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2.2.2 Integrals 101 to 118

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

verified

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

size

40 40 42 36 39 38 0 38 39

N.S.

1 1.00 1.05 0.90 0.98 0.95 0.00 0.95 0.98

time (sec)

N/A 0.226 0.282 2.844 1.008 0.290 0.000 0.951 0.740

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

279 285 0 681 0 0 0 0 0

N.S.

1 1.02 0.00 2.44 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.763 0.000 6.016 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 F A F F F(-1) F F(-1)

verified

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

size

207 213 0 394 0 0 0 0 0

N.S.

1 1.03 0.00 1.90 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.600 0.000 2.973 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 F A F F F(-1) F F(-1)

verified

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

size

141 143 0 171 0 0 0 0 0

N.S.

1 1.01 0.00 1.21 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.450 0.000 0.955 0.000 0.000 0.000 0.000 0.000

Problem 105

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

40 40 42 36 39 48 61 38 39

N.S.

1 1.00 1.05 0.90 0.98 1.20 1.52 0.95 0.98

time (sec)

N/A 0.227 0.471 1.430 0.406 0.254 133.802 0.446 0.482

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

40 40 42 36 293 91 0 38 39

N.S.

1 1.00 1.05 0.90 7.32 2.28 0.00 0.95 0.98

time (sec)

N/A 0.222 4.677 1.422 1.886 0.245 0.000 0.541 1.305

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

84 86 0 102 0 0 0 0 0

N.S.

1 1.02 0.00 1.21 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.359 0.000 1.068 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 A F F A A A F(-1)

verified

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

size

81 74 50 0 0 55 105 82 0

N.S.

1 0.91 0.62 0.00 0.00 0.68 1.30 1.01 0.00

time (sec)

N/A 0.269 0.201 0.000 0.000 0.256 0.583 0.289 0.000

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

82 76 50 0 0 46 85 69 0

N.S.

1 0.93 0.61 0.00 0.00 0.56 1.04 0.84 0.00

time (sec)

N/A 0.261 0.158 0.000 0.000 0.267 0.351 0.284 0.000

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

41 42 30 0 0 36 58 44 0

N.S.

1 1.02 0.73 0.00 0.00 0.88 1.41 1.07 0.00

time (sec)

N/A 0.244 0.051 0.000 0.000 0.249 0.219 0.283 0.000

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

39 42 32 0 0 28 37 31 0

N.S.

1 1.08 0.82 0.00 0.00 0.72 0.95 0.79 0.00

time (sec)

N/A 0.193 0.048 0.000 0.000 0.256 0.110 0.264 0.000

Problem 112

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

45 45 79 0 0 0 0 0 0

N.S.

1 1.00 1.76 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.251 0.072 0.000 0.000 0.000 0.000 0.000 0.000

Problem 113

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

87 88 55 0 0 0 0 0 0

N.S.

1 1.01 0.63 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.299 0.081 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 B A F B F B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

48 49 528 45 0 140 0 95 43

N.S.

1 1.02 11.00 0.94 0.00 2.92 0.00 1.98 0.90

time (sec)

N/A 0.250 0.926 0.629 0.000 0.273 0.000 0.290 0.694

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 56 21 0 0 0 37 0

N.S.

1 1.00 2.15 0.81 0.00 0.00 0.00 1.42 0.00

time (sec)

N/A 0.286 0.112 1.616 0.000 0.000 0.000 0.297 0.000

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

5 5 5 6 0 0 0 5 0

N.S.

1 1.00 1.00 1.20 0.00 0.00 0.00 1.00 0.00

time (sec)

N/A 0.249 0.056 0.776 0.000 0.000 0.000 0.278 0.000

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

39 39 39 0 0 42 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 1.08 0.00 0.00 0.00

time (sec)

N/A 0.269 0.067 0.000 0.000 0.265 0.000 0.000 0.000

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

31 31 25 0 0 27 0 0 25

N.S.

1 1.00 0.81 0.00 0.00 0.87 0.00 0.00 0.81

time (sec)

N/A 0.262 0.040 0.000 0.000 0.234 0.000 0.000 0.340

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