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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 A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 81 69 70 67 63 442 52

N.S.

1 1.00 1.37 1.17 1.19 1.14 1.07 7.49 0.88

time (sec)

N/A 0.022 0.010 0.060 0.291 0.335 0.386 0.458 0.839

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

57 57 62 64 55 69 68 403 53

N.S.

1 1.00 1.09 1.12 0.96 1.21 1.19 7.07 0.93

time (sec)

N/A 0.031 0.009 0.014 0.268 0.337 0.332 0.431 0.821

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 70 60 61 58 53 296 43

N.S.

1 1.00 1.46 1.25 1.27 1.21 1.10 6.17 0.90

time (sec)

N/A 0.022 0.009 0.013 0.266 0.341 0.236 0.425 0.773

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 51 55 44 58 58 258 44

N.S.

1 1.00 1.11 1.20 0.96 1.26 1.26 5.61 0.96

time (sec)

N/A 0.024 0.009 0.013 0.255 0.356 0.202 0.420 0.744

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 59 51 50 48 42 148 35

N.S.

1 1.00 1.59 1.38 1.35 1.30 1.14 4.00 0.95

time (sec)

N/A 0.012 0.008 0.013 0.263 0.340 0.176 0.413 0.727

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 30 29 30 42 27 156 27

N.S.

1 1.00 1.00 0.97 1.00 1.40 0.90 5.20 0.90

time (sec)

N/A 0.009 0.004 0.010 0.255 0.337 0.121 0.414 0.684

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

26 26 24 47 0 0 0 0 -1

N.S.

1 1.00 0.92 1.81 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.011 0.009 0.017 0.000 0.000 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 39 50 39 47 41 94 33

N.S.

1 1.00 1.08 1.39 1.08 1.31 1.14 2.61 0.92

time (sec)

N/A 0.018 0.008 0.019 0.262 0.401 0.312 0.408 0.700

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 59 55 45 43 36 135 46

N.S.

1 1.00 1.59 1.49 1.22 1.16 0.97 3.65 1.24

time (sec)

N/A 0.016 0.008 0.020 0.264 0.346 0.263 0.414 0.728

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 59 62 49 59 70 251 46

N.S.

1 1.00 1.09 1.15 0.91 1.09 1.30 4.65 0.85

time (sec)

N/A 0.026 0.008 0.020 0.256 0.366 0.414 0.435 0.730

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 70 64 60 52 46 292 59

N.S.

1 1.00 1.46 1.33 1.25 1.08 0.96 6.08 1.23

time (sec)

N/A 0.020 0.008 0.020 0.277 0.351 0.313 0.417 1.053

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 70 71 61 70 80 397 71

N.S.

1 1.00 1.08 1.09 0.94 1.08 1.23 6.11 1.09

time (sec)

N/A 0.028 0.009 0.022 0.263 0.380 0.574 0.410 0.911

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 164 290 215 193 211 889 171

N.S.

1 1.00 1.13 2.00 1.48 1.33 1.46 6.13 1.18

time (sec)

N/A 0.219 0.045 0.066 0.264 0.353 0.555 0.435 1.042

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 161 281 0 0 0 0 -1

N.S.

1 1.00 0.99 1.73 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.213 0.332 0.106 0.000 0.000 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 113 132 254 189 160 168 603 134

N.S.

1 1.00 1.17 2.25 1.67 1.42 1.49 5.34 1.19

time (sec)

N/A 0.166 0.035 0.031 0.261 0.347 0.387 0.435 0.916

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

130 130 122 245 0 0 0 0 -1

N.S.

1 1.00 0.94 1.88 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.149 0.183 0.056 0.000 0.000 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 90 215 158 122 114 301 89

N.S.

1 1.00 1.20 2.87 2.11 1.63 1.52 4.01 1.19

time (sec)

N/A 0.083 0.033 0.028 0.277 0.366 0.238 0.402 0.785

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 82 118 0 0 0 0 -1

N.S.

1 1.00 1.11 1.59 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.071 0.096 0.089 0.000 0.000 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 120 701 0 0 0 0 -1

N.S.

1 1.00 1.03 5.99 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.187 0.050 0.783 0.000 0.000 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 94 244 0 0 0 0 -1

N.S.

1 1.00 1.32 3.44 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.101 0.102 0.102 0.000 0.000 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 101 234 151 135 126 278 246

N.S.

1 1.00 1.26 2.92 1.89 1.69 1.58 3.48 3.08

time (sec)

N/A 0.096 0.040 0.043 0.268 0.356 0.400 0.434 1.490

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

130 130 145 305 0 0 0 0 -1

N.S.

1 1.00 1.12 2.35 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.166 0.252 0.089 0.000 0.000 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 164 271 224 173 184 612 303

N.S.

1 1.00 1.40 2.32 1.91 1.48 1.57 5.23 2.59

time (sec)

N/A 0.164 0.043 0.046 0.257 0.361 0.570 0.425 1.903

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

247 247 305 1242 0 0 0 0 -1

N.S.

1 1.00 1.23 5.03 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.668 0.509 2.719 0.000 0.000 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

262 262 383 1188 0 0 0 0 -1

N.S.

1 1.00 1.46 4.53 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.554 0.528 2.388 0.000 0.000 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

185 185 245 1157 0 0 0 0 -1

N.S.

1 1.00 1.32 6.25 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.420 0.347 1.262 0.000 0.000 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

197 197 250 1093 0 0 0 0 -1

N.S.

1 1.00 1.27 5.55 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.363 0.373 1.214 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 161 5831 0 0 0 0 -1

N.S.

1 1.00 1.31 47.41 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.185 0.232 0.489 0.000 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 108 161 245 0 0 0 0 -1

N.S.

1 1.00 1.49 2.27 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.162 0.306 0.242 0.000 0.000 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

184 184 178 1470 0 0 0 0 -1

N.S.

1 1.00 0.97 7.99 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.315 0.150 0.346 0.000 0.000 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 196 1555 0 0 0 0 -1

N.S.

1 1.00 1.92 15.25 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.188 0.245 0.363 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 192 4871 0 0 0 0 -1

N.S.

1 1.00 1.56 39.60 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.208 0.185 0.575 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

200 200 323 1716 0 0 0 0 -1

N.S.

1 1.00 1.62 8.58 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.345 0.638 2.553 0.000 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

187 187 295 1204 0 0 0 0 -1

N.S.

1 1.00 1.58 6.44 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.440 0.470 1.862 0.000 0.000 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

124 124 128 107 134 296 0 0 -1

N.S.

1 1.00 1.03 0.86 1.08 2.39 0.00 0.00 -0.01

time (sec)

N/A 0.059 0.048 0.070 0.473 0.364 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 115 93 118 255 0 0 -1

N.S.

1 1.00 1.08 0.88 1.11 2.41 0.00 0.00 -0.01

time (sec)

N/A 0.048 0.038 0.042 0.468 0.386 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 114 93 119 223 636 0 -1

N.S.

1 1.00 1.08 0.88 1.12 2.10 6.00 0.00 -0.01

time (sec)

N/A 0.044 0.032 0.041 0.466 0.432 5.390 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 98 68 103 211 0 88 -1

N.S.

1 1.00 1.15 0.80 1.21 2.48 0.00 1.04 -0.01

time (sec)

N/A 0.037 0.024 0.040 0.486 0.361 0.000 0.464 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 99 69 94 221 0 93 -1

N.S.

1 1.00 1.16 0.81 1.11 2.60 0.00 1.09 -0.01

time (sec)

N/A 0.037 0.029 0.041 0.464 0.360 0.000 0.445 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

107 107 107 93 101 243 0 117 -1

N.S.

1 1.00 1.00 0.87 0.94 2.27 0.00 1.09 -0.01

time (sec)

N/A 0.046 0.040 0.051 0.463 0.366 0.000 0.444 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

107 107 108 93 112 253 0 117 -1

N.S.

1 1.00 1.01 0.87 1.05 2.36 0.00 1.09 -0.01

time (sec)

N/A 0.046 0.031 0.050 0.474 0.370 0.000 0.442 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 125 122 107 130 272 0 135 -1

N.S.

1 1.00 0.98 0.86 1.04 2.18 0.00 1.08 -0.01

time (sec)

N/A 0.057 0.044 0.053 0.466 0.358 0.000 0.512 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.017 2.686 0.257 0.000 0.000 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.017 1.694 0.246 0.000 0.000 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 59 0 0 0 0 0 -1

N.S.

1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.027 0.052 0.247 0.000 0.000 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.018 0.187 0.237 0.000 0.000 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.018 0.374 0.237 0.000 0.000 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

13 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08

time (sec)

N/A 0.004 0.327 0.062 0.000 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.016 0.243 0.132 0.000 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 78 66 69 64 58 78 69

N.S.

1 1.00 1.44 1.22 1.28 1.19 1.07 1.44 1.28

time (sec)

N/A 0.028 0.016 0.031 0.271 0.335 7.601 0.425 1.064

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 53 45 46 62 85 57 61

N.S.

1 1.00 1.10 0.94 0.96 1.29 1.77 1.19 1.27

time (sec)

N/A 0.026 0.014 0.040 0.253 0.354 5.116 0.412 0.791

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 67 57 58 54 48 181 60

N.S.

1 1.00 1.56 1.33 1.35 1.26 1.12 4.21 1.40

time (sec)

N/A 0.021 0.014 0.042 0.258 0.362 3.614 0.406 0.939

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 42 39 37 50 71 188 52

N.S.

1 1.00 1.14 1.05 1.00 1.35 1.92 5.08 1.41

time (sec)

N/A 0.011 0.009 0.021 0.255 0.327 3.203 0.421 0.765

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 28 124 0 0 0 0 -1

N.S.

1 1.00 0.93 4.13 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.023 0.012 0.054 0.000 0.000 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 45 49 41 55 80 51 55

N.S.

1 1.00 1.12 1.22 1.02 1.38 2.00 1.28 1.38

time (sec)

N/A 0.020 0.011 0.031 0.261 0.385 5.460 0.434 0.855

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 65 55 51 49 41 67 52

N.S.

1 1.00 1.59 1.34 1.24 1.20 1.00 1.63 1.27

time (sec)

N/A 0.020 0.011 0.036 0.265 0.370 3.443 0.425 0.999

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 61 63 51 65 97 65 67

N.S.

1 1.00 1.09 1.12 0.91 1.16 1.73 1.16 1.20

time (sec)

N/A 0.026 0.011 0.036 0.257 0.342 8.953 0.433 0.884

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 93 53 69 197 185 73 72

N.S.

1 1.00 1.43 0.82 1.06 3.03 2.85 1.12 1.11

time (sec)

N/A 0.026 0.018 0.087 0.458 0.363 5.798 0.479 0.984

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 91 51 66 186 670 75 70

N.S.

1 1.00 1.44 0.81 1.05 2.95 10.63 1.19 1.11

time (sec)

N/A 0.024 0.015 0.055 0.482 0.362 3.381 0.461 0.851

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

44 44 57 37 55 160 702 83 55

N.S.

1 1.00 1.30 0.84 1.25 3.64 15.95 1.89 1.25

time (sec)

N/A 0.017 0.015 0.046 0.486 0.424 2.545 0.397 0.790

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 75 42 61 157 1374 79 62

N.S.

1 1.00 1.63 0.91 1.33 3.41 29.87 1.72 1.35

time (sec)

N/A 0.019 0.014 0.058 0.476 0.378 4.696 0.443 0.921

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 91 51 65 181 1904 93 71

N.S.

1 1.00 1.44 0.81 1.03 2.87 30.22 1.48 1.13

time (sec)

N/A 0.023 0.021 0.065 0.461 0.348 6.340 0.418 0.995

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 91 51 66 187 1948 91 71

N.S.

1 1.00 1.44 0.81 1.05 2.97 30.92 1.44 1.13

time (sec)

N/A 0.023 0.022 0.066 0.461 0.358 8.690 0.460 1.026

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 125 146 298 217 176 206 175 335

N.S.

1 1.00 1.17 2.38 1.74 1.41 1.65 1.40 2.68

time (sec)

N/A 0.187 0.048 0.075 0.264 0.368 9.249 0.519 1.733

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

146 146 132 380 0 0 0 0 -1

N.S.

1 1.00 0.90 2.60 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.174 0.199 0.277 0.000 0.000 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 106 287 186 138 163 361 275

N.S.

1 1.00 1.16 3.15 2.04 1.52 1.79 3.97 3.02

time (sec)

N/A 0.111 0.036 0.174 0.264 0.340 5.294 0.448 1.262

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 99 137 0 0 0 0 -1

N.S.

1 1.00 1.05 1.46 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.097 0.109 0.168 0.000 0.000 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

137 137 183 0 0 0 0 0 -1

N.S.

1 1.00 1.34 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.229 0.050 0.021 0.000 0.000 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 119 0 0 0 0 0 -1

N.S.

1 1.00 1.37 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.132 0.104 0.024 0.000 0.000 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 111 257 175 151 175 0 278

N.S.

1 1.00 1.26 2.92 1.99 1.72 1.99 0.00 3.16

time (sec)

N/A 0.134 0.052 0.152 0.265 0.355 7.112 0.000 1.498

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F F F

verified

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

size

1173 1173 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.637 8.450 0.020 0.000 0.000 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F F F

verified

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

size

1129 1129 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.464 8.319 0.023 0.000 0.000 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

958 958 566 0 0 0 0 0 -1

N.S.

1 1.00 0.59 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.993 1.793 0.021 0.000 0.000 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

942 942 566 0 0 0 0 0 -1

N.S.

1 1.00 0.60 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.946 2.322 0.022 0.000 0.000 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F F F

verified

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

size

1102 1102 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.268 2.296 0.022 0.000 0.000 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F F F

verified

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

size

1176 1176 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.388 2.315 0.023 0.000 0.000 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 185 798 0 0 0 0 -1

N.S.

1 1.00 1.31 5.66 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.218 0.337 0.316 0.000 0.000 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 211 280 0 0 0 0 -1

N.S.

1 1.00 1.57 2.09 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.195 0.173 0.320 0.000 0.000 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

207 207 211 0 0 0 0 0 -1

N.S.

1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.373 0.131 0.023 0.000 0.000 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 125 222 0 0 0 0 0 -1

N.S.

1 1.00 1.78 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.232 0.286 0.023 0.000 0.000 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 218 0 0 0 0 0 -1

N.S.

1 1.00 1.57 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.248 0.201 0.023 0.000 0.000 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

317 317 241 303 316 455 0 0 -1

N.S.

1 1.00 0.76 0.96 1.00 1.44 0.00 0.00 -0.00

time (sec)

N/A 0.212 0.084 0.078 0.474 0.402 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

317 317 240 303 310 399 0 0 -1

N.S.

1 1.00 0.76 0.96 0.98 1.26 0.00 0.00 -0.00

time (sec)

N/A 0.187 0.062 0.043 0.468 0.377 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

301 301 227 289 301 400 0 0 -1

N.S.

1 1.00 0.75 0.96 1.00 1.33 0.00 0.00 -0.00

time (sec)

N/A 0.164 0.049 0.040 0.467 0.432 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

285 285 227 257 296 364 0 493 -1

N.S.

1 1.00 0.80 0.90 1.04 1.28 0.00 1.73 -0.00

time (sec)

N/A 0.155 0.040 0.043 0.472 0.392 0.000 0.424 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

285 285 268 259 296 397 0 505 -1

N.S.

1 1.00 0.94 0.91 1.04 1.39 0.00 1.77 -0.00

time (sec)

N/A 0.176 0.066 0.046 0.474 0.392 0.000 0.584 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

301 301 268 279 277 428 0 516 -1

N.S.

1 1.00 0.89 0.93 0.92 1.42 0.00 1.71 -0.00

time (sec)

N/A 0.176 0.069 0.044 0.467 0.399 0.000 0.755 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

317 317 275 291 298 473 0 532 -1

N.S.

1 1.00 0.87 0.92 0.94 1.49 0.00 1.68 -0.00

time (sec)

N/A 0.189 0.055 0.052 0.471 0.378 0.000 1.871 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

317 317 281 301 297 450 0 519 -1

N.S.

1 1.00 0.89 0.95 0.94 1.42 0.00 1.64 -0.00

time (sec)

N/A 0.179 0.061 0.056 0.479 0.453 0.000 5.280 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A NO N/A TBD TBD TBD TBD TBD TBD

size

6327 6327 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 10.663 48.318 0.050 0.000 0.000 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F F F

verified

N/A NO N/A TBD TBD TBD TBD TBD TBD

size

6177 6177 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 9.226 45.605 0.050 0.000 0.000 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F F F

verified

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

size

6334 6334 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 9.671 48.964 0.052 0.000 0.000 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F F F

verified

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

size

6520 6520 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 8.943 39.646 0.052 0.000 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

21 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.017 1.365 0.026 0.000 0.000 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

21 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.016 0.850 0.025 0.000 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 64 0 0 0 0 0 -1

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.026 0.047 0.023 0.000 0.000 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

21 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.018 0.269 0.023 0.000 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.017 0.267 0.023 0.000 0.000 0.000 0.000 0.000

Problem 99

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

54 54 78 66 69 64 0 78 69

N.S.

1 1.00 1.44 1.22 1.28 1.19 0.00 1.44 1.28

time (sec)

N/A 0.028 0.016 0.029 0.251 0.373 0.000 0.428 1.108

Problem 100

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

48 48 53 45 46 62 0 57 61

N.S.

1 1.00 1.10 0.94 0.96 1.29 0.00 1.19 1.27

time (sec)

N/A 0.026 0.015 0.049 0.265 0.339 0.000 0.435 0.824

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