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2.2.1 Integrals 1 to 19

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 A A F(-2) A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 60 56 0 39 54 63 48

N.S.

1 1.00 0.77 0.72 0.00 0.50 0.69 0.81 0.62

time (sec)

N/A 0.053 0.129 0.259 0.000 3.117 0.084 0.426 0.324

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

29 29 42 93 0 26 36 69 74

N.S.

1 1.00 1.45 3.21 0.00 0.90 1.24 2.38 2.55

time (sec)

N/A 0.110 0.096 0.168 0.000 3.016 0.083 0.392 0.485

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 32 37 0 27 34 51 36

N.S.

1 1.00 0.64 0.74 0.00 0.54 0.68 1.02 0.72

time (sec)

N/A 0.042 0.069 0.256 0.000 2.374 0.060 0.407 0.253

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 19 49 0 14 17 31 40

N.S.

1 1.00 1.00 2.58 0.00 0.74 0.89 1.63 2.11

time (sec)

N/A 0.071 0.016 0.210 0.000 3.943 0.054 0.421 0.276

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

18 18 44 34 45 33 0 29 21

N.S.

1 1.00 2.44 1.89 2.50 1.83 0.00 1.61 1.17

time (sec)

N/A 0.072 0.040 0.214 0.278 3.696 0.000 0.408 0.250

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 17 13 12 36 0 53 12

N.S.

1 1.00 0.85 0.65 0.60 1.80 0.00 2.65 0.60

time (sec)

N/A 0.027 0.038 0.243 0.283 4.471 0.000 0.422 0.227

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 48 68 94 73 0 55 47

N.S.

1 1.00 2.18 3.09 4.27 3.32 0.00 2.50 2.14

time (sec)

N/A 0.107 0.160 0.250 0.280 5.672 0.000 0.448 0.303

Problem 8

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

19 19 24 18 13 30 0 13 13

N.S.

1 1.00 1.26 0.95 0.68 1.58 0.00 0.68 0.68

time (sec)

N/A 0.031 0.059 0.197 0.281 2.976 0.000 0.424 0.200

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 61 116 167 123 0 87 81

N.S.

1 1.00 1.52 2.90 4.18 3.08 0.00 2.18 2.02

time (sec)

N/A 0.129 0.649 0.262 0.298 3.498 0.000 0.404 0.460

Problem 10

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

37 37 26 31 25 48 0 25 27

N.S.

1 1.00 0.70 0.84 0.68 1.30 0.00 0.68 0.73

time (sec)

N/A 0.038 0.096 0.254 0.283 2.545 0.000 0.418 0.212

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 179 172 240 178 0 270 279

N.S.

1 1.00 1.42 1.37 1.90 1.41 0.00 2.14 2.21

time (sec)

N/A 0.240 0.646 0.362 0.504 3.487 0.000 0.453 0.497

Problem 12

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

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 0.156 1.196 0.394 0.528 2.901 0.000 0.447 0.671

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 82 98 122 95 0 155 118

N.S.

1 1.00 1.12 1.34 1.67 1.30 0.00 2.12 1.62

time (sec)

N/A 0.121 0.340 0.271 0.534 2.766 0.000 0.429 0.366

Problem 14

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

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 0.065 0.212 0.287 0.512 4.091 0.000 0.438 0.376

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD 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 0.083 0.099 0.369 0.505 3.870 0.000 0.436 0.657

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

29 29 27 21 20 57 0 21 20

N.S.

1 1.00 0.93 0.72 0.69 1.97 0.00 0.72 0.69

time (sec)

N/A 0.040 0.090 0.288 0.285 3.132 0.000 0.428 0.200

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B F B B

verified

N/A Yes Yes TBD 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 0.142 0.503 0.497 0.505 5.978 0.000 0.435 0.580

Problem 18

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

73 73 66 56 56 106 0 60 55

N.S.

1 1.00 0.90 0.77 0.77 1.45 0.00 0.82 0.75

time (sec)

N/A 0.078 0.301 0.367 0.283 2.464 0.000 0.411 0.223

Problem 19

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

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 0.061 0.058 0.276 0.524 2.869 0.000 0.441 0.322

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