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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 B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

114 114 107 184 161 115 221 646 -1

N.S.

1 1.00 0.94 1.61 1.41 1.01 1.94 5.67 -0.01

time (sec)

N/A 0.045 0.094 0.146 0.260 0.472 11.779 0.935 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 72 83 80 62 153 518 -1

N.S.

1 1.00 0.81 0.93 0.90 0.70 1.72 5.82 -0.01

time (sec)

N/A 0.033 0.088 0.148 0.267 0.344 3.082 0.479 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 97 148 132 106 175 480 -1

N.S.

1 1.00 1.09 1.66 1.48 1.19 1.97 5.39 -0.01

time (sec)

N/A 0.036 0.049 0.142 0.270 0.413 4.801 0.716 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 62 74 59 52 107 352 -1

N.S.

1 1.00 0.97 1.16 0.92 0.81 1.67 5.50 -0.02

time (sec)

N/A 0.020 0.067 0.145 0.268 0.359 1.924 0.456 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 85 112 97 94 107 310 -1

N.S.

1 1.00 1.33 1.75 1.52 1.47 1.67 4.84 -0.02

time (sec)

N/A 0.025 0.042 0.144 0.312 0.412 2.635 0.683 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 50 65 36 39 58 182 40

N.S.

1 1.00 1.28 1.67 0.92 1.00 1.49 4.67 1.03

time (sec)

N/A 0.010 0.019 0.152 0.261 0.336 1.415 0.453 0.653

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 58 37 53 64 32 62 33

N.S.

1 1.00 1.87 1.19 1.71 2.06 1.03 2.00 1.06

time (sec)

N/A 0.017 0.045 0.075 0.258 0.347 1.633 0.421 0.872

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 53 140 0 0 0 0 65

N.S.

1 1.00 0.83 2.19 0.00 0.00 0.00 0.00 1.02

time (sec)

N/A 0.064 0.028 0.298 0.000 0.000 0.000 0.000 0.763

Problem 9

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

32 32 41 63 33 26 37 42 37

N.S.

1 1.00 1.28 1.97 1.03 0.81 1.16 1.31 1.16

time (sec)

N/A 0.017 0.022 0.147 0.254 0.390 0.482 0.438 0.636

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 66 114 83 40 121 66 50

N.S.

1 1.00 1.29 2.24 1.63 0.78 2.37 1.29 0.98

time (sec)

N/A 0.026 0.026 0.148 0.472 0.405 2.469 0.427 0.726

Problem 11

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

60 60 59 75 58 39 112 87 -1

N.S.

1 1.00 0.98 1.25 0.97 0.65 1.87 1.45 -0.02

time (sec)

N/A 0.028 0.045 0.145 0.277 0.391 2.146 0.439 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 78 150 125 53 194 117 -1

N.S.

1 1.00 1.03 1.97 1.64 0.70 2.55 1.54 -0.01

time (sec)

N/A 0.034 0.041 0.155 0.472 0.350 4.694 0.418 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 69 83 76 50 158 149 -1

N.S.

1 1.00 0.84 1.01 0.93 0.61 1.93 1.82 -0.01

time (sec)

N/A 0.036 0.061 0.146 0.265 0.343 5.067 0.432 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 88 186 165 63 243 174 -1

N.S.

1 1.00 0.87 1.84 1.63 0.62 2.41 1.72 -0.01

time (sec)

N/A 0.043 0.070 0.141 0.501 0.336 10.912 0.434 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

107 107 124 181 197 146 0 811 -1

N.S.

1 1.00 1.16 1.69 1.84 1.36 0.00 7.58 -0.01

time (sec)

N/A 0.082 0.149 0.411 0.505 0.428 0.000 0.535 0.000

Problem 16

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

139 139 210 304 0 0 0 0 -1

N.S.

1 1.00 1.51 2.19 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.096 0.977 0.779 0.000 0.000 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 89 127 84 111 0 427 -1

N.S.

1 1.00 1.62 2.31 1.53 2.02 0.00 7.76 -0.02

time (sec)

N/A 0.055 0.085 0.407 0.291 0.425 0.000 0.498 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

84 84 147 188 0 0 0 0 -1

N.S.

1 1.00 1.75 2.24 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.054 0.146 0.283 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 B F F F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 137 361 0 0 0 0 -1

N.S.

1 1.00 1.51 3.97 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.095 0.089 0.363 0.000 0.000 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 71 118 79 57 0 104 88

N.S.

1 1.00 1.42 2.36 1.58 1.14 0.00 2.08 1.76

time (sec)

N/A 0.050 0.092 0.268 0.267 0.397 0.000 0.444 0.812

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 102 201 0 82 0 163 -1

N.S.

1 1.00 1.16 2.28 0.00 0.93 0.00 1.85 -0.01

time (sec)

N/A 0.057 0.071 0.266 0.000 0.394 0.000 0.443 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 108 154 197 93 0 224 -1

N.S.

1 1.00 1.06 1.51 1.93 0.91 0.00 2.20 -0.01

time (sec)

N/A 0.078 0.149 0.406 0.519 0.403 0.000 0.449 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 148 274 0 120 0 304 -1

N.S.

1 1.00 1.10 2.04 0.00 0.90 0.00 2.27 -0.01

time (sec)

N/A 0.086 0.110 0.385 0.000 0.353 0.000 0.445 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

207 207 285 458 0 0 0 0 -1

N.S.

1 1.00 1.38 2.21 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.157 0.597 0.819 0.000 0.000 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

220 220 580 603 0 0 0 0 -1

N.S.

1 1.00 2.64 2.74 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.153 7.313 1.003 0.000 0.000 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 182 323 0 0 0 0 -1

N.S.

1 1.00 1.44 2.56 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.111 0.327 0.747 0.000 0.000 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

144 144 265 412 0 0 0 0 -1

N.S.

1 1.00 1.84 2.86 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.091 0.194 0.551 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 B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

124 124 242 666 0 0 0 0 -1

N.S.

1 1.00 1.95 5.37 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.106 0.130 0.401 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 B A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 135 199 147 98 0 195 155

N.S.

1 1.00 1.69 2.49 1.84 1.22 0.00 2.44 1.94

time (sec)

N/A 0.066 0.126 0.289 0.263 0.419 0.000 0.481 0.792

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 125 186 338 0 150 0 302 -1

N.S.

1 1.00 1.49 2.70 0.00 1.20 0.00 2.42 -0.01

time (sec)

N/A 0.075 0.134 0.354 0.000 0.352 0.000 0.464 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

170 170 204 299 0 173 0 428 -1

N.S.

1 1.00 1.20 1.76 0.00 1.02 0.00 2.52 -0.01

time (sec)

N/A 0.119 0.204 0.413 0.000 0.504 0.000 0.479 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

208 208 283 485 0 225 0 576 -1

N.S.

1 1.00 1.36 2.33 0.00 1.08 0.00 2.77 -0.00

time (sec)

N/A 0.125 0.225 0.519 0.000 0.420 0.000 0.447 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F(-2) 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 0.011 2.649 1.458 0.000 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A 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 0.005 2.411 0.910 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 A A A A A A

verified

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

size

17 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 -0.06

time (sec)

N/A 0.017 0.202 0.406 0.000 0.000 0.000 0.000 0.000

Problem 36

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

47 47 43 48 0 0 0 54 -1

N.S.

1 1.00 0.91 1.02 0.00 0.00 0.00 1.15 -0.02

time (sec)

N/A 0.081 0.057 0.243 0.000 0.000 0.000 0.560 0.000

Problem 37

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 56 58 0 0 0 95 -1

N.S.

1 1.00 0.89 0.92 0.00 0.00 0.00 1.51 -0.02

time (sec)

N/A 0.114 0.056 0.200 0.000 0.000 0.000 0.422 0.000

Problem 38

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

117 117 91 102 0 0 0 200 -1

N.S.

1 1.00 0.78 0.87 0.00 0.00 0.00 1.71 -0.01

time (sec)

N/A 0.194 0.132 0.207 0.000 0.000 0.000 0.423 0.000

Problem 39

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

19 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 -0.05

time (sec)

N/A 0.016 4.884 1.760 0.000 0.000 0.000 0.000 0.000

Problem 40

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

19 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 -0.05

time (sec)

N/A 0.017 3.202 1.744 0.000 0.000 0.000 0.000 0.000

Problem 41

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

66 66 83 0 0 0 0 0 -1

N.S.

1 1.00 1.26 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.034 0.113 1.830 0.000 0.000 0.000 0.000 0.000

Problem 42

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

19 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 -0.05

time (sec)

N/A 0.019 0.614 2.691 0.000 0.000 0.000 0.000 0.000

Problem 43

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

19 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 -0.05

time (sec)

N/A 0.020 1.225 1.408 0.000 0.000 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

167 167 165 413 267 283 362 1130 -1

N.S.

1 1.00 0.99 2.47 1.60 1.69 2.17 6.77 -0.01

time (sec)

N/A 0.296 0.191 0.232 0.280 0.474 5.993 2.531 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 122 315 198 208 228 602 -1

N.S.

1 1.00 0.99 2.56 1.61 1.69 1.85 4.89 -0.01

time (sec)

N/A 0.191 0.110 0.227 0.281 0.406 4.897 1.974 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 113 139 94 134 104 341 -1

N.S.

1 1.00 1.36 1.67 1.13 1.61 1.25 4.11 -0.01

time (sec)

N/A 0.117 0.151 0.158 0.271 0.481 3.248 0.592 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 58 37 53 64 32 62 33

N.S.

1 1.00 1.87 1.19 1.71 2.06 1.03 2.00 1.06

time (sec)

N/A 0.017 0.035 0.083 0.255 0.434 1.776 0.422 0.002

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

257 257 411 893 0 0 0 0 -1

N.S.

1 1.00 1.60 3.47 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.288 0.464 1.066 0.000 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 141 216 0 442 0 0 -1

N.S.

1 1.00 1.38 2.12 0.00 4.33 0.00 0.00 -0.01

time (sec)

N/A 0.114 0.140 2.318 0.000 0.420 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

172 172 250 971 0 1062 0 0 -1

N.S.

1 1.00 1.45 5.65 0.00 6.17 0.00 0.00 -0.01

time (sec)

N/A 0.221 0.338 4.423 0.000 0.655 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

496 693 870 1204 0 0 0 0 -1

N.S.

1 1.40 1.75 2.43 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 2.031 40.711 0.729 0.000 0.000 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

404 502 368 827 0 0 0 0 -1

N.S.

1 1.24 0.91 2.05 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.682 10.953 0.655 0.000 0.000 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

315 315 657 386 0 0 0 0 -1

N.S.

1 1.00 2.09 1.23 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.336 28.377 0.566 0.000 0.000 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 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 -0.04

time (sec)

N/A 0.049 180.001 3.827 0.000 0.000 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 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 -0.04

time (sec)

N/A 0.051 6.048 2.533 0.000 0.000 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

372 372 333 798 0 0 0 0 -1

N.S.

1 1.00 0.90 2.15 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.523 10.900 0.584 0.000 0.000 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

714 714 873 1233 0 0 0 0 -1

N.S.

1 1.00 1.22 1.73 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.906 30.533 0.619 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

530 530 784 850 0 0 0 0 -1

N.S.

1 1.00 1.48 1.60 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.463 30.501 0.579 0.000 0.000 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

344 344 289 410 0 0 0 0 -1

N.S.

1 1.00 0.84 1.19 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.203 10.906 0.566 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(-2) F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

212 212 243 252 0 0 0 0 -1

N.S.

1 1.00 1.15 1.19 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.226 3.827 0.553 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 A A A F(-1) A A

verified

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

size

24 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 -0.04

time (sec)

N/A 0.049 4.586 1.427 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 A A A A A A

verified

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

size

24 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 -0.04

time (sec)

N/A 0.055 6.972 3.257 0.000 0.000 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

551 551 814 880 0 0 0 0 -1

N.S.

1 1.00 1.48 1.60 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.859 30.757 0.582 0.000 0.000 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

369 369 750 439 0 0 0 0 -1

N.S.

1 1.00 2.03 1.19 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.411 30.556 0.535 0.000 0.000 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

238 238 226 282 0 0 0 0 -1

N.S.

1 1.00 0.95 1.18 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.202 11.218 0.507 0.000 0.000 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 124 215 0 0 0 0 -1

N.S.

1 1.00 1.04 1.81 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.169 0.161 0.489 0.000 0.000 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 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 -0.04

time (sec)

N/A 0.058 14.464 6.179 0.000 0.000 0.000 0.000 0.000

Problem 68

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

24 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 -0.04

time (sec)

N/A 0.064 15.659 5.211 0.000 0.000 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

602 602 887 1067 0 0 0 0 -1

N.S.

1 1.00 1.47 1.77 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 2.154 30.675 0.960 0.000 0.000 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

440 440 856 1026 0 0 0 0 -1

N.S.

1 1.00 1.95 2.33 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.727 30.592 0.933 0.000 0.000 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

314 314 345 900 0 0 0 0 -1

N.S.

1 1.00 1.10 2.87 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.544 11.081 0.884 0.000 0.000 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

298 298 608 875 0 0 0 0 -1

N.S.

1 1.00 2.04 2.94 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.298 18.791 0.905 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 F(-1) A A

verified

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

size

24 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 -0.04

time (sec)

N/A 0.062 44.758 8.010 0.000 0.000 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 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 -0.04

time (sec)

N/A 0.067 43.613 7.737 0.000 0.000 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

540 637 1002 1620 0 0 0 0 -1

N.S.

1 1.18 1.86 3.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.538 30.852 0.931 0.000 0.000 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

206 206 140 341 298 196 408 1166 -1

N.S.

1 1.00 0.68 1.66 1.45 0.95 1.98 5.66 -0.00

time (sec)

N/A 0.091 0.170 0.409 0.263 0.464 14.913 1.770 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 121 267 234 177 294 822 -1

N.S.

1 1.00 0.75 1.66 1.45 1.10 1.83 5.11 -0.01

time (sec)

N/A 0.075 0.122 0.422 0.261 0.410 6.297 1.278 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

109 109 149 191 155 147 153 473 -1

N.S.

1 1.00 1.37 1.75 1.42 1.35 1.40 4.34 -0.01

time (sec)

N/A 0.037 0.195 0.267 0.269 0.428 4.560 1.095 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 104 137 91 130 73 1052 75

N.S.

1 1.00 1.20 1.57 1.05 1.49 0.84 12.09 0.86

time (sec)

N/A 0.046 0.091 0.273 0.263 0.400 3.431 0.623 0.833

Problem 80

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

105 105 69 121 96 70 151 136 -1

N.S.

1 1.00 0.66 1.15 0.91 0.67 1.44 1.30 -0.01

time (sec)

N/A 0.055 0.079 0.270 0.265 0.360 2.889 0.464 0.000

Problem 81

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

152 152 94 140 139 93 280 245 -1

N.S.

1 1.00 0.62 0.92 0.91 0.61 1.84 1.61 -0.01

time (sec)

N/A 0.068 0.119 0.289 0.265 0.353 6.251 0.447 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

197 197 110 158 174 113 372 367 -1

N.S.

1 1.00 0.56 0.80 0.88 0.57 1.89 1.86 -0.01

time (sec)

N/A 0.087 0.122 0.305 0.265 0.357 34.486 0.438 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

196 196 115 152 185 130 364 1244 -1

N.S.

1 1.00 0.59 0.78 0.94 0.66 1.86 6.35 -0.01

time (sec)

N/A 0.110 0.172 0.415 0.267 0.382 5.362 0.542 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

153 153 97 307 144 111 272 900 -1

N.S.

1 1.00 0.63 2.01 0.94 0.73 1.78 5.88 -0.01

time (sec)

N/A 0.088 0.155 0.522 0.277 0.382 3.796 0.470 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 78 238 100 89 177 556 -1

N.S.

1 1.00 0.57 1.72 0.72 0.64 1.28 4.03 -0.01

time (sec)

N/A 0.068 0.076 0.503 0.259 0.365 2.362 0.452 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

124 124 108 198 0 0 0 0 111

N.S.

1 1.00 0.87 1.60 0.00 0.00 0.00 0.00 0.90

time (sec)

N/A 0.214 0.065 4.875 0.000 0.000 0.000 0.000 0.925

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

137 137 125 204 0 0 0 0 124

N.S.

1 1.00 0.91 1.49 0.00 0.00 0.00 0.00 0.91

time (sec)

N/A 0.214 0.075 1.111 0.000 0.000 0.000 0.000 0.991

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

252 252 184 475 404 272 542 1579 -1

N.S.

1 1.00 0.73 1.88 1.60 1.08 2.15 6.27 -0.00

time (sec)

N/A 0.167 0.225 0.520 0.272 0.568 15.162 5.304 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

191 191 151 358 296 236 355 1033 -1

N.S.

1 1.00 0.79 1.87 1.55 1.24 1.86 5.41 -0.01

time (sec)

N/A 0.084 0.155 0.369 0.264 0.489 7.349 3.451 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

163 163 134 273 197 234 207 2502 -1

N.S.

1 1.00 0.82 1.67 1.21 1.44 1.27 15.35 -0.01

time (sec)

N/A 0.092 0.122 0.367 0.273 0.456 5.552 2.560 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

157 157 125 251 158 233 211 4288 -1

N.S.

1 1.00 0.80 1.60 1.01 1.48 1.34 27.31 -0.01

time (sec)

N/A 0.096 0.180 0.388 0.259 0.414 5.531 101.449 0.000

Problem 92

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

183 183 127 191 181 131 335 314 -1

N.S.

1 1.00 0.69 1.04 0.99 0.72 1.83 1.72 -0.01

time (sec)

N/A 0.116 0.162 0.384 0.257 0.390 6.897 0.443 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

241 241 153 223 241 165 510 491 -1

N.S.

1 1.00 0.63 0.93 1.00 0.68 2.12 2.04 -0.00

time (sec)

N/A 0.140 0.161 0.384 0.277 0.351 35.888 0.475 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

242 242 159 499 253 184 493 1706 -1

N.S.

1 1.00 0.66 2.06 1.05 0.76 2.04 7.05 -0.00

time (sec)

N/A 0.160 0.196 0.614 0.264 0.388 6.470 0.579 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

195 195 124 376 189 150 352 1160 -1

N.S.

1 1.00 0.64 1.93 0.97 0.77 1.81 5.95 -0.01

time (sec)

N/A 0.105 0.183 0.627 0.263 0.367 4.093 0.523 0.000

Problem 96

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

186 186 157 301 0 0 0 0 -1

N.S.

1 1.00 0.84 1.62 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.300 0.245 8.671 0.000 0.000 0.000 0.000 0.000

Problem 97

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

189 189 194 309 0 0 0 0 -1

N.S.

1 1.00 1.03 1.63 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.300 0.493 6.217 0.000 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

565 565 1260 407 0 0 0 0 -1

N.S.

1 1.00 2.23 0.72 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.096 1.246 3.691 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

507 507 1123 420 0 0 0 0 -1

N.S.

1 1.00 2.21 0.83 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.975 0.321 2.313 0.000 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

529 529 1068 272 0 0 0 0 -1

N.S.

1 1.00 2.02 0.51 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.777 0.311 1.954 0.000 0.000 0.000 0.000 0.000

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