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Integrals 101 to 197

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 101

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

40 41 40 32 31 149 88 31 31 28

N.S.

1 1.02 1.00 0.80 0.78 3.72 2.20 0.78 0.78 0.70

time (sec)

N/A 0.232 0.027 0.371 0.107 0.072 0.329 0.124 0.180 0.107

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B B A B B

verified

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

size

55 57 55 40 40 228 292 39 68 37

N.S.

1 1.04 1.00 0.73 0.73 4.15 5.31 0.71 1.24 0.67

time (sec)

N/A 0.244 0.072 0.369 0.110 0.087 1.898 0.122 0.204 0.049

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B B A B B

verified

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

size

81 88 68 52 64 356 666 52 116 56

N.S.

1 1.09 0.84 0.64 0.79 4.40 8.22 0.64 1.43 0.69

time (sec)

N/A 0.270 0.134 0.391 0.107 0.083 7.452 0.120 0.220 0.144

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

42 47 41 33 32 32 39 32 35 32

N.S.

1 1.12 0.98 0.79 0.76 0.76 0.93 0.76 0.83 0.76

time (sec)

N/A 0.281 0.017 0.503 0.027 0.059 0.262 0.116 0.201 0.054

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

29 34 30 22 21 21 27 21 24 21

N.S.

1 1.17 1.03 0.76 0.72 0.72 0.93 0.72 0.83 0.72

time (sec)

N/A 0.261 0.015 0.433 0.031 0.063 0.408 0.119 0.225 0.039

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

14 14 14 11 10 10 12 10 13 10

N.S.

1 1.00 1.00 0.79 0.71 0.71 0.86 0.71 0.93 0.71

time (sec)

N/A 0.208 0.001 0.073 0.027 0.060 0.023 0.120 0.204 0.027

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A C A A B B

verified

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

size

148 222 101 110 176 132 104 186 120 41

N.S.

1 1.50 0.68 0.74 1.19 0.89 0.70 1.26 0.81 0.28

time (sec)

N/A 0.603 0.143 0.371 0.120 0.074 1.120 0.126 0.217 0.159

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A C B A B B

verified

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

size

167 249 134 129 196 230 413 201 319 62

N.S.

1 1.49 0.80 0.77 1.17 1.38 2.47 1.20 1.91 0.37

time (sec)

N/A 0.661 0.331 0.379 0.113 0.080 30.580 0.132 0.187 0.167

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

186 276 146 150 219 340 0 211 498 84

N.S.

1 1.48 0.78 0.81 1.18 1.83 0.00 1.13 2.68 0.45

time (sec)

N/A 0.717 0.259 0.392 0.109 0.086 0.000 0.128 0.224 0.104

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

36 45 36 31 30 33 36 31 33 33

N.S.

1 1.25 1.00 0.86 0.83 0.92 1.00 0.86 0.92 0.92

time (sec)

N/A 0.270 0.021 0.499 0.038 0.060 0.130 0.125 0.205 0.050

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

15 16 25 14 21 21 24 21 21 21

N.S.

1 1.07 1.67 0.93 1.40 1.40 1.60 1.40 1.40 1.40

time (sec)

N/A 0.205 0.016 0.447 0.025 0.059 0.074 0.118 0.208 0.045

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

14 14 14 11 10 10 12 10 10 10

N.S.

1 1.00 1.00 0.79 0.71 0.71 0.86 0.71 0.71 0.71

time (sec)

N/A 0.208 0.001 0.075 0.024 0.060 0.021 0.120 0.180 0.034

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

50 54 51 44 54 43 58 45 43 42

N.S.

1 1.08 1.02 0.88 1.08 0.86 1.16 0.90 0.86 0.84

time (sec)

N/A 0.299 0.026 0.385 0.032 0.068 0.207 0.119 0.217 0.045

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

67 72 80 62 76 100 165 65 78 65

N.S.

1 1.07 1.19 0.93 1.13 1.49 2.46 0.97 1.16 0.97

time (sec)

N/A 0.331 0.043 0.380 0.033 0.071 0.283 0.121 0.188 0.044

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B B A B B

verified

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

size

90 95 97 79 101 159 362 79 117 87

N.S.

1 1.06 1.08 0.88 1.12 1.77 4.02 0.88 1.30 0.97

time (sec)

N/A 0.367 0.085 0.385 0.027 0.081 0.334 0.124 0.213 0.045

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

36 43 36 33 32 35 32 33 35 33

N.S.

1 1.19 1.00 0.92 0.89 0.97 0.89 0.92 0.97 0.92

time (sec)

N/A 0.293 0.023 0.513 0.035 0.063 0.226 0.120 0.187 0.126

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

25 30 25 22 21 27 24 21 24 21

N.S.

1 1.20 1.00 0.88 0.84 1.08 0.96 0.84 0.96 0.84

time (sec)

N/A 0.285 0.018 0.423 0.031 0.066 0.175 0.126 0.226 0.109

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

12 12 12 11 10 10 10 10 10 10

N.S.

1 1.00 1.00 0.92 0.83 0.83 0.83 0.83 0.83 0.83

time (sec)

N/A 0.218 0.001 0.074 0.024 0.064 0.023 0.116 0.186 0.026

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

46 50 46 42 38 161 100 42 38 34

N.S.

1 1.09 1.00 0.91 0.83 3.50 2.17 0.91 0.83 0.74

time (sec)

N/A 0.303 0.040 0.366 0.111 0.073 0.362 0.122 0.212 0.057

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

74 81 76 59 66 285 410 64 87 59

N.S.

1 1.09 1.03 0.80 0.89 3.85 5.54 0.86 1.18 0.80

time (sec)

N/A 0.332 0.097 0.362 0.106 0.077 1.883 0.123 0.241 0.071

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B B A B B

verified

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

size

100 112 89 66 88 403 808 74 138 78

N.S.

1 1.12 0.89 0.66 0.88 4.03 8.08 0.74 1.38 0.78

time (sec)

N/A 0.365 0.140 0.368 0.116 0.086 7.089 0.132 0.227 0.072

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

40 45 40 33 32 37 37 35 37 35

N.S.

1 1.12 1.00 0.82 0.80 0.92 0.92 0.88 0.92 0.88

time (sec)

N/A 0.305 0.027 0.496 0.024 0.065 0.391 0.123 0.195 0.062

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

27 32 27 22 21 29 26 22 26 24

N.S.

1 1.19 1.00 0.81 0.78 1.07 0.96 0.81 0.96 0.89

time (sec)

N/A 0.284 0.022 0.411 0.031 0.064 0.241 0.119 0.219 0.053

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

12 12 12 11 10 16 10 10 13 10

N.S.

1 1.00 1.00 0.92 0.83 1.33 0.83 0.83 1.08 0.83

time (sec)

N/A 0.223 0.002 0.076 0.026 0.061 0.021 0.124 0.208 0.097

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A C A A B B

verified

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

size

153 237 124 117 188 161 117 179 153 52

N.S.

1 1.55 0.81 0.76 1.23 1.05 0.76 1.17 1.00 0.34

time (sec)

N/A 0.675 0.155 0.365 0.110 0.074 1.181 0.132 0.230 0.158

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A C B A B B

verified

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

size

173 268 147 135 213 264 464 195 326 76

N.S.

1 1.55 0.85 0.78 1.23 1.53 2.68 1.13 1.88 0.44

time (sec)

N/A 0.728 0.302 0.369 0.120 0.081 29.947 0.131 0.188 0.105

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

195 299 160 144 235 364 0 207 503 96

N.S.

1 1.53 0.82 0.74 1.21 1.87 0.00 1.06 2.58 0.49

time (sec)

N/A 0.774 0.392 0.364 0.113 0.084 0.000 0.131 0.180 0.178

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

15 16 25 14 21 21 24 21 21 21

N.S.

1 1.07 1.67 0.93 1.40 1.40 1.60 1.40 1.40 1.40

time (sec)

N/A 0.213 0.002 0.393 0.032 0.063 0.078 0.118 0.202 0.002

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

15 15 25 14 13 21 24 21 21 21

N.S.

1 1.00 1.67 0.93 0.87 1.40 1.60 1.40 1.40 1.40

time (sec)

N/A 0.216 0.013 0.418 0.025 0.066 0.081 0.126 0.224 0.040

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B B B B

verified

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

size

65 67 45 44 47 55 884 180 54 37

N.S.

1 1.03 0.69 0.68 0.72 0.85 13.60 2.77 0.83 0.57

time (sec)

N/A 0.290 0.039 0.372 0.031 0.073 1.191 0.126 0.201 0.208

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B B B B

verified

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

size

63 67 54 44 47 44 804 107 43 37

N.S.

1 1.06 0.86 0.70 0.75 0.70 12.76 1.70 0.68 0.59

time (sec)

N/A 0.284 0.033 0.369 0.032 0.070 1.020 0.123 0.182 0.138

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

61 65 45 43 47 35 726 43 34 37

N.S.

1 1.07 0.74 0.70 0.77 0.57 11.90 0.70 0.56 0.61

time (sec)

N/A 0.293 0.027 0.368 0.034 0.071 0.945 0.119 0.210 0.173

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

59 63 42 44 47 67 615 57 35 37

N.S.

1 1.07 0.71 0.75 0.80 1.14 10.42 0.97 0.59 0.63

time (sec)

N/A 0.281 0.029 0.395 0.027 0.078 1.025 0.124 0.209 0.301

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B B A B B

verified

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

size

59 63 43 42 47 101 143 49 45 37

N.S.

1 1.07 0.73 0.71 0.80 1.71 2.42 0.83 0.76 0.63

time (sec)

N/A 0.284 0.031 0.379 0.025 0.105 0.826 0.118 0.190 0.624

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

103 111 98 82 160 0 138 126 82 37

N.S.

1 1.08 0.95 0.80 1.55 0.00 1.34 1.22 0.80 0.36

time (sec)

N/A 0.325 0.299 0.360 0.112 0.000 3.610 0.171 0.212 0.200

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

82 87 83 64 120 0 109 54 62 37

N.S.

1 1.06 1.01 0.78 1.46 0.00 1.33 0.66 0.76 0.45

time (sec)

N/A 0.294 0.200 0.357 0.111 0.000 1.961 0.153 0.192 0.140

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

61 63 69 43 81 0 54 44 45 67

N.S.

1 1.03 1.13 0.70 1.33 0.00 0.89 0.72 0.74 1.10

time (sec)

N/A 0.262 0.131 0.359 0.108 0.000 1.146 0.139 0.213 0.206

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

56 57 66 42 63 0 49 0 95 37

N.S.

1 1.02 1.18 0.75 1.12 0.00 0.88 0.00 1.70 0.66

time (sec)

N/A 0.266 0.102 0.362 0.106 0.000 0.909 0.000 0.170 0.297

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

18 18 18 60 14 0 44 14 65 41

N.S.

1 1.00 1.00 3.33 0.78 0.00 2.44 0.78 3.61 2.28

time (sec)

N/A 0.206 0.056 0.365 0.026 0.000 0.670 0.134 0.218 0.634

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

43 50 33 83 33 0 165 27 110 38

N.S.

1 1.16 0.77 1.93 0.77 0.00 3.84 0.63 2.56 0.88

time (sec)

N/A 0.244 0.074 0.357 0.026 0.000 1.923 0.141 0.209 0.800

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

64 84 46 106 50 0 573 41 153 38

N.S.

1 1.31 0.72 1.66 0.78 0.00 8.95 0.64 2.39 0.59

time (sec)

N/A 0.277 0.088 0.364 0.028 0.000 6.332 0.142 0.213 0.940

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C F F C F F B

verified

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

size

287 295 53 130 0 0 41 0 52 37

N.S.

1 1.03 0.18 0.45 0.00 0.00 0.14 0.00 0.18 0.13

time (sec)

N/A 0.520 10.013 0.424 0.000 0.000 0.617 0.000 0.270 0.233

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C F F C F F B

verified

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

size

266 271 52 114 0 0 41 0 35 37

N.S.

1 1.02 0.20 0.43 0.00 0.00 0.15 0.00 0.13 0.14

time (sec)

N/A 0.481 9.710 0.398 0.000 0.000 0.488 0.000 0.279 0.155

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C F F C F F B

verified

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

size

243 247 52 101 0 0 39 0 20 37

N.S.

1 1.02 0.21 0.42 0.00 0.00 0.16 0.00 0.08 0.15

time (sec)

N/A 0.454 10.013 0.412 0.000 0.000 0.455 0.000 0.252 0.201

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C F F C F F B

verified

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

size

271 276 55 121 0 0 39 0 28 37

N.S.

1 1.02 0.20 0.45 0.00 0.00 0.14 0.00 0.10 0.14

time (sec)

N/A 0.488 10.011 0.518 0.000 0.000 0.484 0.000 0.212 0.347

Problem 146

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD TBD

size

121 125 83 165 148 0 170 127 108 38

N.S.

1 1.03 0.69 1.36 1.22 0.00 1.40 1.05 0.89 0.31

time (sec)

N/A 0.348 0.112 0.394 0.111 0.000 16.034 0.384 0.238 0.375

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD TBD

size

100 105 79 135 131 0 110 122 83 38

N.S.

1 1.05 0.79 1.35 1.31 0.00 1.10 1.22 0.83 0.38

time (sec)

N/A 0.333 0.101 0.374 0.111 0.000 6.481 0.186 0.202 0.249

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD TBD

size

100 107 84 135 135 0 139 109 83 38

N.S.

1 1.07 0.84 1.35 1.35 0.00 1.39 1.09 0.83 0.38

time (sec)

N/A 0.337 0.099 0.363 0.122 0.000 4.423 0.185 0.199 0.132

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD TBD

size

102 113 84 135 137 0 138 123 83 38

N.S.

1 1.11 0.82 1.32 1.34 0.00 1.35 1.21 0.81 0.37

time (sec)

N/A 0.342 0.103 0.373 0.110 0.000 4.992 0.185 0.205 0.164

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD TBD

size

105 119 84 194 137 0 139 0 83 38

N.S.

1 1.13 0.80 1.85 1.30 0.00 1.32 0.00 0.79 0.36

time (sec)

N/A 0.364 0.108 0.560 0.112 0.000 7.431 0.000 0.199 0.189

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD TBD

size

128 146 103 527 154 0 144 131 103 38

N.S.

1 1.14 0.80 4.12 1.20 0.00 1.12 1.02 0.80 0.30

time (sec)

N/A 0.380 0.159 0.561 0.107 0.000 13.245 0.176 0.222 0.367

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD TBD

size

101 110 110 120 110 0 122 0 116 37

N.S.

1 1.09 1.09 1.19 1.09 0.00 1.21 0.00 1.15 0.37

time (sec)

N/A 0.375 5.946 0.379 0.120 0.000 7.503 0.000 0.259 0.229

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD TBD

size

70 77 85 73 72 0 87 126 83 37

N.S.

1 1.10 1.21 1.04 1.03 0.00 1.24 1.80 1.19 0.53

time (sec)

N/A 0.353 5.221 0.368 0.106 0.000 2.609 0.139 0.233 0.197

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B C B B

verified

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

size

18 18 31 28 14 28 42 40 19 38

N.S.

1 1.00 1.72 1.56 0.78 1.56 2.33 2.22 1.06 2.11

time (sec)

N/A 0.230 4.321 0.375 0.032 0.409 0.705 0.124 0.207 0.191

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A C B B

verified

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

size

39 50 33 37 31 29 48 61 21 38

N.S.

1 1.28 0.85 0.95 0.79 0.74 1.23 1.56 0.54 0.97

time (sec)

N/A 0.292 3.764 0.461 0.033 0.537 0.718 0.129 0.267 0.178

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B C B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD TBD

size

58 80 57 48 52 79 230 77 41 38

N.S.

1 1.38 0.98 0.83 0.90 1.36 3.97 1.33 0.71 0.66

time (sec)

N/A 0.342 4.577 0.406 0.029 0.467 1.396 0.135 0.205 0.389

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD TBD

size

136 149 53 135 0 0 46 0 59 38

N.S.

1 1.10 0.39 0.99 0.00 0.00 0.34 0.00 0.43 0.28

time (sec)

N/A 0.394 10.020 1.022 0.000 0.000 3.379 0.000 0.315 0.276

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD TBD

size

114 123 52 133 0 0 46 0 40 38

N.S.

1 1.08 0.46 1.17 0.00 0.00 0.40 0.00 0.35 0.33

time (sec)

N/A 0.351 10.011 0.619 0.000 0.000 1.490 0.000 0.296 0.155

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD TBD

size

119 126 52 126 0 0 44 0 46 37

N.S.

1 1.06 0.44 1.06 0.00 0.00 0.37 0.00 0.39 0.31

time (sec)

N/A 0.369 10.014 0.782 0.000 0.000 1.407 0.000 0.301 0.278

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD TBD

size

143 157 55 134 0 0 44 0 127 37

N.S.

1 1.10 0.38 0.94 0.00 0.00 0.31 0.00 0.89 0.26

time (sec)

N/A 0.441 10.030 1.257 0.000 0.000 2.166 0.000 0.261 0.419

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F C F F B

verified

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

size

50 50 50 0 0 0 37 0 101 41

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.74 0.00 2.02 0.82

time (sec)

N/A 0.300 0.094 0.000 0.000 0.000 19.884 0.000 0.283 0.223

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F C F F B

verified

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

size

50 50 50 0 0 0 24 0 259 41

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.48 0.00 5.18 0.82

time (sec)

N/A 0.277 0.055 0.000 0.000 0.000 2.077 0.000 0.225 0.225

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F A A B B B B

verified

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

size

74 74 68 0 71 98 2628 231 86 41

N.S.

1 1.00 0.92 0.00 0.96 1.32 35.51 3.12 1.16 0.55

time (sec)

N/A 0.326 0.080 0.000 0.047 0.140 1.690 0.127 0.200 0.201

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F C F F B

verified

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

size

46 46 46 0 0 0 41 0 215 57

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.89 0.00 4.67 1.24

time (sec)

N/A 0.280 0.124 0.000 0.000 0.000 10.760 0.000 0.257 0.197

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F C F F B

verified

N/A No Yes N/A TBD TBD TBD TBD TBD TBD

size

50 52 50 0 0 0 27 0 134 41

N.S.

1 1.04 1.00 0.00 0.00 0.00 0.54 0.00 2.68 0.82

time (sec)

N/A 0.295 0.123 0.000 0.000 0.000 14.656 0.000 0.216 0.241

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F C F F B

verified

N/A No Yes N/A TBD TBD TBD TBD TBD TBD

size

50 52 50 0 0 0 42 0 63 41

N.S.

1 1.04 1.00 0.00 0.00 0.00 0.84 0.00 1.26 0.82

time (sec)

N/A 0.320 0.224 0.000 0.000 0.000 81.185 0.000 0.269 0.224

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A B B B B B B

verified

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

size

15 16 38 14 32 32 37 32 31 32

N.S.

1 1.07 2.53 0.93 2.13 2.13 2.47 2.13 2.07 2.13

time (sec)

N/A 0.222 0.017 0.494 0.030 0.111 0.583 0.118 0.280 0.113

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B A B B B

verified

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

size

15 15 38 14 13 32 22 32 31 32

N.S.

1 1.00 2.53 0.93 0.87 2.13 1.47 2.13 2.07 2.13

time (sec)

N/A 0.222 0.014 0.502 0.030 0.080 0.538 0.121 0.202 0.047

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

45 45 43 30 42 29 41 29 29 29

N.S.

1 1.00 0.96 0.67 0.93 0.64 0.91 0.64 0.64 0.64

time (sec)

N/A 0.273 0.018 0.365 0.026 0.075 25.188 0.125 0.191 0.026

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

18 18 31 0 14 0 78 0 13 38

N.S.

1 1.00 1.72 0.00 0.78 0.00 4.33 0.00 0.72 2.11

time (sec)

N/A 0.221 6.002 0.000 0.032 0.000 3.765 0.000 0.212 0.226

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B B B B B

verified

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

size

60 60 54 58 60 130 469 159 146 57

N.S.

1 1.00 0.90 0.97 1.00 2.17 7.82 2.65 2.43 0.95

time (sec)

N/A 0.310 0.090 0.460 0.026 0.087 0.431 0.124 0.237 0.210

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

38 38 34 37 38 65 182 73 66 36

N.S.

1 1.00 0.89 0.97 1.00 1.71 4.79 1.92 1.74 0.95

time (sec)

N/A 0.275 0.060 0.397 0.030 0.112 0.279 0.117 0.232 0.173

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

16 16 16 16 16 20 17 16 17 15

N.S.

1 1.00 1.00 1.00 1.00 1.25 1.06 1.00 1.06 0.94

time (sec)

N/A 0.230 0.006 0.039 0.033 0.082 0.020 0.122 0.206 0.127

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F C F F B

verified

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

size

24 24 24 0 0 0 44 0 11 25

N.S.

1 1.00 1.00 0.00 0.00 0.00 1.83 0.00 0.46 1.04

time (sec)

N/A 0.231 0.019 0.000 0.000 0.000 0.478 0.000 0.241 0.259

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F C F F B

verified

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

size

24 24 24 0 0 0 318 0 24 25

N.S.

1 1.00 1.00 0.00 0.00 0.00 13.25 0.00 1.00 1.04

time (sec)

N/A 0.229 0.014 0.000 0.000 0.000 0.684 0.000 0.222 0.164

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 24 24 0 0 0 0 0 128 25

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 5.33 1.04

time (sec)

N/A 0.224 0.018 0.000 0.000 0.000 0.000 0.000 0.210 0.322

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

49 49 49 0 0 0 49 0 241 43

N.S.

1 1.00 1.00 0.00 0.00 0.00 1.00 0.00 4.92 0.88

time (sec)

N/A 0.263 0.026 0.000 0.000 0.000 0.965 0.000 0.221 0.235

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

48 48 48 0 0 0 49 0 91 43

N.S.

1 1.00 1.00 0.00 0.00 0.00 1.02 0.00 1.90 0.90

time (sec)

N/A 0.260 0.020 0.000 0.000 0.000 0.642 0.000 0.244 0.364

Problem 179

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

48 48 48 0 0 0 49 0 20 43

N.S.

1 1.00 1.00 0.00 0.00 0.00 1.02 0.00 0.42 0.90

time (sec)

N/A 0.261 0.023 0.000 0.000 0.000 0.588 0.000 0.203 0.407

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

51 51 51 0 0 0 49 0 33 43

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.96 0.00 0.65 0.84

time (sec)

N/A 0.257 0.021 0.000 0.000 0.000 0.718 0.000 0.209 0.312

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

51 51 51 0 0 0 49 0 46 43

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.96 0.00 0.90 0.84

time (sec)

N/A 0.258 0.026 0.000 0.000 0.000 1.186 0.000 0.256 0.325

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F C F F B

verified

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

size

46 46 46 0 0 0 46 0 96 47

N.S.

1 1.00 1.00 0.00 0.00 0.00 1.00 0.00 2.09 1.02

time (sec)

N/A 0.258 0.020 0.000 0.000 0.000 0.930 0.000 0.194 0.941

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B F B B F B B

verified

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

size

22 22 41 51 0 50 61 0 28 41

N.S.

1 1.00 1.86 2.32 0.00 2.27 2.77 0.00 1.27 1.86

time (sec)

N/A 0.223 0.087 0.469 0.000 0.100 5.416 0.000 0.216 0.432

Problem 184

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C F F A B F F B

verified

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

size

146 132 55 0 0 192 1724 0 106 64

N.S.

1 0.90 0.38 0.00 0.00 1.32 11.81 0.00 0.73 0.44

time (sec)

N/A 0.408 0.049 0.000 0.000 0.086 1.139 0.000 0.216 0.440

Problem 185

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C F F A B F F B

verified

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

size

96 91 55 0 0 126 695 0 82 64

N.S.

1 0.95 0.57 0.00 0.00 1.31 7.24 0.00 0.85 0.67

time (sec)

N/A 0.334 0.044 0.000 0.000 0.093 0.967 0.000 0.236 0.418

Problem 186

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C F F A B F F B

verified

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

size

50 50 55 0 0 68 250 0 58 64

N.S.

1 1.00 1.10 0.00 0.00 1.36 5.00 0.00 1.16 1.28

time (sec)

N/A 0.273 0.040 0.000 0.000 0.090 0.769 0.000 0.238 0.405

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B F A B F F B

verified

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

size

18 18 18 47 0 31 42 0 34 75

N.S.

1 1.00 1.00 2.61 0.00 1.72 2.33 0.00 1.89 4.17

time (sec)

N/A 0.222 0.038 0.477 0.000 0.078 0.697 0.000 0.202 0.352

Problem 188

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F C F F B

verified

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

size

50 39 50 0 0 0 39 0 15 51

N.S.

1 0.78 1.00 0.00 0.00 0.00 0.78 0.00 0.30 1.02

time (sec)

N/A 0.287 0.016 0.000 0.000 0.000 6.840 0.000 0.211 0.524

Problem 189

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F C F F B

verified

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

size

53 53 53 0 0 0 48 0 39 54

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.91 0.00 0.74 1.02

time (sec)

N/A 0.274 0.022 0.000 0.000 0.000 1.673 0.000 0.255 0.557

Problem 190

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F C F F B

verified

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

size

55 55 55 0 0 0 48 0 68 56

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.87 0.00 1.24 1.02

time (sec)

N/A 0.271 0.020 0.000 0.000 0.000 1.930 0.000 0.252 0.336

Problem 191

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C F F A B F F B

verified

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

size

147 132 55 0 0 192 1911 0 106 64

N.S.

1 0.90 0.37 0.00 0.00 1.31 13.00 0.00 0.72 0.44

time (sec)

N/A 0.400 0.023 0.000 0.000 0.081 4.260 0.000 0.199 0.342

Problem 192

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C F F A B F F B

verified

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

size

97 91 55 0 0 126 767 0 82 64

N.S.

1 0.94 0.57 0.00 0.00 1.30 7.91 0.00 0.85 0.66

time (sec)

N/A 0.338 0.017 0.000 0.000 0.080 4.049 0.000 0.246 0.334

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C F F A B F F B

verified

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

size

51 51 55 0 0 68 241 0 58 64

N.S.

1 1.00 1.08 0.00 0.00 1.33 4.73 0.00 1.14 1.25

time (sec)

N/A 0.278 0.011 0.000 0.000 0.079 2.683 0.000 0.239 0.209

Problem 194

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B F A B F F B

verified

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

size

18 18 18 47 0 31 99 0 34 75

N.S.

1 1.00 1.00 2.61 0.00 1.72 5.50 0.00 1.89 4.17

time (sec)

N/A 0.215 0.009 0.497 0.000 0.076 2.375 0.000 0.186 0.216

Problem 195

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F C F F B

verified

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

size

50 39 50 0 0 0 39 0 15 51

N.S.

1 0.78 1.00 0.00 0.00 0.00 0.78 0.00 0.30 1.02

time (sec)

N/A 0.275 0.000 0.000 0.000 0.000 6.698 0.000 0.195 0.003

Problem 196

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F C F F B

verified

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

size

59 59 53 0 0 0 48 0 39 54

N.S.

1 1.00 0.90 0.00 0.00 0.00 0.81 0.00 0.66 0.92

time (sec)

N/A 0.287 0.001 0.000 0.000 0.000 3.469 0.000 0.276 0.385

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F C F F B

verified

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

size

56 56 55 0 0 0 48 0 68 56

N.S.

1 1.00 0.98 0.00 0.00 0.00 0.86 0.00 1.21 1.00

time (sec)

N/A 0.277 0.002 0.000 0.000 0.000 2.606 0.000 0.260 0.194

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