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Integrals 1 to 98

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 F F A F F F(-1)

verified

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

size

67 67 67 0 0 65 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.97 0.00 0.00 0.00

time (sec)

N/A 0.081 0.419 0.000 0.000 0.083 0.000 0.000 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 141 100 260 309 227 350 8802 260

N.S.

1 1.00 0.71 1.84 2.19 1.61 2.48 62.43 1.84

time (sec)

N/A 0.074 0.465 0.164 0.204 0.286 0.113 0.503 0.167

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 110 78 165 206 147 231 4706 165

N.S.

1 1.00 0.71 1.50 1.87 1.34 2.10 42.78 1.50

time (sec)

N/A 0.048 0.156 0.108 0.222 0.282 0.098 0.463 0.100

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 79 56 91 123 84 133 2214 91

N.S.

1 1.00 0.71 1.15 1.56 1.06 1.68 28.03 1.15

time (sec)

N/A 0.029 0.244 0.126 0.189 0.258 0.092 0.352 0.082

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 34 38 60 38 60 898 38

N.S.

1 1.00 0.71 0.79 1.25 0.79 1.25 18.71 0.79

time (sec)

N/A 0.012 0.142 0.016 0.183 0.264 0.071 0.363 0.061

Problem 6

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 21 21 20 21 20 21 21

N.S.

1 1.00 1.05 1.05 1.00 1.05 1.00 1.05 1.05

time (sec)

N/A 0.002 0.022 0.012 0.177 0.271 0.049 0.332 0.041

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 31 56 0 39 0 0 0

N.S.

1 1.00 1.00 1.81 0.00 1.26 0.00 0.00 0.00

time (sec)

N/A 0.015 0.089 0.112 0.000 0.263 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 57 55 99 0 77 0 0 0

N.S.

1 1.00 0.96 1.74 0.00 1.35 0.00 0.00 0.00

time (sec)

N/A 0.032 0.298 0.094 0.000 0.262 0.000 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 95 88 155 0 134 0 0 0

N.S.

1 1.00 0.93 1.63 0.00 1.41 0.00 0.00 0.00

time (sec)

N/A 0.048 0.237 0.159 0.000 0.263 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 128 99 199 0 209 0 0 0

N.S.

1 1.00 0.77 1.55 0.00 1.63 0.00 0.00 0.00

time (sec)

N/A 0.069 0.250 0.347 0.000 0.264 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 161 121 243 0 300 0 0 0

N.S.

1 1.00 0.75 1.51 0.00 1.86 0.00 0.00 0.00

time (sec)

N/A 0.103 0.240 0.306 0.000 0.282 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 141 100 260 309 227 350 8802 260

N.S.

1 1.00 0.71 1.84 2.19 1.61 2.48 62.43 1.84

time (sec)

N/A 0.085 0.017 0.059 0.206 0.266 0.109 0.602 0.087

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 110 78 165 206 147 231 4706 165

N.S.

1 1.00 0.71 1.50 1.87 1.34 2.10 42.78 1.50

time (sec)

N/A 0.060 0.008 0.037 0.206 0.273 0.101 0.407 0.067

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 79 56 91 123 84 133 2214 91

N.S.

1 1.00 0.71 1.15 1.56 1.06 1.68 28.03 1.15

time (sec)

N/A 0.029 0.016 0.023 0.191 0.256 0.087 0.367 0.056

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 57 55 99 0 77 0 0 0

N.S.

1 1.00 0.96 1.74 0.00 1.35 0.00 0.00 0.00

time (sec)

N/A 0.031 0.011 0.246 0.000 0.269 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 95 88 155 0 134 0 0 0

N.S.

1 1.00 0.93 1.63 0.00 1.41 0.00 0.00 0.00

time (sec)

N/A 0.069 0.011 0.083 0.000 0.282 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 128 99 199 0 209 0 0 0

N.S.

1 1.00 0.77 1.55 0.00 1.63 0.00 0.00 0.00

time (sec)

N/A 0.092 0.013 0.123 0.000 0.266 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 161 121 243 0 300 0 0 0

N.S.

1 1.00 0.75 1.51 0.00 1.86 0.00 0.00 0.00

time (sec)

N/A 0.121 0.014 0.191 0.000 0.279 0.000 0.000 0.000

Problem 19

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

72 72 72 0 0 68 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.94 0.00 0.00 0.00

time (sec)

N/A 0.041 0.086 0.000 0.000 0.090 0.000 0.000 0.000

Problem 20

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

71 71 71 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.048 0.078 0.000 0.000 0.000 0.000 0.000 0.000

Problem 21

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

71 71 71 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.038 0.073 0.000 0.000 0.000 0.000 0.000 0.000

Problem 22

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

71 71 71 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.041 0.042 0.000 0.000 0.000 0.000 0.000 0.000

Problem 23

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 67 0 0 65 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.97 0.00 0.00 0.00

time (sec)

N/A 0.016 0.008 0.000 0.000 0.080 0.000 0.000 0.000

Problem 24

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

69 69 69 0 0 67 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.97 0.00 0.00 0.00

time (sec)

N/A 0.015 0.046 0.000 0.000 0.085 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(-2) F F(-1)

verified

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

size

73 73 73 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.040 0.036 0.000 0.000 0.000 0.000 0.000 0.000

Problem 26

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

73 73 73 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.039 0.036 0.000 0.000 0.000 0.000 0.000 0.000

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

15 15 15 14 13 13 14 13 13

N.S.

1 1.00 1.00 0.93 0.87 0.87 0.93 0.87 0.87

time (sec)

N/A 0.002 0.020 0.013 0.213 0.259 0.042 0.334 0.075

Problem 28

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 15 15 15 15

N.S.

1 1.00 1.00 1.07 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.002 0.015 0.013 0.178 0.248 0.040 0.398 0.060

Problem 29

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 19 19 12 13 13 10 13 11

N.S.

1 1.00 1.00 0.63 0.68 0.68 0.53 0.68 0.58

time (sec)

N/A 0.004 0.018 0.028 0.191 0.255 0.048 0.302 0.067

Problem 30

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

131 131 36 99 24 89 0 94 82

N.S.

1 1.00 0.27 0.76 0.18 0.68 0.00 0.72 0.63

time (sec)

N/A 0.111 0.087 0.022 0.228 0.266 0.000 0.310 0.105

Problem 31

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

108 108 36 87 24 77 0 82 72

N.S.

1 1.00 0.33 0.81 0.22 0.71 0.00 0.76 0.67

time (sec)

N/A 0.063 0.072 0.011 0.229 0.254 0.000 0.339 0.066

Problem 32

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

85 85 36 75 24 65 0 70 75

N.S.

1 1.00 0.42 0.88 0.28 0.76 0.00 0.82 0.88

time (sec)

N/A 0.044 0.096 0.008 0.226 0.252 0.000 0.326 0.068

Problem 33

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

62 62 30 66 24 51 0 58 55

N.S.

1 1.00 0.48 1.06 0.39 0.82 0.00 0.94 0.89

time (sec)

N/A 0.029 0.058 0.008 0.228 0.257 0.000 0.308 0.066

Problem 34

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

38 38 30 27 29 34 0 28 32

N.S.

1 1.00 0.79 0.71 0.76 0.89 0.00 0.74 0.84

time (sec)

N/A 0.018 0.070 0.010 0.225 0.264 0.000 0.469 0.081

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 38 64 24 44 0 0 42

N.S.

1 1.00 0.70 1.19 0.44 0.81 0.00 0.00 0.78

time (sec)

N/A 0.030 0.116 0.010 0.234 0.263 0.000 0.000 0.087

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 49 72 24 58 0 0 61

N.S.

1 1.00 0.64 0.94 0.31 0.75 0.00 0.00 0.79

time (sec)

N/A 0.044 0.106 0.010 0.227 0.259 0.000 0.000 0.095

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 100 61 84 24 74 0 0 80

N.S.

1 1.00 0.61 0.84 0.24 0.74 0.00 0.00 0.80

time (sec)

N/A 0.058 0.125 0.011 0.231 0.254 0.000 0.000 0.100

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 123 73 96 24 86 0 0 99

N.S.

1 1.00 0.59 0.78 0.20 0.70 0.00 0.00 0.80

time (sec)

N/A 0.076 0.148 0.010 0.229 0.269 0.000 0.000 0.098

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

208 208 72 0 0 230 0 1023 0

N.S.

1 1.00 0.35 0.00 0.00 1.11 0.00 4.92 0.00

time (sec)

N/A 0.181 0.193 0.000 0.000 0.259 0.000 0.459 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

173 173 72 0 0 167 0 643 0

N.S.

1 1.00 0.42 0.00 0.00 0.97 0.00 3.72 0.00

time (sec)

N/A 0.102 0.126 0.000 0.000 0.264 0.000 0.429 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

138 138 63 0 0 121 0 372 0

N.S.

1 1.00 0.46 0.00 0.00 0.88 0.00 2.70 0.00

time (sec)

N/A 0.076 0.153 0.000 0.000 0.261 0.000 0.437 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

105 105 63 0 0 90 0 189 0

N.S.

1 1.00 0.60 0.00 0.00 0.86 0.00 1.80 0.00

time (sec)

N/A 0.050 0.093 0.000 0.000 0.258 0.000 0.320 0.000

Problem 43

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

72 72 63 0 0 64 0 56 0

N.S.

1 1.00 0.88 0.00 0.00 0.89 0.00 0.78 0.00

time (sec)

N/A 0.030 0.094 0.000 0.000 0.261 0.000 0.300 0.000

Problem 44

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

97 97 75 0 0 90 0 0 0

N.S.

1 1.00 0.77 0.00 0.00 0.93 0.00 0.00 0.00

time (sec)

N/A 0.057 0.176 0.000 0.000 0.251 0.000 0.000 0.000

Problem 45

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

130 130 92 0 0 140 0 0 0

N.S.

1 1.00 0.71 0.00 0.00 1.08 0.00 0.00 0.00

time (sec)

N/A 0.084 0.277 0.000 0.000 0.249 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

165 165 118 0 0 230 0 0 0

N.S.

1 1.00 0.72 0.00 0.00 1.39 0.00 0.00 0.00

time (sec)

N/A 0.110 0.246 0.000 0.000 0.258 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(-1) F F(-1)

verified

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

size

200 200 144 0 0 321 0 0 0

N.S.

1 1.00 0.72 0.00 0.00 1.60 0.00 0.00 0.00

time (sec)

N/A 0.142 0.328 0.000 0.000 0.259 0.000 0.000 0.000

Problem 48

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

151 151 24 78 79 82 138 80 89

N.S.

1 1.00 0.16 0.52 0.52 0.54 0.91 0.53 0.59

time (sec)

N/A 0.089 0.609 0.096 0.188 0.263 127.004 0.299 0.104

Problem 49

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

71 71 63 0 0 117 0 0 0

N.S.

1 1.00 0.89 0.00 0.00 1.65 0.00 0.00 0.00

time (sec)

N/A 0.020 0.184 0.000 0.000 0.083 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

98 98 78 0 0 133 0 0 0

N.S.

1 1.00 0.80 0.00 0.00 1.36 0.00 0.00 0.00

time (sec)

N/A 0.069 0.200 0.000 0.000 0.086 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 A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 34 38 60 38 60 898 38

N.S.

1 1.00 0.71 0.79 1.25 0.79 1.25 18.71 0.79

time (sec)

N/A 0.013 0.007 0.000 0.190 0.242 0.061 0.347 0.002

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 135 56 80 117 74 116 2068 80

N.S.

1 1.00 0.41 0.59 0.87 0.55 0.86 15.32 0.59

time (sec)

N/A 0.078 0.118 0.020 0.210 0.275 0.075 0.355 0.149

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

229 229 84 138 194 122 190 4188 138

N.S.

1 1.00 0.37 0.60 0.85 0.53 0.83 18.29 0.60

time (sec)

N/A 0.128 0.176 0.027 0.204 0.255 0.088 0.377 0.183

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

348 348 117 212 291 182 284 7630 212

N.S.

1 1.00 0.34 0.61 0.84 0.52 0.82 21.93 0.61

time (sec)

N/A 0.215 0.540 0.033 0.195 0.252 0.120 0.414 0.217

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 116 61 334 123 126 99 0 0

N.S.

1 1.00 0.53 2.88 1.06 1.09 0.85 0.00 0.00

time (sec)

N/A 0.115 0.218 0.342 0.112 0.084 9.756 0.000 0.000

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

397 397 121 178 196 121 236 202 175

N.S.

1 1.00 0.30 0.45 0.49 0.30 0.59 0.51 0.44

time (sec)

N/A 0.341 0.283 0.210 0.206 0.262 0.102 0.300 0.201

Problem 57

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

318 318 130 143 164 102 196 163 126

N.S.

1 1.00 0.41 0.45 0.52 0.32 0.62 0.51 0.40

time (sec)

N/A 0.265 0.218 0.161 0.192 0.250 0.096 0.335 0.199

Problem 58

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

184 184 96 102 132 78 148 123 117

N.S.

1 1.00 0.52 0.55 0.72 0.42 0.80 0.67 0.64

time (sec)

N/A 0.165 0.172 0.197 0.197 0.266 0.087 0.294 0.108

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

80 80 41 68 103 57 104 87 66

N.S.

1 1.00 0.51 0.85 1.29 0.71 1.30 1.09 0.82

time (sec)

N/A 0.042 0.170 0.164 0.184 0.268 0.077 0.297 0.146

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

102 102 52 96 69 50 70 95 69

N.S.

1 1.00 0.51 0.94 0.68 0.49 0.69 0.93 0.68

time (sec)

N/A 0.102 0.177 0.210 0.230 0.268 3.432 0.291 0.233

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

94 94 54 88 61 56 99 92 72

N.S.

1 1.00 0.57 0.94 0.65 0.60 1.05 0.98 0.77

time (sec)

N/A 0.101 0.188 0.205 0.244 0.250 1.465 0.289 0.242

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

130 130 68 112 64 70 56 125 100

N.S.

1 1.00 0.52 0.86 0.49 0.54 0.43 0.96 0.77

time (sec)

N/A 0.134 0.167 0.225 0.242 0.262 1.264 0.287 0.253

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

198 198 81 167 63 83 53 183 142

N.S.

1 1.00 0.41 0.84 0.32 0.42 0.27 0.92 0.72

time (sec)

N/A 0.205 0.203 0.211 0.252 0.257 1.168 0.290 0.228

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 139 86 433 123 161 0 0 0

N.S.

1 1.00 0.62 3.12 0.88 1.16 0.00 0.00 0.00

time (sec)

N/A 0.192 0.271 0.600 0.115 0.084 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

414 414 159 250 328 228 323 9584 249

N.S.

1 1.00 0.38 0.60 0.79 0.55 0.78 23.15 0.60

time (sec)

N/A 0.448 0.291 0.220 0.196 0.257 0.116 0.444 0.265

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

328 328 121 197 262 178 260 6582 196

N.S.

1 1.00 0.37 0.60 0.80 0.54 0.79 20.07 0.60

time (sec)

N/A 0.362 0.256 0.178 0.194 0.263 0.106 0.525 0.207

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

242 242 91 144 196 132 199 4114 143

N.S.

1 1.00 0.38 0.60 0.81 0.55 0.82 17.00 0.59

time (sec)

N/A 0.227 0.214 0.207 0.209 0.257 0.091 0.449 0.182

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 85 58 93 134 85 134 2264 92

N.S.

1 1.00 0.68 1.09 1.58 1.00 1.58 26.64 1.08

time (sec)

N/A 0.078 0.166 0.203 0.187 0.245 0.098 0.465 0.153

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 96 54 118 87 75 0 0 80

N.S.

1 1.00 0.56 1.23 0.91 0.78 0.00 0.00 0.83

time (sec)

N/A 0.159 0.270 0.211 0.242 0.260 0.000 0.000 0.228

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 85 58 153 68 83 0 0 89

N.S.

1 1.00 0.68 1.80 0.80 0.98 0.00 0.00 1.05

time (sec)

N/A 0.175 0.250 0.230 0.259 0.239 0.000 0.000 0.253

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 136 76 208 74 89 0 0 133

N.S.

1 1.00 0.56 1.53 0.54 0.65 0.00 0.00 0.98

time (sec)

N/A 0.230 0.326 0.234 0.269 0.233 0.000 0.000 0.282

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

217 217 116 294 85 137 0 0 202

N.S.

1 1.00 0.53 1.35 0.39 0.63 0.00 0.00 0.93

time (sec)

N/A 0.291 0.277 0.200 0.267 0.237 0.000 0.000 0.302

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

321 321 156 386 93 186 0 0 258

N.S.

1 1.00 0.49 1.20 0.29 0.58 0.00 0.00 0.80

time (sec)

N/A 0.367 0.318 0.239 0.269 0.246 0.000 0.000 0.307

Problem 74

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

754 754 458 900 894 544 1445 1096 803

N.S.

1 1.00 0.61 1.19 1.19 0.72 1.92 1.45 1.06

time (sec)

N/A 0.603 6.787 0.188 0.223 0.244 0.292 0.384 0.485

Problem 75

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

495 495 320 560 599 354 899 674 537

N.S.

1 1.00 0.65 1.13 1.21 0.72 1.82 1.36 1.08

time (sec)

N/A 0.412 2.074 0.219 0.214 0.239 0.229 0.388 0.307

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

271 271 191 276 344 197 447 331 264

N.S.

1 1.00 0.70 1.02 1.27 0.73 1.65 1.22 0.97

time (sec)

N/A 0.222 0.731 0.159 0.204 0.250 0.138 0.330 0.214

Problem 77

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

102 102 50 99 149 83 158 132 120

N.S.

1 1.00 0.49 0.97 1.46 0.81 1.55 1.29 1.18

time (sec)

N/A 0.072 0.255 0.154 0.187 0.237 0.099 0.338 0.111

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

277 277 175 489 0 235 0 546 0

N.S.

1 1.00 0.63 1.77 0.00 0.85 0.00 1.97 0.00

time (sec)

N/A 0.221 0.738 0.263 0.000 0.241 0.000 0.350 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

258 258 163 406 0 353 0 2861 0

N.S.

1 1.00 0.63 1.57 0.00 1.37 0.00 11.09 0.00

time (sec)

N/A 0.244 1.184 0.196 0.000 0.271 0.000 0.366 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

294 294 267 418 0 550 0 1995 0

N.S.

1 1.00 0.91 1.42 0.00 1.87 0.00 6.79 0.00

time (sec)

N/A 0.262 1.888 0.248 0.000 0.265 0.000 0.407 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

396 396 389 511 0 793 0 3178 0

N.S.

1 1.00 0.98 1.29 0.00 2.00 0.00 8.03 0.00

time (sec)

N/A 0.329 2.262 0.204 0.000 0.283 0.000 0.398 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

557 557 669 596 0 1084 0 16988 0

N.S.

1 1.00 1.20 1.07 0.00 1.95 0.00 30.50 0.00

time (sec)

N/A 0.440 2.299 0.269 0.000 0.283 0.000 0.481 0.000

Problem 83

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

24 24 25 26 42 32 0 0 25

N.S.

1 1.00 1.04 1.08 1.75 1.33 0.00 0.00 1.04

time (sec)

N/A 0.089 0.192 307.214 0.263 0.270 0.000 0.000 0.280

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 23 25 42 25 0 0 23

N.S.

1 1.00 1.05 1.14 1.91 1.14 0.00 0.00 1.05

time (sec)

N/A 0.082 0.116 41.589 0.270 0.253 0.000 0.000 0.194

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 23 25 42 25 0 0 23

N.S.

1 1.00 1.05 1.14 1.91 1.14 0.00 0.00 1.05

time (sec)

N/A 0.067 0.106 23.717 0.269 0.274 0.000 0.000 0.186

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 21 23 38 23 0 0 21

N.S.

1 1.00 1.05 1.15 1.90 1.15 0.00 0.00 1.05

time (sec)

N/A 0.030 0.103 13.035 0.250 0.273 0.000 0.000 0.170

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 19 22 36 22 0 0 20

N.S.

1 1.00 1.00 1.16 1.89 1.16 0.00 0.00 1.05

time (sec)

N/A 0.079 0.024 15.115 0.265 0.297 0.000 0.000 0.177

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 23 25 39 25 0 0 23

N.S.

1 1.00 1.05 1.14 1.77 1.14 0.00 0.00 1.05

time (sec)

N/A 0.100 0.197 15.318 0.261 0.284 0.000 0.000 0.242

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 23 25 39 25 0 0 23

N.S.

1 1.00 1.05 1.14 1.77 1.14 0.00 0.00 1.05

time (sec)

N/A 0.085 0.209 15.315 0.266 0.279 0.000 0.000 0.239

Problem 90

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

91 91 45 43 60 43 51 43 45

N.S.

1 1.00 0.49 0.47 0.66 0.47 0.56 0.47 0.49

time (sec)

N/A 0.090 0.109 0.043 0.186 0.257 0.071 0.317 0.172

Problem 91

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 72 37 35 48 35 42 35 37

N.S.

1 1.00 0.51 0.49 0.67 0.49 0.58 0.49 0.51

time (sec)

N/A 0.071 0.093 0.020 0.178 0.259 0.071 0.332 0.052

Problem 92

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

53 53 29 27 36 27 34 27 29

N.S.

1 1.00 0.55 0.51 0.68 0.51 0.64 0.51 0.55

time (sec)

N/A 0.041 0.086 0.017 0.198 0.248 0.053 0.324 0.097

Problem 93

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 34 21 19 24 19 26 19 18

N.S.

1 1.00 0.62 0.56 0.71 0.56 0.76 0.56 0.53

time (sec)

N/A 0.017 0.062 0.020 0.183 0.248 0.054 0.347 0.043

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

16 16 16 14 14 14 14 14 13

N.S.

1 1.00 1.00 0.88 0.88 0.88 0.88 0.88 0.81

time (sec)

N/A 0.004 0.021 0.016 0.199 0.245 0.039 0.349 0.066

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 27 57 10 10 0 10 0

N.S.

1 1.00 1.00 2.11 0.37 0.37 0.00 0.37 0.00

time (sec)

N/A 0.045 0.078 0.014 0.228 0.254 0.000 0.336 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 47 116 13 29 0 29 0

N.S.

1 1.00 0.98 2.42 0.27 0.60 0.00 0.60 0.00

time (sec)

N/A 0.055 0.097 0.020 0.220 0.257 0.000 0.354 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 71 56 155 15 38 0 46 0

N.S.

1 1.00 0.79 2.18 0.21 0.54 0.00 0.65 0.00

time (sec)

N/A 0.078 0.106 0.023 0.230 0.248 0.000 0.332 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 92 64 189 15 46 0 63 0

N.S.

1 1.00 0.70 2.05 0.16 0.50 0.00 0.68 0.00

time (sec)

N/A 0.097 0.115 0.033 0.229 0.240 0.000 0.401 0.000

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