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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 A A B F B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 19 47 0 43 42 74 46

N.S.

1 1.00 1.00 2.47 0.00 2.26 2.21 3.89 2.42

time (sec)

N/A 0.491 0.044 0.398 0.000 0.236 0.202 0.281 0.302

Problem 2

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 19 15 12 12 12 10 12 11

N.S.

1 0.76 0.60 0.48 0.48 0.48 0.40 0.48 0.44

time (sec)

N/A 0.143 0.007 0.092 0.186 0.232 0.037 0.271 11.743

Problem 3

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

32 27 27 26 31 25 27 25 25

N.S.

1 0.84 0.84 0.81 0.97 0.78 0.84 0.78 0.78

time (sec)

N/A 0.335 0.029 0.163 0.304 0.245 0.082 0.313 12.327

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A N/A Yes No TBD TBD TBD TBD TBD

size

23 0 23 126 52 18 0 0 18

N.S.

1 0.00 1.00 5.48 2.26 0.78 0.00 0.00 0.78

time (sec)

N/A 0.000 0.176 0.262 0.415 0.262 0.000 0.000 12.893

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A B B B

verified

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

size

21 0 26 47 27 32 53 63 27

N.S.

1 0.00 1.24 2.24 1.29 1.52 2.52 3.00 1.29

time (sec)

N/A 0.000 2.652 0.540 0.243 0.259 0.214 0.283 12.575

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

17 0 17 16 15 15 17 20 18

N.S.

1 0.00 1.00 0.94 0.88 0.88 1.00 1.18 1.06

time (sec)

N/A 0.000 0.336 0.100 0.261 0.243 0.124 0.271 0.226

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F B A B B B A B

verified

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

size

19 0 46 25 41 45 37 31 29

N.S.

1 0.00 2.42 1.32 2.16 2.37 1.95 1.63 1.53

time (sec)

N/A 0.000 0.305 0.322 0.191 0.263 0.126 0.269 12.459

Problem 8

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

7 7 7 9 8 8 7 9 8

N.S.

1 1.00 1.00 1.29 1.14 1.14 1.00 1.29 1.14

time (sec)

N/A 0.122 0.001 0.351 0.197 0.244 0.030 0.267 0.036

Problem 9

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

19 8 8 9 8 8 7 9 8

N.S.

1 0.42 0.42 0.47 0.42 0.42 0.37 0.47 0.42

time (sec)

N/A 0.134 0.001 0.042 0.184 0.247 0.030 0.262 0.017

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 0 26 46 71 31 27 45 0

N.S.

1 0.00 1.00 1.77 2.73 1.19 1.04 1.73 0.00

time (sec)

N/A 0.000 0.400 5.492 0.362 0.242 0.179 0.864 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 19 19 15 14 41 15 0 14

N.S.

1 0.86 0.86 0.68 0.64 1.86 0.68 0.00 0.64

time (sec)

N/A 0.175 0.045 0.117 0.196 0.257 0.259 0.000 0.163

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 24 24 21 162 20 20 68 20

N.S.

1 0.73 0.73 0.64 4.91 0.61 0.61 2.06 0.61

time (sec)

N/A 0.507 0.060 0.545 0.310 0.242 0.128 0.286 11.862

Problem 13

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

12 12 12 19 10 18 8 10 12

N.S.

1 1.00 1.00 1.58 0.83 1.50 0.67 0.83 1.00

time (sec)

N/A 0.308 0.068 1.777 0.238 0.247 0.092 0.270 11.955

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 135 28 122 576 127 153 126 0

N.S.

1 5.87 1.22 5.30 25.04 5.52 6.65 5.48 0.00

time (sec)

N/A 12.936 0.795 2.600 0.371 0.275 0.715 0.290 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 33 19 18 231 17 15 17 19

N.S.

1 1.74 1.00 0.95 12.16 0.89 0.79 0.89 1.00

time (sec)

N/A 0.190 0.802 0.167 0.269 0.255 0.066 0.291 11.834

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

23 14 14 15 25 14 12 14 11

N.S.

1 0.61 0.61 0.65 1.09 0.61 0.52 0.61 0.48

time (sec)

N/A 0.143 0.003 0.056 0.195 0.246 0.046 0.272 11.403

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A N/A Yes No TBD TBD TBD TBD TBD

size

24 0 24 52 27 36 0 0 0

N.S.

1 0.00 1.00 2.17 1.12 1.50 0.00 0.00 0.00

time (sec)

N/A 0.000 0.160 0.614 0.636 0.243 0.000 0.000 0.000

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

30 43 47 35 34 34 37 36 36

N.S.

1 1.43 1.57 1.17 1.13 1.13 1.23 1.20 1.20

time (sec)

N/A 0.225 0.066 0.085 0.182 0.246 0.125 0.282 0.105

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 38 53 23 45 29 32 29 29

N.S.

1 1.81 2.52 1.10 2.14 1.38 1.52 1.38 1.38

time (sec)

N/A 2.725 9.287 0.129 0.290 0.263 0.096 0.312 12.018

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

19 0 20 20 25 22 22 19 26

N.S.

1 0.00 1.05 1.05 1.32 1.16 1.16 1.00 1.37

time (sec)

N/A 0.000 0.455 0.211 0.356 0.248 0.145 0.305 12.089

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A B A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 37 17 33 31 31 31 31 13

N.S.

1 2.31 1.06 2.06 1.94 1.94 1.94 1.94 0.81

time (sec)

N/A 0.195 0.166 0.145 0.190 0.255 0.066 0.286 0.148

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

31 0 22 27 54 52 53 53 0

N.S.

1 0.00 0.71 0.87 1.74 1.68 1.71 1.71 0.00

time (sec)

N/A 0.000 0.381 0.387 0.339 0.269 0.163 0.342 0.000

Problem 23

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

26 35 36 34 34 30 34 36 34

N.S.

1 1.35 1.38 1.31 1.31 1.15 1.31 1.38 1.31

time (sec)

N/A 0.195 0.012 0.083 0.197 0.251 0.061 0.286 0.062

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

23 0 22 20 19 22 19 22 28

N.S.

1 0.00 0.96 0.87 0.83 0.96 0.83 0.96 1.22

time (sec)

N/A 0.000 0.126 0.366 0.247 0.263 0.211 0.336 13.268

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 0 20 20 22 34 0 36 19

N.S.

1 0.00 1.00 1.00 1.10 1.70 0.00 1.80 0.95

time (sec)

N/A 0.000 0.351 11.850 0.259 0.266 0.000 0.318 13.089

Problem 26

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

20 25 25 21 20 20 22 25 20

N.S.

1 1.25 1.25 1.05 1.00 1.00 1.10 1.25 1.00

time (sec)

N/A 0.247 0.050 0.096 0.220 0.250 0.141 0.293 12.705

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 97 24 22 20 26 26 37 21

N.S.

1 3.03 0.75 0.69 0.62 0.81 0.81 1.16 0.66

time (sec)

N/A 0.464 0.049 1.183 0.316 0.258 0.052 0.291 11.961

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

31 0 31 30 91 32 32 0 32

N.S.

1 0.00 1.00 0.97 2.94 1.03 1.03 0.00 1.03

time (sec)

N/A 0.000 0.166 133.609 0.503 0.250 1.468 0.000 12.362

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A C A A A B

verified

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

size

31 0 27 26 39 32 22 41 28

N.S.

1 0.00 0.87 0.84 1.26 1.03 0.71 1.32 0.90

time (sec)

N/A 0.000 0.428 3.086 0.240 0.252 0.144 0.271 12.140

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

21 0 28 27 25 24 26 24 24

N.S.

1 0.00 1.33 1.29 1.19 1.14 1.24 1.14 1.14

time (sec)

N/A 0.000 0.067 1.722 0.415 0.243 0.956 0.459 13.686

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

22 0 22 35 20 34 32 19 121

N.S.

1 0.00 1.00 1.59 0.91 1.55 1.45 0.86 5.50

time (sec)

N/A 0.000 0.419 55.741 0.428 0.251 0.870 1.641 12.027

Problem 32

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

28 24 24 21 20 20 22 20 22

N.S.

1 0.86 0.86 0.75 0.71 0.71 0.79 0.71 0.79

time (sec)

N/A 0.465 1.732 0.231 0.240 0.245 0.114 0.302 11.729

Problem 33

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 17 13 13 16 16 15 16 18

N.S.

1 1.13 0.87 0.87 1.07 1.07 1.00 1.07 1.20

time (sec)

N/A 0.206 0.062 0.081 0.194 0.255 0.058 0.286 11.437

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

26 35 27 24 22 22 26 22 19

N.S.

1 1.35 1.04 0.92 0.85 0.85 1.00 0.85 0.73

time (sec)

N/A 0.220 0.013 0.068 0.192 0.252 0.152 0.274 0.090

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

25 0 53 49 48 48 0 0 0

N.S.

1 0.00 2.12 1.96 1.92 1.92 0.00 0.00 0.00

time (sec)

N/A 0.000 0.121 0.255 0.227 0.248 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A F B

verified

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

size

23 0 19 27 17 26 22 0 51

N.S.

1 0.00 0.83 1.17 0.74 1.13 0.96 0.00 2.22

time (sec)

N/A 0.000 0.622 0.884 1.411 0.235 0.163 0.000 11.054

Problem 37

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

27 35 37 26 30 30 24 36 35

N.S.

1 1.30 1.37 0.96 1.11 1.11 0.89 1.33 1.30

time (sec)

N/A 0.840 0.213 0.490 0.224 0.241 0.253 0.282 11.276

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A B C B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 197 17 32 109 31 34 31 15

N.S.

1 11.59 1.00 1.88 6.41 1.82 2.00 1.82 0.88

time (sec)

N/A 0.782 0.029 0.181 0.244 0.242 0.063 0.280 10.802

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 28 20 35 28 31 0 0 32

N.S.

1 1.22 0.87 1.52 1.22 1.35 0.00 0.00 1.39

time (sec)

N/A 1.259 0.134 14.129 0.317 0.259 0.000 0.000 11.325

Problem 40

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

34 52 52 36 52 37 36 37 47

N.S.

1 1.53 1.53 1.06 1.53 1.09 1.06 1.09 1.38

time (sec)

N/A 4.085 0.131 0.856 0.250 0.257 0.194 0.334 10.884

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

26 0 25 26 30 23 19 23 25

N.S.

1 0.00 0.96 1.00 1.15 0.88 0.73 0.88 0.96

time (sec)

N/A 0.000 0.059 0.205 0.309 0.250 0.121 0.283 10.660

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 0 59 0 0 159 0 0 91

N.S.

1 0.00 2.03 0.00 0.00 5.48 0.00 0.00 3.14

time (sec)

N/A 0.000 0.169 0.000 0.000 0.256 0.000 0.000 11.808

Problem 43

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 22 31 17 16 16 15 18 20

N.S.

1 0.88 1.24 0.68 0.64 0.64 0.60 0.72 0.80

time (sec)

N/A 0.231 0.015 1.233 0.189 0.260 0.186 0.296 0.106

Problem 44

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

20 21 19 20 19 22 14 19 18

N.S.

1 1.05 0.95 1.00 0.95 1.10 0.70 0.95 0.90

time (sec)

N/A 0.178 0.013 0.580 0.194 0.240 0.067 0.279 10.547

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

25 0 22 20 25 27 22 37 800

N.S.

1 0.00 0.88 0.80 1.00 1.08 0.88 1.48 32.00

time (sec)

N/A 0.000 0.972 1.593 0.312 0.251 0.071 0.302 11.155

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

14 0 12 12 11 11 8 11 12

N.S.

1 0.00 0.86 0.86 0.79 0.79 0.57 0.79 0.86

time (sec)

N/A 0.000 0.056 0.598 0.215 0.267 0.049 0.288 10.695

Problem 47

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

27 24 24 18 17 28 17 17 17

N.S.

1 0.89 0.89 0.67 0.63 1.04 0.63 0.63 0.63

time (sec)

N/A 0.159 0.017 0.384 0.194 0.254 0.066 0.274 0.071

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A F B

verified

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

size

27 0 13 9 8 8 10 0 8

N.S.

1 0.00 0.48 0.33 0.30 0.30 0.37 0.00 0.30

time (sec)

N/A 0.000 0.130 0.082 0.250 0.248 0.178 0.000 10.950

Problem 49

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

20 20 34 27 23 26 27 32 26

N.S.

1 1.00 1.70 1.35 1.15 1.30 1.35 1.60 1.30

time (sec)

N/A 0.356 0.072 0.436 0.287 0.254 0.139 0.295 12.114

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 0 24 31 63 44 42 0 90

N.S.

1 0.00 1.00 1.29 2.62 1.83 1.75 0.00 3.75

time (sec)

N/A 0.000 0.145 3.093 0.444 0.251 0.268 0.000 11.285

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A C A A B B B

verified

N/A N/A Yes No TBD TBD TBD TBD TBD

size

31 0 58 179 32 38 58 178 54

N.S.

1 0.00 1.87 5.77 1.03 1.23 1.87 5.74 1.74

time (sec)

N/A 0.000 0.948 26.056 0.388 0.263 0.556 2.407 11.137

Problem 52

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

34 29 29 25 52 45 22 48 24

N.S.

1 0.85 0.85 0.74 1.53 1.32 0.65 1.41 0.71

time (sec)

N/A 0.350 0.111 0.491 0.252 0.254 0.118 0.287 10.918

Problem 53

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

24 28 28 29 28 31 24 30 26

N.S.

1 1.17 1.17 1.21 1.17 1.29 1.00 1.25 1.08

time (sec)

N/A 0.394 0.016 0.101 0.191 0.246 0.072 0.280 11.071

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

27 0 26 28 46 41 22 33 85

N.S.

1 0.00 0.96 1.04 1.70 1.52 0.81 1.22 3.15

time (sec)

N/A 0.000 0.316 1.647 0.303 0.260 0.085 0.290 11.777

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 0 26 36 42 42 0 42 23

N.S.

1 0.00 1.08 1.50 1.75 1.75 0.00 1.75 0.96

time (sec)

N/A 0.000 5.157 0.048 0.257 0.257 0.000 0.319 12.037

Problem 56

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

23 21 21 20 21 21 19 23 21

N.S.

1 0.91 0.91 0.87 0.91 0.91 0.83 1.00 0.91

time (sec)

N/A 0.333 0.012 0.128 0.191 0.221 0.052 0.270 0.112

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

21 0 13 12 11 22 8 22 11

N.S.

1 0.00 0.62 0.57 0.52 1.05 0.38 1.05 0.52

time (sec)

N/A 0.000 0.081 0.153 0.249 0.246 0.081 0.281 10.770

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 26 33 29 58 28 26 69 29

N.S.

1 0.87 1.10 0.97 1.93 0.93 0.87 2.30 0.97

time (sec)

N/A 2.733 0.837 7.075 0.334 0.263 0.328 0.347 11.371

Problem 59

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 20 20 19 45 18 17 18 20

N.S.

1 0.80 0.80 0.76 1.80 0.72 0.68 0.72 0.80

time (sec)

N/A 0.261 0.049 0.741 0.319 0.261 0.076 0.275 12.072

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

26 0 19 18 17 21 14 21 17

N.S.

1 0.00 0.73 0.69 0.65 0.81 0.54 0.81 0.65

time (sec)

N/A 0.000 1.256 0.260 0.216 0.248 0.066 0.283 0.151

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

20 0 20 25 25 24 26 30 24

N.S.

1 0.00 1.00 1.25 1.25 1.20 1.30 1.50 1.20

time (sec)

N/A 0.000 0.429 33.027 0.325 0.249 2.345 0.337 12.444

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

11 11 11 12 11 11 8 11 10

N.S.

1 1.00 1.00 1.09 1.00 1.00 0.73 1.00 0.91

time (sec)

N/A 0.231 0.008 0.075 0.210 0.268 0.106 0.286 11.704

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 62 122 51 63 61 0 55

N.S.

1 1.00 2.38 4.69 1.96 2.42 2.35 0.00 2.12

time (sec)

N/A 1.163 0.171 90.924 0.268 0.266 11.449 0.000 11.813

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

22 0 27 26 23 25 15 19 21

N.S.

1 0.00 1.23 1.18 1.05 1.14 0.68 0.86 0.95

time (sec)

N/A 0.000 0.432 0.271 0.212 0.263 0.096 0.303 11.158

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A B B B B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 89 35 70 80 59 63 0 58

N.S.

1 2.70 1.06 2.12 2.42 1.79 1.91 0.00 1.76

time (sec)

N/A 0.370 0.263 4.947 0.194 0.250 6.889 0.000 11.318

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 0 0 54 105 103 46 48 0

N.S.

1 0.00 0.00 1.64 3.18 3.12 1.39 1.45 0.00

time (sec)

N/A 0.000 0.000 1.277 0.332 0.260 0.161 0.582 0.000

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

18 18 18 21 21 20 19 21 20

N.S.

1 1.00 1.00 1.17 1.17 1.11 1.06 1.17 1.11

time (sec)

N/A 1.217 0.232 0.713 0.224 0.257 0.136 0.295 13.329

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 29 29 31 189 29 26 29 26

N.S.

1 1.07 1.07 1.15 7.00 1.07 0.96 1.07 0.96

time (sec)

N/A 0.193 0.404 0.094 0.320 0.263 0.080 0.282 0.129

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A F A A A B

verified

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

size

30 0 52 37 0 40 44 39 39

N.S.

1 0.00 1.73 1.23 0.00 1.33 1.47 1.30 1.30

time (sec)

N/A 0.000 0.556 0.171 0.000 0.253 0.306 0.328 12.249

Problem 70

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 23 23 22 21 21 20 21 17

N.S.

1 1.28 1.28 1.22 1.17 1.17 1.11 1.17 0.94

time (sec)

N/A 0.158 0.020 0.147 0.184 0.266 0.110 0.276 11.821

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 28 24 23 25 29 22 35 0

N.S.

1 1.17 1.00 0.96 1.04 1.21 0.92 1.46 0.00

time (sec)

N/A 1.158 0.244 0.184 0.238 0.261 0.145 0.290 0.000

Problem 72

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

33 27 30 27 66 27 24 27 25

N.S.

1 0.82 0.91 0.82 2.00 0.82 0.73 0.82 0.76

time (sec)

N/A 0.484 0.088 0.627 0.216 0.240 0.118 0.287 0.210

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A F B

verified

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

size

30 0 49 44 45 38 42 0 42

N.S.

1 0.00 1.63 1.47 1.50 1.27 1.40 0.00 1.40

time (sec)

N/A 0.000 0.266 0.173 0.221 0.257 0.166 0.000 12.172

Problem 74

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 23 22 21 21 22 19 20 21

N.S.

1 1.05 1.00 0.95 0.95 1.00 0.86 0.91 0.95

time (sec)

N/A 0.174 0.006 0.085 0.192 0.250 0.052 0.289 0.057

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 0 242 243 352 352 170 242 0

N.S.

1 0.00 8.34 8.38 12.14 12.14 5.86 8.34 0.00

time (sec)

N/A 0.000 0.767 7.596 0.861 0.308 2.030 7.179 0.000

Problem 76

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

19 15 15 12 11 12 8 11 12

N.S.

1 0.79 0.79 0.63 0.58 0.63 0.42 0.58 0.63

time (sec)

N/A 0.146 0.002 0.016 0.179 0.257 0.034 0.270 0.025

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

21 0 18 17 16 26 15 16 16

N.S.

1 0.00 0.86 0.81 0.76 1.24 0.71 0.76 0.76

time (sec)

N/A 0.000 0.131 0.061 0.235 0.250 0.095 0.275 11.563

Problem 78

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

8 8 8 9 8 8 7 8 8

N.S.

1 1.00 1.00 1.12 1.00 1.00 0.88 1.00 1.00

time (sec)

N/A 0.121 0.000 0.078 0.173 0.250 0.023 0.311 0.036

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 0 30 30 0 30 0 0 48

N.S.

1 0.00 1.00 1.00 0.00 1.00 0.00 0.00 1.60

time (sec)

N/A 0.000 0.281 196.254 0.000 0.266 0.000 0.000 0.386

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A B B B B B B

verified

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

size

27 0 49 64 75 75 60 76 68

N.S.

1 0.00 1.81 2.37 2.78 2.78 2.22 2.81 2.52

time (sec)

N/A 0.000 0.060 11.361 0.215 0.250 0.087 0.339 11.950

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A B B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 67 20 41 40 36 42 36 18

N.S.

1 3.19 0.95 1.95 1.90 1.71 2.00 1.71 0.86

time (sec)

N/A 0.230 0.184 0.219 0.187 0.247 0.084 0.289 0.149

Problem 82

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 36 31 29 28 28 27 28 26

N.S.

1 1.71 1.48 1.38 1.33 1.33 1.29 1.33 1.24

time (sec)

N/A 0.184 0.075 0.050 0.178 0.236 0.059 0.315 11.103

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

38 0 41 44 48 40 37 88 0

N.S.

1 0.00 1.08 1.16 1.26 1.05 0.97 2.32 0.00

time (sec)

N/A 0.000 0.293 95.365 1.058 0.255 3.358 1.414 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 27 26 24 63 65 73 66 118

N.S.

1 1.08 1.04 0.96 2.52 2.60 2.92 2.64 4.72

time (sec)

N/A 0.557 0.071 0.738 0.310 0.274 0.167 0.349 7.729

Problem 85

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 21 20 18 18 15 19 19

N.S.

1 1.00 0.95 0.91 0.82 0.82 0.68 0.86 0.86

time (sec)

N/A 0.163 0.018 0.438 0.177 0.246 0.095 0.259 0.084

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 60 63 35 42 42 34 124 57

N.S.

1 1.67 1.75 0.97 1.17 1.17 0.94 3.44 1.58

time (sec)

N/A 1.534 0.252 1.388 0.225 0.252 0.291 0.286 0.432

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 23 58 24 29 30 27 29 29

N.S.

1 1.44 3.62 1.50 1.81 1.88 1.69 1.81 1.81

time (sec)

N/A 0.137 0.000 0.008 0.182 0.228 0.022 0.267 0.003

Problem 88

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

27 38 37 30 31 33 27 28 23

N.S.

1 1.41 1.37 1.11 1.15 1.22 1.00 1.04 0.85

time (sec)

N/A 0.220 0.012 0.080 0.187 0.242 0.074 0.276 12.847

Problem 89

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

23 40 23 20 20 20 26 0 19

N.S.

1 1.74 1.00 0.87 0.87 0.87 1.13 0.00 0.83

time (sec)

N/A 0.224 0.084 4.789 0.317 0.249 0.938 0.000 12.604

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

30 0 40 34 38 41 39 43 55

N.S.

1 0.00 1.33 1.13 1.27 1.37 1.30 1.43 1.83

time (sec)

N/A 0.000 0.125 1.365 0.247 0.257 0.158 0.306 13.673

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

32 0 41 51 48 37 37 47 42

N.S.

1 0.00 1.28 1.59 1.50 1.16 1.16 1.47 1.31

time (sec)

N/A 0.000 0.108 12.876 0.214 0.247 0.422 0.387 13.432

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

17 0 15 14 13 13 10 13 13

N.S.

1 0.00 0.88 0.82 0.76 0.76 0.59 0.76 0.76

time (sec)

N/A 0.000 0.252 0.113 0.210 0.262 0.062 0.270 13.226

Problem 93

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

17 19 19 17 18 18 141 18 18

N.S.

1 1.12 1.12 1.00 1.06 1.06 8.29 1.06 1.06

time (sec)

N/A 0.422 0.232 0.446 0.213 0.251 0.204 0.263 11.504

Problem 94

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

27 25 24 18 18 20 15 18 17

N.S.

1 0.93 0.89 0.67 0.67 0.74 0.56 0.67 0.63

time (sec)

N/A 0.222 0.010 0.062 0.178 0.231 0.059 0.304 0.055

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A B A B B

verified

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

size

31 0 35 29 40 71 31 936 87

N.S.

1 0.00 1.13 0.94 1.29 2.29 1.00 30.19 2.81

time (sec)

N/A 0.000 0.235 0.493 0.226 0.270 0.155 0.310 11.263

Problem 96

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

32 34 46 25 42 28 29 28 95

N.S.

1 1.06 1.44 0.78 1.31 0.88 0.91 0.88 2.97

time (sec)

N/A 4.201 3.590 0.658 0.270 0.257 0.139 0.467 11.888

Problem 97

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 18 22 16 18 18 32 18 15

N.S.

1 0.82 1.00 0.73 0.82 0.82 1.45 0.82 0.68

time (sec)

N/A 0.131 0.003 0.050 0.171 0.247 0.027 0.277 11.870

Problem 98

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 9 9 10 9 9 10 9 10

N.S.

1 0.56 0.56 0.62 0.56 0.56 0.62 0.56 0.62

time (sec)

N/A 0.125 0.001 0.059 0.175 0.258 0.024 0.262 0.039

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F B B B B B B B

verified

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

size

33 0 14593 128 39766 124 139 497 127

N.S.

1 0.00 442.21 3.88 1205.03 3.76 4.21 15.06 3.85

time (sec)

N/A 0.000 41.564 1.218 0.716 0.266 0.248 1.234 11.944

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 18 18 18 61 17 15 17 18

N.S.

1 0.75 0.75 0.75 2.54 0.71 0.62 0.71 0.75

time (sec)

N/A 0.278 0.036 0.079 0.301 0.262 0.054 0.279 0.101

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