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Integrals 1 to 19

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

verified

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

size

20 20 107 23 248 24 0 495 66 22

N.S.

1 1.00 5.35 1.15 12.40 1.20 0.00 24.75 3.30 1.10

time (sec)

N/A 0.197 0.259 1.623 0.304 0.081 0.000 1.013 0.190 37.224

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

18 18 59 48 42 42 141 54 18 23

N.S.

1 1.00 3.28 2.67 2.33 2.33 7.83 3.00 1.00 1.28

time (sec)

N/A 0.191 0.150 4.345 0.028 0.074 0.464 0.142 0.187 37.560

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

18 18 39 38 44 35 236 43 18 43

N.S.

1 1.00 2.17 2.11 2.44 1.94 13.11 2.39 1.00 2.39

time (sec)

N/A 0.189 0.207 2.439 0.031 0.080 0.341 0.163 0.180 36.594

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

18 18 44 35 29 29 100 36 18 22

N.S.

1 1.00 2.44 1.94 1.61 1.61 5.56 2.00 1.00 1.22

time (sec)

N/A 0.189 0.124 1.937 0.027 0.096 0.221 0.150 0.193 36.784

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

18 18 31 29 34 28 148 29 18 18

N.S.

1 1.00 1.72 1.61 1.89 1.56 8.22 1.61 1.00 1.00

time (sec)

N/A 0.188 0.078 0.974 0.027 0.077 0.165 0.169 0.185 36.636

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

18 18 51 24 22 22 53 24 18 21

N.S.

1 1.00 2.83 1.33 1.22 1.22 2.94 1.33 1.00 1.17

time (sec)

N/A 0.182 0.097 0.764 0.032 0.073 0.111 0.133 0.179 0.042

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

16 16 33 15 26 16 49 14 16 14

N.S.

1 1.00 2.06 0.94 1.62 1.00 3.06 0.88 1.00 0.88

time (sec)

N/A 0.153 0.006 0.262 0.032 0.079 0.081 0.182 0.182 37.359

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

10 10 22 11 10 10 15 10 10 10

N.S.

1 1.00 2.20 1.10 1.00 1.00 1.50 1.00 1.00 1.00

time (sec)

N/A 0.164 0.014 0.115 0.026 0.070 0.055 0.170 0.177 0.017

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

10 10 10 11 12 18 0 12 18 10

N.S.

1 1.00 1.00 1.10 1.20 1.80 0.00 1.20 1.80 1.00

time (sec)

N/A 0.184 0.025 0.323 0.026 0.066 0.000 0.181 0.186 36.825

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

16 16 82 17 23 24 0 45 18 23

N.S.

1 1.00 5.12 1.06 1.44 1.50 0.00 2.81 1.12 1.44

time (sec)

N/A 0.195 0.085 0.399 0.027 0.065 0.000 0.202 0.178 36.485

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

18 18 18 34 22 32 0 22 18 18

N.S.

1 1.00 1.00 1.89 1.22 1.78 0.00 1.22 1.00 1.00

time (sec)

N/A 0.200 0.339 0.679 0.028 0.066 0.000 0.138 0.186 36.504

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

18 18 39 34 32 32 0 90 18 22

N.S.

1 1.00 2.17 1.89 1.78 1.78 0.00 5.00 1.00 1.22

time (sec)

N/A 0.201 0.145 0.630 0.028 0.072 0.000 0.207 0.183 0.058

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

171 173 1794 0 0 0 0 0 42 0

N.S.

1 1.01 10.49 0.00 0.00 0.00 0.00 0.00 0.25 0.00

time (sec)

N/A 0.638 30.372 0.000 0.000 0.000 0.000 0.000 0.189 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

211 211 0 0 0 0 0 0 42 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.00

time (sec)

N/A 0.563 0.000 0.000 0.000 0.000 0.000 0.000 0.194 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

287 286 0 0 0 0 0 0 42 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.15 0.00

time (sec)

N/A 0.643 0.000 0.000 0.000 0.000 0.000 0.000 0.193 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

73 65 109 73 60 60 153 76 115 58

N.S.

1 0.89 1.49 1.00 0.82 0.82 2.10 1.04 1.58 0.79

time (sec)

N/A 0.249 0.164 4.552 0.028 0.082 0.470 0.136 0.186 37.422

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

184 186 300 0 0 0 0 0 65 0

N.S.

1 1.01 1.63 0.00 0.00 0.00 0.00 0.00 0.35 0.00

time (sec)

N/A 0.687 24.294 0.000 0.000 0.000 0.000 0.000 0.196 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

215 215 0 0 0 0 0 0 88 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.41 0.00

time (sec)

N/A 0.558 0.000 0.000 0.000 0.000 0.000 0.000 0.210 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

305 304 0 0 0 0 0 0 65 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.21 0.00

time (sec)

N/A 0.694 0.000 0.000 0.000 0.000 0.000 0.000 0.198 0.000

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