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2.2.1 Integrals 1 to 24

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 A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 98 163 112 145 161 0 155 242

N.S.

1 1.08 1.79 1.23 1.59 1.77 0.00 1.70 2.66

time (sec)

N/A 0.580 0.289 1.444 0.240 0.249 0.000 0.294 18.940

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

72 85 116 74 87 135 0 123 118

N.S.

1 1.18 1.61 1.03 1.21 1.88 0.00 1.71 1.64

time (sec)

N/A 0.560 0.190 1.037 0.234 0.260 0.000 0.288 18.710

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 59 137 67 80 103 0 93 84

N.S.

1 1.16 2.69 1.31 1.57 2.02 0.00 1.82 1.65

time (sec)

N/A 0.415 0.112 0.760 0.239 0.240 0.000 0.282 19.696

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 41 72 31 50 51 0 47 129

N.S.

1 1.24 2.18 0.94 1.52 1.55 0.00 1.42 3.91

time (sec)

N/A 0.365 0.064 0.822 0.230 0.263 0.000 0.268 19.493

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 50 33 31 47 38 0 79 116

N.S.

1 1.19 0.79 0.74 1.12 0.90 0.00 1.88 2.76

time (sec)

N/A 0.359 0.167 0.699 0.249 0.255 0.000 0.267 18.920

Problem 6

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 68 43 42 60 49 0 95 153

N.S.

1 1.26 0.80 0.78 1.11 0.91 0.00 1.76 2.83

time (sec)

N/A 0.463 0.223 1.005 0.249 0.249 0.000 0.267 19.544

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 64 117 55 120 129 0 107 56

N.S.

1 1.05 1.92 0.90 1.97 2.11 0.00 1.75 0.92

time (sec)

N/A 0.431 0.173 0.957 0.234 0.247 0.000 0.282 19.259

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 17 35 42 36 54 15 15

N.S.

1 1.00 1.00 2.06 2.47 2.12 3.18 0.88 0.88

time (sec)

N/A 0.279 0.021 0.931 0.232 0.235 0.848 0.277 19.010

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 79 45 68 86 0 101 56

N.S.

1 1.00 2.08 1.18 1.79 2.26 0.00 2.66 1.47

time (sec)

N/A 0.319 0.054 0.595 0.243 0.244 0.000 0.276 18.865

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 22 46 26 40 45 0 60 40

N.S.

1 0.81 1.70 0.96 1.48 1.67 0.00 2.22 1.48

time (sec)

N/A 0.268 0.069 0.579 0.240 0.250 0.000 0.264 19.071

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 25 22 37 26 54 35 53

N.S.

1 1.00 0.86 0.76 1.28 0.90 1.86 1.21 1.83

time (sec)

N/A 0.264 0.031 0.506 0.238 0.244 2.332 0.262 19.464

Problem 12

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

17 17 17 31 36 15 0 56 15

N.S.

1 1.00 1.00 1.82 2.12 0.88 0.00 3.29 0.88

time (sec)

N/A 0.273 0.010 0.818 0.233 0.245 0.000 0.269 20.345

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 64 117 55 120 129 0 107 56

N.S.

1 1.05 1.92 0.90 1.97 2.11 0.00 1.75 0.92

time (sec)

N/A 0.422 0.024 0.892 0.228 0.248 0.000 0.283 18.766

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 17 35 42 36 54 15 15

N.S.

1 1.00 1.00 2.06 2.47 2.12 3.18 0.88 0.88

time (sec)

N/A 0.278 0.015 0.861 0.223 0.235 0.830 0.271 18.878

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 79 45 68 86 0 101 56

N.S.

1 1.00 2.08 1.18 1.79 2.26 0.00 2.66 1.47

time (sec)

N/A 0.306 0.022 0.542 0.235 0.262 0.000 0.277 18.846

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 22 46 26 33 45 75 60 40

N.S.

1 0.81 1.70 0.96 1.22 1.67 2.78 2.22 1.48

time (sec)

N/A 0.257 0.019 0.300 0.220 0.255 6.254 0.271 18.684

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 25 22 37 26 85 35 53

N.S.

1 1.00 0.86 0.76 1.28 0.90 2.93 1.21 1.83

time (sec)

N/A 0.260 0.012 0.333 0.233 0.244 3.384 0.275 19.434

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 17 31 36 15 83 56 15

N.S.

1 1.00 1.00 1.82 2.12 0.88 4.88 3.29 0.88

time (sec)

N/A 0.262 0.008 0.592 0.226 0.228 4.949 0.283 18.734

Problem 19

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

91 98 163 112 145 161 0 155 242

N.S.

1 1.08 1.79 1.23 1.59 1.77 0.00 1.70 2.66

time (sec)

N/A 0.555 0.155 1.427 0.236 0.251 0.000 0.282 19.277

Problem 20

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

70 85 116 74 87 135 0 123 119

N.S.

1 1.21 1.66 1.06 1.24 1.93 0.00 1.76 1.70

time (sec)

N/A 0.553 0.099 1.296 0.233 0.249 0.000 0.281 20.139

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 59 137 67 80 103 0 93 86

N.S.

1 1.16 2.69 1.31 1.57 2.02 0.00 1.82 1.69

time (sec)

N/A 0.416 0.082 1.005 0.249 0.254 0.000 0.282 18.786

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 41 72 32 41 51 82 49 129

N.S.

1 1.24 2.18 0.97 1.24 1.55 2.48 1.48 3.91

time (sec)

N/A 0.363 0.024 0.408 0.224 0.259 6.738 0.274 18.964

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 50 35 33 47 38 105 79 116

N.S.

1 1.19 0.83 0.79 1.12 0.90 2.50 1.88 2.76

time (sec)

N/A 0.359 0.180 0.410 0.241 0.240 4.858 0.268 19.154

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 68 44 44 60 49 139 95 153

N.S.

1 1.26 0.81 0.81 1.11 0.91 2.57 1.76 2.83

time (sec)

N/A 0.452 0.189 0.763 0.220 0.248 6.515 0.276 19.665

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