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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 B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 21 11 10 10 12 26 10

N.S.

1 1.00 2.10 1.10 1.00 1.00 1.20 2.60 1.00

time (sec)

N/A 0.163 0.006 0.038 0.179 0.243 0.062 0.262 0.052

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 20 32 22 46 32 18

N.S.

1 1.00 0.92 0.80 1.28 0.88 1.84 1.28 0.72

time (sec)

N/A 0.175 0.011 0.069 0.200 0.244 0.080 0.260 1.542

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 32 26 23 54 32 36 54 22

N.S.

1 1.23 1.00 0.88 2.08 1.23 1.38 2.08 0.85

time (sec)

N/A 0.188 0.002 0.079 0.179 0.242 0.130 0.258 1.541

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 60 49 95 60 31

N.S.

1 1.11 0.72 0.67 1.30 1.07 2.07 1.30 0.67

time (sec)

N/A 0.242 0.032 0.141 0.180 0.241 0.161 0.263 0.090

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 46 41 33 82 66 58 82 31

N.S.

1 1.12 1.00 0.80 2.00 1.61 1.41 2.00 0.76

time (sec)

N/A 0.192 0.012 0.387 0.186 0.242 0.221 0.262 1.569

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 86 90 139 88 42

N.S.

1 1.15 0.64 0.63 1.28 1.34 2.07 1.31 0.63

time (sec)

N/A 0.331 0.038 0.533 0.179 0.240 0.328 0.271 1.739

Problem 7

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

69 74 55 201 0 326 0 0 0

N.S.

1 1.07 0.80 2.91 0.00 4.72 0.00 0.00 0.00

time (sec)

N/A 0.310 0.085 3.507 0.000 0.082 0.000 0.000 0.000

Problem 8

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

46 46 44 188 0 203 0 0 0

N.S.

1 1.00 0.96 4.09 0.00 4.41 0.00 0.00 0.00

time (sec)

N/A 0.240 0.044 0.772 0.000 0.090 0.000 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 81 174 0 102 0 0 0

N.S.

1 1.00 1.76 3.78 0.00 2.22 0.00 0.00 0.00

time (sec)

N/A 0.235 0.074 0.462 0.000 0.079 0.000 0.000 0.000

Problem 10

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

20 20 20 135 0 37 0 0 0

N.S.

1 1.00 1.00 6.75 0.00 1.85 0.00 0.00 0.00

time (sec)

N/A 0.169 0.024 0.384 0.000 0.076 0.000 0.000 0.000

Problem 11

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

20 20 20 135 0 24 0 0 0

N.S.

1 1.00 1.00 6.75 0.00 1.20 0.00 0.00 0.00

time (sec)

N/A 0.168 0.026 0.106 0.000 0.075 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 42 103 0 148 0 0 0

N.S.

1 1.00 1.00 2.45 0.00 3.52 0.00 0.00 0.00

time (sec)

N/A 0.234 0.049 0.304 0.000 0.076 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 84 217 0 310 0 0 0

N.S.

1 1.00 1.83 4.72 0.00 6.74 0.00 0.00 0.00

time (sec)

N/A 0.230 0.051 0.513 0.000 0.081 0.000 0.000 0.000

Problem 14

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

69 70 63 363 0 613 0 0 0

N.S.

1 1.01 0.91 5.26 0.00 8.88 0.00 0.00 0.00

time (sec)

N/A 0.303 0.105 0.958 0.000 0.080 0.000 0.000 0.000

Problem 15

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

65 71 53 145 0 256 0 0 0

N.S.

1 1.09 0.82 2.23 0.00 3.94 0.00 0.00 0.00

time (sec)

N/A 0.359 0.053 2.736 0.000 0.078 0.000 0.000 0.000

Problem 16

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

48 48 41 184 0 161 0 0 0

N.S.

1 1.00 0.85 3.83 0.00 3.35 0.00 0.00 0.00

time (sec)

N/A 0.289 0.044 0.881 0.000 0.085 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 57 130 0 68 0 0 0

N.S.

1 1.00 1.19 2.71 0.00 1.42 0.00 0.00 0.00

time (sec)

N/A 0.284 0.052 0.586 0.000 0.074 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 F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 27 118 0 28 0 0 0

N.S.

1 1.00 1.00 4.37 0.00 1.04 0.00 0.00 0.00

time (sec)

N/A 0.213 0.020 0.516 0.000 0.075 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

27 27 27 100 0 16 0 0 0

N.S.

1 1.00 1.00 3.70 0.00 0.59 0.00 0.00 0.00

time (sec)

N/A 0.216 0.022 0.127 0.000 0.075 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

46 46 34 159 0 101 0 0 0

N.S.

1 1.00 0.74 3.46 0.00 2.20 0.00 0.00 0.00

time (sec)

N/A 0.278 0.030 0.344 0.000 0.076 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 56 177 0 213 0 0 0

N.S.

1 1.00 1.12 3.54 0.00 4.26 0.00 0.00 0.00

time (sec)

N/A 0.295 0.039 0.418 0.000 0.078 0.000 0.000 0.000

Problem 22

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 71 43 254 0 422 0 0 0

N.S.

1 1.06 0.64 3.79 0.00 6.30 0.00 0.00 0.00

time (sec)

N/A 0.364 0.053 0.679 0.000 0.077 0.000 0.000 0.000

Problem 23

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 65 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 0.206 0.049 0.000 0.000 0.000 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 62 53 37 66 100 337 70 70

N.S.

1 1.15 0.98 0.69 1.22 1.85 6.24 1.30 1.30

time (sec)

N/A 0.426 0.280 0.133 0.181 0.254 0.575 0.260 1.759

Problem 25

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

43 43 45 30 56 70 189 51 52

N.S.

1 1.00 1.05 0.70 1.30 1.63 4.40 1.19 1.21

time (sec)

N/A 0.280 0.221 0.102 0.176 0.259 0.373 0.255 1.680

Problem 26

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 24 32 20 41 47 63 35 34

N.S.

1 0.96 1.28 0.80 1.64 1.88 2.52 1.40 1.36

time (sec)

N/A 0.322 0.179 0.061 0.180 0.261 0.216 0.254 1.695

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

18 18 29 13 18 24 8 17 17

N.S.

1 1.00 1.61 0.72 1.00 1.33 0.44 0.94 0.94

time (sec)

N/A 0.241 0.129 0.039 0.186 0.245 0.146 0.255 1.669

Problem 28

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

20 20 22 19 23 29 0 20 31

N.S.

1 1.00 1.10 0.95 1.15 1.45 0.00 1.00 1.55

time (sec)

N/A 0.282 0.105 0.128 0.261 0.249 0.000 0.257 1.684

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 29 43 33 45 127 0 36 58

N.S.

1 1.04 1.54 1.18 1.61 4.54 0.00 1.29 2.07

time (sec)

N/A 0.395 0.161 0.236 0.275 0.234 0.000 0.258 1.725

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 44 49 46 73 325 0 48 73

N.S.

1 1.02 1.14 1.07 1.70 7.56 0.00 1.12 1.70

time (sec)

N/A 0.464 0.168 0.224 0.272 0.263 0.000 0.248 1.701

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 63 60 52 101 600 0 57 107

N.S.

1 1.12 1.07 0.93 1.80 10.71 0.00 1.02 1.91

time (sec)

N/A 0.501 0.239 0.299 0.267 0.251 0.000 0.254 1.676

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 14 14 18 22 17 15 15

N.S.

1 1.00 0.70 0.70 0.90 1.10 0.85 0.75 0.75

time (sec)

N/A 0.178 0.013 0.043 0.175 0.242 0.270 0.255 1.680

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 34 26 90 113 36 25 25

N.S.

1 1.00 0.72 0.55 1.91 2.40 0.77 0.53 0.53

time (sec)

N/A 0.253 0.023 0.060 0.178 0.243 0.419 0.250 0.068

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 75 44 37 205 174 51 36 36

N.S.

1 1.07 0.63 0.53 2.93 2.49 0.73 0.51 0.51

time (sec)

N/A 0.329 0.040 0.067 0.183 0.245 0.843 0.254 1.690

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 103 54 48 364 347 68 47 283

N.S.

1 1.11 0.58 0.52 3.91 3.73 0.73 0.51 3.04

time (sec)

N/A 0.419 0.066 0.083 0.188 0.245 1.753 0.260 1.720

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 14 16 18 24 19 15 15

N.S.

1 1.00 0.61 0.70 0.78 1.04 0.83 0.65 0.65

time (sec)

N/A 0.183 0.087 0.046 0.181 0.243 0.369 0.253 0.060

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 31 26 90 117 39 25 25

N.S.

1 1.00 0.61 0.51 1.76 2.29 0.76 0.49 0.49

time (sec)

N/A 0.254 0.063 0.067 0.180 0.233 0.560 0.259 0.062

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 81 41 37 205 174 56 36 36

N.S.

1 1.07 0.54 0.49 2.70 2.29 0.74 0.47 0.47

time (sec)

N/A 0.336 0.130 0.079 0.195 0.246 1.050 0.282 1.724

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 111 51 48 364 347 73 47 283

N.S.

1 1.10 0.50 0.48 3.60 3.44 0.72 0.47 2.80

time (sec)

N/A 0.438 0.091 0.094 0.186 0.236 2.073 0.249 0.088

Problem 40

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

51 51 34 92 114 62 0 37 0

N.S.

1 1.00 0.67 1.80 2.24 1.22 0.00 0.73 0.00

time (sec)

N/A 0.275 0.017 0.139 0.331 0.248 0.000 0.262 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 44 40 0 92 0 74 0

N.S.

1 1.00 0.83 0.75 0.00 1.74 0.00 1.40 0.00

time (sec)

N/A 0.284 0.122 0.147 0.000 0.266 0.000 0.261 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 93 71 73 121 327 0 105 0

N.S.

1 1.04 0.80 0.82 1.36 3.67 0.00 1.18 0.00

time (sec)

N/A 0.363 0.095 0.139 0.274 0.259 0.000 0.281 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 55 58 81 140 0 75 0

N.S.

1 1.00 0.93 0.98 1.37 2.37 0.00 1.27 0.00

time (sec)

N/A 0.268 0.051 0.114 0.276 0.249 0.000 0.256 0.000

Problem 44

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

26 26 29 43 40 41 0 35 26

N.S.

1 1.00 1.12 1.65 1.54 1.58 0.00 1.35 1.00

time (sec)

N/A 0.179 0.063 0.104 0.276 0.243 0.000 0.251 0.127

Problem 45

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

46 46 40 103 86 149 0 21 0

N.S.

1 1.00 0.87 2.24 1.87 3.24 0.00 0.46 0.00

time (sec)

N/A 0.201 0.014 0.107 0.339 0.251 0.000 0.259 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 63 144 170 222 0 70 0

N.S.

1 1.00 0.82 1.87 2.21 2.88 0.00 0.91 0.00

time (sec)

N/A 0.289 0.064 0.131 0.324 0.253 0.000 0.269 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 112 91 178 250 522 0 0 0

N.S.

1 1.05 0.85 1.66 2.34 4.88 0.00 0.00 0.00

time (sec)

N/A 0.379 0.192 0.143 0.334 0.266 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 96 72 71 190 328 0 194 0

N.S.

1 1.04 0.78 0.77 2.07 3.57 0.00 2.11 0.00

time (sec)

N/A 0.363 0.199 0.173 0.280 0.247 0.000 0.265 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 61 56 56 124 139 0 127 0

N.S.

1 1.00 0.92 0.92 2.03 2.28 0.00 2.08 0.00

time (sec)

N/A 0.276 0.149 0.104 0.294 0.248 0.000 0.266 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 30 41 58 42 0 63 27

N.S.

1 1.00 1.11 1.52 2.15 1.56 0.00 2.33 1.00

time (sec)

N/A 0.192 0.089 0.120 0.275 0.245 0.000 0.266 1.867

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 55 41 0 154 0 40 0

N.S.

1 1.00 1.15 0.85 0.00 3.21 0.00 0.83 0.00

time (sec)

N/A 0.206 0.115 0.091 0.000 0.253 0.000 0.263 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 79 98 87 0 274 0 115 0

N.S.

1 1.00 1.24 1.10 0.00 3.47 0.00 1.46 0.00

time (sec)

N/A 0.290 0.252 0.114 0.000 0.256 0.000 0.276 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 115 129 137 0 580 0 177 0

N.S.

1 1.05 1.17 1.25 0.00 5.27 0.00 1.61 0.00

time (sec)

N/A 0.391 0.283 0.131 0.000 0.253 0.000 0.284 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 129 99 203 0 1625 0 133 209

N.S.

1 1.15 0.88 1.81 0.00 14.51 0.00 1.19 1.87

time (sec)

N/A 0.767 0.171 0.306 0.000 0.290 0.000 0.250 2.080

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 95 78 153 0 903 4559 92 167

N.S.

1 1.12 0.92 1.80 0.00 10.62 53.64 1.08 1.96

time (sec)

N/A 0.529 0.114 0.179 0.000 0.277 157.924 0.258 1.919

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 65 57 94 0 449 1275 62 139

N.S.

1 1.05 0.92 1.52 0.00 7.24 20.56 1.00 2.24

time (sec)

N/A 0.369 0.097 0.109 0.000 0.263 51.494 0.250 1.866

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 52 48 64 0 218 241 42 109

N.S.

1 1.00 0.92 1.23 0.00 4.19 4.63 0.81 2.10

time (sec)

N/A 0.266 0.048 0.074 0.000 0.273 12.257 0.264 1.859

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 54 51 0 227 0 45 286

N.S.

1 1.00 1.00 0.94 0.00 4.20 0.00 0.83 5.30

time (sec)

N/A 0.324 0.068 0.221 0.000 0.273 0.000 0.254 4.430

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 67 63 73 0 515 0 61 294

N.S.

1 1.05 0.98 1.14 0.00 8.05 0.00 0.95 4.59

time (sec)

N/A 0.447 0.122 0.321 0.000 0.282 0.000 0.263 4.043

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 98 82 109 0 1370 0 89 476

N.S.

1 1.13 0.94 1.25 0.00 15.75 0.00 1.02 5.47

time (sec)

N/A 0.722 0.201 0.505 0.000 0.328 0.000 0.261 5.092

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 131 101 145 0 2483 0 123 547

N.S.

1 1.15 0.89 1.27 0.00 21.78 0.00 1.08 4.80

time (sec)

N/A 0.995 0.324 0.738 0.000 0.338 0.000 0.271 5.639

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

183 196 133 132 273 190 314 263 160

N.S.

1 1.07 0.73 0.72 1.49 1.04 1.72 1.44 0.87

time (sec)

N/A 0.733 0.765 0.588 0.186 0.266 0.277 0.292 0.326

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

137 145 104 101 183 123 240 196 114

N.S.

1 1.06 0.76 0.74 1.34 0.90 1.75 1.43 0.83

time (sec)

N/A 0.494 0.400 0.281 0.185 0.251 0.183 0.256 0.198

Problem 64

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

90 93 80 67 116 78 128 131 73

N.S.

1 1.03 0.89 0.74 1.29 0.87 1.42 1.46 0.81

time (sec)

N/A 0.320 0.213 0.166 0.192 0.251 0.146 0.263 1.765

Problem 65

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

50 50 46 43 55 40 78 75 41

N.S.

1 1.00 0.92 0.86 1.10 0.80 1.56 1.50 0.82

time (sec)

N/A 0.211 0.129 0.096 0.181 0.245 0.103 0.261 1.687

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 26 16 15 17 17 32 15

N.S.

1 1.00 1.73 1.07 1.00 1.13 1.13 2.13 1.00

time (sec)

N/A 0.147 0.003 0.034 0.181 0.254 0.066 0.254 0.059

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 48 44 0 237 163 39 53

N.S.

1 1.00 0.98 0.90 0.00 4.84 3.33 0.80 1.08

time (sec)

N/A 0.212 0.049 0.072 0.000 0.275 2.396 0.273 2.004

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 97 84 118 0 743 2332 99 215

N.S.

1 1.13 0.98 1.37 0.00 8.64 27.12 1.15 2.50

time (sec)

N/A 0.324 0.198 0.141 0.000 0.260 40.227 0.264 2.123

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 159 113 186 0 2591 0 195 0

N.S.

1 1.20 0.85 1.40 0.00 19.48 0.00 1.47 0.00

time (sec)

N/A 0.490 0.328 0.256 0.000 0.282 0.000 0.261 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

184 226 160 284 0 5705 0 329 0

N.S.

1 1.23 0.87 1.54 0.00 31.01 0.00 1.79 0.00

time (sec)

N/A 0.735 0.766 0.513 0.000 0.319 0.000 0.274 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 20 18 19 24 24 16 34

N.S.

1 1.00 0.91 0.82 0.86 1.09 1.09 0.73 1.55

time (sec)

N/A 0.188 0.035 0.120 0.266 0.262 0.412 0.266 1.708

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 43 46 64 147 291 54 74

N.S.

1 1.00 0.90 0.96 1.33 3.06 6.06 1.12 1.54

time (sec)

N/A 0.266 0.089 0.149 0.259 0.246 1.101 0.261 1.707

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 78 53 62 108 408 507 76 137

N.S.

1 1.07 0.73 0.85 1.48 5.59 6.95 1.04 1.88

time (sec)

N/A 0.392 0.136 0.195 0.262 0.252 2.040 0.257 1.732

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 108 63 75 152 793 784 98 223

N.S.

1 1.10 0.64 0.77 1.55 8.09 8.00 1.00 2.28

time (sec)

N/A 0.519 0.181 0.271 0.278 0.274 3.747 0.257 1.740

Problem 75

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

31 31 65 30 37 42 41 28 40

N.S.

1 1.00 2.10 0.97 1.19 1.35 1.32 0.90 1.29

time (sec)

N/A 0.186 0.034 0.091 0.188 0.257 0.312 0.274 1.735

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 61 144 64 81 212 199 65 77

N.S.

1 1.09 2.57 1.14 1.45 3.79 3.55 1.16 1.38

time (sec)

N/A 0.263 0.107 0.110 0.188 0.269 0.729 0.284 1.810

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 91 217 90 125 563 445 87 141

N.S.

1 1.12 2.68 1.11 1.54 6.95 5.49 1.07 1.74

time (sec)

N/A 0.379 0.180 0.159 0.187 0.259 1.384 0.273 1.824

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 121 296 112 169 1078 784 109 226

N.S.

1 1.14 2.79 1.06 1.59 10.17 7.40 1.03 2.13

time (sec)

N/A 0.513 0.270 0.209 0.188 0.252 2.694 0.282 0.119

Problem 79

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

153 159 150 685 0 464 0 0 0

N.S.

1 1.04 0.98 4.48 0.00 3.03 0.00 0.00 0.00

time (sec)

N/A 0.904 0.407 6.487 0.000 0.093 0.000 0.000 0.000

Problem 80

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

124 125 111 466 0 265 0 0 0

N.S.

1 1.01 0.90 3.76 0.00 2.14 0.00 0.00 0.00

time (sec)

N/A 0.691 0.181 1.430 0.000 0.088 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 F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 61 61 276 0 196 0 0 0

N.S.

1 1.00 1.00 4.52 0.00 3.21 0.00 0.00 0.00

time (sec)

N/A 0.302 0.107 1.463 0.000 0.084 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

46 46 46 146 0 61 0 0 0

N.S.

1 1.00 1.00 3.17 0.00 1.33 0.00 0.00 0.00

time (sec)

N/A 0.274 0.033 0.198 0.000 0.076 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 F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 84 68 298 0 413 0 0 0

N.S.

1 1.00 0.81 3.55 0.00 4.92 0.00 0.00 0.00

time (sec)

N/A 0.396 0.097 1.184 0.000 0.083 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 F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

177 187 135 459 0 1281 0 0 0

N.S.

1 1.06 0.76 2.59 0.00 7.24 0.00 0.00 0.00

time (sec)

N/A 0.980 0.413 2.631 0.000 0.101 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 No TBD TBD TBD TBD TBD

size

227 253 165 566 0 3315 0 0 0

N.S.

1 1.11 0.73 2.49 0.00 14.60 0.00 0.00 0.00

time (sec)

N/A 1.320 0.546 2.960 0.000 0.152 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 100 73 181 0 174 0 0 0

N.S.

1 1.00 0.73 1.81 0.00 1.74 0.00 0.00 0.00

time (sec)

N/A 0.545 0.284 0.988 0.000 0.081 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 89 60 71 237 563 0 153 0

N.S.

1 0.95 0.64 0.76 2.52 5.99 0.00 1.63 0.00

time (sec)

N/A 0.451 0.096 0.682 0.298 0.258 0.000 0.268 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 66 46 57 163 279 0 113 0

N.S.

1 0.97 0.68 0.84 2.40 4.10 0.00 1.66 0.00

time (sec)

N/A 0.358 0.071 0.311 0.311 0.262 0.000 0.272 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 40 31 39 90 100 0 71 0

N.S.

1 1.00 0.78 0.98 2.25 2.50 0.00 1.78 0.00

time (sec)

N/A 0.276 0.032 0.307 0.286 0.277 0.000 0.263 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 93 61 69 288 564 0 295 0

N.S.

1 0.95 0.62 0.70 2.94 5.76 0.00 3.01 0.00

time (sec)

N/A 0.467 0.249 0.663 0.295 0.264 0.000 0.286 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 69 47 55 199 279 0 212 0

N.S.

1 0.97 0.66 0.77 2.80 3.93 0.00 2.99 0.00

time (sec)

N/A 0.366 0.217 0.373 0.297 0.257 0.000 0.274 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 32 39 109 107 0 131 0

N.S.

1 1.00 0.73 0.89 2.48 2.43 0.00 2.98 0.00

time (sec)

N/A 0.300 0.154 0.321 0.290 0.258 0.000 0.264 0.000

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

18 18 32 15 26 29 15 17 19

N.S.

1 1.00 1.78 0.83 1.44 1.61 0.83 0.94 1.06

time (sec)

N/A 0.244 0.187 0.058 0.177 0.259 0.136 0.257 0.056

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 25 31 129 50 36 30 30

N.S.

1 1.00 0.71 0.89 3.69 1.43 1.03 0.86 0.86

time (sec)

N/A 0.277 0.055 0.086 0.203 0.251 0.227 0.248 0.085

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 54 41 35 263 127 46 46 141

N.S.

1 0.96 0.73 0.62 4.70 2.27 0.82 0.82 2.52

time (sec)

N/A 0.334 0.066 0.104 0.187 0.266 0.389 0.259 1.690

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 71 55 55 449 175 78 60 231

N.S.

1 0.95 0.73 0.73 5.99 2.33 1.04 0.80 3.08

time (sec)

N/A 0.417 0.069 0.147 0.196 0.243 0.780 0.253 1.685

Problem 97

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

20 20 42 19 27 31 15 16 19

N.S.

1 1.00 2.10 0.95 1.35 1.55 0.75 0.80 0.95

time (sec)

N/A 0.254 0.192 0.058 0.174 0.258 0.207 0.254 0.053

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 25 26 131 48 36 32 32

N.S.

1 1.00 0.68 0.70 3.54 1.30 0.97 0.86 0.86

time (sec)

N/A 0.269 0.049 0.077 0.195 0.257 0.324 0.249 1.699

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 58 41 39 267 127 46 46 143

N.S.

1 0.97 0.68 0.65 4.45 2.12 0.77 0.77 2.38

time (sec)

N/A 0.342 0.064 0.115 0.192 0.248 0.551 0.255 0.084

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 77 55 56 451 175 78 60 233

N.S.

1 0.95 0.68 0.69 5.57 2.16 0.96 0.74 2.88

time (sec)

N/A 0.426 0.060 0.125 0.192 0.246 0.996 0.250 1.685

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