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Integrals 101 to 119

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 Reduce Mupad

grade

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

verified

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

size

525 423 141 141 0 23255 0 0 27 99213

N.S.

1 0.81 0.27 0.27 0.00 44.30 0.00 0.00 0.05 188.98

time (sec)

N/A 0.690 0.242 0.090 0.000 57.925 0.000 0.000 200.024 28.340

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

542 439 184 172 0 0 0 0 27 93859

N.S.

1 0.81 0.34 0.32 0.00 0.00 0.00 0.00 0.05 173.17

time (sec)

N/A 0.755 0.319 0.102 0.000 0.000 0.000 0.000 200.023 28.933

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

548 443 170 168 0 0 0 0 24 128217

N.S.

1 0.81 0.31 0.31 0.00 0.00 0.00 0.00 0.04 233.97

time (sec)

N/A 0.750 0.254 0.097 0.000 0.000 0.000 0.000 200.020 31.209

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

659 510 244 214 0 0 0 0 27 142799

N.S.

1 0.77 0.37 0.32 0.00 0.00 0.00 0.00 0.04 216.69

time (sec)

N/A 0.948 0.340 0.167 0.000 0.000 0.000 0.000 200.019 32.987

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

259 303 262 370 0 0 0 643 29 0

N.S.

1 1.17 1.01 1.43 0.00 0.00 0.00 2.48 0.11 0.00

time (sec)

N/A 0.689 0.435 5.454 0.000 0.000 0.000 4.617 200.032 0.000

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

254 296 254 356 0 0 0 498 29 0

N.S.

1 1.17 1.00 1.40 0.00 0.00 0.00 1.96 0.11 0.00

time (sec)

N/A 0.652 0.414 5.306 0.000 0.000 0.000 4.427 200.032 0.000

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

243 288 242 364 0 0 0 500 29 0

N.S.

1 1.19 1.00 1.50 0.00 0.00 0.00 2.06 0.12 0.00

time (sec)

N/A 0.639 0.384 5.140 0.000 0.000 0.000 4.640 200.029 0.000

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

391 387 603 672 0 0 0 1019 29 0

N.S.

1 0.99 1.54 1.72 0.00 0.00 0.00 2.61 0.07 0.00

time (sec)

N/A 0.927 0.576 57.368 0.000 0.000 0.000 4.465 200.035 0.000

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

507 502 735 836 0 0 0 1303 29 0

N.S.

1 0.99 1.45 1.65 0.00 0.00 0.00 2.57 0.06 0.00

time (sec)

N/A 1.224 1.134 52.365 0.000 0.000 0.000 4.441 200.030 0.000

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

633 611 727 807 0 0 0 20106 29 0

N.S.

1 0.97 1.15 1.27 0.00 0.00 0.00 31.76 0.05 0.00

time (sec)

N/A 1.315 2.978 3.191 0.000 0.000 0.000 7.240 200.048 0.000

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

531 586 596 620 0 0 0 18563 29 0

N.S.

1 1.10 1.12 1.17 0.00 0.00 0.00 34.96 0.05 0.00

time (sec)

N/A 1.232 2.031 3.078 0.000 0.000 0.000 6.978 200.044 0.000

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

619 590 612 660 0 0 0 19913 29 0

N.S.

1 0.95 0.99 1.07 0.00 0.00 0.00 32.17 0.05 0.00

time (sec)

N/A 1.050 2.391 3.019 0.000 0.000 0.000 7.405 200.054 0.000

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

759 676 716 859 0 0 0 37269 27 0

N.S.

1 0.89 0.94 1.13 0.00 0.00 0.00 49.10 0.04 0.00

time (sec)

N/A 2.231 2.861 3.517 0.000 0.000 0.000 9.001 200.277 0.000

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

928 888 702 1081 0 0 0 28419 29 0

N.S.

1 0.96 0.76 1.16 0.00 0.00 0.00 30.62 0.03 0.00

time (sec)

N/A 4.145 1.157 7.333 0.000 0.000 0.000 6.789 202.668 0.000

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1267 1316 532 465 0 0 0 0 29 0

N.S.

1 1.04 0.42 0.37 0.00 0.00 0.00 0.00 0.02 0.00

time (sec)

N/A 2.864 6.589 3.250 0.000 0.000 0.000 0.000 200.038 0.000

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1265 1185 531 456 0 0 0 0 29 0

N.S.

1 0.94 0.42 0.36 0.00 0.00 0.00 0.00 0.02 0.00

time (sec)

N/A 2.199 7.446 3.522 0.000 0.000 0.000 0.000 200.033 0.000

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1702 1320 645 573 0 0 0 0 29 0

N.S.

1 0.78 0.38 0.34 0.00 0.00 0.00 0.00 0.02 0.00

time (sec)

N/A 2.531 8.581 3.770 0.000 0.000 0.000 0.000 200.030 0.000

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1534 0 649 573 0 0 0 0 26 0

N.S.

1 0.00 0.42 0.37 0.00 0.00 0.00 0.00 0.02 0.00

time (sec)

N/A 0.000 10.067 5.410 0.000 0.000 0.000 0.000 200.031 0.000

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

2110 0 847 697 0 0 0 0 29 0

N.S.

1 0.00 0.40 0.33 0.00 0.00 0.00 0.00 0.01 0.00

time (sec)

N/A 0.000 10.693 8.977 0.000 0.000 0.000 0.000 200.028 0.000

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