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Integrals 501 to 525

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 501

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

23 23 25 23 25 37 0 25 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.61 0.00 1.09 1.09 1.09

time (sec)

N/A 0.219 2.440 1.481 4.647 0.116 0.000 1.019 0.188 38.510

Problem 502

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

14 14 16 14 16 28 0 16 16 16

N.S.

1 1.00 1.14 1.00 1.14 2.00 0.00 1.14 1.14 1.14

time (sec)

N/A 0.182 0.227 1.189 0.808 0.089 0.000 0.582 0.173 35.952

Problem 503

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

23 23 25 23 25 37 0 25 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.61 0.00 1.09 1.09 1.09

time (sec)

N/A 0.217 2.161 1.454 4.547 0.115 0.000 1.003 0.185 38.476

Problem 504

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

23 23 25 23 25 37 0 25 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.61 0.00 1.09 1.09 1.09

time (sec)

N/A 0.219 15.817 1.602 13.422 0.133 0.000 1.080 0.201 39.202

Problem 505

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

306 306 3544 0 0 0 0 0 92 0

N.S.

1 1.00 11.58 0.00 0.00 0.00 0.00 0.00 0.30 0.00

time (sec)

N/A 0.710 21.696 0.000 0.000 0.000 0.000 0.000 0.183 0.000

Problem 506

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

215 215 2368 0 0 0 0 0 63 0

N.S.

1 1.00 11.01 0.00 0.00 0.00 0.00 0.00 0.29 0.00

time (sec)

N/A 0.526 17.499 0.000 0.000 0.000 0.000 0.000 0.180 0.000

Problem 507

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

124 124 1395 0 0 0 0 0 34 0

N.S.

1 1.00 11.25 0.00 0.00 0.00 0.00 0.00 0.27 0.00

time (sec)

N/A 0.360 14.446 0.000 0.000 0.000 0.000 0.000 0.182 0.000

Problem 508

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

23 23 25 23 25 25 20 25 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.87 1.09 1.09 1.09

time (sec)

N/A 0.229 5.701 0.901 1.220 0.077 3.858 1.005 0.169 35.717

Problem 509

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

23 23 25 23 25 43 22 25 43 25

N.S.

1 1.00 1.09 1.00 1.09 1.87 0.96 1.09 1.87 1.09

time (sec)

N/A 0.228 51.466 0.980 2.376 0.084 58.206 1.224 0.184 36.022

Problem 510

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

47 45 45 38 57 94 0 46 14 0

N.S.

1 0.96 0.96 0.81 1.21 2.00 0.00 0.98 0.30 0.00

time (sec)

N/A 0.258 0.035 1.719 0.115 0.090 0.000 0.347 0.170 0.000

Problem 511

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

29 29 29 24 41 71 0 27 24 0

N.S.

1 1.00 1.00 0.83 1.41 2.45 0.00 0.93 0.83 0.00

time (sec)

N/A 0.257 0.020 0.440 0.113 0.085 0.000 0.350 0.175 0.000

Problem 512

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

23 23 25 23 25 25 0 25 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.00 1.09 1.09 1.09

time (sec)

N/A 0.228 6.220 0.973 3.654 0.095 0.000 5.999 0.175 36.445

Problem 513

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

23 23 25 23 25 25 0 25 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.00 1.09 1.09 1.09

time (sec)

N/A 0.229 27.092 0.716 4.364 0.090 0.000 0.645 0.171 35.901

Problem 514

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

21 21 23 21 23 23 20 23 23 23

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.95 1.10 1.10 1.10

time (sec)

N/A 0.207 1.643 0.673 2.728 0.089 63.508 0.483 0.181 35.763

Problem 515

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

55 55 55 0 0 0 0 0 23 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.42 0.00

time (sec)

N/A 0.259 0.079 0.000 0.000 0.000 0.000 0.000 0.168 0.000

Problem 516

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

136 134 129 0 0 0 0 0 25 0

N.S.

1 0.99 0.95 0.00 0.00 0.00 0.00 0.00 0.18 0.00

time (sec)

N/A 0.396 1.229 0.000 0.000 0.000 0.000 0.000 0.188 0.000

Problem 517

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

23 23 25 23 25 25 0 25 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.00 1.09 1.09 1.09

time (sec)

N/A 0.224 27.275 0.738 5.370 0.091 0.000 13.100 0.180 35.964

Problem 518

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

23 23 25 23 25 25 0 25 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.00 1.09 1.09 1.09

time (sec)

N/A 0.226 3.721 0.707 3.664 0.093 0.000 10.354 0.166 35.934

Problem 519

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

14 14 16 14 16 16 14 16 16 16

N.S.

1 1.00 1.14 1.00 1.14 1.14 1.00 1.14 1.14 1.14

time (sec)

N/A 0.188 0.740 0.315 2.114 0.145 4.359 2.654 0.178 36.000

Problem 520

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

23 23 25 23 25 25 22 25 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.96 1.09 1.09 1.09

time (sec)

N/A 0.228 2.972 0.704 3.827 0.085 148.147 2.972 0.178 36.190

Problem 521

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

23 23 25 23 25 25 0 25 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.00 1.09 1.09 1.09

time (sec)

N/A 0.226 33.690 0.727 5.534 0.091 0.000 3.089 0.180 36.394

Problem 522

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

107 148 102 230 0 125 0 0 131 0

N.S.

1 1.38 0.95 2.15 0.00 1.17 0.00 0.00 1.22 0.00

time (sec)

N/A 0.421 0.229 6.335 0.000 0.106 0.000 0.000 0.193 0.000

Problem 523

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

137 137 135 0 0 0 0 0 40 0

N.S.

1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 0.29 0.00

time (sec)

N/A 0.423 2.700 0.000 0.000 0.000 0.000 0.000 0.194 0.000

Problem 524

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

79 79 325 192065 0 0 0 0 45 0

N.S.

1 1.00 4.11 2431.20 0.00 0.00 0.00 0.00 0.57 0.00

time (sec)

N/A 0.465 2.288 5.745 0.000 0.000 0.000 0.000 0.188 0.000

Problem 525

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

79 79 529 2254 0 1623 0 0 90 0

N.S.

1 1.00 6.70 28.53 0.00 20.54 0.00 0.00 1.14 0.00

time (sec)

N/A 0.478 2.110 4.953 0.000 0.145 0.000 0.000 0.174 0.000

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