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2.2.1 Integrals 1 to 23

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

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 111 84 194 58 0 80 83

N.S.

1 1.00 2.02 1.53 3.53 1.05 0.00 1.45 1.51

time (sec)

N/A 0.070 0.163 0.112 0.472 4.127 0.000 0.428 0.479

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 50 44 58 71 0 52 134

N.S.

1 1.00 0.74 0.65 0.85 1.04 0.00 0.76 1.97

time (sec)

N/A 0.052 0.152 0.109 0.263 3.172 0.000 0.405 0.435

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 62 54 94 38 0 49 51

N.S.

1 1.00 1.59 1.38 2.41 0.97 0.00 1.26 1.31

time (sec)

N/A 0.058 0.109 0.080 0.467 2.780 0.000 0.420 0.291

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 30 28 31 35 0 34 62

N.S.

1 1.00 0.75 0.70 0.78 0.88 0.00 0.85 1.55

time (sec)

N/A 0.037 0.062 0.095 0.262 3.124 0.000 0.426 0.339

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

9 9 9 17 9 9 0 9 25

N.S.

1 1.00 1.00 1.89 1.00 1.00 0.00 1.00 2.78

time (sec)

N/A 0.018 0.012 0.060 0.262 3.769 0.000 0.412 0.294

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 30 18 30 25 0 17 45

N.S.

1 1.00 2.00 1.20 2.00 1.67 0.00 1.13 3.00

time (sec)

N/A 0.029 0.038 0.073 0.467 2.975 0.000 0.411 0.282

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 11 13 18 19 0 14 36

N.S.

1 1.00 0.69 0.81 1.12 1.19 0.00 0.88 2.25

time (sec)

N/A 0.030 0.024 0.069 0.261 3.074 0.000 0.413 0.304

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 90 51 86 64 0 65 85

N.S.

1 1.00 2.90 1.65 2.77 2.06 0.00 2.10 2.74

time (sec)

N/A 0.044 0.043 0.095 0.466 4.479 0.000 0.422 0.298

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 26 25 29 45 0 29 80

N.S.

1 1.00 0.72 0.69 0.81 1.25 0.00 0.81 2.22

time (sec)

N/A 0.036 0.034 0.112 0.267 3.564 0.000 0.415 0.297

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 163 83 134 104 0 109 123

N.S.

1 1.00 3.33 1.69 2.73 2.12 0.00 2.22 2.51

time (sec)

N/A 0.061 0.050 0.097 0.465 3.360 0.000 0.424 0.333

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 39 41 42 70 0 41 113

N.S.

1 1.00 0.67 0.71 0.72 1.21 0.00 0.71 1.95

time (sec)

N/A 0.043 0.058 0.113 0.271 2.621 0.000 0.413 0.431

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

178 178 172 160 251 260 0 252 445

N.S.

1 1.00 0.97 0.90 1.41 1.46 0.00 1.42 2.50

time (sec)

N/A 0.206 0.867 0.272 0.272 3.755 0.000 0.401 2.300

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 113 115 101 120 144 0 139 172

N.S.

1 1.00 1.02 0.89 1.06 1.27 0.00 1.23 1.52

time (sec)

N/A 0.118 0.527 0.162 0.268 2.879 0.000 0.403 1.137

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 56 60 50 58 0 53 80

N.S.

1 1.00 0.85 0.91 0.76 0.88 0.00 0.80 1.21

time (sec)

N/A 0.064 0.066 0.107 0.260 3.195 0.000 0.403 0.442

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 11 21 11 11 0 12 55

N.S.

1 1.00 0.58 1.11 0.58 0.58 0.00 0.63 2.89

time (sec)

N/A 0.017 0.011 0.055 0.263 4.124 0.000 0.430 0.418

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 39 43 42 47 0 44 75

N.S.

1 1.00 1.03 1.13 1.11 1.24 0.00 1.16 1.97

time (sec)

N/A 0.045 0.054 0.117 0.265 3.052 0.000 0.427 0.459

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 85 86 84 151 0 90 157

N.S.

1 1.00 1.18 1.19 1.17 2.10 0.00 1.25 2.18

time (sec)

N/A 0.061 0.150 0.164 0.255 2.503 0.000 0.412 0.567

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 132 149 149 327 0 155 284

N.S.

1 1.00 1.08 1.22 1.22 2.68 0.00 1.27 2.33

time (sec)

N/A 0.090 0.312 0.206 0.262 2.904 0.000 0.406 0.870

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 205 194 190 0 483 0 216 2500

N.S.

1 1.29 1.22 1.19 0.00 3.04 0.00 1.36 15.72

time (sec)

N/A 0.216 1.161 0.204 0.000 3.505 0.000 0.424 7.377

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 112 87 106 0 296 0 103 2341

N.S.

1 1.33 1.04 1.26 0.00 3.52 0.00 1.23 27.87

time (sec)

N/A 0.123 0.276 0.138 0.000 3.433 0.000 0.419 2.258

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

61 61 71 75 0 206 0 80 697

N.S.

1 1.00 1.16 1.23 0.00 3.38 0.00 1.31 11.43

time (sec)

N/A 0.121 0.075 0.123 0.000 4.278 0.000 0.435 0.526

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 158 141 0 453 0 163 2163

N.S.

1 1.00 1.74 1.55 0.00 4.98 0.00 1.79 23.77

time (sec)

N/A 0.190 0.446 0.197 0.000 4.760 0.000 0.405 1.190

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

186 186 312 251 0 852 0 299 2500

N.S.

1 1.00 1.68 1.35 0.00 4.58 0.00 1.61 13.44

time (sec)

N/A 0.184 0.968 0.256 0.000 4.157 0.000 0.443 1.586

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