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2.2.1 Integrals 1 to 19

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 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

323 323 410 372 0 8169 0 0 39682

N.S.

1 1.00 1.27 1.15 0.00 25.29 0.00 0.00 122.85

time (sec)

N/A 2.244 1.223 3.041 0.000 4.768 0.000 0.000 25.962

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

298 298 358 305 0 6531 0 0 21407

N.S.

1 1.00 1.20 1.02 0.00 21.92 0.00 0.00 71.84

time (sec)

N/A 2.268 0.748 2.213 0.000 2.255 0.000 0.000 25.584

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

253 253 310 252 0 4985 0 0 15461

N.S.

1 1.00 1.23 1.00 0.00 19.70 0.00 0.00 61.11

time (sec)

N/A 1.018 1.364 1.612 0.000 0.981 0.000 0.000 28.232

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

226 226 268 217 0 3519 0 0 5048

N.S.

1 1.00 1.19 0.96 0.00 15.57 0.00 0.00 22.34

time (sec)

N/A 0.700 1.370 1.042 0.000 0.572 0.000 0.000 24.568

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

221 229 233 247 0 3495 0 0 5064

N.S.

1 1.04 1.05 1.12 0.00 15.81 0.00 0.00 22.91

time (sec)

N/A 0.486 0.997 1.015 0.000 0.508 0.000 0.000 24.608

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

244 244 306 284 0 5296 0 0 11540

N.S.

1 1.00 1.25 1.16 0.00 21.70 0.00 0.00 47.30

time (sec)

N/A 0.828 1.390 1.995 0.000 73.246 0.000 0.000 26.300

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

271 271 388 337 0 6851 0 0 16102

N.S.

1 1.00 1.43 1.24 0.00 25.28 0.00 0.00 59.42

time (sec)

N/A 0.962 2.521 2.834 0.000 258.462 0.000 0.000 25.087

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

331 331 481 414 0 0 0 0 21909

N.S.

1 1.00 1.45 1.25 0.00 0.00 0.00 0.00 66.19

time (sec)

N/A 2.367 2.945 4.324 0.000 0.000 0.000 0.000 24.743

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 73 79 0 276 0 78 229

N.S.

1 1.00 0.96 1.04 0.00 3.63 0.00 1.03 3.01

time (sec)

N/A 0.329 0.129 0.923 0.000 0.383 0.000 0.319 0.234

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

230 230 314 178 0 971 0 0 11164

N.S.

1 1.00 1.37 0.77 0.00 4.22 0.00 0.00 48.54

time (sec)

N/A 0.747 0.582 0.908 0.000 0.388 0.000 0.000 29.244

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 35 36 0 139 99 35 47

N.S.

1 1.00 1.00 1.03 0.00 3.97 2.83 1.00 1.34

time (sec)

N/A 0.213 0.017 0.523 0.000 0.348 1.487 0.305 15.685

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 125 119 118 0 482 0 131 1001

N.S.

1 0.98 0.93 0.92 0.00 3.77 0.00 1.02 7.82

time (sec)

N/A 0.396 0.237 0.855 0.000 0.789 0.000 0.317 18.912

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

324 324 407 417 0 16739 0 0 37118

N.S.

1 1.00 1.26 1.29 0.00 51.66 0.00 0.00 114.56

time (sec)

N/A 1.580 1.200 7.063 0.000 3.952 0.000 0.000 28.270

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

206 203 202 236 0 1244 0 377 2743

N.S.

1 0.99 0.98 1.15 0.00 6.04 0.00 1.83 13.32

time (sec)

N/A 0.575 0.762 2.186 0.000 5.874 0.000 0.362 34.636

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 15 16 15 17 15 17 9

N.S.

1 1.00 0.71 0.76 0.71 0.81 0.71 0.81 0.43

time (sec)

N/A 0.216 0.011 0.497 0.227 0.268 0.088 0.337 0.201

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 9 14 13 17 12 17 9

N.S.

1 1.00 0.53 0.82 0.76 1.00 0.71 1.00 0.53

time (sec)

N/A 0.216 0.112 0.401 0.246 0.280 0.093 0.380 15.220

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 15 16 15 17 15 17 9

N.S.

1 1.00 0.71 0.76 0.71 0.81 0.71 0.81 0.43

time (sec)

N/A 0.216 0.100 0.490 0.239 0.306 0.090 0.352 0.117

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 11 9 6 5 5 5 5 5

N.S.

1 1.22 1.00 0.67 0.56 0.56 0.56 0.56 0.56

time (sec)

N/A 0.196 0.012 2.259 0.314 0.284 0.110 0.306 0.083

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

5 5 5 6 5 5 5 5 5

N.S.

1 1.00 1.00 1.20 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.196 0.012 1.743 0.360 0.270 0.103 0.285 0.073

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