Integrals 101 to 104

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 Reduce Mupad

grade

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

verified

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

size

82 68 86 59 58 57 65 474 57 0

N.S.

1 0.83 1.05 0.72 0.71 0.70 0.79 5.78 0.70 0.00

time (sec)

N/A 0.487 0.076 0.376 0.027 0.106 0.640 0.218 0.199 0.000

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

160 162 94 107 106 62 139 859 81 0

N.S.

1 1.01 0.59 0.67 0.66 0.39 0.87 5.37 0.51 0.00

time (sec)

N/A 1.031 0.128 0.496 0.034 0.078 0.630 0.184 0.196 0.000

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

190 192 168 121 120 76 165 7916 92 0

N.S.

1 1.01 0.88 0.64 0.63 0.40 0.87 41.66 0.48 0.00

time (sec)

N/A 1.122 0.200 0.819 0.034 0.108 0.659 39.833 0.236 0.000

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

233 235 186 154 153 85 202 271 110 0

N.S.

1 1.01 0.80 0.66 0.66 0.36 0.87 1.16 0.47 0.00

time (sec)

N/A 1.200 0.193 0.954 0.032 0.125 0.770 3.519 0.207 0.000