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2.2 Detailed conclusion table per each integral for all CAS systems

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A A F B F A F A

verified

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

size

28 28 28 27 0 52 0 46 -1 34

N.S.

1 1.00 1.00 0.96 0.00 1.86 0.00 1.64 -0.04 1.21

time (sec)

N/A 0.036 0.027 0.167 0.000 0.342 0.000 0.001 0.000 78.013

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A A A A A A B A

verified

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

size

2 2 2 3 2 2 2 2 2 2

N.S.

1 1.00 1.00 1.50 1.00 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.001 0.002 0.016 0.350 0.331 0.043 0.000 0.045 1.497

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A A B B A B B A

verified

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

size

14 14 14 19 25 25 8 35 10 6

N.S.

1 1.00 1.00 1.36 1.79 1.79 0.57 2.50 0.71 0.43

time (sec)

N/A 0.005 0.011 0.138 0.263 0.334 0.419 0.001 0.070 1.948

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A C A F F A F B C

verified

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

size

252 252 20 158 0 0 31 0 231 19

N.S.

1 1.00 0.08 0.63 0.00 0.00 0.12 0.00 0.92 0.08

time (sec)

N/A 0.051 9.830 0.046 0.000 0.326 0.341 0.000 0.249 1.967

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A A B B A B B C

verified

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

size

16 16 16 13 29 29 31 39 180 23

N.S.

1 1.00 1.00 0.81 1.81 1.81 1.94 2.44 11.25 1.44

time (sec)

N/A 0.007 0.013 0.131 0.265 0.320 0.448 0.001 0.145 2.062

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A C F A F F F F(-2)

verified

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

size

76 76 78 1290 0 72 0 0 -1 0

N.S.

1 1.00 1.03 16.97 0.00 0.95 0.00 0.00 -0.01 0.00

time (sec)

N/A 0.019 3.031 0.635 0.000 0.376 0.000 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A A B A A A B A

verified

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

size

13 13 13 17 144 16 10 18 11 11

N.S.

1 1.00 1.00 1.31 11.08 1.23 0.77 1.38 0.85 0.85

time (sec)

N/A 0.048 0.025 0.021 0.261 0.331 0.076 0.003 0.064 1.681

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A A B B F F B F(-2)

verified

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

size

42 42 42 43 142 85 0 0 32 0

N.S.

1 1.00 1.00 1.02 3.38 2.02 0.00 0.00 0.76 0.00

time (sec)

N/A 0.034 0.013 0.023 0.390 0.357 0.000 0.000 0.220 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A A C A A A F C

verified

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

size

2 2 2 3 13 2 2 2 -1 2

N.S.

1 1.00 1.00 1.50 6.50 1.00 1.00 1.00 -0.50 1.00

time (sec)

N/A 0.007 0.009 0.031 0.323 0.338 0.313 0.001 0.000 1.733

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A F A F(-2) F F B F(-2)

verified

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

size

17 17 17 0 21 0 0 0 14 0

N.S.

1 1.00 1.00 0.00 1.24 0.00 0.00 0.00 0.82 0.00

time (sec)

N/A 0.386 0.548 0.003 0.283 0.000 0.000 0.000 0.269 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A A A B A A B A

verified

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

size

13 13 13 12 11 24 12 16 11 11

N.S.

1 1.00 1.00 0.92 0.85 1.85 0.92 1.23 0.85 0.85

time (sec)

N/A 0.018 0.016 0.009 0.261 0.332 0.386 0.001 0.194 1.855

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A F A F F B F A B F(-1)

verified

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

size

13 0 13 0 0 24 0 15 11 0

N.S.

1 0.00 1.00 0.00 0.00 1.85 0.00 1.15 0.85 0.00

time (sec)

N/A 0.391 0.100 0.002 0.000 0.328 0.000 0.022 0.197 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A A F A A A B C

verified

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

size

23 23 23 26 0 19 19 24 19 19

N.S.

1 1.00 1.00 1.13 0.00 0.83 0.83 1.04 0.83 0.83

time (sec)

N/A 0.153 0.063 0.053 0.000 0.327 0.301 0.008 0.272 1.935

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A C F A A A B A

verified

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

size

39 39 41 40 0 22 24 22 22 21

N.S.

1 1.00 1.05 1.03 0.00 0.56 0.62 0.56 0.56 0.54

time (sec)

N/A 0.017 0.007 0.019 0.000 0.318 0.063 0.004 0.273 1.704

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