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2.2.1 Integrals 1 to 19

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 C A B A F(-1) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 107 23 248 24 0 425 22

N.S.

1 1.00 5.35 1.15 12.40 1.20 0.00 21.25 1.10

time (sec)

N/A 0.198 0.134 3.064 0.558 0.257 0.000 3.536 12.937

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 59 48 42 42 141 54 23

N.S.

1 1.00 3.28 2.67 2.33 2.33 7.83 3.00 1.28

time (sec)

N/A 0.184 0.079 1.495 0.204 0.306 0.438 0.294 12.853

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 39 38 44 35 236 43 43

N.S.

1 1.00 2.17 2.11 2.44 1.94 13.11 2.39 2.39

time (sec)

N/A 0.182 0.108 1.105 0.216 0.264 0.326 0.288 13.546

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 44 35 29 29 100 36 22

N.S.

1 1.00 2.44 1.94 1.61 1.61 5.56 2.00 1.22

time (sec)

N/A 0.192 0.063 1.166 0.203 0.250 0.211 0.297 13.296

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 31 29 34 28 148 29 18

N.S.

1 1.00 1.72 1.61 1.89 1.56 8.22 1.61 1.00

time (sec)

N/A 0.186 0.042 0.776 0.214 0.245 0.156 0.301 13.136

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 51 24 22 22 53 24 21

N.S.

1 1.00 2.83 1.33 1.22 1.22 2.94 1.33 1.17

time (sec)

N/A 0.177 0.050 0.845 0.208 0.250 0.107 0.325 0.049

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 33 15 26 16 49 14 14

N.S.

1 1.00 2.06 0.94 1.62 1.00 3.06 0.88 0.88

time (sec)

N/A 0.144 0.003 0.381 0.211 0.277 0.080 0.285 13.029

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 22 11 10 10 4124 28 10

N.S.

1 1.00 2.20 1.10 1.00 1.00 412.40 2.80 1.00

time (sec)

N/A 0.153 0.007 0.345 0.224 0.270 10.219 0.292 0.018

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 10 11 12 18 0 12 10

N.S.

1 1.00 1.00 1.10 1.20 1.80 0.00 1.20 1.00

time (sec)

N/A 0.168 0.010 0.609 0.213 0.247 0.000 0.294 12.584

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 107 17 23 24 0 45 23

N.S.

1 1.00 6.69 1.06 1.44 1.50 0.00 2.81 1.44

time (sec)

N/A 0.181 0.051 0.937 0.217 0.241 0.000 0.293 12.860

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 34 22 32 0 22 18

N.S.

1 1.00 1.00 1.89 1.22 1.78 0.00 1.22 1.00

time (sec)

N/A 0.185 0.177 1.194 0.220 0.246 0.000 0.303 12.990

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 39 34 32 32 0 90 22

N.S.

1 1.00 2.17 1.89 1.78 1.78 0.00 5.00 1.22

time (sec)

N/A 0.186 0.074 1.061 0.215 0.262 0.000 0.316 13.283

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

171 173 1794 0 0 0 0 0 0

N.S.

1 1.01 10.49 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.615 26.440 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 F F F F F(-1) F F(-1)

verified

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

size

211 211 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.556 0.000 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 F F F F F(-1) F F(-1)

verified

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

size

286 286 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.632 0.000 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 A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 65 109 73 60 60 153 76 58

N.S.

1 0.89 1.49 1.00 0.82 0.82 2.10 1.04 0.79

time (sec)

N/A 0.246 0.080 1.310 0.212 0.261 0.440 0.455 0.074

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

184 186 300 0 0 0 0 0 0

N.S.

1 1.01 1.63 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.667 22.285 0.000 0.000 0.000 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

215 215 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.552 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

304 304 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.670 0.000 0.000 0.000 0.000 0.000 0.000 0.000

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