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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 51 72 71 50 75 67 -1

N.S.

1 1.00 0.68 0.96 0.95 0.67 1.00 0.89 -0.01

time (sec)

N/A 0.032 0.022 0.007 0.483 2.480 0.320 0.412 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 54 60 61 48 66 57 -1

N.S.

1 1.00 0.78 0.87 0.88 0.70 0.96 0.83 -0.01

time (sec)

N/A 0.019 0.022 0.004 0.469 0.825 0.209 0.438 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 42 52 50 41 53 47 -1

N.S.

1 1.00 0.78 0.96 0.93 0.76 0.98 0.87 -0.02

time (sec)

N/A 0.023 0.024 0.006 0.477 3.496 0.129 0.409 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 42 40 40 37 42 37 38

N.S.

1 1.00 0.93 0.89 0.89 0.82 0.93 0.82 0.84

time (sec)

N/A 0.011 0.012 0.006 0.463 1.640 0.090 0.431 0.036

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

26 26 26 27 26 26 24 26 24

N.S.

1 1.00 1.00 1.04 1.00 1.00 0.92 1.00 0.92

time (sec)

N/A 0.005 0.005 0.006 0.472 2.563 0.057 0.407 0.069

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 51 68 0 0 0 0 -1

N.S.

1 1.00 1.00 1.33 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.038 0.014 0.312 0.000 0.000 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 34 29 38 82 34 48 25

N.S.

1 1.00 1.26 1.07 1.41 3.04 1.26 1.78 0.93

time (sec)

N/A 0.015 0.010 0.006 0.487 2.674 1.000 0.432 0.023

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 31 38 28 27 53 68 -1

N.S.

1 1.00 0.91 1.12 0.82 0.79 1.56 2.00 -0.03

time (sec)

N/A 0.010 0.013 0.006 0.477 3.471 0.751 0.447 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 67 53 60 110 109 77 -1

N.S.

1 1.00 1.20 0.95 1.07 1.96 1.95 1.38 -0.02

time (sec)

N/A 0.024 0.019 0.004 0.460 3.264 1.664 0.424 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 41 58 50 37 102 130 -1

N.S.

1 1.00 0.71 1.00 0.86 0.64 1.76 2.24 -0.02

time (sec)

N/A 0.015 0.017 0.006 0.465 3.184 1.073 0.421 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 72 73 82 122 184 101 -1

N.S.

1 1.00 0.90 0.91 1.02 1.52 2.30 1.26 -0.01

time (sec)

N/A 0.031 0.053 0.013 0.456 3.841 3.399 0.411 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 82 76 102 76 121 100 -1

N.S.

1 1.00 0.68 0.63 0.85 0.63 1.01 0.83 -0.01

time (sec)

N/A 0.132 0.042 0.050 0.472 2.976 0.513 0.474 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 74 91 0 70 97 87 -1

N.S.

1 1.00 0.76 0.93 0.00 0.71 0.99 0.89 -0.01

time (sec)

N/A 0.111 0.026 0.060 0.000 2.996 0.335 0.433 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 63 59 72 59 83 68 -1

N.S.

1 1.00 0.77 0.72 0.88 0.72 1.01 0.83 -0.01

time (sec)

N/A 0.080 0.033 0.045 0.477 2.720 0.202 0.421 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 57 63 0 51 58 55 -1

N.S.

1 1.00 0.95 1.05 0.00 0.85 0.97 0.92 -0.02

time (sec)

N/A 0.062 0.020 0.060 0.000 3.428 0.130 0.435 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

35 35 35 37 33 36 37 33 45

N.S.

1 1.00 1.00 1.06 0.94 1.03 1.06 0.94 1.29

time (sec)

N/A 0.031 0.015 0.088 0.480 3.244 0.094 0.430 0.314

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 73 101 0 0 0 0 -1

N.S.

1 1.00 1.00 1.38 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.063 0.017 0.136 0.000 0.000 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 98 136 0 0 0 0 -1

N.S.

1 1.00 1.32 1.84 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.075 0.098 0.105 0.000 0.000 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 43 47 39 44 0 82 -1

N.S.

1 1.00 1.00 1.09 0.91 1.02 0.00 1.91 -0.02

time (sec)

N/A 0.053 0.020 0.112 0.465 3.105 0.000 0.427 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

124 124 152 166 0 0 0 0 -1

N.S.

1 1.00 1.23 1.34 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.123 0.426 0.624 0.000 0.000 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 69 82 74 62 0 185 -1

N.S.

1 1.00 0.79 0.94 0.85 0.71 0.00 2.13 -0.01

time (sec)

N/A 0.097 0.028 0.118 0.486 2.478 0.000 0.519 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

201 201 122 159 171 104 202 175 -1

N.S.

1 1.00 0.61 0.79 0.85 0.52 1.00 0.87 -0.00

time (sec)

N/A 0.262 0.048 0.049 0.486 3.355 0.732 0.435 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

167 167 115 151 0 96 167 141 -1

N.S.

1 1.00 0.69 0.90 0.00 0.57 1.00 0.84 -0.01

time (sec)

N/A 0.200 0.052 0.070 0.000 3.213 0.513 0.438 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 95 106 120 78 134 117 -1

N.S.

1 1.00 0.70 0.78 0.88 0.57 0.99 0.86 -0.01

time (sec)

N/A 0.150 0.035 0.046 0.473 2.355 0.343 0.431 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 99 85 90 0 69 99 83 -1

N.S.

1 1.00 0.86 0.91 0.00 0.70 1.00 0.84 -0.01

time (sec)

N/A 0.102 0.029 0.059 0.000 2.967 0.200 0.476 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 60 57 59 44 60 56 59

N.S.

1 1.00 1.00 0.95 0.98 0.73 1.00 0.93 0.98

time (sec)

N/A 0.052 0.015 0.075 0.470 2.946 0.124 0.418 0.309

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 101 135 0 0 0 0 -1

N.S.

1 1.00 1.00 1.34 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.073 0.017 0.138 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 139 0 0 0 0 0 -1

N.S.

1 1.00 1.14 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.118 0.079 0.372 0.000 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 92 117 0 0 0 0 -1

N.S.

1 1.00 0.90 1.15 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.116 0.141 0.359 0.000 0.000 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

192 192 501 256 0 0 0 0 -1

N.S.

1 1.00 2.61 1.33 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.201 1.081 0.431 0.000 0.000 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

169 169 149 190 0 0 0 0 -1

N.S.

1 1.00 0.88 1.12 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.192 0.358 0.447 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

282 282 167 332 0 153 275 245 -1

N.S.

1 1.00 0.59 1.18 0.00 0.54 0.98 0.87 -0.00

time (sec)

N/A 0.565 0.062 0.165 0.000 2.480 1.532 0.461 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

250 250 150 197 206 134 248 212 -1

N.S.

1 1.00 0.60 0.79 0.82 0.54 0.99 0.85 -0.00

time (sec)

N/A 0.442 0.065 0.048 0.480 3.037 1.071 0.421 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

198 198 135 213 0 121 197 173 -1

N.S.

1 1.00 0.68 1.08 0.00 0.61 0.99 0.87 -0.01

time (sec)

N/A 0.349 0.048 0.070 0.000 3.569 0.750 0.450 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

166 166 114 130 146 99 165 140 -1

N.S.

1 1.00 0.69 0.78 0.88 0.60 0.99 0.84 -0.01

time (sec)

N/A 0.244 0.052 0.043 0.486 2.699 0.503 0.426 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 96 113 0 82 110 101 -1

N.S.

1 1.00 0.86 1.01 0.00 0.73 0.98 0.90 -0.01

time (sec)

N/A 0.158 0.032 0.060 0.000 3.482 0.325 0.429 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 69 67 74 55 70 65 63

N.S.

1 1.00 1.00 0.97 1.07 0.80 1.01 0.94 0.91

time (sec)

N/A 0.079 0.019 0.086 0.481 2.828 0.185 0.432 0.305

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 119 168 0 0 0 0 -1

N.S.

1 1.00 1.00 1.41 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.085 0.017 0.144 0.000 0.000 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

176 176 549 0 0 0 0 0 -1

N.S.

1 1.00 3.12 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.145 0.753 0.305 0.000 0.000 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 115 150 0 0 0 0 -1

N.S.

1 1.00 0.95 1.24 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.143 0.271 0.364 0.000 0.000 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

304 304 1475 419 0 0 0 0 -1

N.S.

1 1.00 4.85 1.38 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.284 12.052 0.450 0.000 0.000 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 40 40 0 0 0 47 -1

N.S.

1 1.00 0.73 0.73 0.00 0.00 0.00 0.85 -0.02

time (sec)

N/A 0.064 0.082 0.172 0.000 0.000 0.000 0.413 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 33 33 0 0 0 37 -1

N.S.

1 1.00 0.77 0.77 0.00 0.00 0.00 0.86 -0.02

time (sec)

N/A 0.056 0.070 0.142 0.000 0.000 0.000 0.455 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 31 31 0 0 0 35 -1

N.S.

1 1.00 0.76 0.76 0.00 0.00 0.00 0.85 -0.02

time (sec)

N/A 0.058 0.063 0.040 0.000 0.000 0.000 0.426 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

29 29 24 24 0 0 0 25 -1

N.S.

1 1.00 0.83 0.83 0.00 0.00 0.00 0.86 -0.03

time (sec)

N/A 0.045 0.052 0.046 0.000 0.000 0.000 0.459 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 20 22 0 0 0 23 -1

N.S.

1 1.00 0.74 0.81 0.00 0.00 0.00 0.85 -0.04

time (sec)

N/A 0.043 0.045 0.042 0.000 0.000 0.000 0.418 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

14 14 14 13 0 0 0 12 -1

N.S.

1 1.00 1.00 0.93 0.00 0.00 0.00 0.86 -0.07

time (sec)

N/A 0.027 0.015 0.035 0.000 0.000 0.000 0.424 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

10 10 10 11 0 0 0 10 -1

N.S.

1 1.00 1.00 1.10 0.00 0.00 0.00 1.00 -0.10

time (sec)

N/A 0.011 0.020 0.073 0.000 0.000 0.000 0.420 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

13 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08

time (sec)

N/A 0.009 0.163 1.016 0.000 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

13 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08

time (sec)

N/A 0.009 0.611 0.829 0.000 0.000 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 86 105 0 0 0 72 -1

N.S.

1 1.00 1.05 1.28 0.00 0.00 0.00 0.88 -0.01

time (sec)

N/A 0.053 0.110 0.178 0.000 0.000 0.000 0.438 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 63 78 0 0 0 62 -1

N.S.

1 1.00 0.90 1.11 0.00 0.00 0.00 0.89 -0.01

time (sec)

N/A 0.049 0.116 0.144 0.000 0.000 0.000 0.439 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 61 81 0 0 0 60 -1

N.S.

1 1.00 0.90 1.19 0.00 0.00 0.00 0.88 -0.01

time (sec)

N/A 0.045 0.114 0.047 0.000 0.000 0.000 0.431 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 50 54 0 0 0 50 -1

N.S.

1 1.00 0.89 0.96 0.00 0.00 0.00 0.89 -0.02

time (sec)

N/A 0.035 0.116 0.049 0.000 0.000 0.000 0.441 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 50 57 0 0 0 48 -1

N.S.

1 1.00 0.93 1.06 0.00 0.00 0.00 0.89 -0.02

time (sec)

N/A 0.034 0.090 0.043 0.000 0.000 0.000 0.432 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 37 30 0 0 0 36 -1

N.S.

1 1.00 0.97 0.79 0.00 0.00 0.00 0.95 -0.03

time (sec)

N/A 0.019 0.069 0.036 0.000 0.000 0.000 0.447 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

35 35 35 32 0 0 0 33 -1

N.S.

1 1.00 1.00 0.91 0.00 0.00 0.00 0.94 -0.03

time (sec)

N/A 0.054 0.033 0.073 0.000 0.000 0.000 0.434 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

13 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08

time (sec)

N/A 0.009 0.717 0.986 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 A A A A A A

verified

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

size

13 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08

time (sec)

N/A 0.009 11.775 0.835 0.000 0.000 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 103 121 0 0 0 86 -1

N.S.

1 1.00 1.05 1.23 0.00 0.00 0.00 0.88 -0.01

time (sec)

N/A 0.234 0.104 0.148 0.000 0.000 0.000 0.443 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 70 82 0 0 0 75 -1

N.S.

1 1.00 0.84 0.99 0.00 0.00 0.00 0.90 -0.01

time (sec)

N/A 0.207 0.116 0.115 0.000 0.000 0.000 0.436 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 65 82 0 0 0 72 -1

N.S.

1 1.00 0.79 1.00 0.00 0.00 0.00 0.88 -0.01

time (sec)

N/A 0.174 0.098 0.042 0.000 0.000 0.000 0.454 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 63 43 0 0 0 57 -1

N.S.

1 1.00 1.00 0.68 0.00 0.00 0.00 0.90 -0.02

time (sec)

N/A 0.117 0.026 0.037 0.000 0.000 0.000 0.414 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 47 43 0 0 0 43 -1

N.S.

1 1.00 0.92 0.84 0.00 0.00 0.00 0.84 -0.02

time (sec)

N/A 0.057 0.023 0.073 0.000 0.000 0.000 0.454 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

13 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08

time (sec)

N/A 0.009 0.519 1.034 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 A A A A A

verified

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

size

13 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08

time (sec)

N/A 0.010 6.486 0.839 0.000 0.000 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

158 158 159 171 0 0 0 138 -1

N.S.

1 1.00 1.01 1.08 0.00 0.00 0.00 0.87 -0.01

time (sec)

N/A 0.229 0.115 0.142 0.000 0.000 0.000 0.436 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

143 143 107 114 0 0 0 125 -1

N.S.

1 1.00 0.75 0.80 0.00 0.00 0.00 0.87 -0.01

time (sec)

N/A 0.193 0.179 0.112 0.000 0.000 0.000 0.451 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 129 117 0 0 0 121 -1

N.S.

1 1.00 0.91 0.83 0.00 0.00 0.00 0.86 -0.01

time (sec)

N/A 0.217 0.087 0.045 0.000 0.000 0.000 0.427 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 86 60 0 0 0 83 -1

N.S.

1 1.00 0.89 0.62 0.00 0.00 0.00 0.86 -0.01

time (sec)

N/A 0.114 0.074 0.038 0.000 0.000 0.000 0.438 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 71 63 0 0 0 66 -1

N.S.

1 1.00 0.91 0.81 0.00 0.00 0.00 0.85 -0.01

time (sec)

N/A 0.102 0.036 0.082 0.000 0.000 0.000 0.412 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

13 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08

time (sec)

N/A 0.009 1.955 1.001 0.000 0.000 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

13 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08

time (sec)

N/A 0.009 19.368 0.844 0.000 0.000 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 212 143 0 0 0 247 -1

N.S.

1 1.00 1.75 1.18 0.00 0.00 0.00 2.04 -0.01

time (sec)

N/A 0.176 0.195 0.420 0.000 0.000 0.000 0.495 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 125 91 0 0 0 153 -1

N.S.

1 1.00 1.32 0.96 0.00 0.00 0.00 1.61 -0.01

time (sec)

N/A 0.136 0.088 0.293 0.000 0.000 0.000 0.483 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 122 96 0 0 0 165 -1

N.S.

1 1.00 1.42 1.12 0.00 0.00 0.00 1.92 -0.01

time (sec)

N/A 0.140 0.134 0.237 0.000 0.000 0.000 0.489 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 49 42 0 0 0 71 -1

N.S.

1 1.00 0.83 0.71 0.00 0.00 0.00 1.20 -0.02

time (sec)

N/A 0.111 0.027 0.152 0.000 0.000 0.000 0.465 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

44 44 76 49 0 0 0 83 -1

N.S.

1 1.00 1.73 1.11 0.00 0.00 0.00 1.89 -0.02

time (sec)

N/A 0.066 0.029 0.143 0.000 0.000 0.000 0.454 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

15 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07

time (sec)

N/A 0.009 0.308 0.174 0.000 0.000 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

282 282 185 193 0 0 0 355 -1

N.S.

1 1.00 0.66 0.68 0.00 0.00 0.00 1.26 -0.00

time (sec)

N/A 0.378 0.090 0.322 0.000 0.000 0.000 0.503 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

157 157 128 121 0 0 0 225 -1

N.S.

1 1.00 0.82 0.77 0.00 0.00 0.00 1.43 -0.01

time (sec)

N/A 0.260 0.055 0.250 0.000 0.000 0.000 0.462 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 125 130 0 0 0 237 -1

N.S.

1 1.00 0.85 0.88 0.00 0.00 0.00 1.61 -0.01

time (sec)

N/A 0.206 0.071 0.221 0.000 0.000 0.000 0.471 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 64 64 0 0 0 107 -1

N.S.

1 1.00 0.72 0.72 0.00 0.00 0.00 1.20 -0.01

time (sec)

N/A 0.121 0.054 0.178 0.000 0.000 0.000 0.483 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 66 72 0 0 0 119 -1

N.S.

1 1.00 0.88 0.96 0.00 0.00 0.00 1.59 -0.01

time (sec)

N/A 0.077 0.021 0.164 0.000 0.000 0.000 0.495 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

15 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07

time (sec)

N/A 0.009 0.297 0.168 0.000 0.000 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

298 298 212 233 0 0 0 463 -1

N.S.

1 1.00 0.71 0.78 0.00 0.00 0.00 1.55 -0.00

time (sec)

N/A 0.535 0.145 0.308 0.000 0.000 0.000 0.496 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

205 205 140 154 0 0 0 297 -1

N.S.

1 1.00 0.68 0.75 0.00 0.00 0.00 1.45 -0.00

time (sec)

N/A 0.400 0.092 0.243 0.000 0.000 0.000 0.489 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

178 178 122 156 0 0 0 309 -1

N.S.

1 1.00 0.69 0.88 0.00 0.00 0.00 1.74 -0.01

time (sec)

N/A 0.308 0.088 0.227 0.000 0.000 0.000 0.478 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 73 79 0 0 0 143 -1

N.S.

1 1.00 0.61 0.66 0.00 0.00 0.00 1.20 -0.01

time (sec)

N/A 0.191 0.068 0.173 0.000 0.000 0.000 0.470 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 76 88 0 0 0 155 -1

N.S.

1 1.00 0.86 1.00 0.00 0.00 0.00 1.76 -0.01

time (sec)

N/A 0.109 0.028 0.151 0.000 0.000 0.000 0.520 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

15 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07

time (sec)

N/A 0.009 0.312 0.166 0.000 0.000 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 192 72 0 0 0 139 -1

N.S.

1 1.00 1.81 0.68 0.00 0.00 0.00 1.31 -0.01

time (sec)

N/A 0.073 0.075 0.218 0.000 0.000 0.000 0.470 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 130 43 0 0 0 81 -1

N.S.

1 1.00 2.00 0.66 0.00 0.00 0.00 1.25 -0.02

time (sec)

N/A 0.055 0.050 0.174 0.000 0.000 0.000 0.455 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 126 50 0 0 0 93 -1

N.S.

1 1.00 1.77 0.70 0.00 0.00 0.00 1.31 -0.01

time (sec)

N/A 0.058 0.061 0.154 0.000 0.000 0.000 0.459 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

28 28 28 21 0 0 0 35 -1

N.S.

1 1.00 1.00 0.75 0.00 0.00 0.00 1.25 -0.04

time (sec)

N/A 0.029 0.019 0.085 0.000 0.000 0.000 0.442 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 68 26 0 0 0 47 -1

N.S.

1 1.00 2.19 0.84 0.00 0.00 0.00 1.52 -0.03

time (sec)

N/A 0.017 0.020 0.088 0.000 0.000 0.000 0.435 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

15 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07

time (sec)

N/A 0.010 0.245 0.135 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(-2) F(-2) A A A

verified

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

size

15 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07

time (sec)

N/A 0.010 2.552 0.730 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 306 182 0 0 0 0 -1

N.S.

1 1.00 1.79 1.06 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.108 0.208 0.360 0.000 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 226 121 0 0 0 0 -1

N.S.

1 1.00 1.78 0.95 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.075 0.346 0.269 0.000 0.000 0.000 0.000 0.000

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