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Integrals 1 to 29

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

verified

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

size

149 173 168 541 333 396 0 0 87 0

N.S.

1 1.16 1.13 3.63 2.23 2.66 0.00 0.00 0.58 0.00

time (sec)

N/A 0.689 0.050 0.428 0.126 0.079 0.000 0.000 0.244 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

99 115 118 306 195 242 0 0 66 0

N.S.

1 1.16 1.19 3.09 1.97 2.44 0.00 0.00 0.67 0.00

time (sec)

N/A 0.449 0.044 0.388 0.124 0.089 0.000 0.000 0.249 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

50 61 90 89 0 119 0 0 43 0

N.S.

1 1.22 1.80 1.78 0.00 2.38 0.00 0.00 0.86 0.00

time (sec)

N/A 0.291 0.020 0.167 0.000 0.089 0.000 0.000 0.230 0.000

Problem 4

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

10 10 12 10 12 12 8 12 12 14

N.S.

1 1.00 1.20 1.00 1.20 1.20 0.80 1.20 1.20 1.40

time (sec)

N/A 0.188 2.783 0.056 0.318 0.073 0.291 0.133 0.227 2.454

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

103 146 185 473 320 1159 0 0 657 0

N.S.

1 1.42 1.80 4.59 3.11 11.25 0.00 0.00 6.38 0.00

time (sec)

N/A 0.712 0.448 0.310 0.207 0.092 0.000 0.000 0.237 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

74 106 137 240 0 623 0 0 327 0

N.S.

1 1.43 1.85 3.24 0.00 8.42 0.00 0.00 4.42 0.00

time (sec)

N/A 0.496 0.312 0.264 0.000 0.091 0.000 0.000 0.257 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

29 33 52 56 91 166 0 80 118 49

N.S.

1 1.14 1.79 1.93 3.14 5.72 0.00 2.76 4.07 1.69

time (sec)

N/A 0.257 0.045 0.280 0.044 0.089 0.000 0.115 0.216 2.521

Problem 8

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

12 12 14 12 73 14 10 14 14 14

N.S.

1 1.00 1.17 1.00 6.08 1.17 0.83 1.17 1.17 1.17

time (sec)

N/A 0.208 5.663 0.061 0.144 0.078 0.305 0.106 0.248 2.462

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

256 294 440 876 605 4008 0 0 0 0

N.S.

1 1.15 1.72 3.42 2.36 15.66 0.00 0.00 0.00 0.00

time (sec)

N/A 1.182 1.860 0.409 0.203 0.144 0.000 0.000 0.233 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

154 184 420 444 393 2218 0 0 1141 0

N.S.

1 1.19 2.73 2.88 2.55 14.40 0.00 0.00 7.41 0.00

time (sec)

N/A 0.734 6.213 0.347 0.192 0.106 0.000 0.000 0.233 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

92 108 271 197 0 1026 0 0 516 0

N.S.

1 1.17 2.95 2.14 0.00 11.15 0.00 0.00 5.61 0.00

time (sec)

N/A 0.497 0.077 0.266 0.000 0.104 0.000 0.000 0.234 0.000

Problem 12

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

12 12 14 12 157 14 10 14 14 14

N.S.

1 1.00 1.17 1.00 13.08 1.17 0.83 1.17 1.17 1.17

time (sec)

N/A 0.225 25.404 0.068 0.182 0.078 0.296 0.341 0.229 2.389

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 24 17 0 0 0 0 0 21 0

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 0.88 0.00

time (sec)

N/A 0.290 0.036 0.000 0.000 0.000 0.000 0.000 0.230 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 24 17 0 0 0 0 0 25 0

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 1.04 0.00

time (sec)

N/A 0.271 0.049 0.000 0.000 0.000 0.000 0.000 0.220 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

47 47 45 0 0 0 0 0 21 0

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 0.45 0.00

time (sec)

N/A 0.319 0.064 0.000 0.000 0.000 0.000 0.000 0.201 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

76 76 67 0 0 0 0 0 25 0

N.S.

1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 0.33 0.00

time (sec)

N/A 0.382 0.178 0.000 0.000 0.000 0.000 0.000 0.226 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

448 452 1792 0 0 1976 0 0 1077 0

N.S.

1 1.01 4.00 0.00 0.00 4.41 0.00 0.00 2.40 0.00

time (sec)

N/A 2.683 19.333 0.000 0.000 0.128 0.000 0.000 0.293 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

330 334 937 0 0 1265 0 0 669 0

N.S.

1 1.01 2.84 0.00 0.00 3.83 0.00 0.00 2.03 0.00

time (sec)

N/A 1.753 11.146 0.000 0.000 0.124 0.000 0.000 0.292 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

212 209 266 483 0 692 0 0 326 0

N.S.

1 0.99 1.25 2.28 0.00 3.26 0.00 0.00 1.54 0.00

time (sec)

N/A 1.056 0.341 0.956 0.000 0.096 0.000 0.000 0.240 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

34 30 30 49 83 132 0 60 82 31

N.S.

1 0.88 0.88 1.44 2.44 3.88 0.00 1.76 2.41 0.91

time (sec)

N/A 0.325 0.015 0.664 0.073 0.098 0.000 0.127 0.228 2.459

Problem 21

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

26 26 28 26 164 34 22 28 163 30

N.S.

1 1.00 1.08 1.00 6.31 1.31 0.85 1.08 6.27 1.15

time (sec)

N/A 0.335 41.753 0.172 0.404 0.074 7.112 0.226 0.313 2.595

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

683 641 2218 0 0 3847 0 0 30 0

N.S.

1 0.94 3.25 0.00 0.00 5.63 0.00 0.00 0.04 0.00

time (sec)

N/A 3.595 9.489 0.000 0.000 0.192 0.000 0.000 200.020 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

510 484 1216 0 0 2410 0 0 1482 0

N.S.

1 0.95 2.38 0.00 0.00 4.73 0.00 0.00 2.91 0.00

time (sec)

N/A 2.815 4.029 0.000 0.000 0.128 0.000 0.000 1.453 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

321 324 610 1012 0 1284 0 0 28 0

N.S.

1 1.01 1.90 3.15 0.00 4.00 0.00 0.00 0.09 0.00

time (sec)

N/A 1.867 1.687 4.509 0.000 0.134 0.000 0.000 200.022 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

95 107 109 167 168 446 0 155 147 212

N.S.

1 1.13 1.15 1.76 1.77 4.69 0.00 1.63 1.55 2.23

time (sec)

N/A 0.676 0.339 4.116 0.160 0.094 0.000 0.143 0.195 2.872

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

864 0 3963 0 0 7980 0 0 30 0

N.S.

1 0.00 4.59 0.00 0.00 9.24 0.00 0.00 0.03 0.00

time (sec)

N/A 0.000 31.034 0.000 0.000 0.204 0.000 0.000 200.019 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

623 0 2129 0 0 4887 0 0 30 0

N.S.

1 0.00 3.42 0.00 0.00 7.84 0.00 0.00 0.05 0.00

time (sec)

N/A 0.000 17.472 0.000 0.000 0.160 0.000 0.000 200.025 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

400 360 696 1102 0 2465 0 0 28 0

N.S.

1 0.90 1.74 2.76 0.00 6.16 0.00 0.00 0.07 0.00

time (sec)

N/A 2.331 1.106 30.654 0.000 0.133 0.000 0.000 200.028 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

85 75 75 244 183 652 0 145 251 180

N.S.

1 0.88 0.88 2.87 2.15 7.67 0.00 1.71 2.95 2.12

time (sec)

N/A 0.393 0.103 17.667 0.054 0.083 0.000 0.135 0.241 2.741

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