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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 F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 106 107 113 115 0 293 111

N.S.

1 1.00 0.70 0.70 0.74 0.76 0.00 1.93 0.73

time (sec)

N/A 0.077 0.143 0.124 0.254 2.615 0.000 0.518 0.131

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 86 87 91 93 0 247 89

N.S.

1 1.00 0.72 0.73 0.76 0.78 0.00 2.08 0.75

time (sec)

N/A 0.072 0.092 0.149 0.266 2.835 0.000 0.478 0.079

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 83 67 69 71 0 201 67

N.S.

1 1.00 0.95 0.77 0.79 0.82 0.00 2.31 0.77

time (sec)

N/A 0.070 0.062 0.141 0.263 2.826 0.000 0.430 0.056

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 57 47 47 49 0 66 45

N.S.

1 1.00 0.98 0.81 0.81 0.84 0.00 1.14 0.78

time (sec)

N/A 0.061 0.037 0.112 0.268 2.105 0.000 0.436 0.063

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

26 26 37 24 23 25 0 32 20

N.S.

1 1.00 1.42 0.92 0.88 0.96 0.00 1.23 0.77

time (sec)

N/A 0.024 0.015 0.040 0.263 2.878 0.000 0.417 0.038

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 63 15 26 31 0 58 17

N.S.

1 1.00 2.10 0.50 0.87 1.03 0.00 1.93 0.57

time (sec)

N/A 0.046 0.026 0.065 0.270 2.660 0.000 0.434 0.124

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 114 41 52 93 0 102 53

N.S.

1 1.00 1.56 0.56 0.71 1.27 0.00 1.40 0.73

time (sec)

N/A 0.076 0.551 0.098 0.276 2.890 0.000 0.447 0.963

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 164 66 95 193 0 149 99

N.S.

1 1.00 1.39 0.56 0.81 1.64 0.00 1.26 0.84

time (sec)

N/A 0.095 0.243 0.115 0.260 3.140 0.000 0.457 0.099

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

163 163 165 89 136 307 0 196 142

N.S.

1 1.00 1.01 0.55 0.83 1.88 0.00 1.20 0.87

time (sec)

N/A 0.115 0.275 0.136 0.271 5.720 0.000 0.490 0.994

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

165 165 106 116 127 123 0 174 150

N.S.

1 1.00 0.64 0.70 0.77 0.75 0.00 1.05 0.91

time (sec)

N/A 0.114 0.222 0.167 0.271 3.141 0.000 0.467 1.144

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 86 96 106 102 0 146 120

N.S.

1 1.00 0.68 0.76 0.83 0.80 0.00 1.15 0.94

time (sec)

N/A 0.103 0.130 0.144 0.266 3.105 0.000 0.463 1.047

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 86 76 81 79 0 118 90

N.S.

1 1.00 0.97 0.85 0.91 0.89 0.00 1.33 1.01

time (sec)

N/A 0.086 0.085 0.126 0.265 4.525 0.000 0.472 1.025

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 54 55 59 55 0 88 80

N.S.

1 1.00 1.06 1.08 1.16 1.08 0.00 1.73 1.57

time (sec)

N/A 0.063 0.040 0.070 0.269 2.639 0.000 0.436 1.069

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 41 42 50 63 0 50 29

N.S.

1 1.00 1.11 1.14 1.35 1.70 0.00 1.35 0.78

time (sec)

N/A 0.075 0.025 0.097 0.268 3.928 0.000 0.624 0.961

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 69 63 76 108 0 79 65

N.S.

1 1.00 1.00 0.91 1.10 1.57 0.00 1.14 0.94

time (sec)

N/A 0.085 0.024 0.108 0.286 3.172 0.000 0.495 0.983

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 91 83 96 190 0 107 97

N.S.

1 1.00 0.90 0.82 0.95 1.88 0.00 1.06 0.96

time (sec)

N/A 0.089 0.024 0.119 0.279 3.296 0.000 0.558 1.005

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 113 103 116 281 0 136 128

N.S.

1 1.00 0.86 0.79 0.89 2.15 0.00 1.04 0.98

time (sec)

N/A 0.093 0.035 0.146 0.281 3.867 0.000 0.521 1.166

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

165 165 135 123 136 366 0 164 159

N.S.

1 1.00 0.82 0.75 0.82 2.22 0.00 0.99 0.96

time (sec)

N/A 0.098 0.041 0.142 0.274 4.394 0.000 0.597 1.643

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

183 183 127 181 146 167 0 370 146

N.S.

1 1.00 0.69 0.99 0.80 0.91 0.00 2.02 0.80

time (sec)

N/A 0.137 0.582 0.089 0.285 3.448 0.000 0.734 0.993

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 107 151 107 128 0 320 105

N.S.

1 1.00 0.82 1.15 0.82 0.98 0.00 2.44 0.80

time (sec)

N/A 0.119 0.384 0.140 0.286 3.015 0.000 0.578 0.950

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 87 121 94 115 0 270 91

N.S.

1 1.00 0.78 1.08 0.84 1.03 0.00 2.41 0.81

time (sec)

N/A 0.115 0.211 0.115 0.271 4.039 0.000 0.683 0.886

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 65 91 56 76 0 74 54

N.S.

1 1.00 1.05 1.47 0.90 1.23 0.00 1.19 0.87

time (sec)

N/A 0.091 0.142 0.091 0.266 3.079 0.000 0.666 0.058

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 31 34 41 51 0 51 41

N.S.

1 1.00 0.72 0.79 0.95 1.19 0.00 1.19 0.95

time (sec)

N/A 0.056 0.077 0.056 0.265 3.167 0.000 0.533 0.059

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 36 29 43 61 0 115 35

N.S.

1 1.00 0.75 0.60 0.90 1.27 0.00 2.40 0.73

time (sec)

N/A 0.082 0.054 0.075 0.272 2.137 0.000 0.546 0.082

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 75 38 68 112 0 135 61

N.S.

1 1.00 1.09 0.55 0.99 1.62 0.00 1.96 0.88

time (sec)

N/A 0.110 0.372 0.118 0.273 2.283 0.000 0.525 0.901

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 103 64 104 209 0 191 109

N.S.

1 1.00 0.90 0.56 0.90 1.82 0.00 1.66 0.95

time (sec)

N/A 0.128 1.032 0.115 0.287 2.791 0.000 0.536 0.095

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

160 160 136 85 143 289 0 238 147

N.S.

1 1.00 0.85 0.53 0.89 1.81 0.00 1.49 0.92

time (sec)

N/A 0.147 0.883 0.133 0.272 3.710 0.000 0.691 0.110

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

205 205 164 112 197 461 0 291 203

N.S.

1 1.00 0.80 0.55 0.96 2.25 0.00 1.42 0.99

time (sec)

N/A 0.177 2.284 0.162 0.274 2.817 0.000 0.757 0.171

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

199 199 144 194 215 185 0 225 293

N.S.

1 1.00 0.72 0.97 1.08 0.93 0.00 1.13 1.47

time (sec)

N/A 0.271 0.628 0.086 0.492 2.461 0.000 0.559 2.540

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

157 157 124 164 174 158 0 193 235

N.S.

1 1.00 0.79 1.04 1.11 1.01 0.00 1.23 1.50

time (sec)

N/A 0.204 0.349 0.121 0.478 2.562 0.000 0.609 2.157

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 94 134 126 133 0 161 177

N.S.

1 1.00 0.82 1.17 1.10 1.16 0.00 1.40 1.54

time (sec)

N/A 0.203 0.177 0.098 0.490 2.554 0.000 0.700 1.825

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 243 78 81 104 0 128 117

N.S.

1 1.00 3.33 1.07 1.11 1.42 0.00 1.75 1.60

time (sec)

N/A 0.107 0.780 0.072 0.490 3.032 0.000 0.536 1.160

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

57 57 401 77 74 101 0 90 70

N.S.

1 1.00 7.04 1.35 1.30 1.77 0.00 1.58 1.23

time (sec)

N/A 0.181 6.116 0.068 0.270 2.494 0.000 0.478 1.126

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 228 117 113 159 0 104 91

N.S.

1 1.00 2.62 1.34 1.30 1.83 0.00 1.20 1.05

time (sec)

N/A 0.218 1.274 0.086 0.274 2.737 0.000 0.470 2.485

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

129 129 317 155 144 206 0 136 124

N.S.

1 1.00 2.46 1.20 1.12 1.60 0.00 1.05 0.96

time (sec)

N/A 0.171 0.633 0.102 0.280 2.615 0.000 0.495 1.284

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

163 163 428 193 175 272 0 168 159

N.S.

1 1.00 2.63 1.18 1.07 1.67 0.00 1.03 0.98

time (sec)

N/A 0.180 0.817 0.116 0.266 2.668 0.000 0.534 0.988

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

201 201 1050 231 204 406 0 200 194

N.S.

1 1.00 5.22 1.15 1.01 2.02 0.00 1.00 0.97

time (sec)

N/A 0.196 6.559 0.120 0.281 2.756 0.000 0.537 0.972

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

203 203 148 252 158 182 0 396 157

N.S.

1 1.00 0.73 1.24 0.78 0.90 0.00 1.95 0.77

time (sec)

N/A 0.143 1.160 0.101 0.273 2.924 0.000 0.646 0.965

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 106 214 107 121 0 239 107

N.S.

1 1.00 0.81 1.63 0.82 0.92 0.00 1.82 0.82

time (sec)

N/A 0.123 0.583 0.092 0.260 3.504 0.000 0.588 0.897

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 108 172 106 130 0 297 107

N.S.

1 1.00 0.81 1.28 0.79 0.97 0.00 2.22 0.80

time (sec)

N/A 0.123 0.409 0.143 0.264 3.224 0.000 0.527 0.887

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 86 114 80 104 0 102 80

N.S.

1 1.00 0.88 1.16 0.82 1.06 0.00 1.04 0.82

time (sec)

N/A 0.073 0.134 0.119 0.262 2.972 0.000 0.489 0.882

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 65 46 55 65 0 64 52

N.S.

1 1.00 1.05 0.74 0.89 1.05 0.00 1.03 0.84

time (sec)

N/A 0.069 0.154 0.061 0.269 2.876 0.000 0.456 0.055

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 81 39 56 76 0 142 49

N.S.

1 1.00 1.21 0.58 0.84 1.13 0.00 2.12 0.73

time (sec)

N/A 0.092 0.090 0.080 0.269 3.126 0.000 0.476 0.074

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 88 50 84 132 0 189 75

N.S.

1 1.00 1.00 0.57 0.95 1.50 0.00 2.15 0.85

time (sec)

N/A 0.121 0.581 0.119 0.267 3.539 0.000 0.540 0.095

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 100 63 103 177 0 186 96

N.S.

1 1.00 0.90 0.57 0.93 1.59 0.00 1.68 0.86

time (sec)

N/A 0.123 0.634 0.125 0.269 4.172 0.000 0.542 0.931

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

157 157 129 85 145 297 0 243 151

N.S.

1 1.00 0.82 0.54 0.92 1.89 0.00 1.55 0.96

time (sec)

N/A 0.146 0.709 0.148 0.272 4.607 0.000 0.557 0.965

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

202 202 159 110 189 419 0 292 195

N.S.

1 1.00 0.79 0.54 0.94 2.07 0.00 1.45 0.97

time (sec)

N/A 0.172 0.806 0.168 0.272 2.911 0.000 0.570 1.013

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

210 210 156 272 291 204 0 244 320

N.S.

1 1.00 0.74 1.30 1.39 0.97 0.00 1.16 1.52

time (sec)

N/A 0.285 1.405 0.102 0.473 3.448 0.000 0.612 2.454

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

182 182 136 232 240 177 0 212 261

N.S.

1 1.00 0.75 1.27 1.32 0.97 0.00 1.16 1.43

time (sec)

N/A 0.215 0.605 0.141 0.487 3.721 0.000 0.594 2.225

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 114 192 182 152 0 180 204

N.S.

1 1.00 0.83 1.39 1.32 1.10 0.00 1.30 1.48

time (sec)

N/A 0.174 0.262 0.116 0.482 3.051 0.000 0.576 1.966

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 300 126 127 125 0 102 90

N.S.

1 1.00 3.06 1.29 1.30 1.28 0.00 1.04 0.92

time (sec)

N/A 0.143 1.587 0.086 0.484 3.875 0.000 0.546 1.278

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 244 127 137 122 0 106 98

N.S.

1 1.00 3.05 1.59 1.71 1.52 0.00 1.32 1.22

time (sec)

N/A 0.139 0.809 0.083 0.275 4.376 0.000 0.510 2.460

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 290 185 188 178 0 123 116

N.S.

1 1.00 2.64 1.68 1.71 1.62 0.00 1.12 1.05

time (sec)

N/A 0.173 5.376 0.112 0.272 2.696 0.000 0.528 5.348

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

165 165 353 241 228 225 0 141 136

N.S.

1 1.00 2.14 1.46 1.38 1.36 0.00 0.85 0.82

time (sec)

N/A 0.307 0.797 0.119 0.282 2.763 0.000 0.549 4.913

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

192 192 430 297 268 278 0 169 169

N.S.

1 1.00 2.24 1.55 1.40 1.45 0.00 0.88 0.88

time (sec)

N/A 0.232 0.811 0.132 0.280 3.580 0.000 0.555 2.896

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

232 232 1000 353 308 375 0 202 204

N.S.

1 1.00 4.31 1.52 1.33 1.62 0.00 0.87 0.88

time (sec)

N/A 0.239 6.453 0.135 0.281 3.153 0.000 0.573 1.039

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 62 89 89 89 0 141 110

N.S.

1 1.00 0.68 0.98 0.98 0.98 0.00 1.55 1.21

time (sec)

N/A 0.116 2.659 0.151 0.269 4.182 0.000 0.434 0.087

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 52 70 69 69 0 119 84

N.S.

1 1.00 0.71 0.96 0.95 0.95 0.00 1.63 1.15

time (sec)

N/A 0.115 1.004 0.122 0.271 2.832 0.000 0.456 0.060

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 42 49 49 49 0 97 58

N.S.

1 1.00 0.76 0.89 0.89 0.89 0.00 1.76 1.05

time (sec)

N/A 0.109 0.231 0.095 0.278 2.443 0.000 0.433 0.074

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 32 30 29 29 0 32 26

N.S.

1 1.00 0.86 0.81 0.78 0.78 0.00 0.86 0.70

time (sec)

N/A 0.093 0.075 0.078 0.273 2.678 0.000 0.460 0.882

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 28 37 30 28 0 34 25

N.S.

1 1.00 0.90 1.19 0.97 0.90 0.00 1.10 0.81

time (sec)

N/A 0.052 0.060 0.033 0.276 3.025 0.000 0.412 0.054

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 67 43 47 60 0 56 33

N.S.

1 1.00 1.16 0.74 0.81 1.03 0.00 0.97 0.57

time (sec)

N/A 0.073 0.080 0.074 0.266 4.218 0.000 0.461 0.919

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 91 55 86 138 0 129 75

N.S.

1 1.00 1.11 0.67 1.05 1.68 0.00 1.57 0.91

time (sec)

N/A 0.120 0.271 0.106 0.275 2.682 0.000 0.481 0.935

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 122 79 130 217 0 182 115

N.S.

1 1.00 1.15 0.75 1.23 2.05 0.00 1.72 1.08

time (sec)

N/A 0.130 0.323 0.118 0.273 2.665 0.000 0.476 1.008

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 125 132 142 360 91 0 139 132

N.S.

1 1.00 1.06 1.14 2.88 0.73 0.00 1.11 1.06

time (sec)

N/A 0.156 0.820 0.155 0.488 3.395 0.000 0.452 3.896

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 99 112 116 278 70 0 113 106

N.S.

1 1.00 1.13 1.17 2.81 0.71 0.00 1.14 1.07

time (sec)

N/A 0.138 0.474 0.128 0.482 3.063 0.000 0.426 3.664

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 83 90 196 51 0 87 55

N.S.

1 1.00 1.14 1.23 2.68 0.70 0.00 1.19 0.75

time (sec)

N/A 0.111 0.420 0.090 0.479 2.776 0.000 0.433 0.984

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

44 44 68 64 112 27 0 58 30

N.S.

1 1.00 1.55 1.45 2.55 0.61 0.00 1.32 0.68

time (sec)

N/A 0.079 0.206 0.076 0.481 2.465 0.000 0.421 0.963

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 66 36 49 41 0 37 32

N.S.

1 1.00 1.78 0.97 1.32 1.11 0.00 1.00 0.86

time (sec)

N/A 0.092 0.162 0.076 0.266 3.496 0.000 0.458 0.927

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 116 62 96 89 0 74 60

N.S.

1 1.00 2.11 1.13 1.75 1.62 0.00 1.35 1.09

time (sec)

N/A 0.105 0.354 0.096 0.269 3.207 0.000 0.452 1.087

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 158 88 136 131 0 103 153

N.S.

1 1.00 2.16 1.21 1.86 1.79 0.00 1.41 2.10

time (sec)

N/A 0.108 0.424 0.105 0.277 3.667 0.000 0.462 1.161

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 200 114 176 177 0 132 201

N.S.

1 1.00 2.20 1.25 1.93 1.95 0.00 1.45 2.21

time (sec)

N/A 0.117 0.649 0.114 0.270 2.824 0.000 0.479 1.454

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

109 109 242 140 216 219 0 161 139

N.S.

1 1.00 2.22 1.28 1.98 2.01 0.00 1.48 1.28

time (sec)

N/A 0.119 0.967 0.118 0.278 3.164 0.000 0.503 3.108

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

137 137 72 88 89 89 0 185 109

N.S.

1 1.00 0.53 0.64 0.65 0.65 0.00 1.35 0.80

time (sec)

N/A 0.135 3.131 0.141 0.269 3.281 0.000 0.530 0.087

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

114 114 62 79 79 79 0 141 96

N.S.

1 1.00 0.54 0.69 0.69 0.69 0.00 1.24 0.84

time (sec)

N/A 0.128 2.279 0.166 0.270 3.346 0.000 0.500 0.910

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 53 50 49 49 0 141 58

N.S.

1 1.00 0.73 0.68 0.67 0.67 0.00 1.93 0.79

time (sec)

N/A 0.115 1.188 0.144 0.265 3.776 0.000 0.456 0.918

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 42 39 39 39 0 119 36

N.S.

1 1.00 0.76 0.71 0.71 0.71 0.00 2.16 0.65

time (sec)

N/A 0.108 0.435 0.112 0.272 3.846 0.000 0.482 0.061

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 51 58 51 48 0 75 56

N.S.

1 1.00 0.77 0.88 0.77 0.73 0.00 1.14 0.85

time (sec)

N/A 0.114 0.138 0.117 0.276 4.597 0.000 0.501 0.064

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

52 52 64 51 46 58 0 52 46

N.S.

1 1.00 1.23 0.98 0.88 1.12 0.00 1.00 0.88

time (sec)

N/A 0.073 0.103 0.043 0.276 4.073 0.000 0.484 0.923

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 83 55 74 106 0 87 60

N.S.

1 1.00 1.38 0.92 1.23 1.77 0.00 1.45 1.00

time (sec)

N/A 0.092 0.122 0.100 0.275 2.872 0.000 0.465 0.096

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 38 57 59 60 0 82 58

N.S.

1 1.00 0.90 1.36 1.40 1.43 0.00 1.95 1.38

time (sec)

N/A 0.089 0.064 0.101 0.270 3.540 0.000 0.471 0.942

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

146 146 152 103 167 283 0 207 152

N.S.

1 1.00 1.04 0.71 1.14 1.94 0.00 1.42 1.04

time (sec)

N/A 0.158 0.519 0.146 0.271 3.488 0.000 0.510 1.053

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

167 167 131 141 378 90 0 139 133

N.S.

1 1.00 0.78 0.84 2.26 0.54 0.00 0.83 0.80

time (sec)

N/A 0.320 1.772 0.153 0.488 3.555 0.000 0.492 3.934

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 111 115 292 71 0 113 107

N.S.

1 1.00 1.07 1.11 2.81 0.68 0.00 1.09 1.03

time (sec)

N/A 0.223 0.589 0.139 0.485 3.752 0.000 0.506 3.750

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 91 89 206 50 0 87 81

N.S.

1 1.00 1.05 1.02 2.37 0.57 0.00 1.00 0.93

time (sec)

N/A 0.170 0.373 0.125 0.483 4.130 0.000 0.441 4.505

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 121 73 140 61 0 75 91

N.S.

1 1.00 1.75 1.06 2.03 0.88 0.00 1.09 1.32

time (sec)

N/A 0.226 0.220 0.116 0.475 2.563 0.000 0.459 1.030

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 105 60 90 71 0 74 71

N.S.

1 1.00 1.44 0.82 1.23 0.97 0.00 1.01 0.97

time (sec)

N/A 0.148 0.299 0.084 0.273 3.064 0.000 0.477 0.982

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 149 86 134 108 0 105 121

N.S.

1 1.00 1.64 0.95 1.47 1.19 0.00 1.15 1.33

time (sec)

N/A 0.240 0.447 0.105 0.271 3.106 0.000 0.500 1.068

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

109 109 191 112 174 169 0 134 106

N.S.

1 1.00 1.75 1.03 1.60 1.55 0.00 1.23 0.97

time (sec)

N/A 0.258 0.652 0.118 0.282 2.820 0.000 0.544 2.185

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 125 233 112 174 204 0 134 201

N.S.

1 1.00 1.86 0.90 1.39 1.63 0.00 1.07 1.61

time (sec)

N/A 0.266 0.924 0.121 0.272 4.595 0.000 0.495 1.687

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 120 90 89 89 0 207 110

N.S.

1 1.00 0.86 0.65 0.64 0.64 0.00 1.49 0.79

time (sec)

N/A 0.142 2.694 0.147 0.274 4.212 0.000 0.551 0.089

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

109 109 100 69 69 69 0 185 84

N.S.

1 1.00 0.92 0.63 0.63 0.63 0.00 1.70 0.77

time (sec)

N/A 0.126 1.850 0.188 0.271 2.750 0.000 0.577 0.921

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 80 50 49 49 0 163 58

N.S.

1 1.00 1.10 0.68 0.67 0.67 0.00 2.23 0.79

time (sec)

N/A 0.118 1.096 0.135 0.277 2.508 0.000 0.551 0.070

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 73 79 73 70 0 172 82

N.S.

1 1.00 0.72 0.77 0.72 0.69 0.00 1.69 0.80

time (sec)

N/A 0.130 0.544 0.151 0.270 2.762 0.000 0.544 0.895

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 99 72 72 82 0 94 75

N.S.

1 1.00 1.11 0.81 0.81 0.92 0.00 1.06 0.84

time (sec)

N/A 0.132 0.274 0.134 0.269 2.617 0.000 0.513 0.888

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 103 63 71 96 0 63 59

N.S.

1 1.00 1.37 0.84 0.95 1.28 0.00 0.84 0.79

time (sec)

N/A 0.089 0.206 0.057 0.264 3.055 0.000 0.491 0.079

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 97 67 98 151 0 113 83

N.S.

1 1.00 1.18 0.82 1.20 1.84 0.00 1.38 1.01

time (sec)

N/A 0.111 0.214 0.115 0.278 2.768 0.000 0.545 0.111

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 138 91 146 240 0 182 130

N.S.

1 1.00 1.10 0.72 1.16 1.90 0.00 1.44 1.03

time (sec)

N/A 0.100 0.394 0.135 0.272 2.689 0.000 0.564 0.167

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

128 128 137 91 188 317 0 232 173

N.S.

1 1.00 1.07 0.71 1.47 2.48 0.00 1.81 1.35

time (sec)

N/A 0.152 3.005 0.148 0.277 2.733 0.000 0.606 1.090

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

157 157 131 142 378 91 0 139 132

N.S.

1 1.00 0.83 0.90 2.41 0.58 0.00 0.89 0.84

time (sec)

N/A 0.327 3.070 0.156 0.486 2.946 0.000 0.538 3.865

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