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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 B F B A F(-1) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 99 253 0 380 121 0 -1

N.S.

1 1.00 0.78 1.99 0.00 2.99 0.95 0.00 -0.01

time (sec)

N/A 0.036 0.061 0.037 0.000 0.349 1.641 0.000 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 88 205 0 263 95 0 -1

N.S.

1 1.00 0.87 2.03 0.00 2.60 0.94 0.00 -0.01

time (sec)

N/A 0.026 0.038 0.009 0.000 0.343 0.607 0.000 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 76 157 0 168 66 0 -1

N.S.

1 1.00 1.01 2.09 0.00 2.24 0.88 0.00 -0.01

time (sec)

N/A 0.017 0.024 0.007 0.000 0.352 0.329 0.000 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

238 238 0 209 0 0 0 0 -1

N.S.

1 1.00 0.00 0.88 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.104 0.030 0.113 0.000 0.000 0.000 0.000 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

53 53 50 111 50 129 0 0 -1

N.S.

1 1.00 0.94 2.09 0.94 2.43 0.00 0.00 -0.02

time (sec)

N/A 0.013 0.023 0.007 0.287 0.355 0.000 0.000 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

79 79 63 62 61 176 0 0 -1

N.S.

1 1.00 0.80 0.78 0.77 2.23 0.00 0.00 -0.01

time (sec)

N/A 0.018 0.030 0.007 0.277 0.353 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

105 105 74 110 102 246 0 0 -1

N.S.

1 1.00 0.70 1.05 0.97 2.34 0.00 0.00 -0.01

time (sec)

N/A 0.025 0.033 0.007 0.260 0.356 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 85 158 123 340 0 0 -1

N.S.

1 1.00 0.65 1.21 0.94 2.60 0.00 0.00 -0.01

time (sec)

N/A 0.032 0.040 0.010 0.285 0.363 0.000 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

114 114 79 224 162 442 116 0 -1

N.S.

1 1.00 0.69 1.96 1.42 3.88 1.02 0.00 -0.01

time (sec)

N/A 0.043 0.039 0.011 0.260 0.364 1.901 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 68 176 132 315 90 0 -1

N.S.

1 1.00 0.75 1.93 1.45 3.46 0.99 0.00 -0.01

time (sec)

N/A 0.035 0.039 0.010 0.281 0.356 0.806 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 56 128 102 209 65 0 -1

N.S.

1 1.00 0.82 1.88 1.50 3.07 0.96 0.00 -0.01

time (sec)

N/A 0.026 0.034 0.008 0.265 0.366 0.428 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 40 76 66 129 36 59 32

N.S.

1 1.00 1.00 1.90 1.65 3.22 0.90 1.48 0.80

time (sec)

N/A 0.006 0.007 0.005 0.279 0.346 0.330 0.416 1.057

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 61 84 0 407 0 0 -1

N.S.

1 1.00 1.11 1.53 0.00 7.40 0.00 0.00 -0.02

time (sec)

N/A 0.021 0.030 0.006 0.000 0.371 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 92 123 0 571 0 0 -1

N.S.

1 1.00 1.08 1.45 0.00 6.72 0.00 0.00 -0.01

time (sec)

N/A 0.030 0.058 0.007 0.000 0.380 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 107 171 0 727 0 0 -1

N.S.

1 1.00 0.96 1.54 0.00 6.55 0.00 0.00 -0.01

time (sec)

N/A 0.040 0.077 0.007 0.000 0.388 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

196 196 161 0 0 402 0 0 -1

N.S.

1 1.00 0.82 0.00 0.00 2.05 0.00 0.00 -0.01

time (sec)

N/A 0.080 0.332 0.231 0.000 0.106 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

168 168 147 0 0 288 0 0 -1

N.S.

1 1.00 0.88 0.00 0.00 1.71 0.00 0.00 -0.01

time (sec)

N/A 0.060 0.282 0.217 0.000 0.107 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 135 0 0 188 0 0 -1

N.S.

1 1.00 0.95 0.00 0.00 1.32 0.00 0.00 -0.01

time (sec)

N/A 0.049 0.203 0.240 0.000 0.098 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 113 111 0 0 112 0 0 -1

N.S.

1 1.00 0.98 0.00 0.00 0.99 0.00 0.00 -0.01

time (sec)

N/A 0.039 0.083 0.178 0.000 0.102 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 142 0 0 187 0 0 -1

N.S.

1 1.00 0.98 0.00 0.00 1.29 0.00 0.00 -0.01

time (sec)

N/A 0.050 0.246 0.162 0.000 0.090 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

173 173 154 0 0 260 0 0 -1

N.S.

1 1.00 0.89 0.00 0.00 1.50 0.00 0.00 -0.01

time (sec)

N/A 0.062 0.205 0.289 0.000 0.099 0.000 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

201 201 163 0 0 355 0 0 -1

N.S.

1 1.00 0.81 0.00 0.00 1.77 0.00 0.00 -0.00

time (sec)

N/A 0.073 0.282 0.293 0.000 0.100 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

297 297 124 0 0 312 0 0 -1

N.S.

1 1.00 0.42 0.00 0.00 1.05 0.00 0.00 -0.00

time (sec)

N/A 0.135 0.086 0.307 0.000 0.109 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

269 269 109 0 0 220 0 0 -1

N.S.

1 1.00 0.41 0.00 0.00 0.82 0.00 0.00 -0.00

time (sec)

N/A 0.112 0.063 0.306 0.000 0.094 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

232 232 85 0 0 128 0 0 -1

N.S.

1 1.00 0.37 0.00 0.00 0.55 0.00 0.00 -0.00

time (sec)

N/A 0.095 0.072 0.296 0.000 0.098 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

272 272 118 0 0 208 0 0 -1

N.S.

1 1.00 0.43 0.00 0.00 0.76 0.00 0.00 -0.00

time (sec)

N/A 0.113 0.106 0.290 0.000 0.091 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

302 302 131 0 0 281 0 0 -1

N.S.

1 1.00 0.43 0.00 0.00 0.93 0.00 0.00 -0.00

time (sec)

N/A 0.135 0.068 0.289 0.000 0.091 0.000 0.000 0.000

Problem 28

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

44 44 39 39 37 59 60 223 90

N.S.

1 1.00 0.89 0.89 0.84 1.34 1.36 5.07 2.05

time (sec)

N/A 0.035 0.015 0.043 0.248 0.366 0.982 0.407 0.316

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 42 121 40 109 0 124 56

N.S.

1 1.00 0.89 2.57 0.85 2.32 0.00 2.64 1.19

time (sec)

N/A 0.035 0.027 0.050 0.258 0.354 0.000 0.405 1.466

Problem 30

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

43 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 -0.02

time (sec)

N/A 0.031 0.066 0.111 0.000 0.000 0.000 0.000 0.000

Problem 31

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

409 409 482 1445 0 0 0 0 -1

N.S.

1 1.00 1.18 3.53 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.364 0.122 0.314 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 B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

268 268 324 674 0 0 0 0 -1

N.S.

1 1.00 1.21 2.51 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.224 0.074 0.016 0.000 0.000 0.000 0.000 0.000

Problem 33

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

89 89 43 117 0 0 0 0 -1

N.S.

1 1.00 0.48 1.31 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.038 0.189 0.016 0.000 0.000 0.000 0.000 0.000

Problem 34

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

43 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 -0.02

time (sec)

N/A 0.032 0.069 0.112 0.000 0.000 0.000 0.000 0.000

Problem 35

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

43 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 -0.02

time (sec)

N/A 0.032 0.531 0.112 0.000 0.000 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 A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 34 41 38 62 0 43 96

N.S.

1 1.00 0.92 1.11 1.03 1.68 0.00 1.16 2.59

time (sec)

N/A 0.023 0.043 0.189 0.261 0.346 0.000 0.402 1.493

Problem 37

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

23 23 20 20 19 13 19 13 19

N.S.

1 1.00 0.87 0.87 0.83 0.57 0.83 0.57 0.83

time (sec)

N/A 0.006 0.013 0.051 0.298 0.340 0.115 0.393 1.005

Problem 38

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

23 23 20 20 19 13 39 13 19

N.S.

1 1.00 0.87 0.87 0.83 0.57 1.70 0.57 0.83

time (sec)

N/A 0.005 0.011 0.049 0.289 0.340 0.105 0.395 0.976

Problem 39

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

16 16 18 15 16 10 19 10 16

N.S.

1 1.00 1.12 0.94 1.00 0.62 1.19 0.62 1.00

time (sec)

N/A 0.002 0.006 0.100 0.291 0.330 0.058 0.391 0.046

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 19 23 34 8 0 9 58

N.S.

1 1.00 0.90 1.10 1.62 0.38 0.00 0.43 2.76

time (sec)

N/A 0.025 0.011 0.056 0.257 0.338 0.000 0.386 1.101

Problem 41

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

17 17 18 18 17 13 14 12 17

N.S.

1 1.00 1.06 1.06 1.00 0.76 0.82 0.71 1.00

time (sec)

N/A 0.010 0.013 0.068 0.295 0.355 0.084 0.383 0.091

Problem 42

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

23 23 18 20 19 11 19 11 16

N.S.

1 1.00 0.78 0.87 0.83 0.48 0.83 0.48 0.70

time (sec)

N/A 0.006 0.012 0.065 0.304 0.327 0.192 0.383 0.951

Problem 43

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

23 23 20 20 19 13 20 13 19

N.S.

1 1.00 0.87 0.87 0.83 0.57 0.87 0.57 0.83

time (sec)

N/A 0.006 0.012 0.060 0.298 0.318 0.250 0.388 0.066

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 62 98 73 161 0 0 203

N.S.

1 1.00 0.87 1.38 1.03 2.27 0.00 0.00 2.86

time (sec)

N/A 0.024 0.083 0.693 0.303 0.359 0.000 0.000 1.126

Problem 45

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

42 42 37 38 36 24 37 24 36

N.S.

1 1.00 0.88 0.90 0.86 0.57 0.88 0.57 0.86

time (sec)

N/A 0.017 0.021 35.963 0.344 0.337 0.261 0.396 0.998

Problem 46

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

42 42 37 38 36 24 37 24 36

N.S.

1 1.00 0.88 0.90 0.86 0.57 0.88 0.57 0.86

time (sec)

N/A 0.016 0.036 30.386 0.335 0.324 0.171 0.402 0.975

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 74 38 36 24 41 24 36

N.S.

1 1.00 2.18 1.12 1.06 0.71 1.21 0.71 1.06

time (sec)

N/A 0.035 0.041 30.592 0.328 0.326 0.148 0.408 0.938

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 15 33 20 20 20 33

N.S.

1 1.00 1.00 0.94 2.06 1.25 1.25 1.25 2.06

time (sec)

N/A 0.005 0.008 0.207 0.340 0.328 0.090 0.399 0.073

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 53 78 20 20 0 21 183

N.S.

1 1.00 1.08 1.59 0.41 0.41 0.00 0.43 3.73

time (sec)

N/A 0.056 0.035 0.135 0.662 0.332 0.000 0.401 0.288

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 37 41 54 24 0 21 198

N.S.

1 1.00 0.95 1.05 1.38 0.62 0.00 0.54 5.08

time (sec)

N/A 0.043 0.035 0.098 0.316 0.344 0.000 0.392 0.187

Problem 51

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

36 36 42 35 34 26 32 22 34

N.S.

1 1.00 1.17 0.97 0.94 0.72 0.89 0.61 0.94

time (sec)

N/A 0.026 0.024 0.215 0.343 0.329 0.198 0.391 0.932

Problem 52

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

31 31 34 38 36 22 37 22 32

N.S.

1 1.00 1.10 1.23 1.16 0.71 1.19 0.71 1.03

time (sec)

N/A 0.014 0.033 0.201 0.334 0.319 0.267 0.392 0.944

Problem 53

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

42 64 37 38 36 24 39 24 36

N.S.

1 1.52 0.88 0.90 0.86 0.57 0.93 0.57 0.86

time (sec)

N/A 0.038 0.022 0.214 0.347 0.348 0.385 0.384 0.955

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 97 177 109 300 0 0 332

N.S.

1 1.00 0.88 1.61 0.99 2.73 0.00 0.00 3.02

time (sec)

N/A 0.064 0.097 6.039 0.348 0.374 0.000 0.000 1.233

Problem 55

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

61 61 54 56 54 35 58 35 53

N.S.

1 1.00 0.89 0.92 0.89 0.57 0.95 0.57 0.87

time (sec)

N/A 0.032 0.019 0.025 0.376 0.324 0.574 0.384 1.048

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

53 53 54 56 54 35 56 35 53

N.S.

1 1.00 1.02 1.06 1.02 0.66 1.06 0.66 1.00

time (sec)

N/A 0.026 0.023 0.023 0.374 0.328 0.443 0.384 0.141

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 99 56 54 34 41 34 53

N.S.

1 1.00 2.91 1.65 1.59 1.00 1.21 1.00 1.56

time (sec)

N/A 0.010 0.046 29.553 0.370 0.328 0.233 0.383 0.977

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 15 51 31 20 31 47

N.S.

1 1.00 1.00 0.94 3.19 1.94 1.25 1.94 2.94

time (sec)

N/A 0.003 0.007 30.429 0.382 0.318 0.126 0.385 0.098

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 104 188 31 31 0 32 306

N.S.

1 1.00 1.35 2.44 0.40 0.40 0.00 0.42 3.97

time (sec)

N/A 0.063 0.046 0.427 0.657 0.337 0.000 0.366 0.142

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 62 96 65 36 0 33 415

N.S.

1 1.00 0.91 1.41 0.96 0.53 0.00 0.49 6.10

time (sec)

N/A 0.030 0.032 0.244 0.694 0.334 0.000 0.383 1.071

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 66 59 72 37 0 31 365

N.S.

1 1.00 1.10 0.98 1.20 0.62 0.00 0.52 6.08

time (sec)

N/A 0.028 0.033 0.272 0.348 0.324 0.000 0.400 0.205

Problem 62

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

55 55 60 52 52 37 51 35 51

N.S.

1 1.00 1.09 0.95 0.95 0.67 0.93 0.64 0.93

time (sec)

N/A 0.027 0.018 0.932 0.372 0.333 0.287 0.387 1.004

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

31 31 50 56 53 33 56 33 48

N.S.

1 1.00 1.61 1.81 1.71 1.06 1.81 1.06 1.55

time (sec)

N/A 0.009 0.019 0.954 0.388 0.338 0.359 0.389 0.969

Problem 64

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

64 64 54 56 54 35 60 35 53

N.S.

1 1.00 0.84 0.88 0.84 0.55 0.94 0.55 0.83

time (sec)

N/A 0.022 0.024 0.908 0.383 0.312 0.551 0.387 0.991

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

154 154 137 278 145 483 0 0 479

N.S.

1 1.00 0.89 1.81 0.94 3.14 0.00 0.00 3.11

time (sec)

N/A 0.068 0.113 33.391 0.386 0.350 0.000 0.000 1.341

Problem 66

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

80 80 71 74 72 46 75 46 242

N.S.

1 1.00 0.89 0.92 0.90 0.58 0.94 0.58 3.02

time (sec)

N/A 0.045 0.040 0.026 0.402 0.340 2.491 0.383 1.032

Problem 67

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

80 80 71 74 72 46 76 46 242

N.S.

1 1.00 0.89 0.92 0.90 0.58 0.95 0.58 3.02

time (sec)

N/A 0.043 0.024 0.026 0.414 0.323 1.571 0.377 0.151

Problem 68

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

80 80 71 74 72 46 78 46 77

N.S.

1 1.00 0.89 0.92 0.90 0.58 0.98 0.58 0.96

time (sec)

N/A 0.040 0.024 0.026 0.421 0.365 1.040 0.396 1.055

Problem 69

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

72 72 71 74 72 45 75 45 70

N.S.

1 1.00 0.99 1.03 1.00 0.62 1.04 0.62 0.97

time (sec)

N/A 0.037 0.018 0.028 0.415 0.378 0.683 0.390 1.020

Problem 70

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

53 53 71 74 72 45 75 45 70

N.S.

1 1.00 1.34 1.40 1.36 0.85 1.42 0.85 1.32

time (sec)

N/A 0.021 0.039 0.015 0.425 0.330 0.423 0.393 0.153

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 125 74 72 46 41 46 70

N.S.

1 1.00 3.68 2.18 2.12 1.35 1.21 1.35 2.06

time (sec)

N/A 0.010 0.056 31.814 0.416 0.325 0.414 0.392 1.001

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 15 69 42 20 42 67

N.S.

1 1.00 1.00 0.94 4.31 2.62 1.25 2.62 4.19

time (sec)

N/A 0.004 0.007 34.815 0.415 0.346 0.287 0.383 0.979

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

105 105 175 358 42 42 0 43 423

N.S.

1 1.00 1.67 3.41 0.40 0.40 0.00 0.41 4.03

time (sec)

N/A 0.055 0.073 1.200 0.667 0.335 0.000 0.377 0.135

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 85 206 77 47 0 44 553

N.S.

1 1.00 0.89 2.17 0.81 0.49 0.00 0.46 5.82

time (sec)

N/A 0.046 0.057 0.703 0.705 0.329 0.000 0.380 0.144

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 81 114 83 47 0 43 672

N.S.

1 1.00 0.93 1.31 0.95 0.54 0.00 0.49 7.72

time (sec)

N/A 0.043 0.027 0.668 0.736 0.343 0.000 0.384 1.537

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 82 77 91 48 0 42 571

N.S.

1 1.00 1.06 1.00 1.18 0.62 0.00 0.55 7.42

time (sec)

N/A 0.041 0.034 1.000 0.381 0.326 0.000 0.389 1.336

Problem 77

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

74 74 78 69 72 48 70 46 68

N.S.

1 1.00 1.05 0.93 0.97 0.65 0.95 0.62 0.92

time (sec)

N/A 0.039 0.026 3.361 0.425 0.314 0.362 0.394 1.135

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 66 74 70 44 75 44 64

N.S.

1 1.00 2.13 2.39 2.26 1.42 2.42 1.42 2.06

time (sec)

N/A 0.010 0.038 2.996 0.423 0.322 0.515 0.400 1.196

Problem 79

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

64 64 71 74 72 46 78 46 70

N.S.

1 1.00 1.11 1.16 1.12 0.72 1.22 0.72 1.09

time (sec)

N/A 0.022 0.024 3.063 0.430 0.328 0.796 0.391 1.039

Problem 80

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

98 98 71 74 72 46 80 46 70

N.S.

1 1.00 0.72 0.76 0.73 0.47 0.82 0.47 0.71

time (sec)

N/A 0.037 0.025 3.009 0.426 0.312 1.164 0.391 1.005

Problem 81

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

80 132 71 74 72 46 76 46 70

N.S.

1 1.65 0.89 0.92 0.90 0.58 0.95 0.58 0.88

time (sec)

N/A 0.053 0.025 3.069 0.423 0.316 1.556 0.395 1.072

Problem 82

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

80 80 71 74 72 46 76 46 70

N.S.

1 1.00 0.89 0.92 0.90 0.58 0.95 0.58 0.88

time (sec)

N/A 0.039 0.044 3.072 0.428 0.331 2.239 0.387 1.105

Problem 83

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

80 80 71 74 72 46 78 46 70

N.S.

1 1.00 0.89 0.92 0.90 0.58 0.98 0.58 0.88

time (sec)

N/A 0.037 0.025 3.096 0.420 0.333 3.534 0.379 1.039

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 177 110 110 68 41 68 104

N.S.

1 1.00 5.21 3.24 3.24 2.00 1.21 2.00 3.06

time (sec)

N/A 0.010 0.076 51.618 0.517 0.343 1.241 0.380 1.100

Problem 85

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

53 53 51 0 0 0 0 0 -1

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.018 0.060 0.019 0.000 0.000 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

81 81 79 202 42 41 0 43 354

N.S.

1 1.00 0.98 2.49 0.52 0.51 0.00 0.53 4.37

time (sec)

N/A 0.044 0.032 2.387 0.547 0.421 0.000 0.406 0.129

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 55 111 29 29 0 30 234

N.S.

1 1.00 0.98 1.98 0.52 0.52 0.00 0.54 4.18

time (sec)

N/A 0.024 0.030 0.648 0.550 0.356 0.000 0.378 0.273

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 31 49 18 17 0 19 108

N.S.

1 1.00 1.00 1.58 0.58 0.55 0.00 0.61 3.48

time (sec)

N/A 0.011 0.024 0.187 0.528 0.338 0.000 0.398 0.154

Problem 89

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

12 12 12 13 13 10 17 11 12

N.S.

1 1.00 1.00 1.08 1.08 0.83 1.42 0.92 1.00

time (sec)

N/A 0.003 0.035 0.065 0.465 0.342 12.130 0.402 1.060

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

44 44 29 43 18 16 0 20 107

N.S.

1 1.00 0.66 0.98 0.41 0.36 0.00 0.45 2.43

time (sec)

N/A 0.020 0.019 7.723 0.520 0.336 0.000 0.387 2.870

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 45 64 28 26 0 30 210

N.S.

1 1.00 0.69 0.98 0.43 0.40 0.00 0.46 3.23

time (sec)

N/A 0.031 0.023 0.021 0.534 0.339 0.000 0.387 2.832

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

92 92 66 87 40 41 0 45 286

N.S.

1 1.00 0.72 0.95 0.43 0.45 0.00 0.49 3.11

time (sec)

N/A 0.049 0.025 0.020 0.529 0.336 0.000 0.395 2.893

Problem 93

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

65 65 51 0 0 0 0 0 -1

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.026 0.485 0.024 0.000 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 106 350 70 73 0 62 669

N.S.

1 1.00 1.08 3.57 0.71 0.74 0.00 0.63 6.83

time (sec)

N/A 0.061 0.064 2.874 0.705 0.324 0.000 0.390 0.177

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 83 223 59 62 0 48 490

N.S.

1 1.00 1.11 2.97 0.79 0.83 0.00 0.64 6.53

time (sec)

N/A 0.038 0.037 0.808 0.698 0.341 0.000 0.376 1.033

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 56 127 44 47 0 34 302

N.S.

1 1.00 1.12 2.54 0.88 0.94 0.00 0.68 6.04

time (sec)

N/A 0.024 0.050 0.236 0.684 0.341 0.000 0.391 1.055

Problem 97

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

28 28 27 56 26 28 36 24 28

N.S.

1 1.00 0.96 2.00 0.93 1.00 1.29 0.86 1.00

time (sec)

N/A 0.011 0.035 0.086 0.667 0.342 25.242 0.389 0.078

Problem 98

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

14 14 14 15 12 13 20 12 14

N.S.

1 1.00 1.00 1.07 0.86 0.93 1.43 0.86 1.00

time (sec)

N/A 0.003 0.007 0.060 0.469 0.316 24.854 0.376 0.081

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 53 67 28 39 0 31 359

N.S.

1 1.00 0.76 0.96 0.40 0.56 0.00 0.44 5.13

time (sec)

N/A 0.032 0.050 0.025 0.639 0.347 0.000 0.377 3.390

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 70 91 45 63 0 45 432

N.S.

1 1.00 0.69 0.89 0.44 0.62 0.00 0.44 4.24

time (sec)

N/A 0.045 0.044 0.027 0.647 0.355 0.000 0.380 3.444

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