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2.2 Detailed conclusion table per each integral for all CAS systems

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA and IntegrateAlgebraic to I.A.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A B A B B F

verified

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

size

189 189 151 1229 338 911 6156 1708 469 0

N.S.

1 1.00 0.80 6.50 1.79 4.82 32.57 9.04 2.48 0.00

time (sec)

N/A 0.227 0.323 0.009 1.878 0.984 11.007 0.570 1.438 0.652

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A B A B B F

verified

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

size

144 144 113 711 242 532 3373 1009 305 0

N.S.

1 1.00 0.78 4.94 1.68 3.69 23.42 7.01 2.12 0.00

time (sec)

N/A 0.121 0.167 0.006 1.814 1.087 7.627 0.561 1.197 0.158

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A B A B B F

verified

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

size

97 97 73 321 146 235 1515 478 185 0

N.S.

1 1.00 0.75 3.31 1.51 2.42 15.62 4.93 1.91 0.00

time (sec)

N/A 0.061 0.078 0.005 1.627 0.756 2.600 0.444 1.028 0.100

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A B B F

verified

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

size

60 60 43 111 70 94 459 167 97 0

N.S.

1 1.00 0.72 1.85 1.17 1.57 7.65 2.78 1.62 0.00

time (sec)

N/A 0.031 0.043 0.004 1.448 0.887 1.935 0.499 0.956 0.060

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A B A B B F

verified

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

size

292 292 247 2443 550 1711 12199 3283 694 0

N.S.

1 1.00 0.85 8.37 1.88 5.86 41.78 11.24 2.38 0.00

time (sec)

N/A 0.287 0.587 0.010 2.268 1.205 13.413 0.814 1.741 1.070

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A B A B B F

verified

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

size

216 216 178 1471 396 1043 7019 2010 499 0

N.S.

1 1.00 0.82 6.81 1.83 4.83 32.50 9.31 2.31 0.00

time (sec)

N/A 0.247 0.354 0.009 2.060 1.025 10.021 0.677 1.388 0.349

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A B A B B F

verified

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

size

144 144 113 711 242 495 3373 1009 305 0

N.S.

1 1.00 0.78 4.94 1.68 3.44 23.42 7.01 2.12 0.00

time (sec)

N/A 0.134 0.173 0.008 1.801 1.009 5.664 0.638 1.182 0.156

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A B A B B F

verified

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

size

91 91 67 263 116 217 1137 380 179 0

N.S.

1 1.00 0.74 2.89 1.27 2.38 12.49 4.18 1.97 0.00

time (sec)

N/A 0.069 0.054 0.007 1.510 0.900 3.167 0.454 1.048 0.085

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B B B F(-1) B B F

verified

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

size

379 379 327 3953 762 2657 0 5234 933 0

N.S.

1 1.00 0.86 10.43 2.01 7.01 0.00 13.81 2.46 0.00

time (sec)

N/A 0.401 0.825 0.010 2.493 0.796 0.000 1.049 2.099 1.215

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A B A B B F

verified

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

size

284 284 239 2443 550 1690 12199 3283 694 0

N.S.

1 1.00 0.84 8.60 1.94 5.95 42.95 11.56 2.44 0.00

time (sec)

N/A 0.284 0.415 0.010 2.317 0.816 13.849 0.946 1.745 0.912

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A B A B B F

verified

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

size

189 189 151 1229 338 837 6156 1708 469 0

N.S.

1 1.00 0.80 6.50 1.79 4.43 32.57 9.04 2.48 0.00

time (sec)

N/A 0.176 0.279 0.009 1.964 0.645 8.211 0.655 1.432 0.651

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A B A B B F

verified

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

size

121 121 90 475 162 381 2220 673 280 0

N.S.

1 1.00 0.74 3.93 1.34 3.15 18.35 5.56 2.31 0.00

time (sec)

N/A 0.079 0.079 0.006 1.637 0.912 8.511 0.507 1.133 0.142

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B A

verified

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

size

84 84 91 112 100 231 97 113 101 111

N.S.

1 1.00 1.08 1.33 1.19 2.75 1.15 1.35 1.20 1.32

time (sec)

N/A 0.077 0.140 0.010 1.377 0.951 59.288 0.432 1.510 0.091

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B A

verified

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

size

84 84 91 112 100 217 97 113 101 111

N.S.

1 1.00 1.08 1.33 1.19 2.58 1.15 1.35 1.20 1.32

time (sec)

N/A 0.077 0.160 0.011 1.366 0.929 54.080 0.569 1.483 0.091

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