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Integrals 1 to 20

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 F F F F F F F(-1)

verified

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

size

71 71 71 0 0 0 0 0 6 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.08 0.00

time (sec)

N/A 0.301 0.102 0.000 0.000 0.000 0.000 0.000 0.165 0.000

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

9 9 9 9 9 8 7 10 9 8

N.S.

1 1.00 1.00 1.00 1.00 0.89 0.78 1.11 1.00 0.89

time (sec)

N/A 0.305 0.121 0.093 0.116 0.083 0.227 0.138 0.150 24.250

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

35 35 28 26 0 28 65 0 26 25

N.S.

1 1.00 0.80 0.74 0.00 0.80 1.86 0.00 0.74 0.71

time (sec)

N/A 0.438 0.426 0.227 0.000 0.073 0.714 0.000 0.156 0.112

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

58 60 38 36 0 46 155 0 41 53

N.S.

1 1.03 0.66 0.62 0.00 0.79 2.67 0.00 0.71 0.91

time (sec)

N/A 0.583 0.613 0.660 0.000 0.071 1.813 0.000 0.145 0.140

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

27 27 25 23 0 30 0 0 29 25

N.S.

1 1.00 0.93 0.85 0.00 1.11 0.00 0.00 1.07 0.93

time (sec)

N/A 0.336 0.156 0.070 0.000 0.078 0.000 0.000 0.170 0.138

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

55 55 51 35 0 50 0 0 46 42

N.S.

1 1.00 0.93 0.64 0.00 0.91 0.00 0.00 0.84 0.76

time (sec)

N/A 0.485 0.278 0.066 0.000 0.078 0.000 0.000 0.157 24.197

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

82 90 95 45 0 68 0 0 61 58

N.S.

1 1.10 1.16 0.55 0.00 0.83 0.00 0.00 0.74 0.71

time (sec)

N/A 0.663 0.344 0.072 0.000 0.083 0.000 0.000 0.177 0.160

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

147 147 89 0 0 0 0 0 26 0

N.S.

1 1.00 0.61 0.00 0.00 0.00 0.00 0.00 0.18 0.00

time (sec)

N/A 0.732 0.250 0.000 0.000 0.000 0.000 0.000 0.166 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

147 147 89 0 0 0 0 0 26 0

N.S.

1 1.00 0.61 0.00 0.00 0.00 0.00 0.00 0.18 0.00

time (sec)

N/A 0.757 0.272 0.000 0.000 0.000 0.000 0.000 0.176 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

207 207 89 0 0 0 0 0 47 0

N.S.

1 1.00 0.43 0.00 0.00 0.00 0.00 0.00 0.23 0.00

time (sec)

N/A 1.011 0.260 0.000 0.000 0.000 0.000 0.000 0.163 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

207 207 89 0 0 0 0 0 47 0

N.S.

1 1.00 0.43 0.00 0.00 0.00 0.00 0.00 0.23 0.00

time (sec)

N/A 1.037 0.274 0.000 0.000 0.000 0.000 0.000 0.174 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

272 269 100 0 0 0 0 0 66 0

N.S.

1 0.99 0.37 0.00 0.00 0.00 0.00 0.00 0.24 0.00

time (sec)

N/A 1.362 0.286 0.000 0.000 0.000 0.000 0.000 0.183 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1 0 46 0 100 59 37 77 17 0

N.S.

1 0.00 46.00 0.00 100.00 59.00 37.00 77.00 17.00 0.00

time (sec)

N/A 0.000 0.068 0.000 0.043 0.067 0.240 0.138 0.164 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1 0 34 0 43 25 20 21 17 0

N.S.

1 0.00 34.00 0.00 43.00 25.00 20.00 21.00 17.00 0.00

time (sec)

N/A 0.000 0.028 0.000 0.038 0.078 0.106 0.135 0.162 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1 0 34 0 43 25 20 21 19 0

N.S.

1 0.00 34.00 0.00 43.00 25.00 20.00 21.00 19.00 0.00

time (sec)

N/A 0.000 0.027 0.000 0.043 0.069 0.105 0.118 0.150 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1 0 46 0 100 59 37 77 19 0

N.S.

1 0.00 46.00 0.00 100.00 59.00 37.00 77.00 19.00 0.00

time (sec)

N/A 0.000 0.059 0.000 0.047 0.068 0.241 0.138 0.174 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1 0 82 0 96 125 0 0 17 0

N.S.

1 0.00 82.00 0.00 96.00 125.00 0.00 0.00 17.00 0.00

time (sec)

N/A 0.000 0.160 0.000 0.072 0.088 0.000 0.000 0.158 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1 0 65 0 61 79 0 0 16 0

N.S.

1 0.00 65.00 0.00 61.00 79.00 0.00 0.00 16.00 0.00

time (sec)

N/A 0.000 0.119 0.000 0.056 0.078 0.000 0.000 0.154 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1 0 65 0 61 79 0 0 18 0

N.S.

1 0.00 65.00 0.00 61.00 79.00 0.00 0.00 18.00 0.00

time (sec)

N/A 0.000 0.114 0.000 0.201 0.075 0.000 0.000 0.155 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1 0 82 0 96 79 0 0 19 0

N.S.

1 0.00 82.00 0.00 96.00 79.00 0.00 0.00 19.00 0.00

time (sec)

N/A 0.000 0.162 0.000 0.194 0.079 0.000 0.000 0.174 0.000

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