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2.2.2 Integrals 101 to 123

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 101

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

175 167 174 197 0 465 384 204 320

N.S.

1 0.95 0.99 1.13 0.00 2.66 2.19 1.17 1.83

time (sec)

N/A 0.343 1.169 0.733 0.000 0.326 0.539 0.299 13.195

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

431 491 539 1547 0 0 0 0 0

N.S.

1 1.14 1.25 3.59 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.897 0.594 0.875 0.000 0.000 0.000 0.000 0.000

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

488 503 1691 4691 0 0 0 0 0

N.S.

1 1.03 3.47 9.61 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.669 2.068 0.979 0.000 0.000 0.000 0.000 0.000

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

564 428 829 1200 0 2179 5942 1132 0

N.S.

1 0.76 1.47 2.13 0.00 3.86 10.54 2.01 0.00

time (sec)

N/A 0.976 11.122 0.986 0.000 0.840 0.856 0.298 0.000

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

236 210 293 398 0 839 1360 403 0

N.S.

1 0.89 1.24 1.69 0.00 3.56 5.76 1.71 0.00

time (sec)

N/A 0.363 2.722 0.664 0.000 0.403 0.630 0.291 0.000

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

679 684 1472 1328 0 0 0 0 0

N.S.

1 1.01 2.17 1.96 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.066 1.920 1.027 0.000 0.000 0.000 0.000 0.000

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

704 716 2854 7856 0 0 0 0 0

N.S.

1 1.02 4.05 11.16 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.641 3.605 1.086 0.000 0.000 0.000 0.000 0.000

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No No No TBD TBD TBD TBD TBD

size

671 693 4727 16309 0 0 0 0 0

N.S.

1 1.03 7.04 24.31 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.127 17.357 1.609 0.000 0.000 0.000 0.000 0.000

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

717 754 618 837 0 1583 1787 818 0

N.S.

1 1.05 0.86 1.17 0.00 2.21 2.49 1.14 0.00

time (sec)

N/A 2.354 4.998 1.246 0.000 0.655 0.995 0.339 0.000

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

316 337 254 286 0 637 641 296 0

N.S.

1 1.07 0.80 0.91 0.00 2.02 2.03 0.94 0.00

time (sec)

N/A 0.852 1.430 1.082 0.000 0.346 0.696 0.325 0.000

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 121 98 86 0 227 226 93 0

N.S.

1 1.04 0.84 0.74 0.00 1.96 1.95 0.80 0.00

time (sec)

N/A 0.284 0.525 0.764 0.000 0.300 0.376 0.304 0.000

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

374 374 218 761 0 11287 0 0 0

N.S.

1 1.00 0.58 2.03 0.00 30.18 0.00 0.00 0.00

time (sec)

N/A 0.533 0.415 0.979 0.000 4.009 0.000 0.000 0.000

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No No Yes TBD TBD TBD TBD TBD

size

789 764 1377 2108 0 0 0 0 0

N.S.

1 0.97 1.75 2.67 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.407 16.758 1.130 0.000 0.000 0.000 0.000 0.000

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

649 709 771 1139 0 3143 0 1093 0

N.S.

1 1.09 1.19 1.76 0.00 4.84 0.00 1.68 0.00

time (sec)

N/A 2.884 5.797 1.677 0.000 1.214 0.000 0.320 0.000

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

309 339 291 439 0 1305 0 399 0

N.S.

1 1.10 0.94 1.42 0.00 4.22 0.00 1.29 0.00

time (sec)

N/A 0.781 1.644 1.126 0.000 0.758 0.000 0.305 0.000

Problem 116

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

111 111 106 201 0 429 0 118 143

N.S.

1 1.00 0.95 1.81 0.00 3.86 0.00 1.06 1.29

time (sec)

N/A 0.272 0.671 0.756 0.000 0.472 0.000 0.309 12.881

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

666 0 806 1906 0 0 0 0 0

N.S.

1 0.00 1.21 2.86 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 1.277 0.861 0.000 0.000 0.000 0.000 0.000

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

891 937 872 3251 0 3995 0 1392 0

N.S.

1 1.05 0.98 3.65 0.00 4.48 0.00 1.56 0.00

time (sec)

N/A 2.377 11.980 1.569 0.000 4.616 0.000 0.325 0.000

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

444 466 392 1129 0 1581 0 579 0

N.S.

1 1.05 0.88 2.54 0.00 3.56 0.00 1.30 0.00

time (sec)

N/A 0.867 2.432 1.003 0.000 2.056 0.000 0.299 0.000

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 131 147 176 0 286 0 234 175

N.S.

1 1.00 1.12 1.34 0.00 2.18 0.00 1.79 1.34

time (sec)

N/A 0.284 1.020 0.649 0.000 1.551 0.000 0.295 12.927

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 53 144 0 154 0 205 0

N.S.

1 1.00 1.04 2.82 0.00 3.02 0.00 4.02 0.00

time (sec)

N/A 0.219 0.157 0.773 0.000 0.268 0.000 0.287 0.000

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No No No TBD TBD TBD TBD TBD

size

1432 1432 670 905 0 0 0 0 0

N.S.

1 1.00 0.47 0.63 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.719 4.796 5.224 0.000 0.000 0.000 0.000 0.000

Problem 123

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 No Yes TBD TBD TBD TBD TBD

size

652 650 390 395 0 0 0 0 0

N.S.

1 1.00 0.60 0.61 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.596 2.245 2.477 0.000 0.000 0.000 0.000 0.000

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