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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 A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 96 72 60 63 63 88 64 108

N.S.

1 1.00 0.75 0.62 0.66 0.66 0.92 0.67 1.12

time (sec)

N/A 0.061 0.019 0.421 0.219 0.258 0.401 0.263 5.185

Problem 2

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

71 71 63 52 55 55 65 56 88

N.S.

1 1.00 0.89 0.73 0.77 0.77 0.92 0.79 1.24

time (sec)

N/A 0.042 0.018 0.265 0.207 0.246 0.233 0.270 0.105

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 42 41 44 42 39 44 48

N.S.

1 1.00 0.91 0.89 0.96 0.91 0.85 0.96 1.04

time (sec)

N/A 0.027 0.023 0.250 0.218 0.251 0.152 0.276 0.143

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 32 23 0 0 26 0 0

N.S.

1 1.00 1.00 0.72 0.00 0.00 0.81 0.00 0.00

time (sec)

N/A 0.011 0.004 0.264 0.000 0.000 0.301 0.000 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 42 41 35 41 36 0 67

N.S.

1 1.00 1.00 0.98 0.83 0.98 0.86 0.00 1.60

time (sec)

N/A 0.030 0.029 0.279 0.251 0.246 0.184 0.000 5.129

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 71 63 62 35 55 60 0 88

N.S.

1 1.00 0.89 0.87 0.49 0.77 0.85 0.00 1.24

time (sec)

N/A 0.044 0.014 0.380 0.263 0.253 0.286 0.000 0.085

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 96 73 70 35 62 87 0 113

N.S.

1 1.00 0.76 0.73 0.36 0.65 0.91 0.00 1.18

time (sec)

N/A 0.059 0.018 0.623 0.305 0.241 0.485 0.000 5.126

Problem 8

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

109 109 72 63 52 59 99 52 52

N.S.

1 1.00 0.66 0.58 0.48 0.54 0.91 0.48 0.48

time (sec)

N/A 0.073 0.014 0.518 0.223 0.251 0.546 0.269 0.126

Problem 9

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

84 84 66 55 44 51 75 44 44

N.S.

1 1.00 0.79 0.65 0.52 0.61 0.89 0.52 0.52

time (sec)

N/A 0.083 0.013 0.314 0.219 0.261 0.297 0.265 5.156

Problem 10

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

59 59 41 47 36 43 51 36 36

N.S.

1 1.00 0.69 0.80 0.61 0.73 0.86 0.61 0.61

time (sec)

N/A 0.036 0.018 0.428 0.220 0.250 0.185 0.264 0.102

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 26 24 25 29 24 23 23

N.S.

1 1.00 1.00 0.92 0.96 1.12 0.92 0.88 0.88

time (sec)

N/A 0.004 0.006 0.339 0.221 0.243 0.131 0.263 5.122

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 26 26 24 30 24 24 24

N.S.

1 1.00 1.00 1.00 0.92 1.15 0.92 0.92 0.92

time (sec)

N/A 0.022 0.014 0.605 0.281 0.264 0.570 0.269 5.424

Problem 13

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

56 56 47 46 27 48 54 51 45

N.S.

1 1.00 0.84 0.82 0.48 0.86 0.96 0.91 0.80

time (sec)

N/A 0.036 0.034 0.413 0.296 0.248 1.037 0.266 5.290

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 81 62 63 27 60 76 68 65

N.S.

1 1.00 0.77 0.78 0.33 0.74 0.94 0.84 0.80

time (sec)

N/A 0.049 0.025 0.659 0.292 0.246 1.774 0.260 5.148

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

289 289 248 467 0 265 746 390 337

N.S.

1 1.00 0.86 1.62 0.00 0.92 2.58 1.35 1.17

time (sec)

N/A 0.234 0.183 1.191 0.000 0.272 1.825 0.294 6.322

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

192 192 138 272 0 163 398 263 204

N.S.

1 1.00 0.72 1.42 0.00 0.85 2.07 1.37 1.06

time (sec)

N/A 0.155 0.133 0.966 0.000 0.255 0.871 0.300 5.920

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 118 88 112 0 91 178 149 126

N.S.

1 1.00 0.75 0.95 0.00 0.77 1.51 1.26 1.07

time (sec)

N/A 0.096 0.073 0.516 0.000 0.253 0.439 0.283 5.852

Problem 18

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

36 36 35 32 31 47 53 59 48

N.S.

1 1.00 0.97 0.89 0.86 1.31 1.47 1.64 1.33

time (sec)

N/A 0.005 0.015 0.316 0.227 0.247 0.229 0.271 0.335

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

14 14 16 14 16 16 12 16 16

N.S.

1 1.00 1.14 1.00 1.14 1.14 0.86 1.14 1.14

time (sec)

N/A 0.012 0.410 0.172 0.332 0.244 0.973 0.270 5.247

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

14 14 16 14 66 27 14 16 16

N.S.

1 1.00 1.14 1.00 4.71 1.93 1.00 1.14 1.14

time (sec)

N/A 0.029 0.591 0.215 0.344 0.265 10.097 0.300 5.380

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

14 14 16 14 94 38 14 16 16

N.S.

1 1.00 1.14 1.00 6.71 2.71 1.00 1.14 1.14

time (sec)

N/A 0.063 1.489 0.234 0.320 0.268 72.581 0.289 6.345

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

178 178 106 160 0 98 168 0 142

N.S.

1 1.00 0.60 0.90 0.00 0.55 0.94 0.00 0.80

time (sec)

N/A 0.193 0.034 0.486 0.000 0.257 0.541 0.000 5.657

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 126 90 116 0 81 117 0 101

N.S.

1 1.00 0.71 0.92 0.00 0.64 0.93 0.00 0.80

time (sec)

N/A 0.118 0.028 0.306 0.000 0.255 0.333 0.000 5.150

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 71 64 72 0 59 65 0 67

N.S.

1 1.00 0.90 1.01 0.00 0.83 0.92 0.00 0.94

time (sec)

N/A 0.056 0.031 0.242 0.000 0.254 0.182 0.000 0.144

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

10 10 12 10 12 12 8 12 12

N.S.

1 1.00 1.20 1.00 1.20 1.20 0.80 1.20 1.20

time (sec)

N/A 0.012 0.022 0.020 0.251 0.242 0.988 0.270 4.977

Problem 26

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 63 0 0 65 0 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.97 0.00 0.00 0.00

time (sec)

N/A 0.071 0.024 0.000 0.000 0.253 0.000 0.000 0.000

Problem 27

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

125 125 97 0 0 94 0 0 0

N.S.

1 1.00 0.78 0.00 0.00 0.75 0.00 0.00 0.00

time (sec)

N/A 0.116 0.061 0.000 0.000 0.247 0.000 0.000 0.000

Problem 28

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

177 177 133 0 0 114 0 0 0

N.S.

1 1.00 0.75 0.00 0.00 0.64 0.00 0.00 0.00

time (sec)

N/A 0.194 0.030 0.000 0.000 0.266 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 165 106 131 0 111 0 170 131

N.S.

1 1.00 0.64 0.79 0.00 0.67 0.00 1.03 0.79

time (sec)

N/A 0.177 0.068 0.538 0.000 0.269 0.000 0.295 5.497

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 113 88 95 0 90 0 111 90

N.S.

1 1.00 0.78 0.84 0.00 0.80 0.00 0.98 0.80

time (sec)

N/A 0.096 0.054 0.542 0.000 0.256 0.000 0.280 0.191

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

56 56 56 48 62 63 0 48 44

N.S.

1 1.00 1.00 0.86 1.11 1.12 0.00 0.86 0.79

time (sec)

N/A 0.034 0.026 0.322 0.292 0.269 0.000 0.267 0.130

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

10 10 12 10 37 12 10 12 12

N.S.

1 1.00 1.20 1.00 3.70 1.20 1.00 1.20 1.20

time (sec)

N/A 0.013 0.029 0.027 0.235 0.239 0.946 0.273 4.997

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

10 10 12 10 37 12 10 12 12

N.S.

1 1.00 1.20 1.00 3.70 1.20 1.00 1.20 1.20

time (sec)

N/A 0.012 0.027 0.024 0.252 0.250 1.063 0.270 5.068

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

10 10 12 10 37 12 10 12 12

N.S.

1 1.00 1.20 1.00 3.70 1.20 1.00 1.20 1.20

time (sec)

N/A 0.015 0.030 0.025 0.252 0.251 1.280 0.271 5.038

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F A F F B

verified

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

size

375 375 226 0 0 281 0 0 359

N.S.

1 1.00 0.60 0.00 0.00 0.75 0.00 0.00 0.96

time (sec)

N/A 0.304 0.717 0.000 0.000 0.267 0.000 0.000 5.611

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F A F F B

verified

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

size

188 188 132 0 0 171 0 0 186

N.S.

1 1.00 0.70 0.00 0.00 0.91 0.00 0.00 0.99

time (sec)

N/A 0.130 0.293 0.000 0.000 0.251 0.000 0.000 0.422

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 71 66 59 0 91 0 0 79

N.S.

1 1.00 0.93 0.83 0.00 1.28 0.00 0.00 1.11

time (sec)

N/A 0.180 0.008 0.375 0.000 0.251 0.000 0.000 5.077

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 18 18 14 18 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.88 1.12 1.12

time (sec)

N/A 0.021 0.044 0.191 0.260 0.250 2.531 0.305 4.924

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 74 29 15 18 18

N.S.

1 1.00 1.12 1.00 4.62 1.81 0.94 1.12 1.12

time (sec)

N/A 0.020 0.074 0.226 0.262 0.253 11.039 0.374 5.070

Problem 40

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

102 102 88 0 0 125 0 85 0

N.S.

1 1.00 0.86 0.00 0.00 1.23 0.00 0.83 0.00

time (sec)

N/A 0.123 0.243 0.000 0.000 0.259 0.000 0.448 0.000

Problem 41

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

94 94 84 0 0 121 0 83 0

N.S.

1 1.00 0.89 0.00 0.00 1.29 0.00 0.88 0.00

time (sec)

N/A 0.109 0.186 0.000 0.000 0.258 0.000 0.457 0.000

Problem 42

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

93 93 80 0 0 122 0 79 0

N.S.

1 1.00 0.86 0.00 0.00 1.31 0.00 0.85 0.00

time (sec)

N/A 0.104 0.167 0.000 0.000 0.267 0.000 0.365 0.000

Problem 43

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

65 65 79 62 58 119 0 67 121

N.S.

1 1.00 1.22 0.95 0.89 1.83 0.00 1.03 1.86

time (sec)

N/A 0.036 0.096 1.209 0.228 0.253 0.000 0.260 5.375

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

92 92 80 0 0 126 0 0 0

N.S.

1 1.00 0.87 0.00 0.00 1.37 0.00 0.00 0.00

time (sec)

N/A 0.132 0.172 0.000 0.000 0.269 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

95 95 77 0 0 124 0 0 0

N.S.

1 1.00 0.81 0.00 0.00 1.31 0.00 0.00 0.00

time (sec)

N/A 0.120 0.173 0.000 0.000 0.267 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

125 125 127 0 0 180 0 0 0

N.S.

1 1.00 1.02 0.00 0.00 1.44 0.00 0.00 0.00

time (sec)

N/A 0.190 0.333 0.000 0.000 0.262 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 17 16 16 19 0 16

N.S.

1 1.00 1.00 0.81 0.76 0.76 0.90 0.00 0.76

time (sec)

N/A 0.030 0.009 0.318 0.234 0.258 0.370 0.000 5.001

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 17 16 16 19 0 93

N.S.

1 1.00 1.00 0.81 0.76 0.76 0.90 0.00 4.43

time (sec)

N/A 0.015 0.006 0.256 0.239 0.251 0.159 0.000 5.292

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 20 0 15 15 17 0 15

N.S.

1 1.00 1.00 0.00 0.75 0.75 0.85 0.00 0.75

time (sec)

N/A 0.021 0.011 0.000 0.220 0.251 0.190 0.000 5.106

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 17 16 16 17 0 16

N.S.

1 1.00 1.00 0.81 0.76 0.76 0.81 0.00 0.76

time (sec)

N/A 0.021 0.006 0.226 0.226 0.252 0.277 0.000 5.188

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 17 16 16 19 0 16

N.S.

1 1.00 1.00 0.81 0.76 0.76 0.90 0.00 0.76

time (sec)

N/A 0.021 0.006 0.243 0.215 0.249 0.442 0.000 0.097

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F A B F B

verified

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

size

28 28 28 0 0 24 63 0 23

N.S.

1 1.00 1.00 0.00 0.00 0.86 2.25 0.00 0.82

time (sec)

N/A 0.029 0.012 0.000 0.000 0.261 1.485 0.000 5.806

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

285 285 138 312 0 260 0 270 244

N.S.

1 1.00 0.48 1.09 0.00 0.91 0.00 0.95 0.86

time (sec)

N/A 0.343 0.294 5.236 0.000 0.269 0.000 0.285 0.876

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

155 155 99 168 0 149 0 141 131

N.S.

1 1.00 0.64 1.08 0.00 0.96 0.00 0.91 0.85

time (sec)

N/A 0.123 0.207 1.436 0.000 0.263 0.000 0.277 0.911

Problem 55

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

57 57 51 67 47 62 0 48 47

N.S.

1 1.00 0.89 1.18 0.82 1.09 0.00 0.84 0.82

time (sec)

N/A 0.032 0.029 0.680 0.230 0.258 0.000 0.268 5.018

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

17 17 19 16 18 18 17 18 18

N.S.

1 1.00 1.12 0.94 1.06 1.06 1.00 1.06 1.06

time (sec)

N/A 0.028 0.111 0.073 0.277 0.249 2.916 0.264 5.246

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

17 17 19 16 18 18 19 18 18

N.S.

1 1.00 1.12 0.94 1.06 1.06 1.12 1.06 1.06

time (sec)

N/A 0.112 0.134 0.190 0.283 0.240 6.196 0.264 6.011

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

17 17 19 16 18 18 19 18 18

N.S.

1 1.00 1.12 0.94 1.06 1.06 1.12 1.06 1.06

time (sec)

N/A 0.270 0.174 0.178 0.279 0.251 31.902 0.271 6.119

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

17 17 19 16 18 18 19 18 18

N.S.

1 1.00 1.12 0.94 1.06 1.06 1.12 1.06 1.06

time (sec)

N/A 0.205 0.204 0.075 0.261 0.260 42.056 0.276 6.964

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

17 17 19 16 18 18 19 18 18

N.S.

1 1.00 1.12 0.94 1.06 1.06 1.12 1.06 1.06

time (sec)

N/A 0.076 0.159 0.133 0.254 0.254 8.058 0.276 6.274

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

14 14 16 13 15 15 15 15 15

N.S.

1 1.00 1.14 0.93 1.07 1.07 1.07 1.07 1.07

time (sec)

N/A 0.014 0.026 0.068 0.292 0.262 2.066 0.268 5.665

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

17 17 19 16 18 18 19 18 18

N.S.

1 1.00 1.12 0.94 1.06 1.06 1.12 1.06 1.06

time (sec)

N/A 0.094 0.151 0.081 0.256 0.254 2.864 0.271 5.758

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

17 17 19 16 18 18 19 18 18

N.S.

1 1.00 1.12 0.94 1.06 1.06 1.12 1.06 1.06

time (sec)

N/A 0.273 0.215 0.178 0.262 0.249 13.669 0.272 5.785

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

118 118 73 88 82 74 119 118 91

N.S.

1 1.00 0.62 0.75 0.69 0.63 1.01 1.00 0.77

time (sec)

N/A 0.106 0.033 2.551 0.205 0.257 33.237 0.273 5.437

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

79 79 57 66 59 55 76 71 65

N.S.

1 1.00 0.72 0.84 0.75 0.70 0.96 0.90 0.82

time (sec)

N/A 0.059 0.027 0.963 0.212 0.243 6.507 0.281 0.225

Problem 66

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

37 37 34 51 34 35 34 31 31

N.S.

1 1.00 0.92 1.38 0.92 0.95 0.92 0.84 0.84

time (sec)

N/A 0.026 0.016 0.162 0.202 0.239 1.188 0.278 0.105

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 32 32 0 0 0 26 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.81 0.00 0.00

time (sec)

N/A 0.032 0.062 0.000 0.000 0.000 5.015 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

71 71 34 0 0 0 29 0 0

N.S.

1 1.00 0.48 0.00 0.00 0.00 0.41 0.00 0.00

time (sec)

N/A 0.076 0.099 0.000 0.000 0.000 26.684 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

115 115 36 0 0 0 0 0 0

N.S.

1 1.00 0.31 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.110 0.099 0.000 0.000 0.000 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

119 119 100 0 0 0 24 0 0

N.S.

1 1.00 0.84 0.00 0.00 0.00 0.20 0.00 0.00

time (sec)

N/A 0.099 0.205 0.000 0.000 0.000 171.601 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

76 76 80 0 0 0 24 0 0

N.S.

1 1.00 1.05 0.00 0.00 0.00 0.32 0.00 0.00

time (sec)

N/A 0.051 0.148 0.000 0.000 0.000 26.636 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 29 0 0 0 0 22 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.76 0.00 0.00

time (sec)

N/A 0.015 0.000 0.000 0.000 0.000 3.808 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

66 66 74 0 0 0 46 0 0

N.S.

1 1.00 1.12 0.00 0.00 0.00 0.70 0.00 0.00

time (sec)

N/A 0.054 0.146 0.000 0.000 0.000 9.923 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

115 115 100 0 0 0 24 0 0

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.21 0.00 0.00

time (sec)

N/A 0.089 0.230 0.000 0.000 0.000 75.746 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 135 86 119 0 97 0 153 192

N.S.

1 1.00 0.64 0.88 0.00 0.72 0.00 1.13 1.42

time (sec)

N/A 0.149 0.052 2.313 0.000 0.255 0.000 0.281 0.478

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 90 68 83 0 76 0 94 106

N.S.

1 1.00 0.76 0.92 0.00 0.84 0.00 1.04 1.18

time (sec)

N/A 0.074 0.035 0.907 0.000 0.259 0.000 0.279 5.288

Problem 77

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

43 43 39 39 34 43 0 35 43

N.S.

1 1.00 0.91 0.91 0.79 1.00 0.00 0.81 1.00

time (sec)

N/A 0.021 0.013 0.437 0.296 0.250 0.000 0.281 5.050

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 19 19 15 19 19

N.S.

1 1.00 1.11 1.00 1.06 1.06 0.83 1.06 1.06

time (sec)

N/A 0.021 0.065 0.063 0.245 0.237 1.565 0.273 5.043

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 19 19 17 19 19

N.S.

1 1.00 1.11 1.00 1.06 1.06 0.94 1.06 1.06

time (sec)

N/A 0.061 0.106 0.163 0.214 0.250 3.513 0.268 5.744

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 19 19 17 19 19

N.S.

1 1.00 1.11 1.00 1.06 1.06 0.94 1.06 1.06

time (sec)

N/A 0.125 0.113 0.162 0.230 0.253 15.338 0.279 5.971

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F A A F B

verified

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

size

112 112 85 0 0 74 109 0 90

N.S.

1 1.00 0.76 0.00 0.00 0.66 0.97 0.00 0.80

time (sec)

N/A 0.093 0.021 0.000 0.000 0.247 6.609 0.000 5.696

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F A A F B

verified

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

size

63 63 56 0 0 52 60 0 80

N.S.

1 1.00 0.89 0.00 0.00 0.83 0.95 0.00 1.27

time (sec)

N/A 0.042 0.028 0.000 0.000 0.242 1.231 0.000 5.263

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 15 14 14 15 0 41

N.S.

1 1.00 1.00 0.83 0.78 0.78 0.83 0.00 2.28

time (sec)

N/A 0.011 0.005 0.260 0.187 0.260 0.305 0.000 0.202

Problem 84

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

52 52 52 0 0 53 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 1.02 0.00 0.00 0.00

time (sec)

N/A 0.046 0.012 0.000 0.000 0.251 0.000 0.000 0.000

Problem 85

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

108 108 85 0 0 84 0 0 0

N.S.

1 1.00 0.79 0.00 0.00 0.78 0.00 0.00 0.00

time (sec)

N/A 0.096 0.046 0.000 0.000 0.262 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F A F A B

verified

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

size

342 342 240 0 0 267 0 288 386

N.S.

1 1.00 0.70 0.00 0.00 0.78 0.00 0.84 1.13

time (sec)

N/A 0.375 3.078 0.000 0.000 0.261 0.000 0.280 6.944

Problem 87

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

86 86 82 139 84 100 0 87 89

N.S.

1 1.00 0.95 1.62 0.98 1.16 0.00 1.01 1.03

time (sec)

N/A 0.050 0.078 0.840 0.210 0.254 0.000 0.276 0.119

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

19 19 21 18 20 20 19 20 20

N.S.

1 1.00 1.11 0.95 1.05 1.05 1.00 1.05 1.05

time (sec)

N/A 0.031 0.148 0.063 0.259 0.251 6.242 0.280 5.531

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

19 19 21 18 20 20 20 20 20

N.S.

1 1.00 1.11 0.95 1.05 1.05 1.05 1.05 1.05

time (sec)

N/A 0.356 0.230 0.197 0.259 0.260 26.881 0.275 5.552

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

19 19 21 18 20 20 0 20 20

N.S.

1 1.00 1.11 0.95 1.05 1.05 0.00 1.05 1.05

time (sec)

N/A 0.720 0.294 0.089 0.271 0.250 0.000 0.275 6.864

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

19 19 21 18 20 20 20 20 20

N.S.

1 1.00 1.11 0.95 1.05 1.05 1.05 1.05 1.05

time (sec)

N/A 0.143 0.263 0.154 0.261 0.270 55.207 0.286 6.834

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 15 17 17 17 17 17

N.S.

1 1.00 1.12 0.94 1.06 1.06 1.06 1.06 1.06

time (sec)

N/A 0.014 0.030 0.076 0.258 0.257 4.935 0.278 6.141

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

19 19 21 18 20 20 20 20 20

N.S.

1 1.00 1.11 0.95 1.05 1.05 1.05 1.05 1.05

time (sec)

N/A 0.155 0.259 0.092 0.258 0.251 7.612 0.278 5.710

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

19 19 21 18 20 20 20 20 20

N.S.

1 1.00 1.11 0.95 1.05 1.05 1.05 1.05 1.05

time (sec)

N/A 0.640 0.320 0.213 0.258 0.250 81.912 0.280 5.921

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 62 62 67 0 66 0 0 52

N.S.

1 1.00 1.00 1.08 0.00 1.06 0.00 0.00 0.84

time (sec)

N/A 0.112 0.091 1.702 0.000 0.256 0.000 0.000 5.001

Problem 96

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

66 66 69 0 0 0 0 0 0

N.S.

1 1.00 1.05 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.055 0.052 0.000 0.000 0.000 0.000 0.000 0.000

Problem 97

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

66 66 67 0 0 0 0 0 0

N.S.

1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.055 0.050 0.000 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 F F F F F F F(-1)

verified

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

size

62 62 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.042 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

62 62 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.043 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

56 56 57 0 0 0 0 0 0

N.S.

1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.049 0.032 0.000 0.000 0.000 0.000 0.000 0.000

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