[tail] [up]

2.2.1 Integrals 1 to 16

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 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

179 185 343 0 0 497 0 0 0

N.S.

1 1.03 1.92 0.00 0.00 2.78 0.00 0.00 0.00

time (sec)

N/A 0.712 0.199 0.000 0.000 0.268 0.000 0.000 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

119 121 199 0 0 305 0 0 0

N.S.

1 1.02 1.67 0.00 0.00 2.56 0.00 0.00 0.00

time (sec)

N/A 0.475 0.082 0.000 0.000 0.269 0.000 0.000 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 61 84 101 0 157 0 0 0

N.S.

1 1.00 1.38 1.66 0.00 2.57 0.00 0.00 0.00

time (sec)

N/A 0.298 0.042 0.309 0.000 0.262 0.000 0.000 0.000

Problem 4

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

14 14 16 14 16 16 12 16 18

N.S.

1 1.00 1.14 1.00 1.14 1.14 0.86 1.14 1.29

time (sec)

N/A 0.207 0.346 0.008 0.459 0.252 0.491 0.357 1.917

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 127 145 298 238 1332 0 0 0

N.S.

1 1.23 1.41 2.89 2.31 12.93 0.00 0.00 0.00

time (sec)

N/A 0.687 0.608 0.717 0.331 0.282 0.000 0.000 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 93 91 159 0 715 0 0 0

N.S.

1 1.27 1.25 2.18 0.00 9.79 0.00 0.00 0.00

time (sec)

N/A 0.483 0.497 0.692 0.000 0.260 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 51 57 72 161 0 78 50

N.S.

1 1.00 1.76 1.97 2.48 5.55 0.00 2.69 1.72

time (sec)

N/A 0.265 0.063 0.557 0.207 0.258 0.000 0.279 0.094

Problem 8

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

16 16 18 16 102 18 14 18 18

N.S.

1 1.00 1.12 1.00 6.38 1.12 0.88 1.12 1.12

time (sec)

N/A 0.216 1.797 0.008 0.296 0.255 0.483 0.263 1.928

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

296 306 455 0 0 4785 0 0 0

N.S.

1 1.03 1.54 0.00 0.00 16.17 0.00 0.00 0.00

time (sec)

N/A 1.233 6.323 0.000 0.000 0.359 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

175 183 270 0 0 2651 0 0 0

N.S.

1 1.05 1.54 0.00 0.00 15.15 0.00 0.00 0.00

time (sec)

N/A 0.725 2.031 0.000 0.000 0.322 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 104 156 216 0 1267 0 0 0

N.S.

1 1.02 1.53 2.12 0.00 12.42 0.00 0.00 0.00

time (sec)

N/A 0.410 0.609 0.585 0.000 0.277 0.000 0.000 0.000

Problem 12

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

16 16 18 16 321 18 14 18 18

N.S.

1 1.00 1.12 1.00 20.06 1.12 0.88 1.12 1.12

time (sec)

N/A 0.221 87.721 0.008 0.491 0.245 0.559 2.601 1.962

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 24 17 0 0 0 0 0 0

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.225 0.046 0.000 0.000 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 24 17 0 0 0 0 0 0

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.222 0.090 0.000 0.000 0.000 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

47 47 45 0 0 0 0 0 0

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.241 0.093 0.000 0.000 0.000 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

66 66 49 0 0 0 0 0 0

N.S.

1 1.00 0.74 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.302 0.094 0.000 0.000 0.000 0.000 0.000 0.000

[front] [up]