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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 F(-2) B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 67 63 73 0 504 0 61 294

N.S.

1 1.05 0.98 1.14 0.00 7.88 0.00 0.95 4.59

time (sec)

N/A 0.558 0.175 0.360 0.000 0.285 0.000 0.267 4.351

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 97 82 109 0 1444 0 89 476

N.S.

1 1.11 0.94 1.25 0.00 16.60 0.00 1.02 5.47

time (sec)

N/A 0.795 0.275 0.567 0.000 0.327 0.000 0.282 5.402

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 57 60 75 93 686 0 69 143

N.S.

1 1.19 1.25 1.56 1.94 14.29 0.00 1.44 2.98

time (sec)

N/A 0.428 0.388 0.669 0.277 0.271 0.000 0.283 2.109

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 26 38 26 74 437 0 61 96

N.S.

1 0.72 1.06 0.72 2.06 12.14 0.00 1.69 2.67

time (sec)

N/A 0.246 0.081 0.435 0.278 0.270 0.000 0.273 2.062

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 35 41 59 51 210 0 42 67

N.S.

1 1.13 1.32 1.90 1.65 6.77 0.00 1.35 2.16

time (sec)

N/A 0.309 0.224 0.332 0.275 0.253 0.000 0.276 2.038

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 15 10 34 33 85 0 35 33

N.S.

1 1.07 0.71 2.43 2.36 6.07 0.00 2.50 2.36

time (sec)

N/A 0.239 0.041 0.234 0.270 0.253 0.000 0.289 2.099

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 15 15 31 16 14 0 14 25

N.S.

1 1.07 1.07 2.21 1.14 1.00 0.00 1.00 1.79

time (sec)

N/A 0.232 0.236 0.170 0.281 0.272 0.000 0.271 2.113

Problem 108

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

9 9 12 17 18 16 19 17 14

N.S.

1 1.00 1.33 1.89 2.00 1.78 2.11 1.89 1.56

time (sec)

N/A 0.202 0.004 0.139 0.197 0.239 0.080 0.264 0.060

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 36 44 38 52 136 0 56 65

N.S.

1 0.90 1.10 0.95 1.30 3.40 0.00 1.40 1.62

time (sec)

N/A 0.252 0.053 0.161 0.190 0.259 0.000 0.277 2.014

Problem 110

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

38 42 33 36 47 46 0 40 94

N.S.

1 1.11 0.87 0.95 1.24 1.21 0.00 1.05 2.47

time (sec)

N/A 0.387 0.307 0.178 0.199 0.254 0.000 0.282 1.985

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 57 66 56 108 773 0 94 160

N.S.

1 0.84 0.97 0.82 1.59 11.37 0.00 1.38 2.35

time (sec)

N/A 0.272 0.166 0.207 0.198 0.267 0.000 0.279 2.096

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 64 69 63 105 151 0 64 264

N.S.

1 1.16 1.25 1.15 1.91 2.75 0.00 1.16 4.80

time (sec)

N/A 0.493 0.271 0.271 0.207 0.253 0.000 0.281 2.198

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 126 121 246 332 4077 0 267 316

N.S.

1 1.04 1.00 2.03 2.74 33.69 0.00 2.21 2.61

time (sec)

N/A 0.350 0.314 2.313 0.288 0.309 0.000 0.311 2.592

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

187 187 185 266 0 4914 0 250 1001

N.S.

1 1.00 0.99 1.42 0.00 26.28 0.00 1.34 5.35

time (sec)

N/A 0.593 0.771 1.637 0.000 0.487 0.000 0.275 8.623

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 77 76 158 164 1280 0 152 155

N.S.

1 1.07 1.06 2.19 2.28 17.78 0.00 2.11 2.15

time (sec)

N/A 0.296 0.197 0.941 0.284 0.287 0.000 0.297 2.401

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 114 113 152 0 1254 0 111 700

N.S.

1 1.21 1.20 1.62 0.00 13.34 0.00 1.18 7.45

time (sec)

N/A 0.730 0.551 0.732 0.000 0.350 0.000 0.281 7.625

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 43 38 75 67 200 0 73 260

N.S.

1 1.23 1.09 2.14 1.91 5.71 0.00 2.09 7.43

time (sec)

N/A 0.263 0.109 0.390 0.285 0.290 0.000 0.273 2.321

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 74 62 84 0 193 0 52 273

N.S.

1 1.19 1.00 1.35 0.00 3.11 0.00 0.84 4.40

time (sec)

N/A 0.638 0.132 0.299 0.000 0.295 0.000 0.301 4.468

Problem 119

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

19 22 11 21 26 27 41 19 23

N.S.

1 1.16 0.58 1.11 1.37 1.42 2.16 1.00 1.21

time (sec)

N/A 0.212 0.050 0.185 0.206 0.273 0.162 0.280 0.099

Problem 120

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

66 81 63 78 67 81 0 67 271

N.S.

1 1.23 0.95 1.18 1.02 1.23 0.00 1.02 4.11

time (sec)

N/A 0.311 0.182 0.331 0.200 0.280 0.000 0.272 0.407

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 104 81 104 0 646 0 82 383

N.S.

1 0.91 0.71 0.91 0.00 5.67 0.00 0.72 3.36

time (sec)

N/A 0.703 0.496 0.457 0.000 0.271 0.000 0.289 2.326

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 139 107 113 164 1222 0 193 339

N.S.

1 1.23 0.95 1.00 1.45 10.81 0.00 1.71 3.00

time (sec)

N/A 0.400 0.506 0.694 0.210 0.301 0.000 0.289 2.879

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

207 181 166 153 0 3530 0 190 713

N.S.

1 0.87 0.80 0.74 0.00 17.05 0.00 0.92 3.44

time (sec)

N/A 1.313 0.893 1.082 0.000 0.315 0.000 0.286 2.509

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

178 211 164 162 366 5181 0 380 623

N.S.

1 1.19 0.92 0.91 2.06 29.11 0.00 2.13 3.50

time (sec)

N/A 0.514 1.089 1.702 0.222 0.372 0.000 0.292 3.472

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

169 132 153 0 0 4363 0 0 0

N.S.

1 0.78 0.91 0.00 0.00 25.82 0.00 0.00 0.00

time (sec)

N/A 0.389 2.652 0.000 0.000 0.683 0.000 0.000 0.000

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

100 81 87 0 0 1589 0 0 0

N.S.

1 0.81 0.87 0.00 0.00 15.89 0.00 0.00 0.00

time (sec)

N/A 0.316 0.961 0.000 0.000 0.691 0.000 0.000 0.000

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 50 50 43 0 605 0 0 47

N.S.

1 0.98 0.98 0.84 0.00 11.86 0.00 0.00 0.92

time (sec)

N/A 0.249 0.233 0.175 0.000 0.653 0.000 0.000 2.357

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

106 118 100 0 0 8620 0 0 0

N.S.

1 1.11 0.94 0.00 0.00 81.32 0.00 0.00 0.00

time (sec)

N/A 0.386 0.348 0.000 0.000 0.641 0.000 0.000 0.000

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

217 268 223 0 0 16532 0 0 0

N.S.

1 1.24 1.03 0.00 0.00 76.18 0.00 0.00 0.00

time (sec)

N/A 0.578 4.086 0.000 0.000 0.995 0.000 0.000 0.000

Problem 130

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

344 345 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 1.341 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 131

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

125 125 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 0.242 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

246 246 539 0 0 0 0 0 0

N.S.

1 1.00 2.19 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.709 18.564 0.000 0.000 0.000 0.000 0.000 0.000

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

148 123 112 0 0 2813 0 0 0

N.S.

1 0.83 0.76 0.00 0.00 19.01 0.00 0.00 0.00

time (sec)

N/A 0.348 1.605 0.000 0.000 0.688 0.000 0.000 0.000

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

79 71 66 0 0 925 0 0 0

N.S.

1 0.90 0.84 0.00 0.00 11.71 0.00 0.00 0.00

time (sec)

N/A 0.300 0.667 0.000 0.000 0.675 0.000 0.000 0.000

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 31 26 0 558 0 0 27

N.S.

1 1.00 1.00 0.84 0.00 18.00 0.00 0.00 0.87

time (sec)

N/A 0.242 0.181 0.208 0.000 0.676 0.000 0.000 2.309

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

106 118 100 0 0 8908 0 0 0

N.S.

1 1.11 0.94 0.00 0.00 84.04 0.00 0.00 0.00

time (sec)

N/A 0.368 0.441 0.000 0.000 0.858 0.000 0.000 0.000

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

262 272 280 0 0 20300 0 0 0

N.S.

1 1.04 1.07 0.00 0.00 77.48 0.00 0.00 0.00

time (sec)

N/A 0.480 3.132 0.000 0.000 4.301 0.000 0.000 0.000

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

610 610 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 1.184 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 139

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

310 310 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 1.073 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 140

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

106 106 168 0 0 0 0 0 0

N.S.

1 1.00 1.58 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.229 0.574 0.000 0.000 0.000 0.000 0.000 0.000

Problem 141

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

362 362 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 1.013 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

148 119 117 0 0 3745 0 0 0

N.S.

1 0.80 0.79 0.00 0.00 25.30 0.00 0.00 0.00

time (sec)

N/A 0.381 0.887 0.000 0.000 0.688 0.000 0.000 0.000

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

88 79 66 0 0 1107 0 0 0

N.S.

1 0.90 0.75 0.00 0.00 12.58 0.00 0.00 0.00

time (sec)

N/A 0.346 0.514 0.000 0.000 0.649 0.000 0.000 0.000

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 53 43 46 0 917 0 0 50

N.S.

1 0.98 0.80 0.85 0.00 16.98 0.00 0.00 0.93

time (sec)

N/A 0.254 0.251 0.169 0.000 0.644 0.000 0.000 2.398

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

142 143 212 0 0 14412 0 0 0

N.S.

1 1.01 1.49 0.00 0.00 101.49 0.00 0.00 0.00

time (sec)

N/A 0.424 1.053 0.000 0.000 3.800 0.000 0.000 0.000

Problem 146

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

316 310 315 0 0 53212 0 0 0

N.S.

1 0.98 1.00 0.00 0.00 168.39 0.00 0.00 0.00

time (sec)

N/A 0.603 1.690 0.000 0.000 6.619 0.000 0.000 0.000

Problem 147

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

907 907 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 1.939 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 148

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

344 381 0 0 0 0 0 0 0

N.S.

1 1.11 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.487 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 149

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

347 376 0 0 0 0 0 0 0

N.S.

1 1.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.341 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

665 665 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 1.763 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

191 105 84 86 386 589 0 64 405

N.S.

1 0.55 0.44 0.45 2.02 3.08 0.00 0.34 2.12

time (sec)

N/A 0.441 0.105 127.386 0.207 0.290 0.000 0.293 0.149

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

141 87 72 65 209 315 0 51 91

N.S.

1 0.62 0.51 0.46 1.48 2.23 0.00 0.36 0.65

time (sec)

N/A 0.357 0.086 140.894 0.205 0.272 0.000 0.281 2.033

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

56 56 44 38 84 120 0 38 78

N.S.

1 1.00 0.79 0.68 1.50 2.14 0.00 0.68 1.39

time (sec)

N/A 0.305 0.073 0.358 0.205 0.254 0.000 0.271 0.121

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

44 44 42 29 21 42 0 20 0

N.S.

1 1.00 0.95 0.66 0.48 0.95 0.00 0.45 0.00

time (sec)

N/A 0.281 0.049 0.378 0.277 0.257 0.000 0.274 0.000

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

74 59 48 60 29 66 0 33 0

N.S.

1 0.80 0.65 0.81 0.39 0.89 0.00 0.45 0.00

time (sec)

N/A 0.328 0.064 0.428 0.209 0.270 0.000 0.268 0.000

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

162 74 81 75 74 126 0 82 0

N.S.

1 0.46 0.50 0.46 0.46 0.78 0.00 0.51 0.00

time (sec)

N/A 0.358 0.121 0.636 0.202 0.255 0.000 0.282 0.000

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

250 102 109 88 112 218 530 110 0

N.S.

1 0.41 0.44 0.35 0.45 0.87 2.12 0.44 0.00

time (sec)

N/A 0.419 0.164 0.672 0.195 0.262 86.597 0.291 0.000

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

108 149 77 130 0 81 0 0 0

N.S.

1 1.38 0.71 1.20 0.00 0.75 0.00 0.00 0.00

time (sec)

N/A 0.324 0.217 0.917 0.000 0.079 0.000 0.000 0.000

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 27 44 39 30 48 0 0 42

N.S.

1 0.96 1.57 1.39 1.07 1.71 0.00 0.00 1.50

time (sec)

N/A 0.252 0.060 0.161 0.312 0.255 0.000 0.000 2.125

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

203 241 65 134 0 120 0 0 0

N.S.

1 1.19 0.32 0.66 0.00 0.59 0.00 0.00 0.00

time (sec)

N/A 0.389 0.143 0.630 0.000 0.081 0.000 0.000 0.000

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

67 72 77 97 0 90 0 0 0

N.S.

1 1.07 1.15 1.45 0.00 1.34 0.00 0.00 0.00

time (sec)

N/A 0.270 0.166 0.190 0.000 0.266 0.000 0.000 0.000

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

87 121 58 114 0 71 0 0 0

N.S.

1 1.39 0.67 1.31 0.00 0.82 0.00 0.00 0.00

time (sec)

N/A 0.286 0.187 0.569 0.000 0.079 0.000 0.000 0.000

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

59 64 75 0 0 100 0 0 0

N.S.

1 1.08 1.27 0.00 0.00 1.69 0.00 0.00 0.00

time (sec)

N/A 0.266 0.138 0.000 0.000 0.265 0.000 0.000 0.000

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 36 167 0 27 0 0 0

N.S.

1 1.00 1.00 4.64 0.00 0.75 0.00 0.00 0.00

time (sec)

N/A 0.271 0.106 0.673 0.000 0.081 0.000 0.000 0.000

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

40 40 55 0 0 57 0 0 0

N.S.

1 1.00 1.38 0.00 0.00 1.42 0.00 0.00 0.00

time (sec)

N/A 0.264 0.160 0.000 0.000 0.257 0.000 0.000 0.000

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

137 190 59 134 0 94 0 0 0

N.S.

1 1.39 0.43 0.98 0.00 0.69 0.00 0.00 0.00

time (sec)

N/A 0.352 0.150 0.659 0.000 0.081 0.000 0.000 0.000

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 28 33 38 42 37 0 0 58

N.S.

1 1.22 1.43 1.65 1.83 1.61 0.00 0.00 2.52

time (sec)

N/A 0.248 0.047 0.149 0.277 0.263 0.000 0.000 2.062

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

80 119 65 117 0 67 0 0 0

N.S.

1 1.49 0.81 1.46 0.00 0.84 0.00 0.00 0.00

time (sec)

N/A 0.297 0.129 0.597 0.000 0.083 0.000 0.000 0.000

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

122 126 98 121 0 109 0 0 0

N.S.

1 1.03 0.80 0.99 0.00 0.89 0.00 0.00 0.00

time (sec)

N/A 0.308 0.234 0.546 0.000 0.272 0.000 0.000 0.000

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

141 177 77 138 0 89 0 0 0

N.S.

1 1.26 0.55 0.98 0.00 0.63 0.00 0.00 0.00

time (sec)

N/A 0.347 0.214 0.609 0.000 0.083 0.000 0.000 0.000

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 27 44 47 30 56 0 0 42

N.S.

1 0.96 1.57 1.68 1.07 2.00 0.00 0.00 1.50

time (sec)

N/A 0.255 0.058 0.160 0.316 0.252 0.000 0.000 2.161

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

251 269 65 147 0 129 0 0 0

N.S.

1 1.07 0.26 0.59 0.00 0.51 0.00 0.00 0.00

time (sec)

N/A 0.424 0.146 0.668 0.000 0.084 0.000 0.000 0.000

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

92 100 90 113 0 101 0 0 0

N.S.

1 1.09 0.98 1.23 0.00 1.10 0.00 0.00 0.00

time (sec)

N/A 0.285 0.190 0.224 0.000 0.285 0.000 0.000 0.000

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

111 149 61 129 0 79 0 0 0

N.S.

1 1.34 0.55 1.16 0.00 0.71 0.00 0.00 0.00

time (sec)

N/A 0.326 0.135 0.590 0.000 0.083 0.000 0.000 0.000

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

88 87 88 0 0 109 0 0 0

N.S.

1 0.99 1.00 0.00 0.00 1.24 0.00 0.00 0.00

time (sec)

N/A 0.298 0.191 0.000 0.000 0.251 0.000 0.000 0.000

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

214 244 65 159 0 0 0 0 0

N.S.

1 1.14 0.30 0.74 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.390 0.196 0.682 0.000 0.000 0.000 0.000 0.000

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

92 92 64 131 0 106 0 0 0

N.S.

1 1.00 0.70 1.42 0.00 1.15 0.00 0.00 0.00

time (sec)

N/A 0.259 0.128 0.225 0.000 0.270 0.000 0.000 0.000

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 45 127 0 82 0 0 0

N.S.

1 1.00 0.80 2.27 0.00 1.46 0.00 0.00 0.00

time (sec)

N/A 0.346 0.160 1.009 0.000 0.086 0.000 0.000 0.000

Problem 179

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

25 30 32 0 39 28 0 0 28

N.S.

1 1.20 1.28 0.00 1.56 1.12 0.00 0.00 1.12

time (sec)

N/A 0.243 0.044 0.000 0.277 0.276 0.000 0.000 2.126

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

92 121 65 0 0 56 0 0 0

N.S.

1 1.32 0.71 0.00 0.00 0.61 0.00 0.00 0.00

time (sec)

N/A 0.301 0.143 0.000 0.000 0.079 0.000 0.000 0.000

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

66 64 51 0 0 93 0 0 0

N.S.

1 0.97 0.77 0.00 0.00 1.41 0.00 0.00 0.00

time (sec)

N/A 0.290 0.144 0.000 0.000 0.253 0.000 0.000 0.000

Problem 182

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

63 63 64 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 0.315 0.841 0.000 0.000 0.000 0.000 0.000 0.000

Problem 183

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

69 69 126 0 0 0 0 0 0

N.S.

1 1.00 1.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.317 5.608 0.000 0.000 0.000 0.000 0.000 0.000

Problem 184

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

70 70 101 0 0 0 0 0 0

N.S.

1 1.00 1.44 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.319 1.595 0.000 0.000 0.000 0.000 0.000 0.000

Problem 185

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

69 69 750 0 0 0 0 0 0

N.S.

1 1.00 10.87 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.324 14.118 0.000 0.000 0.000 0.000 0.000 0.000

Problem 186

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 139 29 50 96 189 0 215 66

N.S.

1 3.48 0.72 1.25 2.40 4.72 0.00 5.38 1.65

time (sec)

N/A 0.337 0.345 33.731 0.362 0.250 0.000 0.757 2.168

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B F B B F A B

verified

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

size

25 26 62 0 74 48 0 38 49

N.S.

1 1.04 2.48 0.00 2.96 1.92 0.00 1.52 1.96

time (sec)

N/A 0.247 0.223 0.000 0.188 0.260 0.000 0.283 2.285

Problem 188

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B F B B F A B

verified

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

size

25 25 64 0 49 49 0 37 36

N.S.

1 1.00 2.56 0.00 1.96 1.96 0.00 1.48 1.44

time (sec)

N/A 0.254 0.125 0.000 0.186 0.260 0.000 0.298 2.141

Problem 189

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

89 96 114 0 0 474 0 0 0

N.S.

1 1.08 1.28 0.00 0.00 5.33 0.00 0.00 0.00

time (sec)

N/A 0.351 2.527 0.000 0.000 0.266 0.000 0.000 0.000

Problem 190

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

65 106 108 0 0 538 0 0 0

N.S.

1 1.63 1.66 0.00 0.00 8.28 0.00 0.00 0.00

time (sec)

N/A 0.361 1.420 0.000 0.000 0.267 0.000 0.000 0.000

Problem 191

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 20 19 34 44 27 41

N.S.

1 1.00 1.00 1.05 1.00 1.79 2.32 1.42 2.16

time (sec)

N/A 0.211 0.069 1.155 0.183 0.287 0.799 0.268 2.039

Problem 192

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 19 28 70 0 28 24

N.S.

1 1.00 1.00 1.06 1.56 3.89 0.00 1.56 1.33

time (sec)

N/A 0.228 0.103 2.072 0.196 0.258 0.000 0.279 2.010

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 53 55 45 0 452 0 115 139

N.S.

1 0.96 1.00 0.82 0.00 8.22 0.00 2.09 2.53

time (sec)

N/A 0.300 0.071 19.636 0.000 0.266 0.000 0.271 2.060

Problem 194

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 45 42 36 91 272 0 47 55

N.S.

1 1.07 1.00 0.86 2.17 6.48 0.00 1.12 1.31

time (sec)

N/A 0.245 0.069 18.950 0.207 0.264 0.000 0.293 2.013

Problem 195

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 89 89 64 0 1326 0 152 314

N.S.

1 1.00 1.00 0.72 0.00 14.90 0.00 1.71 3.53

time (sec)

N/A 0.391 0.087 233.028 0.000 0.276 0.000 0.277 2.028

Problem 196

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 95 74 295 0 315 0 0 0

N.S.

1 0.98 0.76 3.04 0.00 3.25 0.00 0.00 0.00

time (sec)

N/A 0.394 0.201 119.731 0.000 0.093 0.000 0.000 0.000

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 91 72 141 0 159 0 0 0

N.S.

1 0.98 0.77 1.52 0.00 1.71 0.00 0.00 0.00

time (sec)

N/A 0.377 0.106 1.547 0.000 0.080 0.000 0.000 0.000

Problem 198

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 58 58 183 0 39 0 0 0

N.S.

1 1.00 1.00 3.16 0.00 0.67 0.00 0.00 0.00

time (sec)

N/A 0.291 0.072 1.223 0.000 0.076 0.000 0.000 0.000

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 58 58 183 0 248 0 0 0

N.S.

1 1.00 1.00 3.16 0.00 4.28 0.00 0.00 0.00

time (sec)

N/A 0.294 0.084 1.586 0.000 0.087 0.000 0.000 0.000

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 95 76 237 0 370 0 0 0

N.S.

1 0.98 0.78 2.44 0.00 3.81 0.00 0.00 0.00

time (sec)

N/A 0.380 0.126 2.119 0.000 0.089 0.000 0.000 0.000

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