[tail] [up]

Integrals 1 to 22

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 Reduce Mupad

grade

N/A A B C B A F B B B

verified

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

size

33 33 105 68 115 50 0 65 96 46

N.S.

1 1.00 3.18 2.06 3.48 1.52 0.00 1.97 2.91 1.39

time (sec)

N/A 0.357 0.355 0.544 0.028 0.091 0.000 0.344 0.201 40.809

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

19 19 17 18 15 15 0 15 23 13

N.S.

1 1.00 0.89 0.95 0.79 0.79 0.00 0.79 1.21 0.68

time (sec)

N/A 0.271 0.032 0.444 0.026 0.071 0.000 0.381 0.184 40.574

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B C B B F B B B

verified

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

size

15 15 39 44 61 33 0 45 23 30

N.S.

1 1.00 2.60 2.93 4.07 2.20 0.00 3.00 1.53 2.00

time (sec)

N/A 0.289 0.229 0.411 0.032 0.082 0.000 0.402 0.153 40.571

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

18 22 12 16 18 20 0 19 23 14

N.S.

1 1.22 0.67 0.89 1.00 1.11 0.00 1.06 1.28 0.78

time (sec)

N/A 0.203 0.024 0.362 0.031 0.083 0.000 0.361 0.152 40.284

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

33 33 42 28 31 37 0 34 21 21

N.S.

1 1.00 1.27 0.85 0.94 1.12 0.00 1.03 0.64 0.64

time (sec)

N/A 0.360 0.054 0.389 0.025 0.081 0.000 0.353 0.160 40.256

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

30 29 25 29 42 24 0 37 27 35

N.S.

1 0.97 0.83 0.97 1.40 0.80 0.00 1.23 0.90 1.17

time (sec)

N/A 0.352 0.225 0.376 0.033 0.070 0.000 0.351 0.150 40.441

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

46 48 60 44 56 83 0 50 42 40

N.S.

1 1.04 1.30 0.96 1.22 1.80 0.00 1.09 0.91 0.87

time (sec)

N/A 0.448 0.179 0.458 0.027 0.087 0.000 0.369 0.153 40.274

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A F A B B

verified

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

size

40 35 41 45 70 53 0 59 41 45

N.S.

1 0.88 1.02 1.12 1.75 1.32 0.00 1.48 1.02 1.12

time (sec)

N/A 0.357 0.245 0.473 0.031 0.077 0.000 0.333 0.193 41.742

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

33 29 49 28 27 43 0 28 27 20

N.S.

1 0.88 1.48 0.85 0.82 1.30 0.00 0.85 0.82 0.61

time (sec)

N/A 0.225 0.077 0.801 0.029 0.086 0.000 0.343 0.155 41.859

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B F(-2) A F B B B

verified

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

size

113 133 190 219 0 332 0 226 368 1666

N.S.

1 1.18 1.68 1.94 0.00 2.94 0.00 2.00 3.26 14.74

time (sec)

N/A 0.871 1.345 0.910 0.000 0.196 0.000 0.393 0.168 41.058

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

57 59 46 58 56 66 0 66 265 115

N.S.

1 1.04 0.81 1.02 0.98 1.16 0.00 1.16 4.65 2.02

time (sec)

N/A 0.284 0.155 0.648 0.032 0.095 0.000 0.401 0.170 42.448

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A F(-2) A F B B B

verified

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

size

61 75 85 100 0 203 0 111 68 77

N.S.

1 1.23 1.39 1.64 0.00 3.33 0.00 1.82 1.11 1.26

time (sec)

N/A 0.587 0.237 0.569 0.000 0.118 0.000 0.392 0.163 41.002

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

20 22 20 21 20 22 0 22 44 48

N.S.

1 1.10 1.00 1.05 1.00 1.10 0.00 1.10 2.20 2.40

time (sec)

N/A 0.208 0.015 0.401 0.031 0.087 0.000 0.387 0.158 41.813

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

54 59 50 54 48 53 0 54 52 47

N.S.

1 1.09 0.93 1.00 0.89 0.98 0.00 1.00 0.96 0.87

time (sec)

N/A 0.256 0.103 0.551 0.031 0.094 0.000 0.350 0.158 41.714

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A F(-2) A F A B B

verified

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

size

77 88 67 78 0 230 0 91 92 86

N.S.

1 1.14 0.87 1.01 0.00 2.99 0.00 1.18 1.19 1.12

time (sec)

N/A 0.442 0.380 0.680 0.000 0.099 0.000 0.421 0.153 40.756

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

93 135 100 96 116 185 0 138 141 116

N.S.

1 1.45 1.08 1.03 1.25 1.99 0.00 1.48 1.52 1.25

time (sec)

N/A 0.411 0.653 0.843 0.031 0.111 0.000 0.413 0.166 41.802

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A F(-2) A F A B B

verified

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

size

138 151 112 127 0 456 0 210 189 183

N.S.

1 1.09 0.81 0.92 0.00 3.30 0.00 1.52 1.37 1.33

time (sec)

N/A 0.832 0.796 1.245 0.000 0.112 0.000 0.386 0.184 43.423

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD TBD

size

44 32 44 81 63 77 0 68 20 0

N.S.

1 0.73 1.00 1.84 1.43 1.75 0.00 1.55 0.45 0.00

time (sec)

N/A 0.238 0.145 0.813 0.107 0.099 0.000 0.391 0.202 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

37 37 37 123 46 118 0 34 12 0

N.S.

1 1.00 1.00 3.32 1.24 3.19 0.00 0.92 0.32 0.00

time (sec)

N/A 0.238 0.025 0.977 0.107 0.207 0.000 0.393 0.157 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 24 24 103 35 98 0 22 20 0

N.S.

1 1.00 1.00 4.29 1.46 4.08 0.00 0.92 0.83 0.00

time (sec)

N/A 0.229 0.015 0.757 0.109 0.107 0.000 0.297 0.151 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD TBD

size

204 170 363 453 0 0 0 0 25 0

N.S.

1 0.83 1.78 2.22 0.00 0.00 0.00 0.00 0.12 0.00

time (sec)

N/A 0.922 19.182 3.136 0.000 0.000 0.000 0.000 0.172 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

23 23 25 23 25 25 22 25 27 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.96 1.09 1.17 1.09

time (sec)

N/A 0.343 11.472 1.467 1.245 0.226 68.638 1.496 0.171 45.044

[front] [up]