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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 C A A A B A B A

verified

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

size

22 22 77 21 20 25 61 24 16 32

N.S.

1 1.00 3.50 0.95 0.91 1.14 2.77 1.09 0.73 1.45

time (sec)

N/A 0.011 0.045 0.090 0.406 0.355 4.142 0.003 0.141 6.104

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

32 32 41 50 0 44 0 208 49 0

N.S.

1 1.00 1.28 1.56 0.00 1.38 0.00 6.50 1.53 0.00

time (sec)

N/A 0.022 0.089 0.010 0.000 0.346 0.000 0.026 0.622 0.000

Problem 3

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

25 25 16 16 23 20 14 21 14 14

N.S.

1 1.00 0.64 0.64 0.92 0.80 0.56 0.84 0.56 0.56

time (sec)

N/A 0.012 0.008 0.017 0.279 0.373 0.186 0.000 0.163 1.848

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

58 58 68 42 112 46 0 80 -1 0

N.S.

1 1.00 1.17 0.72 1.93 0.79 0.00 1.38 -0.02 0.00

time (sec)

N/A 0.061 0.012 0.059 0.375 0.445 0.000 0.002 0.000 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A A A A B A B B

verified

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

size

50 50 26 42 56 67 838 39 88 86

N.S.

1 1.00 0.52 0.84 1.12 1.34 16.76 0.78 1.76 1.72

time (sec)

N/A 0.020 0.025 0.121 0.273 0.343 3.527 0.002 0.269 15.130

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A C C F B A A B C

verified

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

size

334 334 30 36 0 1058 26 344 313 37

N.S.

1 1.00 0.09 0.11 0.00 3.17 0.08 1.03 0.94 0.11

time (sec)

N/A 0.248 0.004 0.018 0.000 0.390 1.248 0.007 0.262 3.092

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

N/A N/A NO TBD TBD TBD TBD TBD TBD TBD

size

291 0 430 172 366 0 0 0 -1 0

N.S.

1 0.00 1.48 0.59 1.26 0.00 0.00 0.00 -0.00 0.00

time (sec)

N/A 0.031 0.737 0.148 0.377 0.000 0.000 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

308 0 654 199 378 0 0 0 -1 0

N.S.

1 0.00 2.12 0.65 1.23 0.00 0.00 0.00 -0.00 0.00

time (sec)

N/A 0.028 0.442 0.011 0.375 0.000 0.000 0.000 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

84 84 105 0 0 66 0 0 -1 0

N.S.

1 1.00 1.25 0.00 0.00 0.79 0.00 0.00 -0.01 0.00

time (sec)

N/A 0.039 0.120 0.010 0.000 0.336 0.000 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

41 41 41 34 51 101 112 71 -1 0

N.S.

1 1.00 1.00 0.83 1.24 2.46 2.73 1.73 -0.02 0.00

time (sec)

N/A 0.134 0.054 0.056 0.343 0.348 8.044 0.006 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

73 73 69 175 63 112 0 92 -1 0

N.S.

1 1.00 0.95 2.40 0.86 1.53 0.00 1.26 -0.01 0.00

time (sec)

N/A 0.084 0.059 0.096 0.363 0.349 0.000 0.021 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

73 73 52 60 77 110 0 106 -1 0

N.S.

1 1.00 0.71 0.82 1.05 1.51 0.00 1.45 -0.01 0.00

time (sec)

N/A 0.197 0.047 0.018 0.370 0.417 0.000 0.005 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

365 365 217 109 0 5235 0 0 -1 0

N.S.

1 1.00 0.59 0.30 0.00 14.34 0.00 0.00 -0.00 0.00

time (sec)

N/A 0.605 0.155 0.059 0.000 5.354 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

337 337 212 105 0 4535 0 0 -1 0

N.S.

1 1.00 0.63 0.31 0.00 13.46 0.00 0.00 -0.00 0.00

time (sec)

N/A 0.399 0.143 0.059 0.000 3.374 0.000 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

77 77 74 0 0 56 0 0 -1 0

N.S.

1 1.00 0.96 0.00 0.00 0.73 0.00 0.00 -0.01 0.00

time (sec)

N/A 0.047 10.041 0.007 0.000 0.621 0.000 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

118 118 112 0 0 73 0 0 -1 0

N.S.

1 1.00 0.95 0.00 0.00 0.62 0.00 0.00 -0.01 0.00

time (sec)

N/A 0.127 10.055 0.012 0.000 0.825 0.000 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

83 83 77 298 0 81 0 262 -1 0

N.S.

1 1.00 0.93 3.59 0.00 0.98 0.00 3.16 -0.01 0.00

time (sec)

N/A 0.070 0.147 0.018 0.000 1.862 0.000 0.020 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

96 96 89 0 0 122 0 0 -1 0

N.S.

1 1.00 0.93 0.00 0.00 1.27 0.00 0.00 -0.01 0.00

time (sec)

N/A 0.056 0.356 0.014 0.000 1.897 0.000 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A B B A A A B F C

verified

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

size

25 25 65 49 36 34 61 91 -1 61

N.S.

1 1.00 2.60 1.96 1.44 1.36 2.44 3.64 -0.04 2.44

time (sec)

N/A 0.050 0.106 0.036 0.337 0.344 2.023 0.015 0.000 4.681

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

25 25 126 33 35 55 0 93 -1 0

N.S.

1 1.00 5.04 1.32 1.40 2.20 0.00 3.72 -0.04 0.00

time (sec)

N/A 0.034 0.082 0.069 0.386 0.360 0.000 0.015 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD TBD

size

108 786 478 95 0 219 0 128 307 0

N.S.

1 7.28 4.43 0.88 0.00 2.03 0.00 1.19 2.84 0.00

time (sec)

N/A 0.790 6.233 0.129 0.000 0.390 0.000 0.004 1.247 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A A A A B A B A

verified

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

size

29 29 56 27 40 46 66 40 26 33

N.S.

1 1.00 1.93 0.93 1.38 1.59 2.28 1.38 0.90 1.14

time (sec)

N/A 0.013 0.023 0.086 0.273 0.347 0.370 0.002 0.278 2.700

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

26 26 26 20 43 68 0 26 19 0

N.S.

1 1.00 1.00 0.77 1.65 2.62 0.00 1.00 0.73 0.00

time (sec)

N/A 0.009 0.013 0.056 0.360 0.335 0.000 0.006 0.162 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

110 147 121 364 0 859 0 489 -1 0

N.S.

1 1.34 1.10 3.31 0.00 7.81 0.00 4.45 -0.01 0.00

time (sec)

N/A 0.390 0.078 0.097 0.000 0.364 0.000 0.091 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

40 40 54 75 0 0 0 0 -1 0

N.S.

1 1.00 1.35 1.88 0.00 0.00 0.00 0.00 -0.02 0.00

time (sec)

N/A 0.052 32.138 0.151 0.000 0.372 0.000 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD TBD

size

185 349 910 392 0 452 0 404 608 0

N.S.

1 1.89 4.92 2.12 0.00 2.44 0.00 2.18 3.29 0.00

time (sec)

N/A 0.697 0.343 0.101 0.000 0.359 0.000 0.031 2.183 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

102 102 102 83 0 0 0 0 -1 0

N.S.

1 1.00 1.00 0.81 0.00 0.00 0.00 0.00 -0.01 0.00

time (sec)

N/A 0.096 0.014 0.023 0.000 0.329 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

159 159 122 0 0 0 0 0 -1 0

N.S.

1 1.00 0.77 0.00 0.00 0.00 0.00 0.00 -0.01 0.00

time (sec)

N/A 0.127 0.060 0.099 0.000 0.322 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

A A A F F F F(-1) F F F(-2)

verified

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

size

395 395 347 0 0 0 0 0 -1 0

N.S.

1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 -0.00 0.00

time (sec)

N/A 0.354 0.153 0.075 0.000 0.337 0.000 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

981 981 868 722 0 0 0 0 -1 0

N.S.

1 1.00 0.88 0.74 0.00 0.00 0.00 0.00 -0.00 0.00

time (sec)

N/A 0.859 0.323 0.051 0.000 0.341 0.000 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD TBD

size

555 555 1076 0 0 0 0 0 -1 0

N.S.

1 1.00 1.94 0.00 0.00 0.00 0.00 0.00 -0.00 0.00

time (sec)

N/A 0.438 0.890 0.007 0.000 0.342 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

313 313 303 252 0 0 0 0 -1 0

N.S.

1 1.00 0.97 0.81 0.00 0.00 0.00 0.00 -0.00 0.00

time (sec)

N/A 0.234 0.056 0.014 0.000 0.342 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

80 80 262 113 84 220 0 0 -1 0

N.S.

1 1.00 3.28 1.41 1.05 2.75 0.00 0.00 -0.01 0.00

time (sec)

N/A 0.051 0.162 0.253 0.376 0.349 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

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

size

57 57 44 71 31 0 0 0 -1 0

N.S.

1 1.00 0.77 1.25 0.54 0.00 0.00 0.00 -0.02 0.00

time (sec)

N/A 0.047 0.049 0.493 0.386 0.337 0.000 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad Mathics

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD TBD

size

121 121 131 171 0 0 0 0 -1 0

N.S.

1 1.00 1.08 1.41 0.00 0.00 0.00 0.00 -0.01 0.00

time (sec)

N/A 0.065 0.138 0.331 0.000 0.344 0.000 0.000 0.000 0.000

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