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
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 14 | 14 | 11 | 8 | 15 | 12 | 12 | 10 | 13 |
N.S. |
1 | 0.74 | 0.74 | 0.58 | 0.42 | 0.79 | 0.63 | 0.63 | 0.53 | 0.68 |
time (sec) |
N/A | 0.209 | 0.001 | 0.044 | 0.042 | 0.090 | 0.285 | 0.120 | 0.143 | 22.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 16 | 15 | 13 | 8 | 15 | 14 | 12 | 10 | 13 |
N.S. |
1 | 0.84 | 0.79 | 0.68 | 0.42 | 0.79 | 0.74 | 0.63 | 0.53 | 0.68 |
time (sec) |
N/A | 0.215 | 0.002 | 0.046 | 0.024 | 0.066 | 0.304 | 0.135 | 0.169 | 22.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 21 | 20 | 18 | 22 | 37 | 0 | 18 | 22 |
N.S. |
1 | 1.00 | 0.72 | 0.69 | 0.62 | 0.76 | 1.28 | 0.00 | 0.62 | 0.76 |
time (sec) |
N/A | 0.231 | 0.005 | 0.037 | 0.038 | 0.099 | 1.060 | 0.000 | 0.156 | 22.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 21 | 20 | 18 | 19 | 36 | 0 | 17 | 20 |
N.S. |
1 | 1.00 | 0.75 | 0.71 | 0.64 | 0.68 | 1.29 | 0.00 | 0.61 | 0.71 |
time (sec) |
N/A | 0.231 | 0.004 | 0.049 | 0.032 | 0.093 | 0.420 | 0.000 | 0.145 | 22.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 18 | 13 | 22 | 29 | 0 | 15 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.68 | 1.16 | 1.53 | 0.00 | 0.79 | 0.95 |
time (sec) |
N/A | 0.219 | 0.003 | 0.033 | 0.033 | 0.081 | 0.412 | 0.000 | 0.158 | 22.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 21 | 20 | 18 | 29 | 44 | 0 | 20 | 22 |
N.S. |
1 | 1.00 | 0.66 | 0.62 | 0.56 | 0.91 | 1.38 | 0.00 | 0.62 | 0.69 |
time (sec) |
N/A | 0.240 | 0.005 | 0.036 | 0.034 | 0.144 | 0.721 | 0.000 | 0.150 | 22.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 21 | 24 | 24 | 42 | 24 | 20 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.14 | 1.14 | 2.00 | 1.14 | 0.95 | 1.00 |
time (sec) |
N/A | 0.239 | 0.004 | 0.079 | 0.033 | 0.109 | 0.497 | 0.111 | 0.142 | 22.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 22 | 23 | 27 | 32 | 46 | 29 | 23 | 22 |
N.S. |
1 | 1.00 | 0.85 | 0.88 | 1.04 | 1.23 | 1.77 | 1.12 | 0.88 | 0.85 |
time (sec) |
N/A | 0.244 | 0.004 | 0.079 | 0.042 | 0.084 | 0.521 | 0.137 | 0.157 | 22.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 21 | 2 | 2 | 17 | 0 | 2 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.62 | 0.15 | 0.15 | 1.31 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.223 | 0.006 | 0.060 | 0.025 | 0.090 | 0.346 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 18 | 18 | 18 | 17 | 22 | 17 | 19 | 18 |
N.S. |
1 | 1.00 | 0.86 | 0.86 | 0.86 | 0.81 | 1.05 | 0.81 | 0.90 | 0.86 |
time (sec) |
N/A | 0.235 | 0.003 | 0.036 | 0.027 | 0.130 | 0.125 | 0.133 | 0.146 | 22.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 18 | 18 | 19 | 17 | 20 | 19 | 19 | 18 |
N.S. |
1 | 1.00 | 0.86 | 0.86 | 0.90 | 0.81 | 0.95 | 0.90 | 0.90 | 0.86 |
time (sec) |
N/A | 0.226 | 0.003 | 0.042 | 0.028 | 0.117 | 0.103 | 0.132 | 0.159 | 22.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 13 | 12 | 12 | 12 | 13 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.93 | 0.86 | 0.86 | 0.86 | 0.93 | 0.86 |
time (sec) |
N/A | 0.223 | 0.001 | 0.033 | 0.036 | 0.130 | 0.105 | 0.120 | 0.272 | 22.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 18 | 18 | 18 | 17 | 22 | 0 | 18 | 18 |
N.S. |
1 | 1.00 | 0.86 | 0.86 | 0.86 | 0.81 | 1.05 | 0.00 | 0.86 | 0.86 |
time (sec) |
N/A | 0.235 | 0.003 | 0.034 | 0.029 | 0.128 | 0.190 | 0.000 | 0.484 | 22.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 18 | 18 | 18 | 17 | 24 | 0 | 18 | 18 |
N.S. |
1 | 1.00 | 0.78 | 0.78 | 0.78 | 0.74 | 1.04 | 0.00 | 0.78 | 0.78 |
time (sec) |
N/A | 0.233 | 0.003 | 0.040 | 0.031 | 0.098 | 0.221 | 0.000 | 0.245 | 22.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 19 | 18 | 32 | 18 | 19 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.06 | 1.00 | 1.78 | 1.00 | 1.06 | 1.00 |
time (sec) |
N/A | 0.227 | 0.003 | 0.037 | 0.037 | 0.168 | 0.585 | 0.140 | 0.218 | 22.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 19 | 18 | 32 | 18 | 19 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.06 | 1.00 | 1.78 | 1.00 | 1.06 | 1.00 |
time (sec) |
N/A | 0.231 | 0.003 | 0.033 | 0.034 | 0.116 | 0.355 | 0.130 | 0.241 | 22.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 17 | 17 | 16 | 29 | 16 | 17 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.06 | 1.00 | 1.81 | 1.00 | 1.06 | 1.00 |
time (sec) |
N/A | 0.227 | 0.002 | 0.025 | 0.030 | 0.096 | 0.254 | 0.113 | 0.228 | 22.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 18 | 19 | 19 | 18 | 27 | 0 | 19 | 18 |
N.S. |
1 | 1.00 | 0.95 | 1.00 | 1.00 | 0.95 | 1.42 | 0.00 | 1.00 | 0.95 |
time (sec) |
N/A | 0.231 | 0.004 | 0.033 | 0.032 | 0.087 | 0.423 | 0.000 | 0.240 | 22.886 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 18 | 19 | 19 | 18 | 34 | 0 | 19 | 18 |
N.S. |
1 | 1.00 | 0.95 | 1.00 | 1.00 | 0.95 | 1.79 | 0.00 | 1.00 | 0.95 |
time (sec) |
N/A | 0.228 | 0.003 | 0.039 | 0.031 | 0.121 | 0.555 | 0.000 | 0.226 | 23.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 12 | 12 | 12 | 9 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.75 | 0.75 | 0.56 | 0.75 |
time (sec) |
N/A | 0.231 | 0.002 | 0.043 | 0.025 | 0.084 | 0.114 | 0.134 | 0.224 | 23.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 12 | 12 | 10 | 7 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.75 | 0.62 | 0.44 | 0.75 |
time (sec) |
N/A | 0.229 | 0.001 | 0.030 | 0.030 | 0.083 | 0.076 | 0.136 | 0.221 | 24.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 11 | 10 | 10 | 8 | 9 | 6 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.75 | 0.50 | 0.83 |
time (sec) |
N/A | 0.211 | 0.001 | 0.031 | 0.025 | 0.072 | 0.074 | 0.132 | 0.224 | 23.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 10 | 9 | 9 | 8 | 10 | 8 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.82 | 0.82 | 0.73 | 0.91 | 0.73 | 0.82 |
time (sec) |
N/A | 0.221 | 0.001 | 0.036 | 0.030 | 0.081 | 0.066 | 0.116 | 0.231 | 22.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 12 | 12 | 13 | 11 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.75 | 0.81 | 0.69 | 0.75 |
time (sec) |
N/A | 0.222 | 0.001 | 0.050 | 0.024 | 0.069 | 0.087 | 0.117 | 0.241 | 22.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 12 | 14 | 13 | 11 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.88 | 0.81 | 0.69 | 0.75 |
time (sec) |
N/A | 0.228 | 0.001 | 0.036 | 0.029 | 0.067 | 0.180 | 0.134 | 0.266 | 22.785 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 13 | 12 | 13 | 10 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.81 | 0.75 | 0.81 | 0.62 | 0.81 |
time (sec) |
N/A | 0.230 | 0.002 | 0.035 | 0.025 | 0.102 | 0.174 | 0.127 | 0.188 | 23.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 17 | 13 | 12 | 13 | 12 | 11 | 8 | 13 |
N.S. |
1 | 1.00 | 1.06 | 0.81 | 0.75 | 0.81 | 0.75 | 0.69 | 0.50 | 0.81 |
time (sec) |
N/A | 0.224 | 0.001 | 0.034 | 0.024 | 0.098 | 0.155 | 0.140 | 0.194 | 23.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 12 | 12 | 11 | 10 | 10 | 7 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.86 | 0.79 | 0.71 | 0.71 | 0.50 | 0.79 |
time (sec) |
N/A | 0.228 | 0.002 | 0.031 | 0.029 | 0.082 | 0.152 | 0.115 | 0.172 | 23.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 11 | 10 | 10 | 10 | 12 | 9 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.83 | 1.00 | 0.75 | 0.83 |
time (sec) |
N/A | 0.207 | 0.001 | 0.031 | 0.028 | 0.085 | 0.127 | 0.137 | 0.148 | 23.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 10 | 9 | 13 | 10 | 15 | 12 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 1.00 | 0.77 | 1.15 | 0.92 | 1.00 |
time (sec) |
N/A | 0.222 | 0.001 | 0.037 | 0.030 | 0.090 | 0.116 | 0.138 | 0.153 | 23.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 13 | 12 | 15 | 12 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.81 | 0.75 | 0.94 | 0.75 | 0.81 |
time (sec) |
N/A | 0.218 | 0.002 | 0.053 | 0.029 | 0.089 | 0.109 | 0.138 | 0.155 | 22.604 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 13 | 14 | 15 | 12 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.81 | 0.88 | 0.94 | 0.75 | 0.81 |
time (sec) |
N/A | 0.229 | 0.002 | 0.034 | 0.024 | 0.074 | 0.191 | 0.119 | 0.145 | 22.920 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 17 | 13 | 12 | 15 | 12 | 17 | 12 | 15 |
N.S. |
1 | 1.00 | 1.06 | 0.81 | 0.75 | 0.94 | 0.75 | 1.06 | 0.75 | 0.94 |
time (sec) |
N/A | 0.222 | 0.005 | 0.036 | 0.025 | 0.073 | 0.201 | 0.129 | 0.163 | 22.766 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 15 | 12 | 17 | 12 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.94 | 0.75 | 1.06 | 0.75 | 0.94 |
time (sec) |
N/A | 0.223 | 0.003 | 0.035 | 0.028 | 0.092 | 0.225 | 0.139 | 0.159 | 22.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 11 | 10 | 15 | 10 | 15 | 10 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 1.07 | 0.71 | 1.07 | 0.71 | 1.07 |
time (sec) |
N/A | 0.215 | 0.002 | 0.032 | 0.030 | 0.089 | 0.193 | 0.134 | 0.146 | 23.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 15 | 10 | 9 | 13 | 7 | 14 | 9 | 13 |
N.S. |
1 | 1.00 | 1.36 | 0.91 | 0.82 | 1.18 | 0.64 | 1.27 | 0.82 | 1.18 |
time (sec) |
N/A | 0.214 | 0.001 | 0.034 | 0.024 | 0.076 | 0.191 | 0.133 | 0.162 | 24.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 12 | 10 | 11 | 11 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 0.86 | 0.71 | 0.79 | 0.79 | 0.86 |
time (sec) |
N/A | 0.210 | 0.002 | 0.050 | 0.024 | 0.171 | 0.206 | 0.124 | 0.154 | 24.521 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 15 | 14 | 14 | 14 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.94 | 0.88 | 0.88 | 0.88 | 0.94 |
time (sec) |
N/A | 0.212 | 0.002 | 0.035 | 0.029 | 0.136 | 0.222 | 0.114 | 0.141 | 23.842 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 15 | 12 | 17 | 12 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.94 | 0.75 | 1.06 | 0.75 | 0.94 |
time (sec) |
N/A | 0.218 | 0.002 | 0.038 | 0.024 | 0.078 | 0.215 | 0.121 | 0.158 | 22.945 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 17 | 13 | 12 | 15 | 12 | 17 | 12 | 15 |
N.S. |
1 | 1.00 | 1.06 | 0.81 | 0.75 | 0.94 | 0.75 | 1.06 | 0.75 | 0.94 |
time (sec) |
N/A | 0.216 | 0.005 | 0.035 | 0.028 | 0.087 | 0.214 | 0.143 | 0.153 | 23.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 15 | 12 | 17 | 12 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.94 | 0.75 | 1.06 | 0.75 | 0.94 |
time (sec) |
N/A | 0.215 | 0.001 | 0.036 | 0.023 | 0.081 | 0.210 | 0.129 | 0.140 | 23.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 11 | 10 | 15 | 10 | 17 | 12 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 1.07 | 0.71 | 1.21 | 0.86 | 1.07 |
time (sec) |
N/A | 0.209 | 0.001 | 0.037 | 0.024 | 0.085 | 0.269 | 0.117 | 0.154 | 24.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 10 | 9 | 15 | 8 | 15 | 10 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 1.15 | 0.62 | 1.15 | 0.77 | 1.15 |
time (sec) |
N/A | 0.213 | 0.001 | 0.038 | 0.028 | 0.100 | 0.248 | 0.117 | 0.163 | 24.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 15 | 13 | 12 | 13 | 8 | 14 | 9 | 13 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 0.86 | 0.93 | 0.57 | 1.00 | 0.64 | 0.93 |
time (sec) |
N/A | 0.213 | 0.001 | 0.052 | 0.043 | 0.074 | 0.314 | 0.130 | 0.141 | 24.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 12 | 12 | 14 | 11 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 0.86 | 0.86 | 1.00 | 0.79 | 0.86 |
time (sec) |
N/A | 0.212 | 0.002 | 0.033 | 0.029 | 0.078 | 0.291 | 0.113 | 0.151 | 24.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 15 | 12 | 17 | 12 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.94 | 0.75 | 1.06 | 0.75 | 0.94 |
time (sec) |
N/A | 0.213 | 0.002 | 0.046 | 0.031 | 0.075 | 0.303 | 0.115 | 0.157 | 23.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 17 | 13 | 12 | 15 | 12 | 17 | 12 | 15 |
N.S. |
1 | 1.00 | 1.06 | 0.81 | 0.75 | 0.94 | 0.75 | 1.06 | 0.75 | 0.94 |
time (sec) |
N/A | 0.208 | 0.004 | 0.038 | 0.030 | 0.077 | 0.262 | 0.111 | 0.142 | 22.866 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 15 | 12 | 17 | 12 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.94 | 0.75 | 1.06 | 0.75 | 0.94 |
time (sec) |
N/A | 0.219 | 0.002 | 0.039 | 0.024 | 0.083 | 0.261 | 0.122 | 0.154 | 23.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 11 | 10 | 15 | 10 | 17 | 12 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 1.07 | 0.71 | 1.21 | 0.86 | 1.07 |
time (sec) |
N/A | 0.204 | 0.001 | 0.035 | 0.029 | 0.078 | 0.317 | 0.109 | 0.157 | 23.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 10 | 9 | 15 | 8 | 17 | 12 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 1.15 | 0.62 | 1.31 | 0.92 | 1.15 |
time (sec) |
N/A | 0.215 | 0.002 | 0.038 | 0.023 | 0.082 | 0.292 | 0.115 | 0.151 | 24.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 15 | 10 | 15 | 10 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.94 | 0.62 | 0.94 | 0.62 | 0.94 |
time (sec) |
N/A | 0.213 | 0.002 | 0.051 | 0.023 | 0.088 | 0.302 | 0.138 | 0.151 | 24.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 15 | 13 | 12 | 13 | 10 | 14 | 9 | 13 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 0.86 | 0.93 | 0.71 | 1.00 | 0.64 | 0.93 |
time (sec) |
N/A | 0.216 | 0.001 | 0.035 | 0.024 | 0.088 | 0.314 | 0.126 | 0.158 | 23.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 21 | 24 | 0 | 32 | 0 | 21 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.14 | 0.00 | 1.52 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.229 | 0.004 | 0.078 | 0.037 | 0.000 | 0.475 | 0.000 | 0.141 | 23.347 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 22 | 23 | 27 | 34 | 36 | 0 | 24 | 22 |
N.S. |
1 | 1.00 | 0.85 | 0.88 | 1.04 | 1.31 | 1.38 | 0.00 | 0.92 | 0.85 |
time (sec) |
N/A | 0.224 | 0.004 | 0.080 | 0.032 | 0.109 | 0.531 | 0.000 | 0.149 | 22.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 18 | 18 | 18 | 17 | 19 | 0 | 18 | 17 |
N.S. |
1 | 1.00 | 0.90 | 0.90 | 0.90 | 0.85 | 0.95 | 0.00 | 0.90 | 0.85 |
time (sec) |
N/A | 0.230 | 0.004 | 0.036 | 0.026 | 0.105 | 0.149 | 0.000 | 0.157 | 22.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 18 | 18 | 18 | 17 | 19 | 0 | 18 | 17 |
N.S. |
1 | 1.00 | 0.90 | 0.90 | 0.90 | 0.85 | 0.95 | 0.00 | 0.90 | 0.85 |
time (sec) |
N/A | 0.225 | 0.003 | 0.033 | 0.033 | 0.144 | 0.106 | 0.000 | 0.143 | 23.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 18 | 18 | 18 | 17 | 19 | 0 | 18 | 17 |
N.S. |
1 | 1.00 | 0.90 | 0.90 | 0.90 | 0.85 | 0.95 | 0.00 | 0.90 | 0.85 |
time (sec) |
N/A | 0.229 | 0.003 | 0.030 | 0.033 | 0.135 | 0.100 | 0.000 | 0.159 | 23.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 16 | 16 | 16 | 15 | 15 | 0 | 16 | 15 |
N.S. |
1 | 1.00 | 0.89 | 0.89 | 0.89 | 0.83 | 0.83 | 0.00 | 0.89 | 0.83 |
time (sec) |
N/A | 0.216 | 0.002 | 0.023 | 0.057 | 0.096 | 0.083 | 0.000 | 0.159 | 23.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 13 | 13 | 12 | 10 | 12 | 13 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.08 | 1.00 | 0.83 | 1.00 | 1.08 | 1.00 |
time (sec) |
N/A | 0.226 | 0.002 | 0.033 | 0.028 | 0.117 | 0.103 | 0.114 | 0.142 | 23.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 18 | 18 | 18 | 17 | 24 | 0 | 18 | 17 |
N.S. |
1 | 1.00 | 0.95 | 0.95 | 0.95 | 0.89 | 1.26 | 0.00 | 0.95 | 0.89 |
time (sec) |
N/A | 0.231 | 0.003 | 0.035 | 0.032 | 0.149 | 0.199 | 0.000 | 0.155 | 23.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 18 | 18 | 18 | 17 | 24 | 18 | 18 | 17 |
N.S. |
1 | 1.00 | 0.95 | 0.95 | 0.95 | 0.89 | 1.26 | 0.95 | 0.95 | 0.89 |
time (sec) |
N/A | 0.225 | 0.003 | 0.036 | 0.027 | 0.085 | 0.229 | 0.123 | 0.156 | 22.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 31 | 19 | 18 | 17 | 0 | 32 | 0 | 17 | 17 |
N.S. |
1 | 1.63 | 1.00 | 0.95 | 0.89 | 0.00 | 1.68 | 0.00 | 0.89 | 0.89 |
time (sec) |
N/A | 0.228 | 0.005 | 0.043 | 0.030 | 0.000 | 0.531 | 0.000 | 0.142 | 21.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 31 | 19 | 18 | 17 | 0 | 32 | 0 | 17 | 17 |
N.S. |
1 | 1.63 | 1.00 | 0.95 | 0.89 | 0.00 | 1.68 | 0.00 | 0.89 | 0.89 |
time (sec) |
N/A | 0.224 | 0.003 | 0.039 | 0.029 | 0.000 | 0.441 | 0.000 | 0.148 | 22.284 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 31 | 17 | 16 | 15 | 0 | 29 | 0 | 15 | 15 |
N.S. |
1 | 1.82 | 1.00 | 0.94 | 0.88 | 0.00 | 1.71 | 0.00 | 0.88 | 0.88 |
time (sec) |
N/A | 0.220 | 0.002 | 0.037 | 0.045 | 0.000 | 0.440 | 0.000 | 0.162 | 22.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 12 | 19 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 0.86 | 1.36 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.222 | 0.002 | 0.043 | 0.029 | 0.100 | 0.132 | 0.133 | 0.143 | 22.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 33 | 19 | 18 | 0 | 0 | 29 | 0 | 17 | 0 |
N.S. |
1 | 1.57 | 0.90 | 0.86 | 0.00 | 0.00 | 1.38 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.229 | 0.003 | 0.041 | 0.000 | 0.000 | 0.515 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 33 | 19 | 18 | 0 | 0 | 34 | 0 | 17 | 0 |
N.S. |
1 | 1.57 | 0.90 | 0.86 | 0.00 | 0.00 | 1.62 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.236 | 0.003 | 0.040 | 0.000 | 0.000 | 0.576 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 21 | 22 | 20 | 19 | 0 | 42 | 0 | 20 | 22 |
N.S. |
1 | 0.88 | 0.92 | 0.83 | 0.79 | 0.00 | 1.75 | 0.00 | 0.83 | 0.92 |
time (sec) |
N/A | 0.230 | 0.006 | 0.039 | 0.029 | 0.000 | 5.149 | 0.000 | 0.142 | 22.364 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 19 | 20 | 18 | 17 | 0 | 39 | 0 | 18 | 22 |
N.S. |
1 | 0.79 | 0.83 | 0.75 | 0.71 | 0.00 | 1.62 | 0.00 | 0.75 | 0.92 |
time (sec) |
N/A | 0.231 | 0.005 | 0.033 | 0.033 | 0.000 | 1.886 | 0.000 | 0.149 | 22.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 16 | 20 | 0 | 13 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 1.00 | 1.25 | 0.00 | 0.81 | 1.00 |
time (sec) |
N/A | 0.226 | 0.003 | 0.090 | 0.032 | 0.096 | 0.463 | 0.000 | 0.158 | 21.827 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 21 | 22 | 20 | 0 | 0 | 39 | 0 | 20 | 22 |
N.S. |
1 | 0.88 | 0.92 | 0.83 | 0.00 | 0.00 | 1.62 | 0.00 | 0.83 | 0.92 |
time (sec) |
N/A | 0.235 | 0.008 | 0.052 | 0.000 | 0.000 | 4.405 | 0.000 | 0.151 | 21.926 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 35 | 22 | 20 | 0 | 0 | 44 | 0 | 20 | 22 |
N.S. |
1 | 1.46 | 0.92 | 0.83 | 0.00 | 0.00 | 1.83 | 0.00 | 0.83 | 0.92 |
time (sec) |
N/A | 0.247 | 0.007 | 0.043 | 0.000 | 0.000 | 10.058 | 0.000 | 0.158 | 22.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 37 | 22 | 18 | 0 | 0 | 36 | 0 | 18 | 22 |
N.S. |
1 | 1.42 | 0.85 | 0.69 | 0.00 | 0.00 | 1.38 | 0.00 | 0.69 | 0.85 |
time (sec) |
N/A | 0.237 | 0.006 | 0.046 | 0.000 | 0.000 | 1.068 | 0.000 | 0.154 | 22.396 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 19 | 18 | 0 | 0 | 41 | 0 | 22 | 24 |
N.S. |
1 | 1.00 | 0.90 | 0.86 | 0.00 | 0.00 | 1.95 | 0.00 | 1.05 | 1.14 |
time (sec) |
N/A | 0.229 | 0.006 | 0.041 | 0.000 | 0.000 | 0.588 | 0.000 | 0.141 | 22.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 19 | 18 | 0 | 0 | 41 | 0 | 22 | 24 |
N.S. |
1 | 1.00 | 0.90 | 0.86 | 0.00 | 0.00 | 1.95 | 0.00 | 1.05 | 1.14 |
time (sec) |
N/A | 0.225 | 0.005 | 0.039 | 0.000 | 0.000 | 0.582 | 0.000 | 0.152 | 22.676 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 17 | 16 | 0 | 0 | 37 | 0 | 20 | 24 |
N.S. |
1 | 1.00 | 0.89 | 0.84 | 0.00 | 0.00 | 1.95 | 0.00 | 1.05 | 1.26 |
time (sec) |
N/A | 0.222 | 0.004 | 0.039 | 0.000 | 0.000 | 0.463 | 0.000 | 0.156 | 22.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 20 | 20 | 0 | 17 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 1.43 | 1.43 | 0.00 | 1.21 | 1.43 |
time (sec) |
N/A | 0.223 | 0.003 | 0.043 | 0.029 | 0.078 | 0.307 | 0.000 | 0.150 | 22.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 18 | 17 | 0 | 41 | 0 | 22 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.89 | 0.00 | 2.16 | 0.00 | 1.16 | 1.26 |
time (sec) |
N/A | 0.222 | 0.005 | 0.045 | 0.024 | 0.000 | 0.755 | 0.000 | 0.161 | 21.846 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 18 | 17 | 0 | 46 | 0 | 22 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.89 | 0.00 | 2.42 | 0.00 | 1.16 | 1.26 |
time (sec) |
N/A | 0.223 | 0.005 | 0.044 | 0.029 | 0.000 | 0.889 | 0.000 | 0.155 | 21.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 23 | 22 | 18 | 0 | 0 | 42 | 0 | 22 | 0 |
N.S. |
1 | 0.77 | 0.73 | 0.60 | 0.00 | 0.00 | 1.40 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.235 | 0.009 | 0.060 | 0.000 | 0.000 | 0.672 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 21 | 22 | 20 | 0 | 0 | 51 | 0 | 24 | 0 |
N.S. |
1 | 0.75 | 0.79 | 0.71 | 0.00 | 0.00 | 1.82 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.228 | 0.007 | 0.045 | 0.000 | 0.000 | 1.087 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 19 | 20 | 18 | 0 | 0 | 48 | 0 | 22 | 0 |
N.S. |
1 | 0.68 | 0.71 | 0.64 | 0.00 | 0.00 | 1.71 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.223 | 0.006 | 0.041 | 0.000 | 0.000 | 1.035 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 22 | 22 | 0 | 17 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 1.38 | 1.38 | 0.00 | 1.06 | 0.75 |
time (sec) |
N/A | 0.223 | 0.004 | 0.207 | 0.029 | 0.101 | 0.471 | 0.000 | 0.148 | 21.807 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 21 | 22 | 20 | 19 | 0 | 51 | 0 | 24 | 0 |
N.S. |
1 | 0.75 | 0.79 | 0.71 | 0.68 | 0.00 | 1.82 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.229 | 0.009 | 0.046 | 0.032 | 0.000 | 6.310 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 35 | 22 | 20 | 19 | 0 | 56 | 0 | 24 | 0 |
N.S. |
1 | 1.25 | 0.79 | 0.71 | 0.68 | 0.00 | 2.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.235 | 0.009 | 0.046 | 0.029 | 0.000 | 16.279 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 33 | 22 | 18 | 17 | 0 | 48 | 0 | 22 | 0 |
N.S. |
1 | 1.18 | 0.79 | 0.64 | 0.61 | 0.00 | 1.71 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.235 | 0.010 | 0.046 | 0.025 | 0.000 | 1.631 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 26 | 25 | 24 | 24 | 0 | 53 | 0 | 23 | 26 |
N.S. |
1 | 0.93 | 0.89 | 0.86 | 0.86 | 0.00 | 1.89 | 0.00 | 0.82 | 0.93 |
time (sec) |
N/A | 0.237 | 0.008 | 0.056 | 0.038 | 0.000 | 14.831 | 0.000 | 0.163 | 21.988 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 25 | 22 | 22 | 0 | 48 | 0 | 20 | 22 |
N.S. |
1 | 1.00 | 1.04 | 0.92 | 0.92 | 0.00 | 2.00 | 0.00 | 0.83 | 0.92 |
time (sec) |
N/A | 0.236 | 0.005 | 0.053 | 0.035 | 0.000 | 0.973 | 0.000 | 0.148 | 21.858 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 25 | 24 | 24 | 0 | 61 | 0 | 28 | 30 |
N.S. |
1 | 1.00 | 0.96 | 0.92 | 0.92 | 0.00 | 2.35 | 0.00 | 1.08 | 1.15 |
time (sec) |
N/A | 0.238 | 0.008 | 0.056 | 0.041 | 0.000 | 0.891 | 0.000 | 0.149 | 22.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 26 | 25 | 24 | 24 | 0 | 66 | 0 | 28 | 0 |
N.S. |
1 | 0.81 | 0.78 | 0.75 | 0.75 | 0.00 | 2.06 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.242 | 0.010 | 0.053 | 0.038 | 0.000 | 2.196 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 26 | 26 | 27 | 0 | 56 | 0 | 28 | 34 |
N.S. |
1 | 1.00 | 0.84 | 0.84 | 0.87 | 0.00 | 1.81 | 0.00 | 0.90 | 1.10 |
time (sec) |
N/A | 0.246 | 0.011 | 0.085 | 0.038 | 0.000 | 146.156 | 0.000 | 0.159 | 22.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 26 | 26 | 27 | 0 | 56 | 0 | 26 | 30 |
N.S. |
1 | 1.00 | 0.84 | 0.84 | 0.87 | 0.00 | 1.81 | 0.00 | 0.84 | 0.97 |
time (sec) |
N/A | 0.242 | 0.007 | 0.069 | 0.041 | 0.000 | 15.925 | 0.000 | 0.155 | 22.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 26 | 24 | 25 | 0 | 51 | 0 | 23 | 23 |
N.S. |
1 | 1.00 | 0.90 | 0.83 | 0.86 | 0.00 | 1.76 | 0.00 | 0.79 | 0.79 |
time (sec) |
N/A | 0.236 | 0.005 | 0.053 | 0.040 | 0.000 | 1.069 | 0.000 | 0.166 | 22.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 26 | 26 | 27 | 0 | 65 | 0 | 31 | 34 |
N.S. |
1 | 1.00 | 0.84 | 0.84 | 0.87 | 0.00 | 2.10 | 0.00 | 1.00 | 1.10 |
time (sec) |
N/A | 0.236 | 0.005 | 0.060 | 0.040 | 0.000 | 0.928 | 0.000 | 0.161 | 22.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 26 | 26 | 27 | 0 | 70 | 0 | 31 | 34 |
N.S. |
1 | 1.00 | 0.84 | 0.84 | 0.87 | 0.00 | 2.26 | 0.00 | 1.00 | 1.10 |
time (sec) |
N/A | 0.240 | 0.007 | 0.056 | 0.041 | 0.000 | 2.445 | 0.000 | 0.153 | 22.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 26 | 26 | 27 | 0 | 70 | 0 | 31 | 34 |
N.S. |
1 | 1.00 | 0.84 | 0.84 | 0.87 | 0.00 | 2.26 | 0.00 | 1.00 | 1.10 |
time (sec) |
N/A | 0.246 | 0.011 | 0.061 | 0.040 | 0.000 | 17.139 | 0.000 | 0.159 | 22.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 19 | 19 | 23 | 0 | 110 | 22 | 0 | 6 | 0 |
N.S. |
1 | 0.95 | 0.95 | 1.15 | 0.00 | 5.50 | 1.10 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.223 | 0.005 | 0.056 | 0.000 | 2.941 | 6.831 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 22 | 0 | 27 | 20 | 0 | 5 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.16 | 0.00 | 1.42 | 1.05 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.219 | 0.005 | 0.053 | 0.000 | 0.077 | 0.631 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 20 | 0 | 30 | 19 | 20 | 8 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 0.00 | 1.58 | 1.00 | 1.05 | 0.42 | 0.00 |
time (sec) |
N/A | 0.216 | 0.004 | 0.055 | 0.000 | 0.102 | 0.445 | 0.134 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 19 | 19 | 23 | 0 | 20 | 20 | 0 | 8 | 0 |
N.S. |
1 | 0.86 | 0.86 | 1.05 | 0.00 | 0.91 | 0.91 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.222 | 0.004 | 0.056 | 0.000 | 0.074 | 1.082 | 0.000 | 0.145 | 0.000 |