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2.2.1 Integrals 1 to 16

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 B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 46 40 27 157 30 0 78 25

N.S.

1 1.05 0.91 0.61 3.57 0.68 0.00 1.77 0.57

time (sec)

N/A 0.426 0.194 0.375 0.305 0.242 0.000 0.257 19.161

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

23 23 17 18 18 22 0 18 15

N.S.

1 1.00 0.74 0.78 0.78 0.96 0.00 0.78 0.65

time (sec)

N/A 0.337 0.029 0.302 0.229 0.239 0.000 0.261 17.949

Problem 3

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

27 27 27 19 81 18 0 44 17

N.S.

1 1.00 1.00 0.70 3.00 0.67 0.00 1.63 0.63

time (sec)

N/A 0.336 0.148 0.293 0.316 0.240 0.000 0.269 18.024

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

17 19 17 23 17 15 0 17 15

N.S.

1 1.12 1.00 1.35 1.00 0.88 0.00 1.00 0.88

time (sec)

N/A 0.269 0.019 0.351 0.230 0.247 0.000 0.264 0.068

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 17 28 31 35 0 34 20

N.S.

1 1.00 0.52 0.85 0.94 1.06 0.00 1.03 0.61

time (sec)

N/A 0.387 0.037 0.486 0.202 0.241 0.000 0.268 0.079

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 56 22 67 25 0 37 37

N.S.

1 1.00 2.43 0.96 2.91 1.09 0.00 1.61 1.61

time (sec)

N/A 0.365 0.227 0.464 0.214 0.245 0.000 0.273 18.157

Problem 7

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

46 48 25 36 54 70 0 48 44

N.S.

1 1.04 0.54 0.78 1.17 1.52 0.00 1.04 0.96

time (sec)

N/A 0.494 0.061 0.670 0.218 0.257 0.000 0.265 18.103

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 85 29 167 45 0 75 69

N.S.

1 1.00 2.50 0.85 4.91 1.32 0.00 2.21 2.03

time (sec)

N/A 0.395 0.270 0.779 0.209 0.240 0.000 0.278 18.330

Problem 9

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

130 150 127 255 0 335 0 278 2055

N.S.

1 1.15 0.98 1.96 0.00 2.58 0.00 2.14 15.81

time (sec)

N/A 0.762 0.909 0.974 0.000 0.276 0.000 0.278 19.214

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 60 60 60 60 60 0 62 58

N.S.

1 0.98 0.98 0.98 0.98 0.98 0.00 1.02 0.95

time (sec)

N/A 0.335 0.168 0.651 0.217 0.267 0.000 0.269 0.085

Problem 11

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

80 92 75 121 0 205 0 121 362

N.S.

1 1.15 0.94 1.51 0.00 2.56 0.00 1.51 4.52

time (sec)

N/A 0.507 0.194 0.521 0.000 0.269 0.000 0.275 18.631

Problem 12

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 19 19 31 20 20 0 21 20

N.S.

1 0.95 0.95 1.55 1.00 1.00 0.00 1.05 1.00

time (sec)

N/A 0.267 0.025 0.339 0.217 0.247 0.000 0.278 19.414

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

54 59 49 55 48 47 0 53 53

N.S.

1 1.09 0.91 1.02 0.89 0.87 0.00 0.98 0.98

time (sec)

N/A 0.293 0.094 0.530 0.228 0.254 0.000 0.281 18.153

Problem 14

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

65 71 97 92 0 243 0 95 104

N.S.

1 1.09 1.49 1.42 0.00 3.74 0.00 1.46 1.60

time (sec)

N/A 0.383 0.416 0.543 0.000 0.270 0.000 0.274 18.981

Problem 15

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

85 128 139 89 108 119 0 129 96

N.S.

1 1.51 1.64 1.05 1.27 1.40 0.00 1.52 1.13

time (sec)

N/A 0.425 0.602 0.964 0.234 0.296 0.000 0.256 19.524

Problem 16

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

109 128 121 176 0 395 0 187 298

N.S.

1 1.17 1.11 1.61 0.00 3.62 0.00 1.72 2.73

time (sec)

N/A 0.590 0.986 1.022 0.000 0.268 0.000 0.286 19.353

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