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.420 0.377 7.330 0.691 0.000 0.000 0.000 0.000

Problem 205

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 201 5972 0 0 0 0 -1

N.S.

1 1.00 1.42 42.06 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.197 0.185 6.803 0.000 0.000 0.000 0.000 0.000

Problem 206

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

224 224 248 1542 0 0 0 0 -1

N.S.

1 1.00 1.11 6.88 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.359 0.136 5.506 0.000 0.000 0.000 0.000 0.000

Problem 207

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 230 4974 528 0 0 0 -1

N.S.

1 1.00 1.62 35.03 3.72 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.246 0.212 7.177 1.097 0.000 0.000 0.000 0.000

Problem 208

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

234 234 333 1289 703 0 0 0 -1

N.S.

1 1.00 1.42 5.51 3.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.475 0.492 8.174 1.229 0.000 0.000 0.000 0.000

Problem 209

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

38 38 31 35 24 36 121 170 24

N.S.

1 1.00 0.82 0.92 0.63 0.95 3.18 4.47 0.63

time (sec)

N/A 0.012 0.013 0.069 0.266 0.377 1.035 0.407 0.862

Problem 210

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 25 30 19 31 39 121 -1

N.S.

1 1.00 0.81 0.97 0.61 1.00 1.26 3.90 -0.03

time (sec)

N/A 0.009 0.009 0.039 0.252 0.390 0.548 0.414 0.000

Problem 211

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 17 16 25 87 72 14

N.S.

1 1.00 1.00 0.85 0.80 1.25 4.35 3.60 0.70

time (sec)

N/A 0.006 0.008 0.054 0.272 0.355 0.214 0.466 0.801

Problem 212

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

24 24 24 29 18 37 126 72 22

N.S.

1 1.00 1.00 1.21 0.75 1.54 5.25 3.00 0.92

time (sec)

N/A 0.007 0.015 0.070 0.249 0.375 0.417 0.419 0.786

Problem 213

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

190 190 222 194 172 1803 0 227 231

N.S.

1 1.00 1.17 1.02 0.91 9.49 0.00 1.19 1.22

time (sec)

N/A 0.249 0.041 0.054 0.471 1.179 0.000 0.490 13.380

Problem 214

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 75 60 58 64 0 97 110

N.S.

1 1.00 1.53 1.22 1.18 1.31 0.00 1.98 2.24

time (sec)

N/A 0.045 0.022 0.100 0.252 0.340 0.000 0.415 1.757

Problem 215

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

190 190 222 194 172 1848 0 0 247

N.S.

1 1.00 1.17 1.02 0.91 9.73 0.00 0.00 1.30

time (sec)

N/A 0.245 0.026 0.056 0.471 1.219 0.000 0.000 11.967

Problem 216

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

170 170 114 179 158 1682 0 186 107

N.S.

1 1.00 0.67 1.05 0.93 9.89 0.00 1.09 0.63

time (sec)

N/A 0.212 0.107 0.057 0.479 1.216 0.000 0.427 5.100

Problem 217

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 32 63 62 0 0 0 -1

N.S.

1 1.00 0.94 1.85 1.82 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.023 0.016 0.115 0.370 0.000 0.000 0.000 0.000

Problem 218

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

172 172 205 167 163 234 0 172 220

N.S.

1 1.00 1.19 0.97 0.95 1.36 0.00 1.00 1.28

time (sec)

N/A 0.163 0.030 0.053 0.485 0.369 0.000 0.488 7.456

Problem 219

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

188 188 220 180 168 214 0 194 228

N.S.

1 1.00 1.17 0.96 0.89 1.14 0.00 1.03 1.21

time (sec)

N/A 0.214 0.042 0.056 0.469 0.377 0.000 0.487 7.375

Problem 220

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 73 55 51 59 0 67 114

N.S.

1 1.00 1.55 1.17 1.09 1.26 0.00 1.43 2.43

time (sec)

N/A 0.024 0.023 0.056 0.269 0.353 0.000 0.440 1.358

Problem 221

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 122 258 186 179 0 0 105

N.S.

1 1.00 1.21 2.55 1.84 1.77 0.00 0.00 1.04

time (sec)

N/A 0.109 0.060 0.270 0.258 0.384 0.000 0.000 1.307

Problem 222

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

156 156 167 785 0 0 0 0 -1

N.S.

1 1.00 1.07 5.03 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.225 0.089 6.804 0.000 0.000 0.000 0.000 0.000

Problem 223

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 123 0 175 173 0 0 281

N.S.

1 1.00 1.28 0.00 1.82 1.80 0.00 0.00 2.93

time (sec)

N/A 0.126 0.090 0.107 0.282 0.365 0.000 0.000 2.037

Problem 224

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

66 66 73 0 0 0 0 0 -1

N.S.

1 1.00 1.11 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.023 0.037 0.011 0.000 0.000 0.000 0.000 0.000

Problem 225

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

67 67 73 0 0 0 0 0 -1

N.S.

1 1.00 1.09 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.018 0.034 0.013 0.000 0.000 0.000 0.000 0.000

Problem 226

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

58 58 58 0 0 0 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.021 0.094 0.011 0.000 0.000 0.000 0.000 0.000

Problem 227

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 39 65 0 141 0 0 -1

N.S.

1 1.00 1.08 1.81 0.00 3.92 0.00 0.00 -0.03

time (sec)

N/A 0.024 0.057 0.144 0.000 0.378 0.000 0.000 0.000

Problem 228

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

67 67 66 0 0 0 0 0 -1

N.S.

1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.023 0.045 0.012 0.000 0.000 0.000 0.000 0.000

Problem 229

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

70 70 73 0 0 0 0 0 -1

N.S.

1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.023 0.032 0.013 0.000 0.000 0.000 0.000 0.000

Problem 230

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

72 72 73 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 0.022 0.033 0.014 0.000 0.000 0.000 0.000 0.000

Problem 231

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

17 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06

time (sec)

N/A 0.010 7.776 0.014 0.000 0.000 0.000 0.000 0.000

Problem 232

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

15 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07

time (sec)

N/A 0.005 1.725 0.012 0.000 0.000 0.000 0.000 0.000

Problem 233

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

148 148 183 827 0 0 0 0 -1

N.S.

1 1.00 1.24 5.59 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.232 0.136 5.898 0.000 0.000 0.000 0.000 0.000

Problem 234

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.017 10.438 0.014 0.000 0.000 0.000 0.000 0.000

Problem 235

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.020 10.395 0.015 0.000 0.000 0.000 0.000 0.000

Problem 236

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 33 53 147 129 0 0 -1

N.S.

1 1.00 1.10 1.77 4.90 4.30 0.00 0.00 -0.03

time (sec)

N/A 0.015 0.031 0.128 0.321 0.357 0.000 0.000 0.000

Problem 237

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 22 95 104 0 0 0 -1

N.S.

1 1.00 0.92 3.96 4.33 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.016 0.010 0.096 0.259 0.000 0.000 0.000 0.000

Problem 238

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 17 30 15 22 15 101 15

N.S.

1 1.00 0.89 1.58 0.79 1.16 0.79 5.32 0.79

time (sec)

N/A 0.005 0.002 0.144 0.251 0.349 0.079 0.407 0.071

Problem 239

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.017 6.300 0.023 0.000 0.000 0.000 0.000 0.000

Problem 240

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.017 5.101 0.020 0.000 0.000 0.000 0.000 0.000

Problem 241

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

84 84 77 0 0 0 0 0 -1

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.043 0.064 0.019 0.000 0.000 0.000 0.000 0.000

Problem 242

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

21 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.022 0.274 0.016 0.000 0.000 0.000 0.000 0.000

Problem 243

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.018 1.242 0.010 0.000 0.000 0.000 0.000 0.000

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