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Integrals 301 to 316

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 301

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

136 140 153 370 0 684 0 153 410 0

N.S.

1 1.03 1.12 2.72 0.00 5.03 0.00 1.12 3.01 0.00

time (sec)

N/A 0.283 2.679 1.412 0.000 0.096 0.000 0.283 0.226 0.000

Problem 302

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

220 192 253 494 0 588 0 0 492 0

N.S.

1 0.87 1.15 2.25 0.00 2.67 0.00 0.00 2.24 0.00

time (sec)

N/A 0.316 1.949 1.355 0.000 0.117 0.000 0.000 0.233 0.000

Problem 303

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

172 156 205 350 0 488 0 0 347 0

N.S.

1 0.91 1.19 2.03 0.00 2.84 0.00 0.00 2.02 0.00

time (sec)

N/A 0.280 5.215 1.394 0.000 0.109 0.000 0.000 0.204 0.000

Problem 304

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

128 124 185 234 0 406 0 117 227 0

N.S.

1 0.97 1.45 1.83 0.00 3.17 0.00 0.91 1.77 0.00

time (sec)

N/A 0.260 5.095 1.310 0.000 0.109 0.000 0.415 0.234 0.000

Problem 305

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

115 141 171 272 0 454 0 117 117 0

N.S.

1 1.23 1.49 2.37 0.00 3.95 0.00 1.02 1.02 0.00

time (sec)

N/A 0.281 10.316 1.377 0.000 0.112 0.000 0.454 0.247 0.000

Problem 306

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

119 126 165 422 0 631 0 158 241 0

N.S.

1 1.06 1.39 3.55 0.00 5.30 0.00 1.33 2.03 0.00

time (sec)

N/A 0.250 10.929 1.497 0.000 0.111 0.000 0.442 0.207 0.000

Problem 307

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

97 97 68 58 0 200 0 122 118 172

N.S.

1 1.00 0.70 0.60 0.00 2.06 0.00 1.26 1.22 1.77

time (sec)

N/A 0.243 10.069 1.410 0.000 0.086 0.000 0.599 0.206 11.708

Problem 308

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

145 140 91 90 0 325 0 218 233 251

N.S.

1 0.97 0.63 0.62 0.00 2.24 0.00 1.50 1.61 1.73

time (sec)

N/A 0.265 10.101 1.522 0.000 0.094 0.000 0.728 0.238 11.875

Problem 309

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

193 185 120 135 0 476 0 341 383 336

N.S.

1 0.96 0.62 0.70 0.00 2.47 0.00 1.77 1.98 1.74

time (sec)

N/A 0.286 7.930 1.578 0.000 0.098 0.000 0.767 0.210 11.910

Problem 310

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

241 230 152 191 0 653 0 491 566 436

N.S.

1 0.95 0.63 0.79 0.00 2.71 0.00 2.04 2.35 1.81

time (sec)

N/A 0.303 8.336 1.451 0.000 0.112 0.000 0.415 0.220 12.910

Problem 311

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

145 145 135 0 0 0 0 0 38 0

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 0.26 0.00

time (sec)

N/A 0.363 0.793 0.000 0.000 0.000 0.000 0.000 200.038 0.000

Problem 312

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

143 143 124 0 0 0 0 0 36 0

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 0.25 0.00

time (sec)

N/A 0.311 0.498 0.000 0.000 0.000 0.000 0.000 200.033 0.000

Problem 313

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

134 134 123 0 0 0 0 0 31 0

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 0.23 0.00

time (sec)

N/A 0.265 0.317 0.000 0.000 0.000 0.000 0.000 200.033 0.000

Problem 314

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

142 142 132 0 0 0 0 0 38 0

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 0.27 0.00

time (sec)

N/A 0.319 0.433 0.000 0.000 0.000 0.000 0.000 200.058 0.000

Problem 315

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

143 143 133 0 0 0 0 0 38 0

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 0.27 0.00

time (sec)

N/A 0.322 0.418 0.000 0.000 0.000 0.000 0.000 200.045 0.000

Problem 316

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

147 148 138 0 0 0 0 0 38 0

N.S.

1 1.01 0.94 0.00 0.00 0.00 0.00 0.00 0.26 0.00

time (sec)

N/A 0.315 0.420 0.000 0.000 0.000 0.000 0.000 200.045 0.000

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