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2.2.1 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 B A B B

verified

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

size

40 40 23 20 23 36 116 23 32 23

N.S.

1 1.00 0.58 0.50 0.58 0.90 2.90 0.58 0.80 0.58

time (sec)

N/A 0.149 0.021 0.420 0.215 0.218 0.290 0.324 0.001 0.349

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 24 24 19 35 40 20 38 34 18

N.S.

1 1.00 1.00 0.79 1.46 1.67 0.83 1.58 1.42 0.75

time (sec)

N/A 0.159 0.043 0.050 0.289 0.228 0.062 0.292 0.001 0.515

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

42 42 41 36 0 137 144 61 51 38

N.S.

1 1.00 0.98 0.86 0.00 3.26 3.43 1.45 1.21 0.90

time (sec)

N/A 0.197 0.038 0.108 0.000 0.254 1.696 0.289 0.001 0.668

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

15 15 34 12 15 23 10 12 11 11

N.S.

1 1.00 2.27 0.80 1.00 1.53 0.67 0.80 0.73 0.73

time (sec)

N/A 0.170 0.022 0.216 0.213 0.227 0.122 0.293 0.000 0.084

Problem 5

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 39 20 29 21 19 21 19 11

N.S.

1 1.00 1.86 0.95 1.38 1.00 0.90 1.00 0.90 0.52

time (sec)

N/A 0.171 0.020 0.217 0.214 0.238 0.120 0.291 0.001 0.386

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

12 21 26 11 15 20 8 10 15 10

N.S.

1 1.75 2.17 0.92 1.25 1.67 0.67 0.83 1.25 0.83

time (sec)

N/A 0.169 0.074 0.172 0.210 0.237 0.208 0.328 0.000 0.353

Problem 7

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

43 27 24 20 23 39 42 49 18 21

N.S.

1 0.63 0.56 0.47 0.53 0.91 0.98 1.14 0.42 0.49

time (sec)

N/A 0.182 0.027 0.208 0.300 0.229 0.205 0.296 0.000 0.048

Problem 8

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

30 33 31 35 34 38 32 36 53 28

N.S.

1 1.10 1.03 1.17 1.13 1.27 1.07 1.20 1.77 0.93

time (sec)

N/A 0.158 0.006 0.042 0.226 0.228 0.078 0.302 0.001 0.382

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