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2.2.1 Integrals 1 to 19

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 A A F(-2) A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 80 60 39 0 39 54 63 48

N.S.

1 1.03 0.77 0.50 0.00 0.50 0.69 0.81 0.62

time (sec)

N/A 0.261 0.483 0.095 0.000 0.260 0.100 0.264 12.528

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 31 42 29 0 26 36 69 74

N.S.

1 1.07 1.45 1.00 0.00 0.90 1.24 2.38 2.55

time (sec)

N/A 0.392 0.186 0.086 0.000 0.277 0.103 0.265 12.981

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 52 32 19 0 27 34 51 36

N.S.

1 1.04 0.64 0.38 0.00 0.54 0.68 1.02 0.72

time (sec)

N/A 0.239 0.358 0.130 0.000 0.266 0.075 0.263 12.274

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 23 19 16 0 14 17 31 40

N.S.

1 1.21 1.00 0.84 0.00 0.74 0.89 1.63 2.11

time (sec)

N/A 0.346 0.016 0.096 0.000 0.261 0.072 0.257 12.839

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 44 33 45 33 0 29 21

N.S.

1 1.00 2.44 1.83 2.50 1.83 0.00 1.61 1.17

time (sec)

N/A 0.338 0.087 0.099 0.221 0.277 0.000 0.261 12.707

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 19 16 13 12 36 0 53 12

N.S.

1 0.95 0.80 0.65 0.60 1.80 0.00 2.65 0.60

time (sec)

N/A 0.216 0.073 0.105 0.218 0.277 0.000 0.255 12.766

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 26 22 49 94 73 0 55 47

N.S.

1 1.18 1.00 2.23 4.27 3.32 0.00 2.50 2.14

time (sec)

N/A 0.385 0.157 0.099 0.247 0.279 0.000 0.264 13.034

Problem 8

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

19 19 16 15 13 30 0 13 13

N.S.

1 1.00 0.84 0.79 0.68 1.58 0.00 0.68 0.68

time (sec)

N/A 0.215 0.083 0.078 0.227 0.254 0.000 0.261 12.886

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 40 37 66 167 123 0 87 81

N.S.

1 1.00 0.92 1.65 4.18 3.08 0.00 2.18 2.02

time (sec)

N/A 0.411 0.156 0.122 0.235 0.278 0.000 0.257 12.910

Problem 10

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

37 37 30 28 25 48 0 25 27

N.S.

1 1.00 0.81 0.76 0.68 1.30 0.00 0.68 0.73

time (sec)

N/A 0.231 0.110 0.087 0.218 0.257 0.000 0.261 12.480

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 211 179 172 240 178 0 270 279

N.S.

1 1.67 1.42 1.37 1.90 1.41 0.00 2.14 2.21

time (sec)

N/A 0.556 0.946 2.458 0.396 0.296 0.000 0.260 13.132

Problem 12

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

123 123 112 170 279 214 0 201 291

N.S.

1 1.00 0.91 1.38 2.27 1.74 0.00 1.63 2.37

time (sec)

N/A 0.766 1.279 1.141 0.420 0.296 0.000 0.280 13.039

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 124 82 98 122 95 0 155 118

N.S.

1 1.70 1.12 1.34 1.67 1.30 0.00 2.12 1.62

time (sec)

N/A 0.355 0.497 0.404 0.412 0.297 0.000 0.256 12.621

Problem 14

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

65 65 61 81 105 144 0 94 93

N.S.

1 1.00 0.94 1.25 1.62 2.22 0.00 1.45 1.43

time (sec)

N/A 0.442 0.214 0.200 0.379 0.299 0.000 0.276 12.537

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 76 63 98 140 0 90 408

N.S.

1 1.00 1.62 1.34 2.09 2.98 0.00 1.91 8.68

time (sec)

N/A 0.353 0.188 0.201 0.380 0.325 0.000 0.286 12.618

Problem 16

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

29 35 19 21 20 57 0 21 20

N.S.

1 1.21 0.66 0.72 0.69 1.97 0.00 0.72 0.69

time (sec)

N/A 0.244 0.121 0.429 0.314 0.289 0.000 0.258 12.547

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 79 192 150 203 166 0 158 346

N.S.

1 1.00 2.43 1.90 2.57 2.10 0.00 2.00 4.38

time (sec)

N/A 0.439 0.760 1.215 0.342 0.328 0.000 0.284 13.022

Problem 18

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

73 81 56 56 56 106 0 60 55

N.S.

1 1.11 0.77 0.77 0.77 1.45 0.00 0.82 0.75

time (sec)

N/A 0.293 0.301 3.703 0.273 0.299 0.000 0.266 12.702

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 57 37 67 66 0 54 54

N.S.

1 1.00 2.28 1.48 2.68 2.64 0.00 2.16 2.16

time (sec)

N/A 0.310 0.130 0.131 0.356 0.294 0.000 0.288 12.811

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