[tail] [up]

2.2.1 Integrals 1 to 14

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 A F B F A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 28 21 0 52 0 34 0

N.S.

1 1.00 1.00 0.75 0.00 1.86 0.00 1.21 0.00

time (sec)

N/A 0.205 0.027 0.957 0.000 0.249 0.000 0.288 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

2 2 2 3 2 2 2 2 2

N.S.

1 1.00 1.00 1.50 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.106 0.002 0.056 0.279 0.241 0.039 0.277 0.050

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 11 25 25 8 25 10

N.S.

1 1.00 1.00 0.79 1.79 1.79 0.57 1.79 0.71

time (sec)

N/A 0.131 0.012 0.402 0.192 0.265 0.550 0.284 0.077

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

252 267 20 15 0 9 31 0 231

N.S.

1 1.06 0.08 0.06 0.00 0.04 0.12 0.00 0.92

time (sec)

N/A 0.317 10.019 0.158 0.000 0.069 0.401 0.000 0.245

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 13 29 29 31 30 180

N.S.

1 1.00 1.00 0.81 1.81 1.81 1.94 1.88 11.25

time (sec)

N/A 0.140 0.020 0.291 0.197 0.239 0.574 0.316 0.115

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 78 148 0 72 0 0 0

N.S.

1 1.00 1.03 1.95 0.00 0.95 0.00 0.00 0.00

time (sec)

N/A 0.192 3.950 1.160 0.000 0.300 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 26 17 144 16 10 16 11

N.S.

1 1.00 2.00 1.31 11.08 1.23 0.77 1.23 0.85

time (sec)

N/A 0.222 0.036 0.097 0.204 0.250 0.069 0.290 0.059

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 42 43 142 85 0 0 32

N.S.

1 1.00 1.00 1.02 3.38 2.02 0.00 0.00 0.76

time (sec)

N/A 0.193 0.010 0.078 0.307 0.265 0.000 0.000 0.192

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

2 2 2 3 13 2 2 2 0

N.S.

1 1.00 1.00 1.50 6.50 1.00 1.00 1.00 0.00

time (sec)

N/A 0.151 0.011 0.081 0.243 0.242 0.459 0.310 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

17 17 17 0 21 0 0 0 14

N.S.

1 1.00 1.00 0.00 1.24 0.00 0.00 0.00 0.82

time (sec)

N/A 0.693 0.592 0.000 0.256 0.000 0.000 0.000 0.288

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 13 12 11 24 12 12 11

N.S.

1 1.00 1.00 0.92 0.85 1.85 0.92 0.92 0.85

time (sec)

N/A 0.161 0.023 0.041 0.200 0.251 0.410 0.266 0.249

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A F F B F A B

verified

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

size

13 0 13 0 0 24 0 11 11

N.S.

1 0.00 1.00 0.00 0.00 1.85 0.00 0.85 0.85

time (sec)

N/A 0.000 0.177 0.000 0.000 0.242 0.000 0.333 0.229

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 23 26 0 19 19 24 19

N.S.

1 1.00 1.00 1.13 0.00 0.83 0.83 1.04 0.83

time (sec)

N/A 0.434 0.132 0.145 0.000 0.240 0.232 0.367 0.248

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 41 23 0 22 24 22 22

N.S.

1 1.00 1.05 0.59 0.00 0.56 0.62 0.56 0.56

time (sec)

N/A 0.180 0.009 0.076 0.000 0.236 0.055 0.281 0.252

[front] [up]