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Integrals 1 to 8

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 Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

10 10 9 11 9 9 7 9 10 10

N.S.

1 1.00 0.90 1.10 0.90 0.90 0.70 0.90 1.00 1.00

time (sec)

N/A 0.164 0.008 0.047 0.032 0.071 0.029 0.151 0.192 0.028

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

21 21 21 18 17 17 20 20 17 17

N.S.

1 1.00 1.00 0.86 0.81 0.81 0.95 0.95 0.81 0.81

time (sec)

N/A 0.191 0.008 0.056 0.027 0.128 0.062 0.118 0.201 0.044

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

25 25 25 18 17 17 20 20 17 17

N.S.

1 1.00 1.00 0.72 0.68 0.68 0.80 0.80 0.68 0.68

time (sec)

N/A 0.192 0.008 0.057 0.032 0.081 0.080 0.119 0.213 12.123

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C A F A F F F B

verified

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

size

153 175 142 132 0 36 0 0 71 88

N.S.

1 1.14 0.93 0.86 0.00 0.24 0.00 0.00 0.46 0.58

time (sec)

N/A 0.423 22.314 0.431 0.000 0.093 0.000 0.000 0.261 0.047

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A F C A F A F F F B

verified

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

size

131 0 133 115 0 20 0 0 55 56

N.S.

1 0.00 1.02 0.88 0.00 0.15 0.00 0.00 0.42 0.43

time (sec)

N/A 0.000 22.254 0.188 0.000 0.074 0.000 0.000 0.236 0.026

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C A F A F F F B

verified

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

size

53 53 68 48 0 8 0 0 28 43

N.S.

1 1.00 1.28 0.91 0.00 0.15 0.00 0.00 0.53 0.81

time (sec)

N/A 0.221 22.103 0.102 0.000 0.102 0.000 0.000 0.203 0.017

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A B C A F F F F F B

verified

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

size

61 133 93 50 0 0 0 0 33 44

N.S.

1 2.18 1.52 0.82 0.00 0.00 0.00 0.00 0.54 0.72

time (sec)

N/A 0.327 22.536 0.318 0.000 0.000 0.000 0.000 0.212 0.015

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C A F F F F F B

verified

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

size

221 277 209 186 0 0 0 0 44 153

N.S.

1 1.25 0.95 0.84 0.00 0.00 0.00 0.00 0.20 0.69

time (sec)

N/A 0.778 23.095 0.466 0.000 0.000 0.000 0.000 0.228 0.024

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