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2.2.2 Integrals 101 to 113

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 101

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

20 18 18 15 14 14 24 14 14

N.S.

1 0.90 0.90 0.75 0.70 0.70 1.20 0.70 0.70

time (sec)

N/A 0.153 0.035 0.053 0.265 0.250 0.051 0.296 0.073

Problem 102

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

33 40 33 27 26 32 31 26 26

N.S.

1 1.21 1.00 0.82 0.79 0.97 0.94 0.79 0.79

time (sec)

N/A 0.151 0.011 0.028 0.283 0.250 0.054 0.280 0.002

Problem 103

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

21 21 21 20 19 31 15 19 19

N.S.

1 1.00 1.00 0.95 0.90 1.48 0.71 0.90 0.90

time (sec)

N/A 0.134 0.000 0.035 0.187 0.253 0.016 0.274 0.003

Problem 104

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

26 26 26 25 24 40 19 24 24

N.S.

1 1.00 1.00 0.96 0.92 1.54 0.73 0.92 0.92

time (sec)

N/A 0.142 0.000 0.039 0.184 0.252 0.018 0.268 0.002

Problem 105

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

27 27 27 26 25 43 22 25 25

N.S.

1 1.00 1.00 0.96 0.93 1.59 0.81 0.93 0.93

time (sec)

N/A 0.141 0.000 0.043 0.186 0.238 0.017 0.273 0.002

Problem 106

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

32 32 32 31 30 52 26 30 30

N.S.

1 1.00 1.00 0.97 0.94 1.62 0.81 0.94 0.94

time (sec)

N/A 0.147 0.000 0.049 0.189 0.240 0.018 0.262 0.003

Problem 107

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

24 24 25 24 23 41 20 23 23

N.S.

1 1.00 1.04 1.00 0.96 1.71 0.83 0.96 0.96

time (sec)

N/A 0.144 0.000 0.043 0.189 0.238 0.015 0.300 0.003

Problem 108

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

29 29 30 29 28 50 24 28 28

N.S.

1 1.00 1.03 1.00 0.97 1.72 0.83 0.97 0.97

time (sec)

N/A 0.148 0.000 0.050 0.188 0.241 0.017 0.266 0.003

Problem 109

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

19 19 19 19 18 18 17 18 18

N.S.

1 1.00 1.00 1.00 0.95 0.95 0.89 0.95 0.95

time (sec)

N/A 0.132 0.000 0.030 0.178 0.240 0.012 0.268 0.003

Problem 110

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

24 24 24 24 23 23 20 23 23

N.S.

1 1.00 1.00 1.00 0.96 0.96 0.83 0.96 0.96

time (sec)

N/A 0.134 0.000 0.029 0.185 0.233 0.012 0.271 0.003

Problem 111

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

25 25 25 25 24 44 24 24 24

N.S.

1 1.00 1.00 1.00 0.96 1.76 0.96 0.96 0.96

time (sec)

N/A 0.137 0.000 0.030 0.178 0.230 0.012 0.276 0.003

Problem 112

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

30 30 30 30 29 52 27 29 29

N.S.

1 1.00 1.00 1.00 0.97 1.73 0.90 0.97 0.97

time (sec)

N/A 0.141 0.000 0.032 0.184 0.227 0.013 0.265 0.003

Problem 113

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

27 27 28 27 26 26 24 26 26

N.S.

1 1.00 1.04 1.00 0.96 0.96 0.89 0.96 0.96

time (sec)

N/A 0.137 0.000 0.027 0.180 0.236 0.012 0.273 0.002

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