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2.2.11 Integrals 1001 to 1025

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.

Problem 1001

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 44 0 0 0 0 0 -1

N.S.

1 1.00 1.07 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.101 0.836 0.034 0.000 0.000 0.000 0.000 0.000

Problem 1002

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

184 184 330 1528 0 0 0 0 -1

N.S.

1 1.00 1.79 8.30 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.162 10.399 0.560 0.000 0.000 0.000 0.000 0.000

Problem 1003

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 90 1036 0 0 0 0 -1

N.S.

1 1.00 0.69 7.91 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.068 20.068 0.054 0.000 0.000 0.000 0.000 0.000

Problem 1004

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 419 514 0 318 0 0 -1

N.S.

1 1.00 7.76 9.52 0.00 5.89 0.00 0.00 -0.02

time (sec)

N/A 0.163 10.561 0.082 0.000 7.989 0.000 0.000 0.000

Problem 1005

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

53 53 416 517 0 319 0 0 -1

N.S.

1 1.00 7.85 9.75 0.00 6.02 0.00 0.00 -0.02

time (sec)

N/A 0.166 10.529 0.085 0.000 8.148 0.000 0.000 0.000

Problem 1006

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 90 69 0 154 0 164 -1

N.S.

1 1.00 1.07 0.82 0.00 1.83 0.00 1.95 -0.01

time (sec)

N/A 0.082 0.237 0.543 0.000 0.373 0.000 2.140 0.000

Problem 1007

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 17 23 7 22 26 15 13

N.S.

1 1.00 0.85 1.15 0.35 1.10 1.30 0.75 0.65

time (sec)

N/A 0.004 0.004 0.025 0.485 0.376 0.164 1.915 3.413

Problem 1008

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F(-2) F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 38 0 0 0 0 0 -1

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.012 0.012 0.010 0.000 0.000 0.000 0.000 0.000

Problem 1009

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 83 242984 0 326 0 0 -1

N.S.

1 1.00 0.94 2761.18 0.00 3.70 0.00 0.00 -0.01

time (sec)

N/A 0.163 0.724 0.374 0.000 2.234 0.000 0.000 0.000

Problem 1010

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F A F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

88 88 15147 269221 0 333 0 0 -1

N.S.

1 1.00 172.12 3059.33 0.00 3.78 0.00 0.00 -0.01

time (sec)

N/A 0.217 16.386 0.333 0.000 2.282 0.000 0.000 0.000

Problem 1011

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 107 0 0 161 0 0 -1

N.S.

1 1.00 2.33 0.00 0.00 3.50 0.00 0.00 -0.02

time (sec)

N/A 0.389 4.938 0.034 0.000 5.846 0.000 0.000 0.000

Problem 1012

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 114 0 0 161 0 0 -1

N.S.

1 1.00 2.48 0.00 0.00 3.50 0.00 0.00 -0.02

time (sec)

N/A 0.401 4.487 0.038 0.000 5.476 0.000 0.000 0.000

Problem 1013

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 107 0 0 161 0 0 -1

N.S.

1 1.00 2.33 0.00 0.00 3.50 0.00 0.00 -0.02

time (sec)

N/A 0.744 0.035 0.039 0.000 5.763 0.000 0.000 0.000

Problem 1014

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 114 0 0 161 0 0 -1

N.S.

1 1.00 2.48 0.00 0.00 3.50 0.00 0.00 -0.02

time (sec)

N/A 0.762 0.010 0.038 0.000 5.274 0.000 0.000 0.000

Problem 1015

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 27 147 94 96 17 58 132

N.S.

1 1.00 1.42 7.74 4.95 5.05 0.89 3.05 6.95

time (sec)

N/A 0.369 0.266 0.404 0.326 0.359 157.078 3.326 6.098

Problem 1016

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

90 90 180 2499 0 458 0 0 -1

N.S.

1 1.00 2.00 27.77 0.00 5.09 0.00 0.00 -0.01

time (sec)

N/A 0.039 0.361 9.401 0.000 5.249 0.000 0.000 0.000

Problem 1017

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A B A C F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 425 181 690 0 289 0 0 -1

N.S.

1 4.13 1.76 6.70 0.00 2.81 0.00 0.00 -0.01

time (sec)

N/A 0.404 1.155 5.433 0.000 3.241 0.000 0.000 0.000

Problem 1018

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A C C B F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 47 53 101 0 51 0 0 -1

N.S.

1 0.96 1.08 2.06 0.00 1.04 0.00 0.00 -0.02

time (sec)

N/A 0.081 0.151 0.500 0.000 0.395 0.000 0.000 0.000

Problem 1019

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 383 555 0 477 0 0 -1

N.S.

1 1.00 4.79 6.94 0.00 5.96 0.00 0.00 -0.01

time (sec)

N/A 0.281 10.561 0.278 0.000 29.132 0.000 0.000 0.000

Problem 1020

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

1 1 1 2 1 1 0 1 1

N.S.

1 1.00 1.00 2.00 1.00 1.00 0.00 1.00 1.00

time (sec)

N/A 0.001 0.000 0.221 0.271 0.342 0.006 1.984 0.005

Problem 1021

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A C C C F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 122 56 234 0 73 0 193 549

N.S.

1 2.90 1.33 5.57 0.00 1.74 0.00 4.60 13.07

time (sec)

N/A 0.108 0.201 0.225 0.000 0.363 0.000 2.615 3.925

Problem 1022

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 149 56 234 0 73 0 193 549

N.S.

1 3.55 1.33 5.57 0.00 1.74 0.00 4.60 13.07

time (sec)

N/A 0.258 0.173 0.244 0.000 0.361 0.000 1.427 3.895

Problem 1023

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A F A A A A B B B

verified

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

size

34 0 31 32 16 31 73 81 31

N.S.

1 0.00 0.91 0.94 0.47 0.91 2.15 2.38 0.91

time (sec)

N/A 0.047 0.093 0.250 0.483 0.358 20.915 2.577 3.452

Problem 1024

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 182 1597 0 164 0 0 -1

N.S.

1 1.00 1.03 9.02 0.00 0.93 0.00 0.00 -0.01

time (sec)

N/A 0.060 6.520 0.679 0.000 0.445 0.000 0.000 0.000

Problem 1025

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A B A C F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 243 100 2992 0 97 0 0 -1

N.S.

1 2.43 1.00 29.92 0.00 0.97 0.00 0.00 -0.01

time (sec)

N/A 0.093 5.043 1.035 0.000 0.420 0.000 0.000 0.000

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