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2.2.1 Integrals 1 to 22

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 Mupad

grade

N/A A B C B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 105 68 115 50 0 65 46

N.S.

1 1.00 3.18 2.06 3.48 1.52 0.00 1.97 1.39

time (sec)

N/A 0.371 0.198 0.636 0.207 0.293 0.000 0.323 13.922

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 17 18 15 15 0 15 13

N.S.

1 1.00 0.89 0.95 0.79 0.79 0.00 0.79 0.68

time (sec)

N/A 0.285 0.018 0.479 0.205 0.274 0.000 0.317 13.484

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 39 44 61 33 0 45 30

N.S.

1 1.00 2.60 2.93 4.07 2.20 0.00 3.00 2.00

time (sec)

N/A 0.295 0.132 0.513 0.211 0.333 0.000 0.333 13.527

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 22 12 16 18 20 0 19 14

N.S.

1 1.22 0.67 0.89 1.00 1.11 0.00 1.06 0.78

time (sec)

N/A 0.210 0.013 0.608 0.225 0.280 0.000 0.298 13.728

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 42 28 31 37 0 34 21

N.S.

1 1.00 1.27 0.85 0.94 1.12 0.00 1.03 0.64

time (sec)

N/A 0.359 0.027 0.514 0.232 0.270 0.000 0.304 14.066

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 29 25 29 42 24 0 37 35

N.S.

1 0.97 0.83 0.97 1.40 0.80 0.00 1.23 1.17

time (sec)

N/A 0.347 0.130 0.464 0.222 0.283 0.000 0.306 14.039

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 48 60 44 56 83 0 50 40

N.S.

1 1.04 1.30 0.96 1.22 1.80 0.00 1.09 0.87

time (sec)

N/A 0.456 0.104 0.543 0.237 0.279 0.000 0.307 13.841

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 35 41 45 70 53 0 59 45

N.S.

1 0.88 1.02 1.12 1.75 1.32 0.00 1.48 1.12

time (sec)

N/A 0.348 0.142 0.646 0.216 0.256 0.000 0.366 13.404

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 29 49 28 27 43 0 28 20

N.S.

1 0.88 1.48 0.85 0.82 1.30 0.00 0.85 0.61

time (sec)

N/A 0.218 0.045 0.953 0.220 0.256 0.000 0.291 14.137

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 133 190 219 0 332 0 226 1666

N.S.

1 1.18 1.68 1.94 0.00 2.94 0.00 2.00 14.74

time (sec)

N/A 0.858 0.806 1.099 0.000 0.377 0.000 0.310 14.846

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 59 46 58 56 66 0 66 115

N.S.

1 1.04 0.81 1.02 0.98 1.16 0.00 1.16 2.02

time (sec)

N/A 0.282 0.083 0.659 0.278 0.290 0.000 0.329 14.537

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 75 85 100 0 203 0 111 77

N.S.

1 1.23 1.39 1.64 0.00 3.33 0.00 1.82 1.26

time (sec)

N/A 0.576 0.142 0.643 0.000 0.303 0.000 0.329 14.256

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 22 20 21 20 22 0 22 48

N.S.

1 1.10 1.00 1.05 1.00 1.10 0.00 1.10 2.40

time (sec)

N/A 0.208 0.007 0.503 0.217 0.262 0.000 0.310 13.923

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 59 50 54 48 53 0 54 47

N.S.

1 1.09 0.93 1.00 0.89 0.98 0.00 1.00 0.87

time (sec)

N/A 0.248 0.059 0.666 0.224 0.262 0.000 0.324 14.061

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 88 67 78 0 230 0 91 86

N.S.

1 1.14 0.87 1.01 0.00 2.99 0.00 1.18 1.12

time (sec)

N/A 0.427 0.227 0.830 0.000 0.282 0.000 0.335 14.707

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 135 100 96 116 185 0 138 116

N.S.

1 1.45 1.08 1.03 1.25 1.99 0.00 1.48 1.25

time (sec)

N/A 0.387 0.380 0.902 0.211 0.316 0.000 0.320 14.304

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 151 112 127 0 456 0 210 183

N.S.

1 1.09 0.81 0.92 0.00 3.30 0.00 1.52 1.33

time (sec)

N/A 0.826 0.470 1.357 0.000 0.332 0.000 0.297 14.332

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

44 32 44 81 63 77 0 68 0

N.S.

1 0.73 1.00 1.84 1.43 1.75 0.00 1.55 0.00

time (sec)

N/A 0.228 0.083 1.683 0.305 0.292 0.000 0.311 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 37 123 46 109 0 34 0

N.S.

1 1.00 1.00 3.32 1.24 2.95 0.00 0.92 0.00

time (sec)

N/A 0.238 0.014 2.230 0.294 0.400 0.000 0.313 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 24 103 35 98 0 22 0

N.S.

1 1.00 1.00 4.29 1.46 4.08 0.00 0.92 0.00

time (sec)

N/A 0.230 0.008 1.707 0.295 0.294 0.000 0.312 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

204 170 363 454 0 0 0 0 0

N.S.

1 0.83 1.78 2.23 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.933 14.916 3.755 0.000 0.000 0.000 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

23 23 25 23 25 25 22 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.96 1.09 1.09

time (sec)

N/A 0.339 6.954 1.618 1.679 0.439 73.314 1.530 14.783

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