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2.2.1 Integrals 1 to 33

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 B B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

225 225 149 252 755 430 0 163 -1

N.S.

1 1.00 0.66 1.12 3.36 1.91 0.00 0.72 -0.00

time (sec)

N/A 0.108 0.217 0.516 0.483 0.431 0.000 0.424 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 130 124 611 343 0 121 -1

N.S.

1 1.00 1.17 1.12 5.50 3.09 0.00 1.09 -0.01

time (sec)

N/A 0.034 0.128 0.236 0.459 0.405 0.000 0.421 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 105 83 464 111 0 79 -1

N.S.

1 1.00 1.15 0.91 5.10 1.22 0.00 0.87 -0.01

time (sec)

N/A 0.023 0.060 0.251 0.410 0.461 0.000 0.438 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

18 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06

time (sec)

N/A 0.007 10.889 0.108 0.000 0.000 0.000 0.000 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

107 107 132 0 0 331 0 0 -1

N.S.

1 1.00 1.23 0.00 0.00 3.09 0.00 0.00 -0.01

time (sec)

N/A 0.059 0.451 2.096 0.000 0.456 0.000 0.000 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

227 227 152 244 834 467 0 167 -1

N.S.

1 1.00 0.67 1.07 3.67 2.06 0.00 0.74 -0.00

time (sec)

N/A 0.105 0.214 0.471 0.494 0.418 0.000 0.415 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 134 120 674 385 0 123 -1

N.S.

1 1.00 1.20 1.07 6.02 3.44 0.00 1.10 -0.01

time (sec)

N/A 0.036 0.126 0.236 0.462 0.411 0.000 0.422 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 109 79 512 115 0 81 -1

N.S.

1 1.00 1.20 0.87 5.63 1.26 0.00 0.89 -0.01

time (sec)

N/A 0.022 0.047 0.257 0.423 0.381 0.000 0.407 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.008 12.199 0.112 0.000 0.000 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 108 136 0 0 371 0 0 -1

N.S.

1 1.00 1.26 0.00 0.00 3.44 0.00 0.00 -0.01

time (sec)

N/A 0.059 0.512 2.105 0.000 0.401 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 72 75 183 58 0 53 -1

N.S.

1 1.00 1.09 1.14 2.77 0.88 0.00 0.80 -0.02

time (sec)

N/A 0.041 0.111 0.326 0.341 0.369 0.000 0.442 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

52 52 75 49 123 50 0 43 -1

N.S.

1 1.00 1.44 0.94 2.37 0.96 0.00 0.83 -0.02

time (sec)

N/A 0.017 0.055 0.238 0.338 0.404 0.000 0.428 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 24 25 94 16 0 21 -1

N.S.

1 1.00 0.62 0.64 2.41 0.41 0.00 0.54 -0.03

time (sec)

N/A 0.010 0.019 0.260 0.332 0.434 0.000 0.418 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

16 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06

time (sec)

N/A 0.007 7.063 0.122 0.000 0.000 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

69 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.026 8.653 0.112 0.000 0.000 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

268 268 176 281 294 766 0 182 -1

N.S.

1 1.00 0.66 1.05 1.10 2.86 0.00 0.68 -0.00

time (sec)

N/A 0.190 0.523 1.620 0.368 0.397 0.000 0.414 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 155 141 200 648 0 142 -1

N.S.

1 1.00 1.14 1.04 1.47 4.76 0.00 1.04 -0.01

time (sec)

N/A 0.070 0.278 1.056 0.358 0.445 0.000 0.418 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 140 94 96 128 0 94 -1

N.S.

1 1.00 1.27 0.85 0.87 1.16 0.00 0.85 -0.01

time (sec)

N/A 0.047 0.100 0.833 0.466 0.390 0.000 0.417 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

33 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.021 40.709 0.583 0.000 0.000 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

268 268 181 273 322 843 0 186 -1

N.S.

1 1.00 0.68 1.02 1.20 3.15 0.00 0.69 -0.00

time (sec)

N/A 0.169 0.554 1.562 0.363 0.578 0.000 0.429 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 159 137 216 730 0 144 -1

N.S.

1 1.00 1.17 1.01 1.59 5.37 0.00 1.06 -0.01

time (sec)

N/A 0.065 0.297 1.049 0.355 0.654 0.000 0.423 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 144 90 96 132 0 96 -1

N.S.

1 1.00 1.31 0.82 0.87 1.20 0.00 0.87 -0.01

time (sec)

N/A 0.046 0.100 0.835 0.479 0.372 0.000 0.440 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

33 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.023 44.016 0.586 0.000 0.000 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 99 77 113 268 0 61 -1

N.S.

1 1.00 1.46 1.13 1.66 3.94 0.00 0.90 -0.01

time (sec)

N/A 0.066 0.148 1.790 0.509 0.445 0.000 0.426 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 88 75 121 90 0 70 -1

N.S.

1 1.00 1.17 1.00 1.61 1.20 0.00 0.93 -0.01

time (sec)

N/A 0.036 0.151 1.598 0.520 0.386 0.000 0.441 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 48 49 45 40 0 42 -1

N.S.

1 1.00 0.86 0.88 0.80 0.71 0.00 0.75 -0.02

time (sec)

N/A 0.023 0.050 1.308 0.481 0.360 0.000 0.423 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

31 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.021 15.599 1.749 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

261 261 194 493 532 1084 0 227 -1

N.S.

1 1.00 0.74 1.89 2.04 4.15 0.00 0.87 -0.00

time (sec)

N/A 0.139 0.409 0.245 0.430 0.571 0.000 0.407 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

128 128 146 211 254 488 0 139 -1

N.S.

1 1.00 1.14 1.65 1.98 3.81 0.00 1.09 -0.01

time (sec)

N/A 0.039 0.203 0.249 0.348 0.400 0.000 0.432 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

22 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.010 4.859 180.000 0.000 0.000 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

311 311 240 558 601 1902 0 263 -1

N.S.

1 1.00 0.77 1.79 1.93 6.12 0.00 0.85 -0.00

time (sec)

N/A 0.277 0.958 1.029 0.625 0.378 0.000 0.434 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

160 160 177 241 300 921 0 165 -1

N.S.

1 1.00 1.11 1.51 1.88 5.76 0.00 1.03 -0.01

time (sec)

N/A 0.110 0.490 1.072 0.560 0.376 0.000 0.424 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

44 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.033 10.857 180.000 0.000 0.000 0.000 0.000 0.000

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