[tail] [up]

2.2.1 Integrals 1 to 34

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 A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

436 436 495 440 621 668 2288 854 713

N.S.

1 1.00 1.14 1.01 1.42 1.53 5.25 1.96 1.64

time (sec)

N/A 0.271 0.570 0.118 0.316 1.067 114.327 0.751 3.903

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

324 324 323 319 387 410 1510 558 514

N.S.

1 1.00 1.00 0.98 1.19 1.27 4.66 1.72 1.59

time (sec)

N/A 0.188 0.326 0.100 0.284 0.954 74.684 0.634 3.488

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

212 212 184 198 198 204 848 309 351

N.S.

1 1.00 0.87 0.93 0.93 0.96 4.00 1.46 1.66

time (sec)

N/A 0.114 0.161 0.098 0.290 0.729 41.624 0.553 3.301

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 82 128 128 90 354 128 128

N.S.

1 1.00 0.71 1.11 1.11 0.78 3.08 1.11 1.11

time (sec)

N/A 0.048 0.067 0.095 0.318 0.982 8.440 0.549 2.846

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

188 188 161 220 0 565 192 248 -1

N.S.

1 1.00 0.86 1.17 0.00 3.01 1.02 1.32 -0.01

time (sec)

N/A 0.140 0.312 0.098 0.000 1.705 26.933 0.551 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

201 201 231 226 0 1004 0 271 -1

N.S.

1 1.00 1.15 1.12 0.00 5.00 0.00 1.35 -0.00

time (sec)

N/A 0.340 0.754 0.099 0.000 1.457 0.000 0.586 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

279 279 298 347 0 1661 0 529 -1

N.S.

1 1.00 1.07 1.24 0.00 5.95 0.00 1.90 -0.00

time (sec)

N/A 0.466 1.149 0.100 0.000 1.184 0.000 0.614 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

375 375 409 548 0 2446 0 976 -1

N.S.

1 1.00 1.09 1.46 0.00 6.52 0.00 2.60 -0.00

time (sec)

N/A 0.567 1.663 0.101 0.000 1.662 0.000 0.566 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

495 495 602 786 0 3624 0 1512 -1

N.S.

1 1.00 1.22 1.59 0.00 7.32 0.00 3.05 -0.00

time (sec)

N/A 0.682 4.321 0.102 0.000 1.735 0.000 0.555 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

434 434 500 1023 629 677 707 1067 -1

N.S.

1 1.00 1.15 2.36 1.45 1.56 1.63 2.46 -0.00

time (sec)

N/A 0.225 0.599 0.101 0.299 1.176 92.939 0.678 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

322 322 326 616 395 419 435 651 -1

N.S.

1 1.00 1.01 1.91 1.23 1.30 1.35 2.02 -0.00

time (sec)

N/A 0.171 0.388 0.099 0.322 0.882 46.664 0.585 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

210 210 188 294 206 213 230 323 -1

N.S.

1 1.00 0.90 1.40 0.98 1.01 1.10 1.54 -0.00

time (sec)

N/A 0.112 0.195 0.099 0.334 0.685 21.146 0.572 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 113 82 110 102 100 114 127 -1

N.S.

1 1.00 0.73 0.97 0.90 0.88 1.01 1.12 -0.01

time (sec)

N/A 0.045 0.064 0.097 0.287 1.357 8.189 0.599 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

193 193 191 179 0 866 172 200 -1

N.S.

1 1.00 0.99 0.93 0.00 4.49 0.89 1.04 -0.01

time (sec)

N/A 0.161 0.462 0.100 0.000 1.538 32.511 0.655 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

253 253 259 228 0 1583 0 388 -1

N.S.

1 1.00 1.02 0.90 0.00 6.26 0.00 1.53 -0.00

time (sec)

N/A 0.404 0.806 0.102 0.000 0.936 0.000 0.614 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

350 350 387 395 0 2594 0 617 -1

N.S.

1 1.00 1.11 1.13 0.00 7.41 0.00 1.76 -0.00

time (sec)

N/A 0.538 1.805 0.101 0.000 1.032 0.000 0.554 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

463 463 561 681 0 3834 0 1085 -1

N.S.

1 1.00 1.21 1.47 0.00 8.28 0.00 2.34 -0.00

time (sec)

N/A 0.738 2.979 0.101 0.000 1.570 0.000 0.549 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

434 434 485 927 627 689 583 1030 -1

N.S.

1 1.00 1.12 2.14 1.44 1.59 1.34 2.37 -0.00

time (sec)

N/A 0.221 0.662 0.103 0.305 0.991 109.214 0.567 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

322 322 317 547 393 431 377 622 -1

N.S.

1 1.00 0.98 1.70 1.22 1.34 1.17 1.93 -0.00

time (sec)

N/A 0.160 0.439 0.312 0.275 1.137 61.692 0.536 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

210 210 177 253 204 225 230 302 -1

N.S.

1 1.00 0.84 1.20 0.97 1.07 1.10 1.44 -0.00

time (sec)

N/A 0.115 0.215 0.099 0.273 1.584 30.710 0.555 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 113 75 98 98 110 425 115 -1

N.S.

1 1.00 0.66 0.87 0.87 0.97 3.76 1.02 -0.01

time (sec)

N/A 0.047 0.074 0.098 0.287 1.393 0.449 0.542 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

210 210 230 202 0 1287 214 281 -1

N.S.

1 1.00 1.10 0.96 0.00 6.13 1.02 1.34 -0.00

time (sec)

N/A 0.202 0.549 0.100 0.000 1.318 55.169 0.837 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

336 336 354 275 0 2444 0 439 -1

N.S.

1 1.00 1.05 0.82 0.00 7.27 0.00 1.31 -0.00

time (sec)

N/A 0.529 1.164 0.101 0.000 1.220 0.000 0.956 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

438 438 554 459 0 3889 0 767 -1

N.S.

1 1.00 1.26 1.05 0.00 8.88 0.00 1.75 -0.00

time (sec)

N/A 0.809 1.931 0.101 0.000 1.452 0.000 0.662 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B B B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

455 455 977 3932 1802 4115 65321 9032 -1

N.S.

1 1.00 2.15 8.64 3.96 9.04 143.56 19.85 -0.00

time (sec)

N/A 0.237 2.855 0.107 0.353 1.854 12.745 0.673 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B B B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

338 338 619 2175 1118 2258 32849 4972 -1

N.S.

1 1.00 1.83 6.43 3.31 6.68 97.19 14.71 -0.00

time (sec)

N/A 0.169 1.218 0.102 0.326 1.500 7.197 1.357 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B B B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

226 226 341 964 596 988 13522 2224 -1

N.S.

1 1.00 1.51 4.27 2.64 4.37 59.83 9.84 -0.00

time (sec)

N/A 0.112 0.627 0.099 0.317 1.242 2.800 1.002 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 148 308 234 394 3798 728 -1

N.S.

1 1.00 1.17 2.44 1.86 3.13 30.14 5.78 -0.01

time (sec)

N/A 0.049 0.167 0.091 0.304 1.202 1.118 0.884 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

203 203 186 0 0 0 0 0 -1

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.129 0.420 0.023 0.000 0.000 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

220 220 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.350 0.776 0.023 0.000 0.000 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

329 329 215 0 0 0 0 0 -1

N.S.

1 1.00 0.65 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.394 2.025 0.030 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 117 0 0 0 0 0 -1

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.061 0.116 0.020 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

268 266 189 0 0 0 0 0 -1

N.S.

1 0.99 0.71 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.208 0.370 0.017 0.000 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

610 605 242 0 0 0 0 0 -1

N.S.

1 0.99 0.40 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.703 0.582 0.016 0.000 0.000 0.000 0.000 0.000

[front] [up]