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2.2.1 Integrals 1 to 33

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 F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

144 144 180 205 0 0 0 0 -1

N.S.

1 1.00 1.25 1.42 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.134 0.151 0.892 0.000 0.000 0.000 0.000 0.000

Problem 2

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

115 115 138 186 0 0 0 0 -1

N.S.

1 1.00 1.20 1.62 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.093 0.101 0.621 0.000 0.000 0.000 0.000 0.000

Problem 3

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

82 82 115 163 0 0 0 0 -1

N.S.

1 1.00 1.40 1.99 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.075 0.054 0.234 0.000 0.000 0.000 0.000 0.000

Problem 4

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

76 76 107 156 0 0 0 0 -1

N.S.

1 1.00 1.41 2.05 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.044 0.044 0.365 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 A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 104 168 0 0 0 0 -1

N.S.

1 1.00 1.46 2.37 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.079 0.094 0.376 0.000 0.000 0.000 0.000 0.000

Problem 6

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

107 107 158 168 0 0 0 0 -1

N.S.

1 1.00 1.48 1.57 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.104 0.152 0.619 0.000 0.000 0.000 0.000 0.000

Problem 7

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

124 124 150 283 0 0 0 0 -1

N.S.

1 1.00 1.21 2.28 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.133 0.284 0.964 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 F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

180 180 294 264 0 0 0 0 -1

N.S.

1 1.00 1.63 1.47 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.168 0.172 1.092 0.000 0.000 0.000 0.000 0.000

Problem 9

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

155 155 203 281 0 0 0 0 -1

N.S.

1 1.00 1.31 1.81 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.132 0.261 0.999 0.000 0.000 0.000 0.000 0.000

Problem 10

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

136 136 251 228 0 0 0 0 -1

N.S.

1 1.00 1.85 1.68 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.094 0.129 0.487 0.000 0.000 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

57 57 49 98 136 54 0 100 -1

N.S.

1 1.00 0.86 1.72 2.39 0.95 0.00 1.75 -0.02

time (sec)

N/A 0.035 0.043 0.168 0.479 2.680 0.000 0.441 0.000

Problem 12

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

132 132 220 228 0 0 0 0 -1

N.S.

1 1.00 1.67 1.73 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.067 0.139 0.202 0.000 0.000 0.000 0.000 0.000

Problem 13

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

122 122 152 340 0 0 0 0 -1

N.S.

1 1.00 1.25 2.79 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.123 0.292 1.216 0.000 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 251 257 0 0 0 0 -1

N.S.

1 1.00 1.42 1.45 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.134 0.254 0.632 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 A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 217 347 0 0 0 0 -1

N.S.

1 1.00 1.36 2.18 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.188 0.428 0.635 0.000 0.000 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

149 149 153 177 167 127 211 165 -1

N.S.

1 1.00 1.03 1.19 1.12 0.85 1.42 1.11 -0.01

time (sec)

N/A 0.087 0.100 0.187 0.475 2.729 0.492 0.419 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 125 161 146 113 177 141 -1

N.S.

1 1.00 1.04 1.34 1.22 0.94 1.48 1.18 -0.01

time (sec)

N/A 0.092 0.081 0.108 0.470 2.880 0.344 0.407 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 131 172 126 107 158 121 -1

N.S.

1 1.00 1.07 1.41 1.03 0.88 1.30 0.99 -0.01

time (sec)

N/A 0.062 0.074 0.158 0.487 2.473 0.245 0.441 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

81 81 91 112 96 87 114 91 -1

N.S.

1 1.00 1.12 1.38 1.19 1.07 1.41 1.12 -0.01

time (sec)

N/A 0.050 0.052 0.006 0.481 2.563 0.147 0.421 0.000

Problem 20

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

132 132 124 130 0 0 0 0 -1

N.S.

1 1.00 0.94 0.98 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.177 0.136 0.569 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 A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 80 79 83 160 78 859 71

N.S.

1 1.00 1.21 1.20 1.26 2.42 1.18 13.02 1.08

time (sec)

N/A 0.053 0.045 0.010 0.487 2.990 2.358 0.735 0.376

Problem 22

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

119 119 105 148 0 0 0 0 -1

N.S.

1 1.00 0.88 1.24 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.167 0.100 1.383 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 A A B A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 130 119 121 184 170 3082 -1

N.S.

1 1.00 1.53 1.40 1.42 2.16 2.00 36.26 -0.01

time (sec)

N/A 0.062 0.045 0.010 0.478 3.893 3.018 122.203 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 99 169 160 110 197 160 -1

N.S.

1 1.00 0.73 1.25 1.19 0.81 1.46 1.19 -0.01

time (sec)

N/A 0.096 0.074 0.133 0.476 3.325 0.342 0.416 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

205 205 149 270 267 168 326 270 -1

N.S.

1 1.00 0.73 1.32 1.30 0.82 1.59 1.32 -0.00

time (sec)

N/A 0.174 0.098 0.133 0.469 2.342 0.719 0.448 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

292 292 212 393 400 239 502 408 -1

N.S.

1 1.00 0.73 1.35 1.37 0.82 1.72 1.40 -0.00

time (sec)

N/A 0.238 0.112 0.155 0.464 2.281 1.491 0.436 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

521 521 811 224 0 0 0 0 -1

N.S.

1 1.00 1.56 0.43 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.559 0.772 11.921 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

727 727 1065 796 0 0 0 0 -1

N.S.

1 1.00 1.46 1.09 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.735 1.527 7.592 0.000 0.000 0.000 0.000 0.000

Problem 29

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 0.012 2.099 0.603 0.000 0.000 0.000 0.000 0.000

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

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 0.011 1.554 0.724 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 F F(-2) B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 68 0 0 276 0 75 -1

N.S.

1 1.00 1.03 0.00 0.00 4.18 0.00 1.14 -0.02

time (sec)

N/A 0.067 0.056 0.417 0.000 2.835 0.000 0.439 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 120 0 0 580 0 185 -1

N.S.

1 1.00 0.88 0.00 0.00 4.26 0.00 1.36 -0.01

time (sec)

N/A 0.108 0.144 0.417 0.000 3.851 0.000 0.521 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

211 211 162 0 0 1066 0 398 -1

N.S.

1 1.00 0.77 0.00 0.00 5.05 0.00 1.89 -0.00

time (sec)

N/A 0.581 0.220 0.405 0.000 2.958 0.000 0.648 0.000

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