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2.2.1 Integrals 1 to 100

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

verified

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

size

32 32 34 32 0 34 0 0 34

N.S.

1 1.00 1.06 1.00 0.00 1.06 0.00 0.00 1.06

time (sec)

N/A 0.447 0.900 0.428 0.000 0.313 0.000 0.000 1.666

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

231 231 223 0 0 0 0 0 0

N.S.

1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.571 0.469 0.000 0.000 0.000 0.000 0.000 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

156 156 149 0 0 0 0 0 0

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.460 0.287 0.000 0.000 0.000 0.000 0.000 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

81 81 77 0 0 0 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.327 0.111 0.000 0.000 0.000 0.000 0.000 0.000

Problem 5

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

15 15 15 16 15 25 34 16 15

N.S.

1 1.00 1.00 1.07 1.00 1.67 2.27 1.07 1.00

time (sec)

N/A 0.163 0.003 1.417 0.197 0.308 0.534 0.526 1.438

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 32 34 32 75 33 0 34 34

N.S.

1 1.00 1.06 1.00 2.34 1.03 0.00 1.06 1.06

time (sec)

N/A 0.437 0.172 0.045 0.318 0.315 0.000 0.426 1.428

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 32 34 32 240 57 0 34 34

N.S.

1 1.00 1.06 1.00 7.50 1.78 0.00 1.06 1.06

time (sec)

N/A 0.471 0.450 0.063 0.330 0.393 0.000 0.398 1.472

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 32 34 32 1170 81 0 34 34

N.S.

1 1.00 1.06 1.00 36.56 2.53 0.00 1.06 1.06

time (sec)

N/A 0.441 0.966 0.073 0.403 0.739 0.000 0.436 1.547

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

272 272 230 271 1115 655 411 766 0

N.S.

1 1.00 0.85 1.00 4.10 2.41 1.51 2.82 0.00

time (sec)

N/A 0.524 0.148 12.893 0.243 0.320 24.793 0.354 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 125 115 129 530 267 216 286 0

N.S.

1 1.00 0.92 1.03 4.24 2.14 1.73 2.29 0.00

time (sec)

N/A 0.344 0.075 2.968 0.226 0.324 13.323 0.324 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 41 47 186 81 65 73 0

N.S.

1 1.00 1.00 1.15 4.54 1.98 1.59 1.78 0.00

time (sec)

N/A 0.231 0.026 0.817 0.211 0.333 8.604 0.316 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 14 13 13 65 13 13

N.S.

1 1.00 1.00 0.93 0.87 0.87 4.33 0.87 0.87

time (sec)

N/A 0.146 0.002 0.485 0.204 0.315 1.171 0.307 1.425

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

28 28 30 28 30 29 24 30 30

N.S.

1 1.00 1.07 1.00 1.07 1.04 0.86 1.07 1.07

time (sec)

N/A 0.390 1.297 0.046 0.258 0.376 5.883 0.337 1.426

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

28 28 30 28 343 51 26 30 30

N.S.

1 1.00 1.07 1.00 12.25 1.82 0.93 1.07 1.07

time (sec)

N/A 0.388 1.127 0.060 0.275 0.354 10.042 0.375 1.533

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

28 28 30 28 1467 73 26 30 30

N.S.

1 1.00 1.07 1.00 52.39 2.61 0.93 1.07 1.07

time (sec)

N/A 0.383 2.264 0.050 0.385 0.395 15.993 1.208 1.794

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 26 26 0 0 42 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 1.62 0.00 0.00 0.00

time (sec)

N/A 0.295 0.064 0.000 0.000 0.323 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

22 22 22 204 0 65 61 0 20

N.S.

1 1.00 1.00 9.27 0.00 2.95 2.77 0.00 0.91

time (sec)

N/A 0.291 0.031 0.081 0.000 0.357 66.404 0.000 1.911

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

22 22 22 135 0 42 39 0 20

N.S.

1 1.00 1.00 6.14 0.00 1.91 1.77 0.00 0.91

time (sec)

N/A 0.241 0.025 187.626 0.000 0.378 20.866 0.000 2.095

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

16 16 16 17 16 28 49 17 16

N.S.

1 1.00 1.00 1.06 1.00 1.75 3.06 1.06 1.00

time (sec)

N/A 0.182 0.015 2.406 0.192 0.347 1.421 0.315 1.470

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

17 17 17 213 22 18 0 0 0

N.S.

1 1.00 1.00 12.53 1.29 1.06 0.00 0.00 0.00

time (sec)

N/A 0.296 0.235 5.581 0.316 0.316 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

20 20 20 68 21 21 0 0 0

N.S.

1 1.00 1.00 3.40 1.05 1.05 0.00 0.00 0.00

time (sec)

N/A 0.296 0.028 15.772 0.352 0.324 0.000 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

22 22 22 68 49 45 0 0 0

N.S.

1 1.00 1.00 3.09 2.23 2.05 0.00 0.00 0.00

time (sec)

N/A 0.308 0.030 116.322 0.429 0.337 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 53 211 195 70 198 52

N.S.

1 1.00 1.00 2.65 10.55 9.75 3.50 9.90 2.60

time (sec)

N/A 0.341 0.016 2.341 0.214 0.316 3.668 0.359 1.596

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 38 35 74 89 51 90 18

N.S.

1 1.00 1.90 1.75 3.70 4.45 2.55 4.50 0.90

time (sec)

N/A 0.276 0.007 0.862 0.192 0.328 2.518 0.497 1.524

Problem 25

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

14 14 14 15 14 21 73 20 14

N.S.

1 1.00 1.00 1.07 1.00 1.50 5.21 1.43 1.00

time (sec)

N/A 0.151 0.003 0.312 0.183 0.334 1.213 0.337 1.488

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 16 32 28 24 28 16

N.S.

1 1.00 1.00 1.07 2.13 1.87 1.60 1.87 1.07

time (sec)

N/A 0.238 0.082 0.264 0.229 0.307 0.730 0.332 1.648

Problem 27

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

18 18 18 19 31 31 15 31 18

N.S.

1 1.00 1.00 1.06 1.72 1.72 0.83 1.72 1.00

time (sec)

N/A 0.310 0.012 0.474 0.234 0.297 11.296 0.331 1.539

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 19 95 101 0 306 39

N.S.

1 1.00 1.00 0.95 4.75 5.05 0.00 15.30 1.95

time (sec)

N/A 0.330 0.012 1.161 0.267 0.314 0.000 0.331 1.481

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

19 19 23 216 26 23 0 0 0

N.S.

1 1.00 1.21 11.37 1.37 1.21 0.00 0.00 0.00

time (sec)

N/A 0.463 0.746 24.973 0.316 0.299 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

40 40 42 40 0 42 0 0 42

N.S.

1 1.00 1.05 1.00 0.00 1.05 0.00 0.00 1.05

time (sec)

N/A 0.473 1.460 0.530 0.000 0.321 0.000 0.000 1.889

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

331 279 445 0 0 0 0 0 0

N.S.

1 0.84 1.34 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.763 1.098 0.000 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

235 200 298 0 0 0 0 0 0

N.S.

1 0.85 1.27 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.630 0.670 0.000 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

139 124 157 0 0 0 0 0 0

N.S.

1 0.89 1.13 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.369 0.299 0.000 0.000 0.000 0.000 0.000 0.000

Problem 34

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

25 25 25 26 25 42 44 26 25

N.S.

1 1.00 1.00 1.04 1.00 1.68 1.76 1.04 1.00

time (sec)

N/A 0.184 0.018 0.659 0.194 0.338 1.419 0.358 1.541

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

40 40 42 40 95 41 0 42 42

N.S.

1 1.00 1.05 1.00 2.38 1.02 0.00 1.05 1.05

time (sec)

N/A 0.444 6.712 0.095 0.327 0.309 0.000 0.381 1.638

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

40 40 42 40 312 65 0 42 42

N.S.

1 1.00 1.05 1.00 7.80 1.62 0.00 1.05 1.05

time (sec)

N/A 0.453 20.804 0.080 0.380 0.350 0.000 0.429 2.100

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

40 40 42 40 1583 89 0 42 42

N.S.

1 1.00 1.05 1.00 39.58 2.22 0.00 1.05 1.05

time (sec)

N/A 0.458 58.910 0.090 0.496 0.742 0.000 0.472 1.953

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 26 27 31 30 22 0 26

N.S.

1 1.00 1.00 1.04 1.19 1.15 0.85 0.00 1.00

time (sec)

N/A 0.379 0.499 10.788 0.359 0.357 22.160 0.000 1.517

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

29 29 31 29 59 52 26 31 31

N.S.

1 1.00 1.07 1.00 2.03 1.79 0.90 1.07 1.07

time (sec)

N/A 0.358 79.503 0.008 0.355 0.373 15.640 0.364 1.625

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

49 49 625 238 0 44 0 0 0

N.S.

1 1.00 12.76 4.86 0.00 0.90 0.00 0.00 0.00

time (sec)

N/A 0.241 0.305 1.491 0.000 0.372 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 642 243 0 45 0 0 0

N.S.

1 1.00 12.84 4.86 0.00 0.90 0.00 0.00 0.00

time (sec)

N/A 0.232 0.299 1.354 0.000 0.341 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

53 53 320 0 0 44 0 0 0

N.S.

1 1.00 6.04 0.00 0.00 0.83 0.00 0.00 0.00

time (sec)

N/A 0.238 0.152 0.000 0.000 0.313 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

52 52 316 0 0 43 0 0 0

N.S.

1 1.00 6.08 0.00 0.00 0.83 0.00 0.00 0.00

time (sec)

N/A 0.219 0.131 0.000 0.000 0.309 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 641 233 0 43 0 0 0

N.S.

1 1.00 13.08 4.76 0.00 0.88 0.00 0.00 0.00

time (sec)

N/A 0.238 0.253 1.614 0.000 0.314 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 645 238 0 44 0 0 0

N.S.

1 1.00 12.90 4.76 0.00 0.88 0.00 0.00 0.00

time (sec)

N/A 0.219 0.177 1.480 0.000 0.355 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

67 67 56 0 0 83 0 0 0

N.S.

1 1.00 0.84 0.00 0.00 1.24 0.00 0.00 0.00

time (sec)

N/A 0.280 0.160 0.000 0.000 0.352 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

79 79 59 0 0 90 0 0 0

N.S.

1 1.00 0.75 0.00 0.00 1.14 0.00 0.00 0.00

time (sec)

N/A 0.289 0.121 0.000 0.000 0.333 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

55 55 49 0 0 70 0 56 0

N.S.

1 1.00 0.89 0.00 0.00 1.27 0.00 1.02 0.00

time (sec)

N/A 0.250 0.053 0.000 0.000 0.309 0.000 0.353 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

55 55 49 0 0 70 0 56 0

N.S.

1 1.00 0.89 0.00 0.00 1.27 0.00 1.02 0.00

time (sec)

N/A 0.237 0.051 0.000 0.000 0.332 0.000 0.330 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

45 45 43 0 0 53 0 42 0

N.S.

1 1.00 0.96 0.00 0.00 1.18 0.00 0.93 0.00

time (sec)

N/A 0.174 0.042 0.000 0.000 0.355 0.000 0.335 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 40 39 64 45 0 54 32

N.S.

1 1.00 1.25 1.22 2.00 1.41 0.00 1.69 1.00

time (sec)

N/A 0.163 0.028 1.661 0.196 0.349 0.000 0.340 1.690

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

48 48 45 0 0 46 0 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.96 0.00 0.00 0.00

time (sec)

N/A 0.238 0.043 0.000 0.000 0.317 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

55 55 49 0 0 53 0 0 0

N.S.

1 1.00 0.89 0.00 0.00 0.96 0.00 0.00 0.00

time (sec)

N/A 0.244 0.043 0.000 0.000 0.383 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

55 55 49 0 0 53 0 0 0

N.S.

1 1.00 0.89 0.00 0.00 0.96 0.00 0.00 0.00

time (sec)

N/A 0.238 0.044 0.000 0.000 0.339 0.000 0.000 0.000

Problem 55

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

22 22 22 26 23 26 19 26 22

N.S.

1 1.00 1.00 1.18 1.05 1.18 0.86 1.18 1.00

time (sec)

N/A 0.159 0.013 0.404 0.233 0.351 0.420 0.307 1.570

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 22 23 22 24 0 32 20

N.S.

1 1.00 1.10 1.15 1.10 1.20 0.00 1.60 1.00

time (sec)

N/A 0.157 0.006 0.547 0.188 0.295 0.000 0.351 1.493

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

40 40 39 0 0 45 0 36 0

N.S.

1 1.00 0.98 0.00 0.00 1.12 0.00 0.90 0.00

time (sec)

N/A 0.204 0.015 0.000 0.000 0.331 0.000 0.331 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 34 33 55 37 0 43 27

N.S.

1 1.00 1.26 1.22 2.04 1.37 0.00 1.59 1.00

time (sec)

N/A 0.161 0.009 1.289 0.195 0.302 0.000 0.331 1.473

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

66 74 48 0 0 0 0 0 0

N.S.

1 1.12 0.73 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.218 0.017 0.000 0.000 0.000 0.000 0.000 0.000

Problem 60

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

99 94 85 86 87 98 112 89 85

N.S.

1 0.95 0.86 0.87 0.88 0.99 1.13 0.90 0.86

time (sec)

N/A 0.250 0.034 0.349 0.197 0.338 4.447 0.331 1.570

Problem 61

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

85 81 74 75 75 86 97 75 73

N.S.

1 0.95 0.87 0.88 0.88 1.01 1.14 0.88 0.86

time (sec)

N/A 0.238 0.028 0.225 0.187 0.321 2.437 0.310 1.481

Problem 62

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

71 68 63 64 65 74 85 65 61

N.S.

1 0.96 0.89 0.90 0.92 1.04 1.20 0.92 0.86

time (sec)

N/A 0.230 0.021 0.172 0.197 0.285 1.307 0.315 1.494

Problem 63

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

57 51 49 53 51 59 70 51 49

N.S.

1 0.89 0.86 0.93 0.89 1.04 1.23 0.89 0.86

time (sec)

N/A 0.213 0.016 0.145 0.192 0.283 0.723 0.327 1.522

Problem 64

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

33 36 31 37 36 38 44 37 33

N.S.

1 1.09 0.94 1.12 1.09 1.15 1.33 1.12 1.00

time (sec)

N/A 0.184 0.007 0.105 0.194 0.304 0.368 0.356 1.570

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 51 50 62 80 0 0 0 0

N.S.

1 0.96 0.94 1.17 1.51 0.00 0.00 0.00 0.00

time (sec)

N/A 0.321 0.015 0.130 0.190 0.000 0.000 0.000 0.000

Problem 66

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

47 47 45 48 46 46 66 47 43

N.S.

1 1.00 0.96 1.02 0.98 0.98 1.40 1.00 0.91

time (sec)

N/A 0.210 0.010 0.122 0.192 0.288 0.981 0.335 1.981

Problem 67

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

72 67 65 62 62 70 94 65 54

N.S.

1 0.93 0.90 0.86 0.86 0.97 1.31 0.90 0.75

time (sec)

N/A 0.221 0.022 0.187 0.196 0.330 1.902 0.402 1.661

Problem 68

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

86 79 77 72 75 82 112 80 68

N.S.

1 0.92 0.90 0.84 0.87 0.95 1.30 0.93 0.79

time (sec)

N/A 0.235 0.023 0.237 0.194 0.305 3.846 0.362 1.677

Problem 69

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

100 93 87 84 86 94 122 92 79

N.S.

1 0.93 0.87 0.84 0.86 0.94 1.22 0.92 0.79

time (sec)

N/A 0.249 0.033 0.335 0.190 0.333 7.517 0.347 1.759

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

157 154 137 0 0 0 0 0 0

N.S.

1 0.98 0.87 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.356 0.123 0.000 0.000 0.000 0.000 0.000 0.000

Problem 71

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

207 201 190 238 0 444 0 221 395

N.S.

1 0.97 0.92 1.15 0.00 2.14 0.00 1.07 1.91

time (sec)

N/A 0.403 0.135 1.056 0.000 0.324 0.000 0.419 1.652

Problem 72

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

167 162 151 190 0 364 0 176 288

N.S.

1 0.97 0.90 1.14 0.00 2.18 0.00 1.05 1.72

time (sec)

N/A 0.367 0.097 0.753 0.000 0.335 0.000 0.351 1.644

Problem 73

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

136 132 122 154 0 299 0 146 229

N.S.

1 0.97 0.90 1.13 0.00 2.20 0.00 1.07 1.68

time (sec)

N/A 0.324 0.073 0.623 0.000 0.347 0.000 0.332 1.660

Problem 74

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

109 102 94 122 0 245 359 113 166

N.S.

1 0.94 0.86 1.12 0.00 2.25 3.29 1.04 1.52

time (sec)

N/A 0.287 0.057 0.543 0.000 0.349 90.937 0.343 1.649

Problem 75

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

79 81 78 89 0 190 274 92 120

N.S.

1 1.03 0.99 1.13 0.00 2.41 3.47 1.16 1.52

time (sec)

N/A 0.246 0.038 0.466 0.000 0.333 34.757 0.353 1.504

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 123 150 166 0 0 0 0 0

N.S.

1 0.95 1.16 1.29 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.373 0.135 0.247 0.000 0.000 0.000 0.000 0.000

Problem 77

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

86 86 87 95 0 199 211 99 262

N.S.

1 1.00 1.01 1.10 0.00 2.31 2.45 1.15 3.05

time (sec)

N/A 0.287 0.070 0.579 0.000 0.368 152.532 0.377 2.133

Problem 78

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

121 117 105 145 0 261 0 129 474

N.S.

1 0.97 0.87 1.20 0.00 2.16 0.00 1.07 3.92

time (sec)

N/A 0.329 0.153 0.574 0.000 0.359 0.000 0.332 1.886

Problem 79

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

149 141 132 181 0 318 0 164 505

N.S.

1 0.95 0.89 1.21 0.00 2.13 0.00 1.10 3.39

time (sec)

N/A 0.369 0.232 0.850 0.000 0.361 0.000 0.336 2.115

Problem 80

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

190 184 172 225 0 404 0 210 627

N.S.

1 0.97 0.91 1.18 0.00 2.13 0.00 1.11 3.30

time (sec)

N/A 0.404 0.288 1.049 0.000 0.357 0.000 0.344 2.202

Problem 81

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

42 42 35 38 37 33 46 37 39

N.S.

1 1.00 0.83 0.90 0.88 0.79 1.10 0.88 0.93

time (sec)

N/A 0.198 0.013 0.248 0.285 0.284 0.072 0.317 0.071

Problem 82

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

485 483 468 876 0 1270 0 741 1240

N.S.

1 1.00 0.96 1.81 0.00 2.62 0.00 1.53 2.56

time (sec)

N/A 0.925 0.532 3.810 0.000 0.376 0.000 0.386 2.206

Problem 83

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

338 337 324 594 0 880 0 495 775

N.S.

1 1.00 0.96 1.76 0.00 2.60 0.00 1.46 2.29

time (sec)

N/A 0.677 0.319 2.378 0.000 0.329 0.000 0.361 1.920

Problem 84

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

226 226 204 384 0 567 0 307 457

N.S.

1 1.00 0.90 1.70 0.00 2.51 0.00 1.36 2.02

time (sec)

N/A 0.481 0.238 1.608 0.000 0.316 0.000 0.343 1.753

Problem 85

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

154 152 123 170 0 336 379 167 242

N.S.

1 0.99 0.80 1.10 0.00 2.18 2.46 1.08 1.57

time (sec)

N/A 0.355 0.122 0.674 0.000 0.327 88.720 0.345 1.643

Problem 86

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

79 81 78 89 0 190 274 92 120

N.S.

1 1.03 0.99 1.13 0.00 2.41 3.47 1.16 1.52

time (sec)

N/A 0.254 0.030 0.148 0.000 0.319 33.635 0.458 0.002

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

228 213 200 300 0 0 0 0 0

N.S.

1 0.93 0.88 1.32 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.580 0.268 1.367 0.000 0.000 0.000 0.000 0.000

Problem 88

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

165 163 166 184 0 429 0 189 590

N.S.

1 0.99 1.01 1.12 0.00 2.60 0.00 1.15 3.58

time (sec)

N/A 0.406 0.201 1.747 0.000 0.374 0.000 0.358 4.536

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

259 248 215 310 0 1341 0 490 1715

N.S.

1 0.96 0.83 1.20 0.00 5.18 0.00 1.89 6.62

time (sec)

N/A 0.539 0.337 2.734 0.000 1.549 0.000 0.396 5.921

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

356 341 310 486 0 3013 0 1128 2707

N.S.

1 0.96 0.87 1.37 0.00 8.46 0.00 3.17 7.60

time (sec)

N/A 0.739 0.635 4.726 0.000 9.965 0.000 0.459 12.796

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

519 500 469 725 0 5824 0 2191 4334

N.S.

1 0.96 0.90 1.40 0.00 11.22 0.00 4.22 8.35

time (sec)

N/A 1.031 1.135 8.090 0.000 48.896 0.000 0.591 20.485

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

175 174 131 292 0 0 0 0 0

N.S.

1 0.99 0.75 1.67 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.541 0.042 1.603 0.000 0.000 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

258 248 339 433 0 0 0 0 0

N.S.

1 0.96 1.31 1.68 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.825 0.222 2.460 0.000 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

762 762 626 555 0 0 0 0 0

N.S.

1 1.00 0.82 0.73 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.466 0.640 1.878 0.000 0.000 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

782 782 663 637 0 0 0 0 0

N.S.

1 1.00 0.85 0.81 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.574 0.739 2.783 0.000 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

144 136 111 0 123 0 0 0 0

N.S.

1 0.94 0.77 0.00 0.85 0.00 0.00 0.00 0.00

time (sec)

N/A 0.463 0.045 0.000 0.198 0.000 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

587 583 478 0 0 0 0 0 0

N.S.

1 0.99 0.81 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.111 0.557 0.000 0.000 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

311 311 290 279 0 0 0 0 0

N.S.

1 1.00 0.93 0.90 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.663 0.123 1.385 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

371 386 365 0 0 0 0 0 0

N.S.

1 1.04 0.98 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.700 0.112 0.000 0.000 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

443 443 826 219 0 0 0 0 0

N.S.

1 1.00 1.86 0.49 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.910 0.457 0.321 0.000 0.000 0.000 0.000 0.000

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