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2.2.2 Integrals 101 to 200

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 Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 100 91 77 94 328 194 80 92

N.S.

1 1.06 0.97 0.82 1.00 3.49 2.06 0.85 0.98

time (sec)

N/A 0.251 0.048 2.543 0.282 0.324 0.582 0.275 4.999

Problem 102

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

89 94 83 76 92 301 155 78 82

N.S.

1 1.06 0.93 0.85 1.03 3.38 1.74 0.88 0.92

time (sec)

N/A 0.214 0.054 2.543 0.291 0.301 0.396 0.275 4.990

Problem 103

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

92 92 84 77 92 300 150 78 82

N.S.

1 1.00 0.91 0.84 1.00 3.26 1.63 0.85 0.89

time (sec)

N/A 0.192 0.042 2.542 0.285 0.285 0.300 0.280 5.131

Problem 104

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

97 108 96 82 96 324 194 82 113

N.S.

1 1.11 0.99 0.85 0.99 3.34 2.00 0.85 1.16

time (sec)

N/A 0.268 0.039 2.499 0.287 0.268 0.385 0.279 5.111

Problem 105

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

117 131 116 98 128 368 226 108 114

N.S.

1 1.12 0.99 0.84 1.09 3.15 1.93 0.92 0.97

time (sec)

N/A 0.381 0.058 2.536 0.277 0.293 0.424 0.298 5.198

Problem 106

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

142 161 139 119 154 426 260 135 135

N.S.

1 1.13 0.98 0.84 1.08 3.00 1.83 0.95 0.95

time (sec)

N/A 0.719 0.066 2.664 0.280 0.281 0.474 0.278 5.034

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 12 13 12 12 26 12 12

N.S.

1 1.00 1.00 1.08 1.00 1.00 2.17 1.00 1.00

time (sec)

N/A 0.140 0.005 2.622 0.274 0.279 0.083 0.281 0.035

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 28 20 23 23 22 25 11

N.S.

1 1.00 2.55 1.82 2.09 2.09 2.00 2.27 1.00

time (sec)

N/A 0.142 0.007 2.539 0.205 0.246 0.091 0.275 5.158

Problem 109

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

11 11 10 11 10 10 7 11 10

N.S.

1 1.00 0.91 1.00 0.91 0.91 0.64 1.00 0.91

time (sec)

N/A 0.137 0.003 2.511 0.201 0.278 0.033 0.289 0.030

Problem 110

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

9 9 9 10 9 9 5 7 9

N.S.

1 1.00 1.00 1.11 1.00 1.00 0.56 0.78 1.00

time (sec)

N/A 0.135 0.003 2.515 0.200 0.239 0.035 0.286 0.033

Problem 111

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

19 19 19 16 15 20 14 15 16

N.S.

1 1.00 1.00 0.84 0.79 1.05 0.74 0.79 0.84

time (sec)

N/A 0.141 0.006 2.548 0.300 0.274 0.045 0.285 0.029

Problem 112

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

19 19 19 16 15 21 15 15 17

N.S.

1 1.00 1.00 0.84 0.79 1.11 0.79 0.79 0.89

time (sec)

N/A 0.141 0.006 2.525 0.266 0.257 0.045 0.297 5.134

Problem 113

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

14 14 14 15 14 19 10 14 14

N.S.

1 1.00 1.00 1.07 1.00 1.36 0.71 1.00 1.00

time (sec)

N/A 0.138 0.005 2.551 0.264 0.245 0.042 0.303 0.025

Problem 114

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

12 12 14 13 14 14 8 14 12

N.S.

1 1.00 1.17 1.08 1.17 1.17 0.67 1.17 1.00

time (sec)

N/A 0.135 0.005 2.514 0.185 0.286 0.085 0.286 0.043

Problem 115

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

12 12 14 13 14 14 8 14 12

N.S.

1 1.00 1.17 1.08 1.17 1.17 0.67 1.17 1.00

time (sec)

N/A 0.133 0.004 2.511 0.199 0.244 0.089 0.288 0.002

Problem 116

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

39 39 39 37 49 98 75 36 31

N.S.

1 1.00 1.00 0.95 1.26 2.51 1.92 0.92 0.79

time (sec)

N/A 0.155 0.015 2.538 0.281 0.250 0.155 0.282 0.101

Problem 117

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

35 40 35 25 30 39 27 25 30

N.S.

1 1.14 1.00 0.71 0.86 1.11 0.77 0.71 0.86

time (sec)

N/A 0.153 0.010 2.560 0.270 0.247 0.060 0.304 4.996

Problem 118

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

14 14 14 13 16 16 17 11 20

N.S.

1 1.00 1.00 0.93 1.14 1.14 1.21 0.79 1.43

time (sec)

N/A 0.143 0.006 2.509 0.188 0.236 0.048 0.285 0.040

Problem 119

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

1 1 1 2 1 1 0 1 1

N.S.

1 1.00 1.00 2.00 1.00 1.00 0.00 1.00 1.00

time (sec)

N/A 0.123 0.000 2.556 0.189 0.264 0.016 0.274 0.002

Problem 120

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

8 8 8 7 6 6 5 6 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.62 0.75 0.75

time (sec)

N/A 0.135 0.000 2.510 0.184 0.249 0.021 0.282 0.023

Problem 121

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

8 8 8 7 6 6 5 6 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.62 0.75 0.75

time (sec)

N/A 0.135 0.000 2.510 0.184 0.250 0.024 0.280 0.012

Problem 122

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

8 8 8 7 6 6 5 6 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.62 0.75 0.75

time (sec)

N/A 0.133 0.000 2.518 0.201 0.248 0.019 0.274 0.013

Problem 123

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

3 3 3 4 3 3 2 3 3

N.S.

1 1.00 1.00 1.33 1.00 1.00 0.67 1.00 1.00

time (sec)

N/A 0.128 0.000 2.495 0.196 0.254 0.026 0.276 0.007

Problem 124

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

4 4 4 5 7 4 3 5 4

N.S.

1 1.00 1.00 1.25 1.75 1.00 0.75 1.25 1.00

time (sec)

N/A 0.126 0.000 2.478 0.203 0.247 0.021 0.278 0.013

Problem 125

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

6 6 6 7 6 6 3 6 6

N.S.

1 1.00 1.00 1.17 1.00 1.00 0.50 1.00 1.00

time (sec)

N/A 0.128 0.000 2.515 0.186 0.251 0.023 0.288 0.013

Problem 126

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

8 8 8 7 6 6 7 6 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.88 0.75 0.75

time (sec)

N/A 0.126 0.000 2.498 0.185 0.249 0.024 0.273 0.018

Problem 127

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

29 27 29 25 25 24 22 47 23

N.S.

1 0.93 1.00 0.86 0.86 0.83 0.76 1.62 0.79

time (sec)

N/A 0.165 0.003 2.505 0.190 0.244 0.062 0.293 5.432

Problem 128

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

33 33 33 29 28 86 58 28 25

N.S.

1 1.00 1.00 0.88 0.85 2.61 1.76 0.85 0.76

time (sec)

N/A 0.155 0.006 2.538 0.276 0.272 0.076 0.305 0.043

Problem 129

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

16 16 16 15 14 14 12 63 14

N.S.

1 1.00 1.00 0.94 0.88 0.88 0.75 3.94 0.88

time (sec)

N/A 0.140 0.001 2.524 0.185 0.319 0.053 0.282 5.175

Problem 130

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 25 17 16 69 54 16 17

N.S.

1 1.00 1.00 0.68 0.64 2.76 2.16 0.64 0.68

time (sec)

N/A 0.140 0.003 2.534 0.273 0.281 0.065 0.272 5.155

Problem 131

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

24 27 24 23 25 21 17 26 19

N.S.

1 1.12 1.00 0.96 1.04 0.88 0.71 1.08 0.79

time (sec)

N/A 0.145 0.004 2.538 0.196 0.267 0.102 0.288 5.064

Problem 132

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

36 36 36 32 31 86 66 31 28

N.S.

1 1.00 1.00 0.89 0.86 2.39 1.83 0.86 0.78

time (sec)

N/A 0.153 0.009 2.545 0.264 0.245 0.087 0.288 0.062

Problem 133

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

38 37 37 34 36 36 32 47 34

N.S.

1 0.97 0.97 0.89 0.95 0.95 0.84 1.24 0.89

time (sec)

N/A 0.182 0.005 2.557 0.199 0.233 0.136 0.273 5.174

Problem 134

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

35 32 28 32 34 40 31 32 31

N.S.

1 0.91 0.80 0.91 0.97 1.14 0.89 0.91 0.89

time (sec)

N/A 0.178 0.006 2.535 0.196 0.308 0.092 0.294 5.121

Problem 135

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

47 47 47 38 38 128 80 37 35

N.S.

1 1.00 1.00 0.81 0.81 2.72 1.70 0.79 0.74

time (sec)

N/A 0.162 0.014 2.580 0.273 0.284 0.099 0.281 0.050

Problem 136

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

17 17 17 16 16 16 15 15 15

N.S.

1 1.00 1.00 0.94 0.94 0.94 0.88 0.88 0.88

time (sec)

N/A 0.139 0.002 2.597 0.189 0.259 0.077 0.275 0.028

Problem 137

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

47 47 47 38 37 128 80 37 35

N.S.

1 1.00 1.00 0.81 0.79 2.72 1.70 0.79 0.74

time (sec)

N/A 0.161 0.016 2.580 0.286 0.281 0.105 0.284 5.118

Problem 138

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

41 40 34 38 40 54 36 51 37

N.S.

1 0.98 0.83 0.93 0.98 1.32 0.88 1.24 0.90

time (sec)

N/A 0.181 0.011 2.570 0.186 0.285 0.148 0.285 0.051

Problem 139

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

60 63 56 47 52 144 94 50 48

N.S.

1 1.05 0.93 0.78 0.87 2.40 1.57 0.83 0.80

time (sec)

N/A 0.176 0.025 2.581 0.282 0.324 0.152 0.273 5.461

Problem 140

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

53 53 42 57 57 80 53 56 55

N.S.

1 1.00 0.79 1.08 1.08 1.51 1.00 1.06 1.04

time (sec)

N/A 0.197 0.023 2.592 0.192 0.269 0.189 0.282 5.204

Problem 141

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

55 55 55 52 51 51 56 53 51

N.S.

1 1.00 1.00 0.95 0.93 0.93 1.02 0.96 0.93

time (sec)

N/A 0.194 0.006 2.613 0.187 0.306 0.024 0.270 5.179

Problem 142

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

55 59 55 52 51 51 53 53 51

N.S.

1 1.07 1.00 0.95 0.93 0.93 0.96 0.96 0.93

time (sec)

N/A 0.205 0.006 2.681 0.182 0.283 0.020 0.272 0.046

Problem 143

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

55 55 55 52 51 51 56 53 51

N.S.

1 1.00 1.00 0.95 0.93 0.93 1.02 0.96 0.93

time (sec)

N/A 0.193 0.006 2.615 0.188 0.289 0.021 0.285 0.046

Problem 144

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

42 46 51 52 51 51 53 53 51

N.S.

1 1.10 1.21 1.24 1.21 1.21 1.26 1.26 1.21

time (sec)

N/A 0.191 0.009 2.675 0.194 0.293 0.025 0.274 0.046

Problem 145

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 50 49 48 48 53 50 48

N.S.

1 1.00 1.00 0.98 0.96 0.96 1.06 1.00 0.96

time (sec)

N/A 0.187 0.005 2.583 0.195 0.283 0.023 0.280 0.044

Problem 146

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

43 50 51 49 52 49 49 53 48

N.S.

1 1.16 1.19 1.14 1.21 1.14 1.14 1.23 1.12

time (sec)

N/A 0.186 0.010 2.578 0.250 0.267 0.060 0.284 0.044

Problem 147

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

48 48 48 49 48 53 48 48 48

N.S.

1 1.00 1.00 1.02 1.00 1.10 1.00 1.00 1.00

time (sec)

N/A 0.190 0.012 2.555 0.266 0.279 0.061 0.277 0.048

Problem 148

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

51 52 49 48 52 54 48 70 48

N.S.

1 1.02 0.96 0.94 1.02 1.06 0.94 1.37 0.94

time (sec)

N/A 0.200 0.016 2.603 0.245 0.330 0.115 0.292 0.047

Problem 149

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

48 48 50 46 50 52 51 50 50

N.S.

1 1.00 1.04 0.96 1.04 1.08 1.06 1.04 1.04

time (sec)

N/A 0.193 0.014 2.557 0.244 0.277 0.133 0.275 0.050

Problem 150

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

87 87 87 89 85 85 100 94 78

N.S.

1 1.00 1.00 1.02 0.98 0.98 1.15 1.08 0.90

time (sec)

N/A 0.234 0.011 2.610 0.188 0.283 0.024 0.281 0.059

Problem 151

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

87 91 81 89 85 85 92 94 78

N.S.

1 1.05 0.93 1.02 0.98 0.98 1.06 1.08 0.90

time (sec)

N/A 0.254 0.017 2.579 0.202 0.287 0.023 0.282 0.033

Problem 152

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

87 87 87 89 85 85 100 94 78

N.S.

1 1.00 1.00 1.02 0.98 0.98 1.15 1.08 0.90

time (sec)

N/A 0.227 0.011 2.595 0.217 0.278 0.025 0.288 0.030

Problem 153

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 75 81 89 85 85 94 94 78

N.S.

1 1.06 1.14 1.25 1.20 1.20 1.32 1.32 1.10

time (sec)

N/A 0.227 0.015 2.626 0.219 0.306 0.030 0.283 0.036

Problem 154

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

82 82 82 86 82 82 97 91 75

N.S.

1 1.00 1.00 1.05 1.00 1.00 1.18 1.11 0.91

time (sec)

N/A 0.219 0.010 2.577 0.193 0.322 0.026 0.286 0.029

Problem 155

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

80 87 80 84 85 82 85 92 74

N.S.

1 1.09 1.00 1.05 1.06 1.02 1.06 1.15 0.92

time (sec)

N/A 0.226 0.016 2.649 0.206 0.300 0.089 0.294 0.037

Problem 156

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

81 81 81 90 83 87 92 90 76

N.S.

1 1.00 1.00 1.11 1.02 1.07 1.14 1.11 0.94

time (sec)

N/A 0.224 0.025 2.624 0.197 0.269 0.081 0.276 0.032

Problem 157

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 82 83 88 85 88 87 114 82

N.S.

1 0.98 0.99 1.05 1.01 1.05 1.04 1.36 0.98

time (sec)

N/A 0.240 0.028 2.595 0.202 0.254 0.146 0.288 0.038

Problem 158

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

80 80 80 81 84 87 92 88 82

N.S.

1 1.00 1.00 1.01 1.05 1.09 1.15 1.10 1.02

time (sec)

N/A 0.228 0.027 2.597 0.197 0.271 0.162 0.276 0.055

Problem 159

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

127 127 127 126 127 127 143 135 119

N.S.

1 1.00 1.00 0.99 1.00 1.00 1.13 1.06 0.94

time (sec)

N/A 0.279 0.017 2.718 0.189 0.236 0.029 0.295 0.057

Problem 160

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

106 110 119 126 127 127 138 135 119

N.S.

1 1.04 1.12 1.19 1.20 1.20 1.30 1.27 1.12

time (sec)

N/A 0.281 0.022 2.614 0.194 0.280 0.031 0.278 0.041

Problem 161

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

127 127 127 126 127 127 143 135 119

N.S.

1 1.00 1.00 0.99 1.00 1.00 1.13 1.06 0.94

time (sec)

N/A 0.263 0.014 2.635 0.198 0.267 0.037 0.271 0.039

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 75 119 125 127 127 136 134 118

N.S.

1 1.06 1.68 1.76 1.79 1.79 1.92 1.89 1.66

time (sec)

N/A 0.231 0.020 2.620 0.200 0.243 0.030 0.276 0.039

Problem 163

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

122 122 122 122 124 124 136 131 116

N.S.

1 1.00 1.00 1.00 1.02 1.02 1.11 1.07 0.95

time (sec)

N/A 0.256 0.013 2.589 0.197 0.259 0.032 0.276 0.042

Problem 164

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

123 126 123 122 128 125 133 134 116

N.S.

1 1.02 1.00 0.99 1.04 1.02 1.08 1.09 0.94

time (sec)

N/A 0.259 0.020 2.700 0.189 0.243 0.113 0.276 0.045

Problem 165

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

120 120 120 126 124 129 131 130 115

N.S.

1 1.00 1.00 1.05 1.03 1.08 1.09 1.08 0.96

time (sec)

N/A 0.244 0.026 2.711 0.218 0.285 0.108 0.278 0.042

Problem 166

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

123 124 120 127 128 131 133 160 121

N.S.

1 1.01 0.98 1.03 1.04 1.07 1.08 1.30 0.98

time (sec)

N/A 0.263 0.032 2.598 0.192 0.269 0.181 0.271 5.147

Problem 167

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

120 120 120 124 126 129 131 129 121

N.S.

1 1.00 1.00 1.03 1.05 1.08 1.09 1.08 1.01

time (sec)

N/A 0.254 0.028 2.820 0.192 0.266 0.190 0.278 0.044

Problem 168

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

104 104 104 143 139 302 246 153 169

N.S.

1 1.00 1.00 1.38 1.34 2.90 2.37 1.47 1.62

time (sec)

N/A 0.255 0.061 2.690 0.302 0.266 0.315 0.276 5.183

Problem 169

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 78 82 95 100 101 83 107 106

N.S.

1 0.99 1.04 1.20 1.27 1.28 1.05 1.35 1.34

time (sec)

N/A 0.238 0.029 2.606 0.192 0.263 0.231 0.290 0.064

Problem 170

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

83 83 83 102 104 228 194 113 128

N.S.

1 1.00 1.00 1.23 1.25 2.75 2.34 1.36 1.54

time (sec)

N/A 0.237 0.045 2.732 0.276 0.254 0.280 0.279 0.065

Problem 171

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

61 60 49 64 65 66 49 67 68

N.S.

1 0.98 0.80 1.05 1.07 1.08 0.80 1.10 1.11

time (sec)

N/A 0.199 0.016 2.723 0.189 0.285 0.206 0.277 4.980

Problem 172

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

63 63 59 64 68 179 172 72 90

N.S.

1 1.00 0.94 1.02 1.08 2.84 2.73 1.14 1.43

time (sec)

N/A 0.205 0.032 2.650 0.267 0.264 0.226 0.284 0.081

Problem 173

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

51 52 50 59 61 59 41 62 58

N.S.

1 1.02 0.98 1.16 1.20 1.16 0.80 1.22 1.14

time (sec)

N/A 0.204 0.015 2.622 0.194 0.257 0.737 0.283 5.083

Problem 174

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

55 55 55 65 63 164 165 63 80

N.S.

1 1.00 1.00 1.18 1.15 2.98 3.00 1.15 1.45

time (sec)

N/A 0.204 0.030 2.618 0.279 0.273 0.292 0.282 5.005

Problem 175

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

58 59 60 66 70 74 49 91 67

N.S.

1 1.02 1.03 1.14 1.21 1.28 0.84 1.57 1.16

time (sec)

N/A 0.217 0.021 2.643 0.193 0.274 0.825 0.288 5.070

Problem 176

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

66 66 64 68 71 192 172 71 90

N.S.

1 1.00 0.97 1.03 1.08 2.91 2.61 1.08 1.36

time (sec)

N/A 0.212 0.036 2.676 0.281 0.252 0.376 0.291 5.312

Problem 177

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

75 77 72 91 96 98 66 139 93

N.S.

1 1.03 0.96 1.21 1.28 1.31 0.88 1.85 1.24

time (sec)

N/A 0.240 0.028 2.744 0.197 0.256 0.807 0.290 5.667

Problem 178

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

87 87 86 100 107 236 207 112 129

N.S.

1 1.00 0.99 1.15 1.23 2.71 2.38 1.29 1.48

time (sec)

N/A 0.232 0.046 2.703 0.278 0.273 0.432 0.289 5.669

Problem 179

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

98 99 108 123 134 136 105 184 129

N.S.

1 1.01 1.10 1.26 1.37 1.39 1.07 1.88 1.32

time (sec)

N/A 0.258 0.040 2.750 0.200 0.261 0.880 0.279 0.138

Problem 180

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

145 116 138 141 149 400 286 156 200

N.S.

1 0.80 0.95 0.97 1.03 2.76 1.97 1.08 1.38

time (sec)

N/A 0.268 0.063 2.683 0.290 0.273 0.549 0.281 0.088

Problem 181

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 88 87 80 107 161 99 163 112

N.S.

1 0.98 0.97 0.89 1.19 1.79 1.10 1.81 1.24

time (sec)

N/A 0.252 0.044 2.763 0.195 0.246 0.526 0.281 5.072

Problem 182

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

118 104 105 101 109 342 246 114 146

N.S.

1 0.88 0.89 0.86 0.92 2.90 2.08 0.97 1.24

time (sec)

N/A 0.235 0.049 2.650 0.274 0.249 0.463 0.274 5.017

Problem 183

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

62 61 56 63 74 101 68 110 77

N.S.

1 0.98 0.90 1.02 1.19 1.63 1.10 1.77 1.24

time (sec)

N/A 0.213 0.032 2.708 0.198 0.270 0.412 0.288 0.089

Problem 184

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 82 89 92 96 302 236 95 124

N.S.

1 1.00 1.09 1.12 1.17 3.68 2.88 1.16 1.51

time (sec)

N/A 0.250 0.040 2.601 0.275 0.281 0.386 0.285 5.050

Problem 185

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

67 68 70 67 86 116 80 99 80

N.S.

1 1.01 1.04 1.00 1.28 1.73 1.19 1.48 1.19

time (sec)

N/A 0.229 0.029 2.584 0.187 0.254 0.738 0.277 5.078

Problem 186

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

106 106 91 97 100 305 238 102 128

N.S.

1 1.00 0.86 0.92 0.94 2.88 2.25 0.96 1.21

time (sec)

N/A 0.230 0.041 2.623 0.273 0.259 0.481 0.314 0.157

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 83 72 77 100 159 92 109 100

N.S.

1 1.02 0.89 0.95 1.23 1.96 1.14 1.35 1.23

time (sec)

N/A 0.245 0.060 2.665 0.203 0.252 0.758 0.287 5.118

Problem 188

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

126 131 107 107 118 356 248 111 147

N.S.

1 1.04 0.85 0.85 0.94 2.83 1.97 0.88 1.17

time (sec)

N/A 0.307 0.043 2.694 0.277 0.255 0.553 0.302 5.103

Problem 189

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

163 174 148 137 159 522 240 154 159

N.S.

1 1.07 0.91 0.84 0.98 3.20 1.47 0.94 0.98

time (sec)

N/A 0.388 0.058 2.631 0.285 0.259 1.086 0.285 5.108

Problem 190

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

99 96 114 105 120 178 122 107 123

N.S.

1 0.97 1.15 1.06 1.21 1.80 1.23 1.08 1.24

time (sec)

N/A 0.267 0.034 2.658 0.213 0.245 3.569 0.295 5.065

Problem 191

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 139 130 123 143 475 223 133 135

N.S.

1 1.09 1.02 0.97 1.13 3.74 1.76 1.05 1.06

time (sec)

N/A 0.305 0.067 2.701 0.304 0.248 0.826 0.289 5.151

Problem 192

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

67 69 54 73 87 108 87 76 83

N.S.

1 1.03 0.81 1.09 1.30 1.61 1.30 1.13 1.24

time (sec)

N/A 0.226 0.018 2.646 0.196 0.258 0.870 0.290 0.075

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 129 106 124 138 449 223 126 130

N.S.

1 1.11 0.91 1.07 1.19 3.87 1.92 1.09 1.12

time (sec)

N/A 0.255 0.059 2.610 0.272 0.367 0.559 0.276 5.099

Problem 194

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 87 75 88 109 163 107 110 106

N.S.

1 1.01 0.87 1.02 1.27 1.90 1.24 1.28 1.23

time (sec)

N/A 0.258 0.053 2.619 0.185 0.329 0.685 0.274 5.094

Problem 195

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

152 136 133 128 146 475 224 135 135

N.S.

1 0.89 0.88 0.84 0.96 3.12 1.47 0.89 0.89

time (sec)

N/A 0.261 0.056 2.777 0.272 0.307 0.643 0.285 5.079

Problem 196

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 109 99 114 142 256 139 177 132

N.S.

1 1.03 0.93 1.08 1.34 2.42 1.31 1.67 1.25

time (sec)

N/A 0.283 0.056 2.656 0.194 0.267 1.218 0.279 5.406

Problem 197

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

161 174 148 142 167 536 240 151 156

N.S.

1 1.08 0.92 0.88 1.04 3.33 1.49 0.94 0.97

time (sec)

N/A 0.375 0.052 2.648 0.280 0.285 0.715 0.275 5.580

Problem 198

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

75 74 71 68 74 75 70 77 76

N.S.

1 0.99 0.95 0.91 0.99 1.00 0.93 1.03 1.01

time (sec)

N/A 0.238 0.021 2.600 0.212 0.263 0.179 0.287 0.069

Problem 199

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

77 66 77 75 77 178 153 84 96

N.S.

1 0.86 1.00 0.97 1.00 2.31 1.99 1.09 1.25

time (sec)

N/A 0.207 0.035 2.611 0.274 0.279 0.209 0.289 5.194

Problem 200

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

54 53 47 49 50 51 46 52 52

N.S.

1 0.98 0.87 0.91 0.93 0.94 0.85 0.96 0.96

time (sec)

N/A 0.210 0.014 2.640 0.198 0.278 0.167 0.271 0.070

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