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Integrals 1 to 21

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 B F(-2) A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 57 56 96 0 227 688 361 1537

N.S.

1 1.00 0.98 1.68 0.00 3.98 12.07 6.33 26.96

time (sec)

N/A 0.145 0.112 0.354 0.000 0.265 10.690 0.317 6.172

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 19 19 19 28 17 18 18

N.S.

1 1.00 1.00 1.00 1.00 1.47 0.89 0.95 0.95

time (sec)

N/A 0.080 0.032 0.198 0.225 0.246 0.146 0.299 3.113

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 20 31 19 25 27 39 30

N.S.

1 1.00 0.87 1.35 0.83 1.09 1.17 1.70 1.30

time (sec)

N/A 0.089 0.166 0.205 0.200 0.230 0.235 0.314 2.718

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 58 57 97 0 231 804 407 2219

N.S.

1 1.00 0.98 1.67 0.00 3.98 13.86 7.02 38.26

time (sec)

N/A 0.143 0.088 0.312 0.000 0.264 11.396 0.316 13.516

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 58 55 85 0 235 748 103 2213

N.S.

1 1.00 0.95 1.47 0.00 4.05 12.90 1.78 38.16

time (sec)

N/A 0.158 0.140 0.319 0.000 0.262 11.271 0.305 13.900

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 65 61 108 0 263 0 121 1540

N.S.

1 1.00 0.94 1.66 0.00 4.05 0.00 1.86 23.69

time (sec)

N/A 0.171 0.253 0.512 0.000 0.300 0.000 0.293 6.282

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 100 134 96 0 266 0 116 419

N.S.

1 1.00 1.34 0.96 0.00 2.66 0.00 1.16 4.19

time (sec)

N/A 0.200 0.334 0.529 0.000 2.767 0.000 0.318 4.195

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 99 116 95 0 265 0 115 417

N.S.

1 1.00 1.17 0.96 0.00 2.68 0.00 1.16 4.21

time (sec)

N/A 0.302 0.280 0.395 0.000 3.585 0.000 0.311 3.626

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

247 247 526 484 0 1049 0 607 9992

N.S.

1 1.00 2.13 1.96 0.00 4.25 0.00 2.46 40.45

time (sec)

N/A 0.475 5.444 2.135 0.000 94.181 0.000 0.393 13.036

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

170 170 335 291 0 747 0 340 6735

N.S.

1 1.00 1.97 1.71 0.00 4.39 0.00 2.00 39.62

time (sec)

N/A 0.359 2.468 1.322 0.000 21.241 0.000 0.376 10.762

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 103 135 165 0 505 0 196 3577

N.S.

1 1.00 1.31 1.60 0.00 4.90 0.00 1.90 34.73

time (sec)

N/A 0.308 2.023 0.842 0.000 2.940 0.000 0.363 7.959

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 112 92 0 296 0 128 345

N.S.

1 1.00 1.47 1.21 0.00 3.89 0.00 1.68 4.54

time (sec)

N/A 0.159 0.492 0.559 0.000 0.516 0.000 0.319 5.078

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 121 106 108 0 1022 0 507 2665

N.S.

1 1.00 0.88 0.89 0.00 8.45 0.00 4.19 22.02

time (sec)

N/A 0.316 0.653 1.043 0.000 1.619 0.000 0.408 5.248

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

187 187 205 210 0 2835 0 333 20827

N.S.

1 1.00 1.10 1.12 0.00 15.16 0.00 1.78 111.37

time (sec)

N/A 0.724 1.459 2.897 0.000 81.938 0.000 0.382 17.788

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

458 458 319 412 0 0 0 748 52103

N.S.

1 1.00 0.70 0.90 0.00 0.00 0.00 1.63 113.76

time (sec)

N/A 1.134 2.953 7.633 0.000 0.000 0.000 0.539 23.607

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

213 213 184 318 0 0 0 0 0

N.S.

1 1.00 0.86 1.49 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.423 8.944 6.349 0.000 0.000 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 102 187 204 0 0 0 0 0

N.S.

1 1.00 1.83 2.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.220 9.666 2.838 0.000 0.000 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 87 82 142 0 326 672 454 886

N.S.

1 1.00 0.94 1.63 0.00 3.75 7.72 5.22 10.18

time (sec)

N/A 0.162 0.509 0.551 0.000 0.301 14.147 0.338 5.870

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 120 115 141 0 444 0 167 126

N.S.

1 1.00 0.96 1.18 0.00 3.70 0.00 1.39 1.05

time (sec)

N/A 0.186 0.632 0.545 0.000 0.305 0.000 0.331 2.923

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

187 187 175 270 0 830 0 480 283

N.S.

1 1.00 0.94 1.44 0.00 4.44 0.00 2.57 1.51

time (sec)

N/A 0.336 0.955 0.875 0.000 0.314 0.000 0.370 6.576

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

260 260 302 456 0 1334 0 918 502

N.S.

1 1.00 1.16 1.75 0.00 5.13 0.00 3.53 1.93

time (sec)

N/A 0.564 1.316 1.342 0.000 0.348 0.000 0.385 5.715

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