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2.2.3 Integrals 201 to 224

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 49 43 61 0 305 0 0 39

N.S.

1 1.02 0.90 1.27 0.00 6.35 0.00 0.00 0.81

time (sec)

N/A 0.260 0.093 0.492 0.000 0.281 0.000 0.000 2.215

Problem 202

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 49 47 37 0 303 0 0 36

N.S.

1 1.04 1.00 0.79 0.00 6.45 0.00 0.00 0.77

time (sec)

N/A 0.253 0.125 0.504 0.000 0.282 0.000 0.000 2.335

Problem 203

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 71 97 76 0 625 0 0 65

N.S.

1 1.00 1.37 1.07 0.00 8.80 0.00 0.00 0.92

time (sec)

N/A 0.329 0.179 0.500 0.000 0.273 0.000 0.000 2.431

Problem 204

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 73 101 74 0 1104 0 0 64

N.S.

1 1.01 1.40 1.03 0.00 15.33 0.00 0.00 0.89

time (sec)

N/A 0.322 0.272 0.494 0.000 0.283 0.000 0.000 3.156

Problem 205

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

135 92 198 149 0 8951 0 0 0

N.S.

1 0.68 1.47 1.10 0.00 66.30 0.00 0.00 0.00

time (sec)

N/A 0.478 2.301 0.865 0.000 1.108 0.000 0.000 0.000

Problem 206

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

105 53 160 90 0 6695 0 0 0

N.S.

1 0.50 1.52 0.86 0.00 63.76 0.00 0.00 0.00

time (sec)

N/A 0.401 0.569 0.729 0.000 0.904 0.000 0.000 0.000

Problem 207

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

58 29 98 52 0 1752 0 0 0

N.S.

1 0.50 1.69 0.90 0.00 30.21 0.00 0.00 0.00

time (sec)

N/A 0.297 0.313 0.783 0.000 0.681 0.000 0.000 0.000

Problem 208

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes N/A TBD TBD TBD TBD TBD

size

106 111 159 0 0 6705 0 0 0

N.S.

1 1.05 1.50 0.00 0.00 63.25 0.00 0.00 0.00

time (sec)

N/A 0.431 0.427 0.000 0.000 0.891 0.000 0.000 0.000

Problem 209

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes N/A TBD TBD TBD TBD TBD

size

183 191 193 0 0 9148 0 0 0

N.S.

1 1.04 1.05 0.00 0.00 49.99 0.00 0.00 0.00

time (sec)

N/A 0.521 1.054 0.000 0.000 1.134 0.000 0.000 0.000

Problem 210

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

132 85 184 165 0 7964 0 0 0

N.S.

1 0.64 1.39 1.25 0.00 60.33 0.00 0.00 0.00

time (sec)

N/A 0.444 1.191 0.824 0.000 1.437 0.000 0.000 0.000

Problem 211

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

319 169 164 195 167 1617 0 181 0

N.S.

1 0.53 0.51 0.61 0.52 5.07 0.00 0.57 0.00

time (sec)

N/A 0.929 6.290 1.210 0.312 0.267 0.000 0.626 0.000

Problem 212

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

197 107 334 131 112 613 0 155 0

N.S.

1 0.54 1.70 0.66 0.57 3.11 0.00 0.79 0.00

time (sec)

N/A 0.452 4.155 0.577 0.282 0.258 0.000 0.451 0.000

Problem 213

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 53 51 213 56 70 0 94 0

N.S.

1 0.64 0.61 2.57 0.67 0.84 0.00 1.13 0.00

time (sec)

N/A 0.336 0.070 0.772 0.286 0.261 0.000 0.279 0.000

Problem 214

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

83 53 51 48 35 53 0 60 0

N.S.

1 0.64 0.61 0.58 0.42 0.64 0.00 0.72 0.00

time (sec)

N/A 0.381 0.139 0.448 0.285 0.265 0.000 0.302 0.000

Problem 215

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

193 103 104 131 90 458 0 130 0

N.S.

1 0.53 0.54 0.68 0.47 2.37 0.00 0.67 0.00

time (sec)

N/A 0.885 0.349 0.608 0.290 0.266 0.000 0.277 0.000

Problem 216

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

311 161 133 195 145 1226 0 185 0

N.S.

1 0.52 0.43 0.63 0.47 3.94 0.00 0.59 0.00

time (sec)

N/A 1.527 0.523 0.588 0.308 0.275 0.000 0.296 0.000

Problem 217

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 137 124 118 0 696 0 0 0

N.S.

1 0.87 0.79 0.75 0.00 4.43 0.00 0.00 0.00

time (sec)

N/A 0.574 0.615 2.676 0.000 0.293 0.000 0.000 0.000

Problem 218

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 101 88 88 0 230 0 0 0

N.S.

1 0.88 0.77 0.77 0.00 2.00 0.00 0.00 0.00

time (sec)

N/A 0.465 0.500 1.261 0.000 0.273 0.000 0.000 0.000

Problem 219

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 69 59 58 0 216 0 0 0

N.S.

1 0.90 0.77 0.75 0.00 2.81 0.00 0.00 0.00

time (sec)

N/A 0.331 0.189 0.784 0.000 0.265 0.000 0.000 0.000

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

7 7 9 7 9 9 8 9 11

N.S.

1 1.00 1.29 1.00 1.29 1.29 1.14 1.29 1.57

time (sec)

N/A 0.299 3.119 0.275 0.403 0.250 4.123 0.354 2.353

Problem 221

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 137 124 118 0 698 0 0 0

N.S.

1 0.87 0.79 0.75 0.00 4.45 0.00 0.00 0.00

time (sec)

N/A 0.579 0.675 2.546 0.000 0.307 0.000 0.000 0.000

Problem 222

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 101 88 88 0 230 0 0 0

N.S.

1 0.88 0.77 0.77 0.00 2.00 0.00 0.00 0.00

time (sec)

N/A 0.448 0.546 1.188 0.000 0.267 0.000 0.000 0.000

Problem 223

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 69 62 58 0 216 0 0 0

N.S.

1 0.90 0.81 0.75 0.00 2.81 0.00 0.00 0.00

time (sec)

N/A 0.330 0.169 0.747 0.000 0.263 0.000 0.000 0.000

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

7 7 9 7 9 9 8 9 11

N.S.

1 1.00 1.29 1.00 1.29 1.29 1.14 1.29 1.57

time (sec)

N/A 0.305 6.181 0.253 0.636 0.258 3.951 0.374 2.312

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