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2.2.2 Integrals 101 to 115

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

426 430 617 989 0 0 0 0 0

N.S.

1 1.01 1.45 2.32 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.712 6.210 6.064 0.000 0.000 0.000 0.000 0.000

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

485 447 587 973 0 0 0 0 0

N.S.

1 0.92 1.21 2.01 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.633 4.310 4.894 0.000 0.000 0.000 0.000 0.000

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

34 34 36 28 30 0 31 30 30

N.S.

1 1.00 1.06 0.82 0.88 0.00 0.91 0.88 0.88

time (sec)

N/A 0.177 18.211 0.020 0.239 0.000 12.864 0.351 5.900

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

545 545 503 0 0 0 0 0 0

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.782 3.278 0.000 0.000 0.000 0.000 0.000 0.000

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

163 163 162 0 0 0 0 0 0

N.S.

1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.286 2.654 0.000 0.000 0.000 0.000 0.000 0.000

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

148 148 148 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.261 4.650 0.000 0.000 0.000 0.000 0.000 0.000

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

34 34 36 28 30 50 31 30 30

N.S.

1 1.00 1.06 0.82 0.88 1.47 0.91 0.88 0.88

time (sec)

N/A 0.181 20.482 0.084 0.273 54.452 17.592 0.404 6.217

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

484 748 0 0 0 0 0 0 0

N.S.

1 1.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.850 0.000 0.000 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 F F F F F F(-1)

verified

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

size

319 568 148 0 0 0 0 0 0

N.S.

1 1.78 0.46 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.583 5.174 0.000 0.000 0.000 0.000 0.000 0.000

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

34 34 36 28 30 111 31 30 30

N.S.

1 1.00 1.06 0.82 0.88 3.26 0.91 0.88 0.88

time (sec)

N/A 0.180 21.111 0.087 0.265 0.261 11.111 0.359 6.260

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

541 540 512 0 0 0 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.735 3.484 0.000 0.000 0.000 0.000 0.000 0.000

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

34 34 36 28 30 53 31 30 30

N.S.

1 1.00 1.06 0.82 0.88 1.56 0.91 0.88 0.88

time (sec)

N/A 0.181 5.068 0.088 0.267 60.517 9.861 0.367 7.785

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

159 159 159 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.282 2.599 0.000 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 F F F F F F(-1)

verified

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

size

148 148 148 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.258 2.939 0.000 0.000 0.000 0.000 0.000 0.000

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

34 34 36 28 30 127 32 30 30

N.S.

1 1.00 1.06 0.82 0.88 3.74 0.94 0.88 0.88

time (sec)

N/A 0.183 10.594 0.088 0.285 0.278 7.327 0.352 9.043

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