[tail] [up]

2.2.1 Integrals 1 to 21

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 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

57 57 56 96 0 227 688 361 1537

N.S.

1 1.00 0.98 1.68 0.00 3.98 12.07 6.33 26.96

time (sec)

N/A 0.097 0.094 0.135 0.000 0.416 12.662 0.465 5.572

Problem 2

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

19 19 19 19 19 28 17 18 18

N.S.

1 1.00 1.00 1.00 1.00 1.47 0.89 0.95 0.95

time (sec)

N/A 0.051 0.040 0.041 0.267 0.426 0.120 0.489 2.177

Problem 3

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

23 23 20 31 19 25 27 39 30

N.S.

1 1.00 0.87 1.35 0.83 1.09 1.17 1.70 1.30

time (sec)

N/A 0.059 0.055 0.049 0.261 0.358 0.220 0.441 2.215

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 57 97 0 231 804 407 2219

N.S.

1 1.00 0.98 1.67 0.00 3.98 13.86 7.02 38.26

time (sec)

N/A 0.090 0.086 0.144 0.000 0.418 12.875 0.473 11.810

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 55 85 0 235 748 103 2213

N.S.

1 1.00 0.95 1.47 0.00 4.05 12.90 1.78 38.16

time (sec)

N/A 0.098 0.105 0.146 0.000 0.377 12.122 0.475 11.904

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 61 108 0 263 0 121 1540

N.S.

1 1.00 0.94 1.66 0.00 4.05 0.00 1.86 23.69

time (sec)

N/A 0.110 0.165 0.168 0.000 0.418 0.000 0.531 5.659

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 134 96 0 266 0 116 419

N.S.

1 1.00 1.34 0.96 0.00 2.66 0.00 1.16 4.19

time (sec)

N/A 0.122 0.295 0.205 0.000 3.223 0.000 0.521 3.581

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 99 116 95 0 265 0 115 417

N.S.

1 1.00 1.17 0.96 0.00 2.68 0.00 1.16 4.21

time (sec)

N/A 0.192 0.223 0.171 0.000 4.078 0.000 0.451 3.544

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

247 247 526 484 0 1075 0 629 2500

N.S.

1 1.00 2.13 1.96 0.00 4.35 0.00 2.55 10.12

time (sec)

N/A 0.288 4.040 0.614 0.000 102.641 0.000 0.541 11.819

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

170 170 335 291 0 771 0 352 2500

N.S.

1 1.00 1.97 1.71 0.00 4.54 0.00 2.07 14.71

time (sec)

N/A 0.236 1.379 0.443 0.000 23.119 0.000 0.554 9.930

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 135 165 0 527 0 203 2500

N.S.

1 1.00 1.31 1.60 0.00 5.12 0.00 1.97 24.27

time (sec)

N/A 0.194 0.921 0.346 0.000 3.773 0.000 0.494 7.465

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 112 92 0 308 0 133 345

N.S.

1 1.00 1.47 1.21 0.00 4.05 0.00 1.75 4.54

time (sec)

N/A 0.098 0.173 0.275 0.000 0.687 0.000 0.501 3.553

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 106 108 0 1054 0 511 2665

N.S.

1 1.00 0.88 0.89 0.00 8.71 0.00 4.22 22.02

time (sec)

N/A 0.186 0.264 0.432 0.000 1.873 0.000 0.531 4.789

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

187 187 205 210 0 2883 0 342 2500

N.S.

1 1.00 1.10 1.12 0.00 15.42 0.00 1.83 13.37

time (sec)

N/A 0.446 0.891 1.126 0.000 85.128 0.000 0.500 15.228

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

458 458 319 412 0 0 0 770 2500

N.S.

1 1.00 0.70 0.90 0.00 0.00 0.00 1.68 5.46

time (sec)

N/A 0.703 2.567 3.346 0.000 0.000 0.000 0.743 20.251

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

213 213 184 357 0 0 0 0 -1

N.S.

1 1.00 0.86 1.68 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.246 6.898 3.727 0.000 0.000 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 187 237 0 0 0 0 -1

N.S.

1 1.00 1.83 2.32 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.131 7.187 0.602 0.000 0.000 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 82 142 0 338 672 459 886

N.S.

1 1.00 0.94 1.63 0.00 3.89 7.72 5.28 10.18

time (sec)

N/A 0.103 0.259 0.383 0.000 0.416 14.549 0.504 4.165

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 115 141 0 462 0 173 126

N.S.

1 1.00 0.96 1.18 0.00 3.85 0.00 1.44 1.05

time (sec)

N/A 0.122 0.464 0.276 0.000 0.435 0.000 0.462 2.566

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

187 187 175 270 0 856 0 502 283

N.S.

1 1.00 0.94 1.44 0.00 4.58 0.00 2.68 1.51

time (sec)

N/A 0.202 0.904 0.387 0.000 0.507 0.000 0.525 5.495

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

260 260 302 456 0 1368 0 960 502

N.S.

1 1.00 1.16 1.75 0.00 5.26 0.00 3.69 1.93

time (sec)

N/A 0.348 1.236 0.527 0.000 0.449 0.000 0.547 5.220

[front] [up]