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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 B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 21 11 10 10 12 10 10

N.S.

1 1.00 2.10 1.10 1.00 1.00 1.20 1.00 1.00

time (sec)

N/A 0.152 0.012 0.268 0.239 0.265 0.060 0.294 14.677

Problem 2

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

25 25 23 19 22 22 46 18 18

N.S.

1 1.00 0.92 0.76 0.88 0.88 1.84 0.72 0.72

time (sec)

N/A 0.164 0.028 0.476 0.255 0.310 0.091 0.289 15.283

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

26 26 26 22 22 21 36 22 24

N.S.

1 1.00 1.00 0.85 0.85 0.81 1.38 0.85 0.92

time (sec)

N/A 0.176 0.010 0.911 0.254 0.262 0.124 0.293 13.520

Problem 4

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

46 51 33 31 33 36 95 32 31

N.S.

1 1.11 0.72 0.67 0.72 0.78 2.07 0.70 0.67

time (sec)

N/A 0.226 0.047 0.754 0.251 0.271 0.175 0.299 13.694

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

41 38 41 32 34 33 58 34 31

N.S.

1 0.93 1.00 0.78 0.83 0.80 1.41 0.83 0.76

time (sec)

N/A 0.184 0.016 0.996 0.240 0.286 0.238 0.296 0.054

Problem 6

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

67 77 43 42 48 46 139 46 42

N.S.

1 1.15 0.64 0.63 0.72 0.69 2.07 0.69 0.63

time (sec)

N/A 0.297 0.046 1.135 0.231 0.271 0.375 0.294 14.250

Problem 7

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

54 46 54 42 44 43 78 44 43

N.S.

1 0.85 1.00 0.78 0.81 0.80 1.44 0.81 0.80

time (sec)

N/A 0.183 0.015 1.276 0.244 0.270 0.508 0.319 13.988

Problem 8

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

88 103 55 55 59 56 184 60 53

N.S.

1 1.17 0.62 0.62 0.67 0.64 2.09 0.68 0.60

time (sec)

N/A 0.381 0.062 1.148 0.260 0.279 0.710 0.293 14.508

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 70 51 199 0 80 0 0 42

N.S.

1 1.08 0.78 3.06 0.00 1.23 0.00 0.00 0.65

time (sec)

N/A 0.289 0.124 4.632 0.000 0.096 0.000 0.000 14.502

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 40 202 0 74 0 0 42

N.S.

1 1.00 0.95 4.81 0.00 1.76 0.00 0.00 1.00

time (sec)

N/A 0.219 0.064 2.886 0.000 0.102 0.000 0.000 14.441

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 36 179 0 68 0 0 35

N.S.

1 1.00 0.86 4.26 0.00 1.62 0.00 0.00 0.83

time (sec)

N/A 0.222 0.052 2.154 0.000 0.091 0.000 0.000 14.407

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 133 0 57 0 0 15

N.S.

1 1.00 1.00 8.31 0.00 3.56 0.00 0.00 0.94

time (sec)

N/A 0.157 0.033 1.612 0.000 0.086 0.000 0.000 14.414

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 18 0 51 0 0 15

N.S.

1 1.00 1.00 1.12 0.00 3.19 0.00 0.00 0.94

time (sec)

N/A 0.158 0.038 0.246 0.000 0.090 0.000 0.000 13.594

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 38 182 0 93 0 0 42

N.S.

1 1.00 1.00 4.79 0.00 2.45 0.00 0.00 1.11

time (sec)

N/A 0.219 0.074 1.302 0.000 0.096 0.000 0.000 14.078

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 36 213 0 92 0 0 42

N.S.

1 1.00 0.86 5.07 0.00 2.19 0.00 0.00 1.00

time (sec)

N/A 0.221 0.072 1.456 0.000 0.087 0.000 0.000 14.248

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 66 59 358 0 110 0 0 42

N.S.

1 1.02 0.91 5.51 0.00 1.69 0.00 0.00 0.65

time (sec)

N/A 0.297 0.116 2.307 0.000 0.090 0.000 0.000 14.850

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 104 76 210 0 95 0 0 0

N.S.

1 1.06 0.78 2.14 0.00 0.97 0.00 0.00 0.00

time (sec)

N/A 0.417 0.126 4.013 0.000 0.096 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 62 213 0 91 0 0 0

N.S.

1 1.00 0.89 3.04 0.00 1.30 0.00 0.00 0.00

time (sec)

N/A 0.314 0.105 2.784 0.000 0.096 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 58 190 0 77 0 0 0

N.S.

1 1.00 0.83 2.71 0.00 1.10 0.00 0.00 0.00

time (sec)

N/A 0.311 0.065 2.322 0.000 0.093 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 38 142 0 63 0 0 0

N.S.

1 1.00 1.00 3.74 0.00 1.66 0.00 0.00 0.00

time (sec)

N/A 0.230 0.036 1.915 0.000 0.089 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 38 54 0 60 0 0 33

N.S.

1 1.00 1.00 1.42 0.00 1.58 0.00 0.00 0.87

time (sec)

N/A 0.224 0.042 0.388 0.000 0.082 0.000 0.000 0.157

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 50 198 0 104 0 0 0

N.S.

1 1.00 0.74 2.91 0.00 1.53 0.00 0.00 0.00

time (sec)

N/A 0.312 0.048 1.450 0.000 0.093 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 51 241 0 103 0 0 0

N.S.

1 1.00 0.71 3.35 0.00 1.43 0.00 0.00 0.00

time (sec)

N/A 0.310 0.082 1.646 0.000 0.093 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 104 68 366 0 121 0 0 0

N.S.

1 1.04 0.68 3.66 0.00 1.21 0.00 0.00 0.00

time (sec)

N/A 0.412 0.123 2.339 0.000 0.097 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

53 53 53 0 0 0 0 0 42

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.79

time (sec)

N/A 0.178 0.065 0.000 0.000 0.000 0.000 0.000 13.888

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F B

verified

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

size

53 53 53 0 0 0 0 0 42

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.79

time (sec)

N/A 0.179 0.035 0.000 0.000 0.000 0.000 0.000 15.288

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F B

verified

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

size

53 53 53 0 0 0 0 0 42

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.79

time (sec)

N/A 0.177 0.035 0.000 0.000 0.000 0.000 0.000 15.053

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F B

verified

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

size

53 53 53 0 0 0 0 0 42

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.79

time (sec)

N/A 0.180 0.031 0.000 0.000 0.000 0.000 0.000 14.948

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F B

verified

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

size

51 51 51 0 0 0 0 0 42

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.82

time (sec)

N/A 0.175 0.028 0.000 0.000 0.000 0.000 0.000 15.290

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F B

verified

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

size

51 51 51 0 0 0 0 0 42

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.82

time (sec)

N/A 0.175 0.029 0.000 0.000 0.000 0.000 0.000 15.332

Problem 31

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

58 58 55 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 0.184 0.053 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 F F F F(-1)

verified

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

size

58 58 55 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 0.185 0.041 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 F F F F(-1)

verified

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

size

58 58 55 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 0.186 0.040 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 F F F F F F(-1)

verified

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

size

58 58 55 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 0.188 0.046 0.000 0.000 0.000 0.000 0.000 0.000

Problem 35

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

56 56 53 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 0.186 0.044 0.000 0.000 0.000 0.000 0.000 0.000

Problem 36

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

56 56 53 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 0.189 0.044 0.000 0.000 0.000 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F B

verified

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

size

64 64 64 0 0 0 0 0 57

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.89

time (sec)

N/A 0.190 0.050 0.000 0.000 0.000 0.000 0.000 14.946

Problem 38

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

69 69 64 0 0 0 0 0 0

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.195 0.049 0.000 0.000 0.000 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 56 33 32 31 40 0 34 0

N.S.

1 1.06 0.62 0.60 0.58 0.75 0.00 0.64 0.00

time (sec)

N/A 0.359 0.015 1.229 0.365 0.296 0.000 0.347 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 23 24 17 26 0 17 0

N.S.

1 1.00 0.68 0.71 0.50 0.76 0.00 0.50 0.00

time (sec)

N/A 0.272 0.008 0.783 0.388 0.301 0.000 0.319 0.000

Problem 41

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

13 13 13 15 6 15 15 9 46

N.S.

1 1.00 1.00 1.15 0.46 1.15 1.15 0.69 3.54

time (sec)

N/A 0.205 0.005 0.819 0.375 0.296 0.230 0.378 14.477

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 48 38 65 0 0 0

N.S.

1 1.00 1.00 3.00 2.38 4.06 0.00 0.00 0.00

time (sec)

N/A 0.220 0.004 0.905 0.385 0.284 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 26 70 304 40 0 20 0

N.S.

1 1.00 0.62 1.67 7.24 0.95 0.00 0.48 0.00

time (sec)

N/A 0.293 0.013 1.045 0.395 0.284 0.000 0.355 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 69 36 89 933 49 0 29 0

N.S.

1 1.13 0.59 1.46 15.30 0.80 0.00 0.48 0.00

time (sec)

N/A 0.381 0.038 1.077 0.622 0.300 0.000 0.311 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 95 61 117 0 92 0 0 0

N.S.

1 0.81 0.52 1.00 0.00 0.79 0.00 0.00 0.00

time (sec)

N/A 0.475 0.152 12.326 0.000 0.122 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 59 50 271 0 66 0 0 0

N.S.

1 0.88 0.75 4.04 0.00 0.99 0.00 0.00 0.00

time (sec)

N/A 0.335 0.099 6.035 0.000 0.123 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 41 37 92 0 59 0 0 0

N.S.

1 0.93 0.84 2.09 0.00 1.34 0.00 0.00 0.00

time (sec)

N/A 0.274 0.046 2.910 0.000 0.089 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 37 31 244 0 71 0 0 0

N.S.

1 0.88 0.74 5.81 0.00 1.69 0.00 0.00 0.00

time (sec)

N/A 0.273 0.039 3.470 0.000 0.101 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 61 44 101 0 74 0 0 0

N.S.

1 0.86 0.62 1.42 0.00 1.04 0.00 0.00 0.00

time (sec)

N/A 0.334 0.086 5.052 0.000 0.100 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 91 57 297 0 92 0 0 0

N.S.

1 0.78 0.49 2.54 0.00 0.79 0.00 0.00 0.00

time (sec)

N/A 0.476 0.135 8.308 0.000 0.131 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 92 53 56 85 68 0 57 0

N.S.

1 0.70 0.40 0.42 0.64 0.52 0.00 0.43 0.00

time (sec)

N/A 0.477 0.151 13.264 0.329 0.278 0.000 0.331 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 60 38 38 55 42 0 25 0

N.S.

1 0.77 0.49 0.49 0.71 0.54 0.00 0.32 0.00

time (sec)

N/A 0.337 0.097 0.821 0.352 0.291 0.000 0.295 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 29 25 20 22 21 0 13 0

N.S.

1 0.81 0.69 0.56 0.61 0.58 0.00 0.36 0.00

time (sec)

N/A 0.224 0.034 1.013 0.471 0.260 0.000 0.314 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 14 6 18 0 6 6

N.S.

1 1.00 1.00 0.93 0.40 1.20 0.00 0.40 0.40

time (sec)

N/A 0.220 0.008 1.138 0.343 0.268 0.000 0.290 14.202

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 40 30 33 22 33 0 22 36

N.S.

1 0.60 0.45 0.49 0.33 0.49 0.00 0.33 0.54

time (sec)

N/A 0.249 0.038 0.855 0.335 0.270 0.000 0.286 14.808

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 56 47 46 34 45 0 34 306

N.S.

1 0.48 0.40 0.39 0.29 0.38 0.00 0.29 2.62

time (sec)

N/A 0.266 0.074 0.956 0.329 0.291 0.000 0.291 18.029

Problem 57

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

78 78 72 0 0 0 0 0 0

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.279 0.073 0.000 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

89 89 74 0 0 0 0 0 0

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.283 0.191 0.000 0.000 0.000 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

83 83 72 0 0 0 0 0 0

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.278 0.130 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 F F F(-2) F F F(-1)

verified

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

size

74 88 68 0 0 0 0 0 0

N.S.

1 1.19 0.92 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.279 0.082 0.000 0.000 0.000 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

80 80 72 0 0 0 0 0 0

N.S.

1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.279 0.084 0.000 0.000 0.000 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

89 89 72 0 0 0 0 0 0

N.S.

1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.278 0.118 0.000 0.000 0.000 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

89 89 74 0 0 0 0 0 0

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.284 0.116 0.000 0.000 0.000 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 24 44 0 15 61 300 40

N.S.

1 1.00 1.00 1.83 0.00 0.62 2.54 12.50 1.67

time (sec)

N/A 0.239 0.047 1.199 0.000 0.264 0.470 0.565 14.224

Problem 65

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

80 80 74 0 0 0 0 0 0

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.295 0.062 0.000 0.000 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 F C F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 142 83 234 0 98 0 0 0

N.S.

1 1.15 0.67 1.90 0.00 0.80 0.00 0.00 0.00

time (sec)

N/A 0.562 0.355 6.764 0.000 0.113 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 108 75 221 0 101 0 0 0

N.S.

1 1.11 0.77 2.28 0.00 1.04 0.00 0.00 0.00

time (sec)

N/A 0.450 0.286 4.485 0.000 0.122 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 108 73 208 0 88 0 0 0

N.S.

1 1.14 0.77 2.19 0.00 0.93 0.00 0.00 0.00

time (sec)

N/A 0.435 0.263 3.465 0.000 0.114 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 74 62 211 0 88 0 0 0

N.S.

1 1.07 0.90 3.06 0.00 1.28 0.00 0.00 0.00

time (sec)

N/A 0.337 0.163 2.844 0.000 0.122 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 74 61 188 0 76 0 0 0

N.S.

1 1.10 0.91 2.81 0.00 1.13 0.00 0.00 0.00

time (sec)

N/A 0.332 0.079 2.211 0.000 0.088 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 38 142 0 63 0 0 0

N.S.

1 1.00 1.00 3.74 0.00 1.66 0.00 0.00 0.00

time (sec)

N/A 0.228 0.039 2.045 0.000 0.091 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 39 142 0 57 0 0 0

N.S.

1 1.00 1.00 3.64 0.00 1.46 0.00 0.00 0.00

time (sec)

N/A 0.262 0.048 1.437 0.000 0.088 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 72 48 196 0 101 0 0 0

N.S.

1 1.14 0.76 3.11 0.00 1.60 0.00 0.00 0.00

time (sec)

N/A 0.360 0.200 1.782 0.000 0.112 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 76 49 239 0 100 0 0 0

N.S.

1 1.09 0.70 3.41 0.00 1.43 0.00 0.00 0.00

time (sec)

N/A 0.352 0.224 1.837 0.000 0.105 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 108 69 364 0 118 0 0 0

N.S.

1 1.14 0.73 3.83 0.00 1.24 0.00 0.00 0.00

time (sec)

N/A 0.461 0.375 2.546 0.000 0.095 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 112 69 396 0 112 0 0 0

N.S.

1 1.14 0.70 4.04 0.00 1.14 0.00 0.00 0.00

time (sec)

N/A 0.467 0.336 2.135 0.000 0.097 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 144 79 414 0 128 0 0 0

N.S.

1 1.17 0.64 3.37 0.00 1.04 0.00 0.00 0.00

time (sec)

N/A 0.583 0.388 3.063 0.000 0.098 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 142 83 236 0 102 0 0 0

N.S.

1 1.13 0.66 1.87 0.00 0.81 0.00 0.00 0.00

time (sec)

N/A 0.553 0.264 5.704 0.000 0.102 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 108 75 223 0 103 0 0 0

N.S.

1 1.14 0.79 2.35 0.00 1.08 0.00 0.00 0.00

time (sec)

N/A 0.436 0.266 4.483 0.000 0.102 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 108 73 210 0 91 0 0 0

N.S.

1 1.10 0.74 2.14 0.00 0.93 0.00 0.00 0.00

time (sec)

N/A 0.432 0.202 3.411 0.000 0.100 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 74 65 213 0 89 0 0 0

N.S.

1 1.10 0.97 3.18 0.00 1.33 0.00 0.00 0.00

time (sec)

N/A 0.335 0.108 2.671 0.000 0.157 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 58 190 0 77 0 0 0

N.S.

1 1.00 0.83 2.71 0.00 1.10 0.00 0.00 0.00

time (sec)

N/A 0.314 0.045 2.162 0.000 0.095 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 39 144 0 63 0 0 0

N.S.

1 1.00 1.00 3.69 0.00 1.62 0.00 0.00 0.00

time (sec)

N/A 0.267 0.014 1.798 0.000 0.097 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 41 144 0 57 0 0 0

N.S.

1 1.00 1.00 3.51 0.00 1.39 0.00 0.00 0.00

time (sec)

N/A 0.268 0.025 1.269 0.000 0.102 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 72 50 198 0 102 0 0 0

N.S.

1 1.09 0.76 3.00 0.00 1.55 0.00 0.00 0.00

time (sec)

N/A 0.353 0.222 1.782 0.000 0.112 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 76 51 241 0 101 0 0 0

N.S.

1 1.06 0.71 3.35 0.00 1.40 0.00 0.00 0.00

time (sec)

N/A 0.355 0.177 1.781 0.000 0.089 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 108 69 365 0 119 0 0 0

N.S.

1 1.10 0.70 3.72 0.00 1.21 0.00 0.00 0.00

time (sec)

N/A 0.458 0.267 2.375 0.000 0.105 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 112 69 398 0 115 0 0 0

N.S.

1 1.12 0.69 3.98 0.00 1.15 0.00 0.00 0.00

time (sec)

N/A 0.453 0.374 2.136 0.000 0.104 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 144 79 416 0 132 0 0 0

N.S.

1 1.14 0.63 3.30 0.00 1.05 0.00 0.00 0.00

time (sec)

N/A 0.579 0.553 2.990 0.000 0.105 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 142 83 236 0 108 0 0 0

N.S.

1 1.14 0.66 1.89 0.00 0.86 0.00 0.00 0.00

time (sec)

N/A 0.548 0.364 10.455 0.000 0.112 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 108 75 223 0 107 0 0 0

N.S.

1 1.10 0.77 2.28 0.00 1.09 0.00 0.00 0.00

time (sec)

N/A 0.428 0.256 5.656 0.000 0.105 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 108 76 210 0 95 0 0 0

N.S.

1 1.11 0.78 2.16 0.00 0.98 0.00 0.00 0.00

time (sec)

N/A 0.433 0.145 3.607 0.000 0.097 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 62 213 0 91 0 0 0

N.S.

1 1.00 0.89 3.04 0.00 1.30 0.00 0.00 0.00

time (sec)

N/A 0.309 0.093 2.853 0.000 0.108 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 59 190 0 79 0 0 0

N.S.

1 1.00 0.82 2.64 0.00 1.10 0.00 0.00 0.00

time (sec)

N/A 0.344 0.048 2.771 0.000 0.099 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 41 144 0 63 0 0 0

N.S.

1 1.00 1.00 3.51 0.00 1.54 0.00 0.00 0.00

time (sec)

N/A 0.266 0.017 6.788 0.000 0.108 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 38 144 0 57 0 0 0

N.S.

1 1.00 0.93 3.51 0.00 1.39 0.00 0.00 0.00

time (sec)

N/A 0.261 0.208 27.801 0.000 0.093 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 72 50 198 0 104 0 0 0

N.S.

1 1.06 0.74 2.91 0.00 1.53 0.00 0.00 0.00

time (sec)

N/A 0.360 0.177 98.968 0.000 0.089 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 76 51 241 0 103 0 0 0

N.S.

1 1.06 0.71 3.35 0.00 1.43 0.00 0.00 0.00

time (sec)

N/A 0.356 0.251 1.135 0.000 0.105 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 108 69 367 0 123 0 0 0

N.S.

1 1.08 0.69 3.67 0.00 1.23 0.00 0.00 0.00

time (sec)

N/A 0.462 0.431 1.673 0.000 0.114 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 112 69 398 0 119 0 0 0

N.S.

1 1.12 0.69 3.98 0.00 1.19 0.00 0.00 0.00

time (sec)

N/A 0.457 0.682 1.065 0.000 0.101 0.000 0.000 0.000

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