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2.2.1 Integrals 1 to 9

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 A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 24 11 10 13 15 22 14 18

N.S.

1 1.50 0.69 0.62 0.81 0.94 1.38 0.88 1.12

time (sec)

N/A 0.161 0.028 0.239 0.298 0.250 0.183 0.283 0.262

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 38 46 13 0 48 0 18 12

N.S.

1 2.00 2.42 0.68 0.00 2.53 0.00 0.95 0.63

time (sec)

N/A 2.618 1.413 0.805 0.000 0.264 0.000 0.306 0.309

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 42 19 35 53 43 32 36 32

N.S.

1 2.21 1.00 1.84 2.79 2.26 1.68 1.89 1.68

time (sec)

N/A 0.685 2.592 0.562 0.278 0.258 0.477 0.298 0.851

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 31 19 24 39 41 0 26 23

N.S.

1 1.63 1.00 1.26 2.05 2.16 0.00 1.37 1.21

time (sec)

N/A 1.491 0.192 0.506 0.290 0.267 0.000 0.295 0.553

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

43 0 61 17 63 31 0 18 27

N.S.

1 0.00 1.42 0.40 1.47 0.72 0.00 0.42 0.63

time (sec)

N/A 0.000 4.765 0.587 1.609 0.268 0.000 0.292 0.374

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

25 0 63 19 63 37 0 16 25

N.S.

1 0.00 2.52 0.76 2.52 1.48 0.00 0.64 1.00

time (sec)

N/A 0.000 0.582 0.565 1.629 0.267 0.000 0.279 0.342

Problem 7

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

14 22 79 12 15 13 27 25 20

N.S.

1 1.57 5.64 0.86 1.07 0.93 1.93 1.79 1.43

time (sec)

N/A 0.169 0.027 0.254 0.276 0.253 0.136 0.264 0.225

Problem 8

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

34 16 15 13 12 31 60 45 24

N.S.

1 0.47 0.44 0.38 0.35 0.91 1.76 1.32 0.71

time (sec)

N/A 0.170 0.063 0.184 0.290 0.248 0.251 0.273 0.221

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 60 50 53 0 364 2453 72 68

N.S.

1 1.11 0.93 0.98 0.00 6.74 45.43 1.33 1.26

time (sec)

N/A 0.224 0.109 0.325 0.000 0.306 116.384 0.277 0.330

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