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2.2.1 Integrals 1 to 27

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 B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 112 149 129 706 929 0 334 1088

N.S.

1 0.98 1.31 1.13 6.19 8.15 0.00 2.93 9.54

time (sec)

N/A 0.302 3.450 2.008 0.198 0.258 0.000 0.305 2.317

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 75 113 83 334 461 0 182 508

N.S.

1 1.01 1.53 1.12 4.51 6.23 0.00 2.46 6.86

time (sec)

N/A 0.268 2.722 1.549 0.189 0.246 0.000 0.269 2.261

Problem 3

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

43 47 84 45 121 180 0 81 166

N.S.

1 1.09 1.95 1.05 2.81 4.19 0.00 1.88 3.86

time (sec)

N/A 0.235 0.584 1.210 0.181 0.276 0.000 0.268 2.350

Problem 4

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

16 16 16 17 23 36 0 23 23

N.S.

1 1.00 1.00 1.06 1.44 2.25 0.00 1.44 1.44

time (sec)

N/A 0.160 0.007 0.837 0.184 0.251 0.000 0.250 2.316

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 52 124 0 457 0 0 471

N.S.

1 1.00 1.04 2.48 0.00 9.14 0.00 0.00 9.42

time (sec)

N/A 0.290 2.173 0.423 0.000 0.276 0.000 0.000 2.792

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F(-2) B F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 122 199 315 0 1747 0 0 0

N.S.

1 1.22 1.99 3.15 0.00 17.47 0.00 0.00 0.00

time (sec)

N/A 0.300 6.505 0.546 0.000 0.297 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F(-2) B F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 192 210 442 0 6569 0 0 0

N.S.

1 1.23 1.35 2.83 0.00 42.11 0.00 0.00 0.00

time (sec)

N/A 0.393 7.020 0.999 0.000 0.339 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F(-2) B F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

220 268 273 672 0 17376 0 0 0

N.S.

1 1.22 1.24 3.05 0.00 78.98 0.00 0.00 0.00

time (sec)

N/A 0.492 8.437 2.313 0.000 0.439 0.000 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F B F F(-2) F(-1)

verified

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

size

174 175 231 0 0 12590 0 0 0

N.S.

1 1.01 1.33 0.00 0.00 72.36 0.00 0.00 0.00

time (sec)

N/A 0.401 3.390 0.000 0.000 0.728 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F B F F(-2) F(-1)

verified

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

size

126 125 193 0 0 6645 0 0 0

N.S.

1 0.99 1.53 0.00 0.00 52.74 0.00 0.00 0.00

time (sec)

N/A 0.298 0.649 0.000 0.000 0.450 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F B F F(-2) F(-1)

verified

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

size

84 82 143 0 0 4389 0 0 0

N.S.

1 0.98 1.70 0.00 0.00 52.25 0.00 0.00 0.00

time (sec)

N/A 0.260 0.216 0.000 0.000 0.365 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B F F B F F(-2) F(-1)

verified

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

size

38 41 97 0 0 1645 0 0 0

N.S.

1 1.08 2.55 0.00 0.00 43.29 0.00 0.00 0.00

time (sec)

N/A 0.219 0.201 0.000 0.000 0.289 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

82 80 148 0 0 3009 0 0 0

N.S.

1 0.98 1.80 0.00 0.00 36.70 0.00 0.00 0.00

time (sec)

N/A 0.253 0.348 0.000 0.000 0.347 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

135 148 174 0 0 7831 0 0 0

N.S.

1 1.10 1.29 0.00 0.00 58.01 0.00 0.00 0.00

time (sec)

N/A 0.318 1.258 0.000 0.000 0.607 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

193 220 234 0 0 18681 0 0 0

N.S.

1 1.14 1.21 0.00 0.00 96.79 0.00 0.00 0.00

time (sec)

N/A 0.392 1.093 0.000 0.000 1.802 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

29 32 28 26 44 190 0 73 0

N.S.

1 1.10 0.97 0.90 1.52 6.55 0.00 2.52 0.00

time (sec)

N/A 0.337 0.065 0.473 0.267 0.260 0.000 0.282 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

14 14 18 17 22 18 0 27 0

N.S.

1 1.00 1.29 1.21 1.57 1.29 0.00 1.93 0.00

time (sec)

N/A 0.287 0.012 0.397 0.271 0.254 0.000 0.282 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 79 13 18 0 30 0

N.S.

1 1.00 1.00 5.64 0.93 1.29 0.00 2.14 0.00

time (sec)

N/A 0.291 0.010 0.227 0.269 0.253 0.000 0.257 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

46 46 92 0 0 528 0 253 0

N.S.

1 1.00 2.00 0.00 0.00 11.48 0.00 5.50 0.00

time (sec)

N/A 0.242 0.198 0.000 0.000 0.258 0.000 0.321 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 26 65 0 0 221 0 110 0

N.S.

1 1.00 2.50 0.00 0.00 8.50 0.00 4.23 0.00

time (sec)

N/A 0.214 0.067 0.000 0.000 0.267 0.000 0.277 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

16 16 45 0 0 163 0 85 0

N.S.

1 1.00 2.81 0.00 0.00 10.19 0.00 5.31 0.00

time (sec)

N/A 0.203 0.063 0.000 0.000 0.267 0.000 0.291 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

47 47 90 0 0 666 0 412 0

N.S.

1 1.00 1.91 0.00 0.00 14.17 0.00 8.77 0.00

time (sec)

N/A 0.232 0.097 0.000 0.000 0.258 0.000 0.391 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 33 68 0 0 358 0 157 0

N.S.

1 1.00 2.06 0.00 0.00 10.85 0.00 4.76 0.00

time (sec)

N/A 0.216 0.049 0.000 0.000 0.266 0.000 0.302 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

14 14 48 0 0 213 0 69 0

N.S.

1 1.00 3.43 0.00 0.00 15.21 0.00 4.93 0.00

time (sec)

N/A 0.196 0.043 0.000 0.000 0.254 0.000 0.282 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 30 95 44 59 0 84 0

N.S.

1 1.00 0.88 2.79 1.29 1.74 0.00 2.47 0.00

time (sec)

N/A 0.335 0.034 0.257 0.271 0.251 0.000 0.279 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 20 26 22 13 0 32 0

N.S.

1 1.00 1.25 1.62 1.38 0.81 0.00 2.00 0.00

time (sec)

N/A 0.275 0.012 0.364 0.278 0.266 0.000 0.261 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 29 13 13 0 35 0

N.S.

1 1.00 1.00 1.81 0.81 0.81 0.00 2.19 0.00

time (sec)

N/A 0.271 0.008 0.430 0.263 0.258 0.000 0.272 0.000

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