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2.2.2 Integrals 101 to 116

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 Reduce Mupad

grade

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

verified

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

size

135 383 145 737 0 318 0 0 81 0

N.S.

1 2.84 1.07 5.46 0.00 2.36 0.00 0.00 0.60 0.00

time (sec)

N/A 0.564 1.122 5.957 0.000 5.248 0.000 0.000 0.023 0.000

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

119 357 139 714 0 268 0 0 69 0

N.S.

1 3.00 1.17 6.00 0.00 2.25 0.00 0.00 0.58 0.00

time (sec)

N/A 0.525 1.088 6.401 0.000 5.265 0.000 0.000 0.022 0.000

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

43 43 43 34 0 0 0 0 133 0

N.S.

1 1.00 1.00 0.79 0.00 0.00 0.00 0.00 3.09 0.00

time (sec)

N/A 0.202 10.181 0.862 0.000 0.000 0.000 0.000 0.019 0.000

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

43 43 43 34 0 0 0 0 81 0

N.S.

1 1.00 1.00 0.79 0.00 0.00 0.00 0.00 1.88 0.00

time (sec)

N/A 0.221 10.141 0.606 0.000 0.000 0.000 0.000 0.015 0.000

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

39 39 43 34 0 0 0 0 81 0

N.S.

1 1.00 1.10 0.87 0.00 0.00 0.00 0.00 2.08 0.00

time (sec)

N/A 0.174 10.017 0.534 0.000 0.000 0.000 0.000 0.015 0.000

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

67 70 101 12 105 94 31 0 34 10

N.S.

1 1.04 1.51 0.18 1.57 1.40 0.46 0.00 0.51 0.15

time (sec)

N/A 0.154 0.082 1.276 0.287 0.250 0.550 0.000 0.008 0.457

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

70 76 90 66 73 75 41 74 35 91

N.S.

1 1.09 1.29 0.94 1.04 1.07 0.59 1.06 0.50 1.30

time (sec)

N/A 0.177 0.050 1.934 0.290 0.249 0.576 0.295 0.009 0.449

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

384 375 0 0 0 0 0 0 88 0

N.S.

1 0.98 0.00 0.00 0.00 0.00 0.00 0.00 0.23 0.00

time (sec)

N/A 0.702 0.000 0.000 0.000 0.000 0.000 0.000 0.030 0.000

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

234 234 0 0 0 0 0 0 32 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.14 0.00

time (sec)

N/A 0.376 0.000 0.000 0.000 0.000 0.000 0.000 0.055 0.000

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

199 250 0 618 0 2298 0 0 648 0

N.S.

1 1.26 0.00 3.11 0.00 11.55 0.00 0.00 3.26 0.00

time (sec)

N/A 0.456 0.000 26.803 0.000 1.184 0.000 0.000 0.155 0.000

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

177 182 0 0 0 0 0 0 69 0

N.S.

1 1.03 0.00 0.00 0.00 0.00 0.00 0.00 0.39 0.00

time (sec)

N/A 0.379 0.000 0.000 0.000 0.000 0.000 0.000 0.019 0.000

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

177 182 0 0 0 0 0 0 69 0

N.S.

1 1.03 0.00 0.00 0.00 0.00 0.00 0.00 0.39 0.00

time (sec)

N/A 0.407 0.000 0.000 0.000 0.000 0.000 0.000 0.020 0.000

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

132 138 204 179 0 191 0 0 19 0

N.S.

1 1.05 1.55 1.36 0.00 1.45 0.00 0.00 0.14 0.00

time (sec)

N/A 0.203 0.331 1.854 0.000 0.225 0.000 0.000 0.004 0.000

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

250 272 26 0 0 0 0 0 20 0

N.S.

1 1.09 0.10 0.00 0.00 0.00 0.00 0.00 0.08 0.00

time (sec)

N/A 0.410 10.012 0.000 0.000 0.000 0.000 0.000 0.003 0.000

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

383 655 138 0 0 0 0 0 42 0

N.S.

1 1.71 0.36 0.00 0.00 0.00 0.00 0.00 0.11 0.00

time (sec)

N/A 1.115 15.090 0.000 0.000 0.000 0.000 0.000 0.017 0.000

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

272 295 283 1147 0 341 0 0 19 0

N.S.

1 1.08 1.04 4.22 0.00 1.25 0.00 0.00 0.07 0.00

time (sec)

N/A 0.335 1.905 5.600 0.000 1.540 0.000 0.000 0.003 0.000

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