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 | 33 | 31 | 31 | 23 | 23 | 25 | 39 | 23 | 25 | 25 |
N.S. |
1 | 0.94 | 0.94 | 0.70 | 0.70 | 0.76 | 1.18 | 0.70 | 0.76 | 0.76 |
time (sec) |
N/A | 0.243 | 0.007 | 0.448 | 0.027 | 0.076 | 0.115 | 0.123 | 0.150 | 0.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 2 | 3 | 13 | 2 | 2 | 2 | 2 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 6.50 | 1.00 | 1.00 | 1.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.136 | 0.008 | 0.105 | 0.061 | 0.069 | 0.342 | 0.120 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 2 | 3 | 13 | 2 | 12 | 2 | 2 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 6.50 | 1.00 | 6.00 | 1.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.146 | 0.002 | 0.144 | 0.057 | 0.072 | 0.493 | 0.121 | 0.141 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 11 | 15 | 13 | 17 | 13 | 13 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.50 | 1.30 | 1.70 | 1.30 | 1.30 | 0.00 |
time (sec) |
N/A | 0.194 | 0.002 | 0.177 | 0.054 | 0.070 | 0.735 | 0.123 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 17 | 11 | 10 | 11 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.13 | 0.73 | 0.67 | 0.73 | 0.73 | 0.00 |
time (sec) |
N/A | 0.172 | 0.009 | 0.277 | 0.065 | 0.075 | 0.577 | 0.120 | 0.153 | 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 | 12 | 12 | 12 | 17 | 20 | 18 | 12 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.42 | 1.67 | 1.50 | 1.00 | 1.33 | 1.33 | 1.33 |
time (sec) |
N/A | 0.177 | 0.006 | 0.060 | 0.029 | 0.076 | 0.041 | 0.116 | 0.149 | 0.012 |
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 | 22 | 12 | 11 | 11 | 14 | 11 | 11 | 11 |
N.S. |
1 | 1.00 | 2.00 | 1.09 | 1.00 | 1.00 | 1.27 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.135 | 0.008 | 0.152 | 0.031 | 0.073 | 0.059 | 0.118 | 0.152 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 21 | 11 | 10 | 10 | 12 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 2.10 | 1.10 | 1.00 | 1.00 | 1.20 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.143 | 0.007 | 0.122 | 0.032 | 0.076 | 0.064 | 0.114 | 0.156 | 0.013 |
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 | 17 | 11 | 18 | 19 | 13 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.42 | 0.92 | 1.50 | 1.58 | 1.08 | 1.33 | 1.33 |
time (sec) |
N/A | 0.139 | 0.006 | 0.032 | 0.023 | 0.083 | 0.054 | 0.123 | 0.151 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 13 | 11 | 26 | 11 | 27 | 29 | 31 | 28 | 28 |
N.S. |
1 | 1.18 | 1.00 | 2.36 | 1.00 | 2.45 | 2.64 | 2.82 | 2.55 | 2.55 |
time (sec) |
N/A | 0.144 | 0.004 | 0.046 | 0.027 | 0.078 | 0.067 | 0.135 | 0.154 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 15 | 26 | 30 | 17 | 51 | 14 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.25 | 2.17 | 2.50 | 1.42 | 4.25 | 1.17 | 1.00 |
time (sec) |
N/A | 0.142 | 0.002 | 0.104 | 0.027 | 0.082 | 0.252 | 0.116 | 0.155 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 19 | 26 | 28 | 34 | 28 | 31 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.73 | 2.36 | 2.55 | 3.09 | 2.55 | 2.82 | 1.00 |
time (sec) |
N/A | 0.139 | 0.002 | 0.145 | 0.031 | 0.082 | 0.285 | 0.128 | 0.153 | 0.013 |
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 | 25 | 25 | 23 | 19 | 24 | 23 | 46 | 18 | 23 | 18 |
N.S. |
1 | 1.00 | 0.92 | 0.76 | 0.96 | 0.92 | 1.84 | 0.72 | 0.92 | 0.72 |
time (sec) |
N/A | 0.149 | 0.019 | 0.300 | 0.029 | 0.077 | 0.083 | 0.122 | 0.154 | 0.107 |
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 | 27 | 24 | 29 | 22 | 22 | 22 | 37 | 25 | 31 | 24 |
N.S. |
1 | 0.89 | 1.07 | 0.81 | 0.81 | 0.81 | 1.37 | 0.93 | 1.15 | 0.89 |
time (sec) |
N/A | 0.161 | 0.009 | 0.493 | 0.029 | 0.075 | 0.102 | 0.115 | 0.146 | 0.079 |
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 | 25 | 25 | 23 | 19 | 22 | 22 | 46 | 18 | 22 | 18 |
N.S. |
1 | 1.00 | 0.92 | 0.76 | 0.88 | 0.88 | 1.84 | 0.72 | 0.88 | 0.72 |
time (sec) |
N/A | 0.148 | 0.013 | 0.237 | 0.030 | 0.081 | 0.081 | 0.112 | 0.159 | 0.093 |
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 | 26 | 26 | 26 | 22 | 22 | 21 | 36 | 22 | 23 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.85 | 0.81 | 1.38 | 0.85 | 0.88 | 0.92 |
time (sec) |
N/A | 0.164 | 0.005 | 0.465 | 0.024 | 0.077 | 0.104 | 0.118 | 0.149 | 0.014 |
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 | 10 | 10 | 10 | 11 | 10 | 18 | 58 | 10 | 18 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.80 | 5.80 | 1.00 | 1.80 | 1.00 |
time (sec) |
N/A | 0.150 | 0.003 | 0.132 | 0.030 | 0.068 | 0.498 | 0.118 | 0.155 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 6 | 5 | 9 | 9 | 3 | 30 | 4 | 4 |
N.S. |
1 | 1.00 | 0.67 | 0.56 | 1.00 | 1.00 | 0.33 | 3.33 | 0.44 | 0.44 |
time (sec) |
N/A | 0.145 | 0.003 | 0.040 | 0.029 | 0.066 | 0.082 | 0.116 | 0.156 | 0.084 |
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 | 8 | 7 | 10 | 10 | 7 | 8 | 8 | 6 |
N.S. |
1 | 1.00 | 0.67 | 0.58 | 0.83 | 0.83 | 0.58 | 0.67 | 0.67 | 0.50 |
time (sec) |
N/A | 0.148 | 0.032 | 0.060 | 0.025 | 0.078 | 0.155 | 0.113 | 0.156 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 23 | 11 | 15 | 18 | 8 | 10 | 14 | 10 |
N.S. |
1 | 1.00 | 2.30 | 1.10 | 1.50 | 1.80 | 0.80 | 1.00 | 1.40 | 1.00 |
time (sec) |
N/A | 0.138 | 0.010 | 0.069 | 0.035 | 0.068 | 0.167 | 0.110 | 0.160 | 0.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 25 | 11 | 15 | 17 | 8 | 10 | 14 | 10 |
N.S. |
1 | 1.00 | 2.27 | 1.00 | 1.36 | 1.55 | 0.73 | 0.91 | 1.27 | 0.91 |
time (sec) |
N/A | 0.147 | 0.011 | 0.081 | 0.031 | 0.072 | 0.169 | 0.115 | 0.149 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 46 | 40 | 39 | 0 | 148 | 100 | 48 | 45 | 45 |
N.S. |
1 | 1.15 | 1.00 | 0.98 | 0.00 | 3.70 | 2.50 | 1.20 | 1.12 | 1.12 |
time (sec) |
N/A | 0.179 | 0.029 | 0.104 | 0.000 | 0.093 | 1.702 | 0.124 | 0.157 | 0.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 52 | 44 | 43 | 0 | 287 | 1872 | 60 | 54 | 58 |
N.S. |
1 | 1.11 | 0.94 | 0.91 | 0.00 | 6.11 | 39.83 | 1.28 | 1.15 | 1.23 |
time (sec) |
N/A | 0.199 | 0.045 | 0.204 | 0.000 | 0.101 | 60.132 | 0.128 | 0.146 | 0.097 |
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 | 73 | 78 | 47 | 46 | 117 | 54 | 105 | 45 | 67 | 52 |
N.S. |
1 | 1.07 | 0.64 | 0.63 | 1.60 | 0.74 | 1.44 | 0.62 | 0.92 | 0.71 |
time (sec) |
N/A | 0.247 | 0.086 | 0.383 | 0.033 | 0.086 | 0.225 | 0.121 | 0.152 | 0.083 |
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 | 15 | 15 | 15 | 12 | 11 | 12 | 20 | 11 | 17 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 0.80 | 1.33 | 0.73 | 1.13 | 0.60 |
time (sec) |
N/A | 0.151 | 0.003 | 0.338 | 0.025 | 0.077 | 0.123 | 0.117 | 0.150 | 0.015 |
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 | 73 | 78 | 47 | 46 | 113 | 54 | 105 | 45 | 64 | 52 |
N.S. |
1 | 1.07 | 0.64 | 0.63 | 1.55 | 0.74 | 1.44 | 0.62 | 0.88 | 0.71 |
time (sec) |
N/A | 0.246 | 0.078 | 0.408 | 0.032 | 0.090 | 0.236 | 0.123 | 0.155 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 22 | 14 | 31 | 14 | 29 | 29 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.57 | 1.00 | 2.21 | 1.00 | 2.07 | 2.07 | 1.50 |
time (sec) |
N/A | 0.181 | 0.004 | 0.043 | 0.024 | 0.076 | 0.039 | 0.123 | 0.149 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 125 | 101 | 138 | 491 | 182 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.20 | 0.97 | 1.33 | 4.72 | 1.75 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.714 | 0.100 | 0.117 | 0.156 | 0.083 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 294 | 133 | 237 | 777 | 212 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.92 | 0.87 | 1.55 | 5.08 | 1.39 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 1.493 | 0.204 | 0.132 | 0.377 | 0.089 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 20 | 107 | 21 | 19 | 23 | 19 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 7.13 | 1.40 | 1.27 | 1.53 | 1.27 | 0.87 |
time (sec) |
N/A | 0.183 | 0.010 | 0.054 | 0.105 | 0.082 | 0.068 | 0.125 | 0.157 | 0.014 |
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 | 15 | 15 | 15 | 12 | 11 | 13 | 26 | 11 | 21 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 0.87 | 1.73 | 0.73 | 1.40 | 0.87 |
time (sec) |
N/A | 0.149 | 0.019 | 0.389 | 0.023 | 0.074 | 0.125 | 0.121 | 0.154 | 0.025 |
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 | 24 | 29 | 14 | 11 | 10 | 19 | 14 | 10 | 18 | 18 |
N.S. |
1 | 1.21 | 0.58 | 0.46 | 0.42 | 0.79 | 0.58 | 0.42 | 0.75 | 0.75 |
time (sec) |
N/A | 0.195 | 0.016 | 0.325 | 0.026 | 0.075 | 0.025 | 0.120 | 0.153 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 6 | 15 | 9 | 18 | 12 | 9 | 17 | 6 |
N.S. |
1 | 1.00 | 0.86 | 2.14 | 1.29 | 2.57 | 1.71 | 1.29 | 2.43 | 0.86 |
time (sec) |
N/A | 0.162 | 0.021 | 0.165 | 0.029 | 0.068 | 0.023 | 0.128 | 0.151 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 22 | 23 | 25 | 22 | 104 | 328 | 22 | 22 |
N.S. |
1 | 1.00 | 0.69 | 0.72 | 0.78 | 0.69 | 3.25 | 10.25 | 0.69 | 0.69 |
time (sec) |
N/A | 0.153 | 0.013 | 0.184 | 0.031 | 0.077 | 0.267 | 0.125 | 0.143 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 20 | 21 | 24 | 20 | 107 | 329 | 20 | 20 |
N.S. |
1 | 1.00 | 0.65 | 0.68 | 0.77 | 0.65 | 3.45 | 10.61 | 0.65 | 0.65 |
time (sec) |
N/A | 0.146 | 0.012 | 0.190 | 0.031 | 0.077 | 0.249 | 0.131 | 0.147 | 0.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 50 | 56 | 60 | 60 | 308 | 1156 | 63 | 57 |
N.S. |
1 | 1.00 | 0.60 | 0.67 | 0.71 | 0.71 | 3.67 | 13.76 | 0.75 | 0.68 |
time (sec) |
N/A | 0.223 | 0.033 | 0.271 | 0.037 | 0.079 | 0.447 | 0.145 | 0.149 | 0.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 49 | 54 | 58 | 58 | 304 | 1155 | 61 | 55 |
N.S. |
1 | 1.00 | 0.59 | 0.65 | 0.70 | 0.70 | 3.66 | 13.92 | 0.73 | 0.66 |
time (sec) |
N/A | 0.218 | 0.031 | 0.233 | 0.036 | 0.078 | 0.414 | 0.139 | 0.149 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 94 | 102 | 107 | 115 | 665 | 2631 | 139 | 133 |
N.S. |
1 | 1.00 | 0.58 | 0.63 | 0.66 | 0.71 | 4.10 | 16.24 | 0.86 | 0.82 |
time (sec) |
N/A | 0.367 | 0.054 | 0.321 | 0.077 | 0.088 | 0.745 | 0.158 | 0.153 | 0.218 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 162 | 93 | 100 | 105 | 111 | 668 | 2631 | 137 | 132 |
N.S. |
1 | 1.01 | 0.58 | 0.62 | 0.65 | 0.69 | 4.15 | 16.34 | 0.85 | 0.82 |
time (sec) |
N/A | 0.367 | 0.047 | 0.346 | 0.042 | 0.087 | 0.729 | 0.154 | 0.147 | 0.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 263 | 169 | 166 | 186 | 203 | 1355 | 5069 | 264 | 231 |
N.S. |
1 | 1.01 | 0.65 | 0.64 | 0.71 | 0.78 | 5.19 | 19.42 | 1.01 | 0.89 |
time (sec) |
N/A | 0.583 | 0.093 | 0.461 | 0.059 | 0.082 | 1.352 | 0.181 | 0.155 | 0.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 262 | 168 | 164 | 184 | 202 | 1352 | 5065 | 262 | 232 |
N.S. |
1 | 1.01 | 0.65 | 0.63 | 0.71 | 0.78 | 5.20 | 19.48 | 1.01 | 0.89 |
time (sec) |
N/A | 0.573 | 0.078 | 0.457 | 0.057 | 0.088 | 1.400 | 0.176 | 0.152 | 0.350 |
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 | 25 | 25 | 25 | 20 | 19 | 17 | 116 | 13 | 89 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.76 | 0.68 | 4.64 | 0.52 | 3.56 | 0.56 |
time (sec) |
N/A | 0.185 | 0.049 | 1.608 | 0.024 | 0.080 | 0.800 | 0.118 | 0.154 | 0.097 |
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 | 30 | 30 | 30 | 23 | 22 | 25 | 114 | 22 | 89 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.73 | 0.83 | 3.80 | 0.73 | 2.97 | 0.73 |
time (sec) |
N/A | 0.188 | 0.031 | 1.556 | 0.025 | 0.076 | 0.772 | 0.114 | 0.162 | 0.159 |
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 | 85 | 97 | 55 | 61 | 55 | 59 | 100 | 60 | 73 | 67 |
N.S. |
1 | 1.14 | 0.65 | 0.72 | 0.65 | 0.69 | 1.18 | 0.71 | 0.86 | 0.79 |
time (sec) |
N/A | 0.447 | 0.047 | 0.527 | 0.027 | 0.073 | 0.301 | 0.116 | 0.150 | 0.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | C | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 13 | 15 | 240 | 22 | 17 | 17 | 17 | 17 |
N.S. |
1 | 1.00 | 1.18 | 1.36 | 21.82 | 2.00 | 1.55 | 1.55 | 1.55 | 1.55 |
time (sec) |
N/A | 0.437 | 0.535 | 0.126 | 0.046 | 0.087 | 41.866 | 0.129 | 0.153 | 0.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 18 | 12 | 11 | 41 | 16 | 0 | 18 | 16 | 10 |
N.S. |
1 | 1.50 | 1.00 | 0.92 | 3.42 | 1.33 | 0.00 | 1.50 | 1.33 | 0.83 |
time (sec) |
N/A | 0.180 | 0.016 | 0.289 | 0.032 | 0.072 | 0.000 | 0.128 | 0.156 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 83 | 76 | 107 | 0 | 312 | 0 | 98 | 150 | 133 |
N.S. |
1 | 1.08 | 0.99 | 1.39 | 0.00 | 4.05 | 0.00 | 1.27 | 1.95 | 1.73 |
time (sec) |
N/A | 0.297 | 0.276 | 0.306 | 0.000 | 0.097 | 0.000 | 0.132 | 0.161 | 0.309 |
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 | 17 | 17 | 17 | 13 | 12 | 13 | 15 | 13 | 12 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.71 | 0.76 | 0.88 | 0.76 | 0.71 | 0.76 |
time (sec) |
N/A | 0.132 | 0.005 | 0.073 | 0.028 | 0.081 | 0.115 | 0.122 | 0.154 | 0.092 |
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 | 17 | 17 | 17 | 11 | 10 | 13 | 15 | 13 | 10 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.65 | 0.59 | 0.76 | 0.88 | 0.76 | 0.59 | 0.76 |
time (sec) |
N/A | 0.135 | 0.005 | 0.076 | 0.030 | 0.077 | 0.103 | 0.119 | 0.163 | 0.089 |
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 | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 3 | 2 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.67 | 0.67 | 0.67 | 0.67 | 1.00 | 0.67 |
time (sec) |
N/A | 0.115 | 0.000 | 0.019 | 0.024 | 0.064 | 0.022 | 0.128 | 0.161 | 0.005 |
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 | 8 | 8 | 8 | 9 | 8 | 8 | 8 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.120 | 0.000 | 0.029 | 0.029 | 0.069 | 0.031 | 0.123 | 0.154 | 0.103 |
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 | 9 | 9 | 9 | 9 | 8 | 8 | 7 | 8 | 9 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.89 | 0.89 | 0.78 | 0.89 | 1.00 | 0.89 |
time (sec) |
N/A | 0.129 | 0.005 | 0.032 | 0.029 | 0.060 | 0.030 | 0.116 | 0.166 | 0.018 |
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 | 4 | 4 | 4 | 9 | 4 | 4 | 3 | 4 | 4 | 4 |
N.S. |
1 | 1.00 | 1.00 | 2.25 | 1.00 | 1.00 | 0.75 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.124 | 0.009 | 0.042 | 0.073 | 0.065 | 0.336 | 0.120 | 0.165 | 0.009 |
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 | 24 | 30 | 38 | 23 | 23 | 22 | 15 | 24 | 23 | 22 |
N.S. |
1 | 1.25 | 1.58 | 0.96 | 0.96 | 0.92 | 0.62 | 1.00 | 0.96 | 0.92 |
time (sec) |
N/A | 0.147 | 0.016 | 0.025 | 0.032 | 0.076 | 0.048 | 0.121 | 0.167 | 0.055 |
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 | 10 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 1.00 | 0.83 |
time (sec) |
N/A | 0.148 | 0.012 | 0.030 | 0.028 | 0.079 | 0.035 | 0.130 | 0.186 | 0.029 |
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 | 13 | 14 | 12 | 14 | 14 | 15 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.08 | 0.92 | 1.08 | 1.08 | 1.15 | 1.08 |
time (sec) |
N/A | 0.129 | 0.006 | 0.030 | 0.024 | 0.064 | 0.031 | 0.124 | 0.162 | 0.031 |
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 | 31 | 31 | 31 | 22 | 23 | 85 | 26 | 21 | 30 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.71 | 0.74 | 2.74 | 0.84 | 0.68 | 0.97 | 0.68 |
time (sec) |
N/A | 0.160 | 0.025 | 0.057 | 0.105 | 0.080 | 0.071 | 0.119 | 0.163 | 0.138 |
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 | 14 | 14 | 13 | 13 | 19 | 13 | 14 | 13 |
N.S. |
1 | 1.00 | 0.67 | 0.67 | 0.62 | 0.62 | 0.90 | 0.62 | 0.67 | 0.62 |
time (sec) |
N/A | 0.145 | 0.009 | 0.040 | 0.032 | 0.061 | 0.039 | 0.118 | 0.153 | 0.016 |
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 | 163 | 201 | 102 | 102 | 101 | 101 | 102 | 101 | 102 | 101 |
N.S. |
1 | 1.23 | 0.63 | 0.63 | 0.62 | 0.62 | 0.63 | 0.62 | 0.63 | 0.62 |
time (sec) |
N/A | 1.019 | 0.066 | 0.094 | 0.031 | 0.063 | 0.046 | 0.116 | 0.147 | 0.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 0 | 18 | 0 | 216 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 0.00 | 1.00 | 0.00 | 12.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.156 | 0.018 | 0.070 | 0.000 | 0.067 | 0.000 | 0.132 | 0.164 | 0.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 0 | 14 | 31 | 237 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 0.00 | 1.00 | 2.21 | 16.93 | 1.00 | 1.00 |
time (sec) |
N/A | 0.148 | 0.011 | 0.065 | 0.000 | 0.067 | 0.239 | 0.136 | 0.152 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 21 | 10 | 19 | 0 | 0 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.24 | 0.59 | 1.12 | 0.00 | 0.00 | 1.12 | 1.12 |
time (sec) |
N/A | 0.151 | 0.012 | 0.088 | 0.065 | 0.070 | 0.000 | 0.000 | 0.147 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 43 | 79 | 0 | 54 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.00 | 0.67 | 1.23 | 0.00 | 0.84 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.237 | 0.220 | 0.244 | 0.000 | 0.067 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 16 | 16 | 16 | 12 | 45 | 16 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.75 | 2.81 | 1.00 | 0.94 |
time (sec) |
N/A | 0.152 | 0.096 | 0.209 | 0.030 | 0.063 | 0.059 | 0.125 | 0.149 | 0.119 |
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 | 12 | 11 | 11 | 15 | 11 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 1.15 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.133 | 0.009 | 0.045 | 0.024 | 0.070 | 0.059 | 0.123 | 0.150 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 8 | 9 | 7 | 8 | 9 | 9 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.82 | 0.64 | 0.73 | 0.82 | 0.82 | 0.64 |
time (sec) |
N/A | 0.122 | 0.010 | 0.019 | 0.027 | 0.071 | 0.090 | 0.124 | 0.145 | 0.011 |
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 | 9 | 9 | 9 | 7 | 6 | 6 | 5 | 6 | 7 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.67 | 0.67 | 0.56 | 0.67 | 0.78 | 0.67 |
time (sec) |
N/A | 0.129 | 0.008 | 0.030 | 0.023 | 0.067 | 0.034 | 0.115 | 0.148 | 0.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 17 | 18 | 17 | 17 | 14 | 24 | 17 | 17 |
N.S. |
1 | 1.00 | 0.63 | 0.67 | 0.63 | 0.63 | 0.52 | 0.89 | 0.63 | 0.63 |
time (sec) |
N/A | 0.245 | 0.008 | 0.052 | 0.049 | 0.063 | 0.045 | 0.118 | 0.147 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 23 | 22 | 36 | 31 | 36 | 25 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.88 | 1.44 | 1.24 | 1.44 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.088 | 0.107 | 0.089 | 0.075 | 0.150 | 0.131 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 11 | 5 | 7 | 7 | 8 | 7 | 11 | 7 |
N.S. |
1 | 1.00 | 1.22 | 0.56 | 0.78 | 0.78 | 0.89 | 0.78 | 1.22 | 0.78 |
time (sec) |
N/A | 0.200 | 0.013 | 0.013 | 0.072 | 0.068 | 0.446 | 0.116 | 0.160 | 0.096 |
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 | 12 | 10 | 10 | 8 | 10 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 0.91 | 0.91 | 0.73 | 0.91 | 1.00 | 0.91 |
time (sec) |
N/A | 0.157 | 0.005 | 0.052 | 0.055 | 0.068 | 1.037 | 0.122 | 0.165 | 0.016 |
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 | 22 | 22 | 17 | 21 | 15 | 15 | 17 | 15 | 22 | 28 |
N.S. |
1 | 1.00 | 0.77 | 0.95 | 0.68 | 0.68 | 0.77 | 0.68 | 1.00 | 1.27 |
time (sec) |
N/A | 0.198 | 0.010 | 0.073 | 0.054 | 0.076 | 1.796 | 0.117 | 0.156 | 0.132 |
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 | 23 | 23 | 17 | 17 | 11 | 11 | 10 | 11 | 12 | 11 |
N.S. |
1 | 1.00 | 0.74 | 0.74 | 0.48 | 0.48 | 0.43 | 0.48 | 0.52 | 0.48 |
time (sec) |
N/A | 0.154 | 0.004 | 0.029 | 0.028 | 0.068 | 0.059 | 0.119 | 0.143 | 0.026 |
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 | 11 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.75 | 0.75 | 0.69 | 0.75 |
time (sec) |
N/A | 0.126 | 0.000 | 0.059 | 0.106 | 0.061 | 0.017 | 0.119 | 0.149 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 43 | 43 | 58 | 86 | 1166 | 48 | 44 | 49 |
N.S. |
1 | 1.00 | 0.75 | 0.75 | 1.02 | 1.51 | 20.46 | 0.84 | 0.77 | 0.86 |
time (sec) |
N/A | 0.170 | 0.014 | 0.119 | 0.105 | 0.088 | 2.381 | 0.124 | 0.154 | 0.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 114 | 95 | 140 | 0 | 300 | 0 | 232 | 196 | 88 |
N.S. |
1 | 0.98 | 0.82 | 1.21 | 0.00 | 2.59 | 0.00 | 2.00 | 1.69 | 0.76 |
time (sec) |
N/A | 0.184 | 0.153 | 0.130 | 0.000 | 0.088 | 0.000 | 0.153 | 0.152 | 0.086 |
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 | 16 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.75 | 0.75 | 1.00 | 0.75 |
time (sec) |
N/A | 0.111 | 0.002 | 0.074 | 0.027 | 0.063 | 0.016 | 0.122 | 0.146 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 21 | 26 | 30 | 202 | 66 | 29 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.62 | 0.76 | 0.88 | 5.94 | 1.94 | 0.85 | 0.74 |
time (sec) |
N/A | 0.136 | 0.015 | 0.115 | 0.027 | 0.064 | 0.590 | 0.113 | 0.146 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 35 | 32 | 41 | 42 | 666 | 93 | 41 | 37 |
N.S. |
1 | 1.00 | 0.66 | 0.60 | 0.77 | 0.79 | 12.57 | 1.75 | 0.77 | 0.70 |
time (sec) |
N/A | 0.146 | 0.043 | 0.117 | 0.023 | 0.066 | 0.969 | 0.124 | 0.144 | 0.026 |
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 | 35 | 35 | 35 | 28 | 42 | 70 | 68 | 32 | 38 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.20 | 2.00 | 1.94 | 0.91 | 1.09 | 0.77 |
time (sec) |
N/A | 0.134 | 0.020 | 0.095 | 0.104 | 0.073 | 0.790 | 0.127 | 0.149 | 0.084 |
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 | 39 | 39 | 39 | 32 | 47 | 90 | 44 | 38 | 51 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.21 | 2.31 | 1.13 | 0.97 | 1.31 | 0.79 |
time (sec) |
N/A | 0.135 | 0.045 | 0.112 | 0.101 | 0.079 | 0.992 | 0.124 | 0.158 | 0.030 |
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 | 12 | 11 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 0.86 | 0.71 | 0.86 | 0.79 | 0.86 |
time (sec) |
N/A | 0.114 | 0.001 | 0.103 | 0.026 | 0.066 | 0.018 | 0.120 | 0.156 | 0.011 |
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 | 32 | 32 | 23 | 21 | 26 | 19 | 162 | 23 | 18 | 25 |
N.S. |
1 | 1.00 | 0.72 | 0.66 | 0.81 | 0.59 | 5.06 | 0.72 | 0.56 | 0.78 |
time (sec) |
N/A | 0.138 | 0.012 | 0.099 | 0.030 | 0.073 | 0.625 | 0.117 | 0.157 | 0.016 |
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 | 51 | 51 | 35 | 32 | 41 | 31 | 600 | 37 | 30 | 37 |
N.S. |
1 | 1.00 | 0.69 | 0.63 | 0.80 | 0.61 | 11.76 | 0.73 | 0.59 | 0.73 |
time (sec) |
N/A | 0.151 | 0.017 | 0.092 | 0.033 | 0.070 | 0.916 | 0.120 | 0.150 | 0.021 |
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 | 23 | 23 | 23 | 18 | 32 | 53 | 24 | 21 | 31 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 1.39 | 2.30 | 1.04 | 0.91 | 1.35 | 0.74 |
time (sec) |
N/A | 0.123 | 0.014 | 0.097 | 0.100 | 0.081 | 0.538 | 0.123 | 0.151 | 0.086 |
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 | 41 | 41 | 41 | 34 | 60 | 90 | 44 | 44 | 51 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.46 | 2.20 | 1.07 | 1.07 | 1.24 | 0.80 |
time (sec) |
N/A | 0.138 | 0.040 | 0.105 | 0.101 | 0.077 | 1.109 | 0.121 | 0.152 | 0.031 |
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 | 23 | 23 | 26 | 25 | 21 | 25 | 24 | 21 | 24 | 21 |
N.S. |
1 | 1.00 | 1.13 | 1.09 | 0.91 | 1.09 | 1.04 | 0.91 | 1.04 | 0.91 |
time (sec) |
N/A | 0.121 | 0.004 | 0.102 | 0.030 | 0.076 | 0.020 | 0.111 | 0.164 | 0.142 |
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 | 48 | 48 | 38 | 43 | 45 | 58 | 216 | 86 | 51 | 94 |
N.S. |
1 | 1.00 | 0.79 | 0.90 | 0.94 | 1.21 | 4.50 | 1.79 | 1.06 | 1.96 |
time (sec) |
N/A | 0.148 | 0.023 | 0.099 | 0.030 | 0.077 | 0.315 | 0.126 | 0.160 | 0.253 |
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 | 55 | 54 | 48 | 37 | 52 | 37 | 230 | 52 | 36 | 43 |
N.S. |
1 | 0.98 | 0.87 | 0.67 | 0.95 | 0.67 | 4.18 | 0.95 | 0.65 | 0.78 |
time (sec) |
N/A | 0.219 | 0.018 | 0.213 | 0.099 | 0.085 | 0.438 | 0.121 | 0.146 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 38 | 11 | 14 | 14 | 10 | 26 | 9 | 10 |
N.S. |
1 | 1.00 | 3.17 | 0.92 | 1.17 | 1.17 | 0.83 | 2.17 | 0.75 | 0.83 |
time (sec) |
N/A | 0.116 | 0.002 | 0.105 | 0.026 | 0.068 | 0.056 | 0.124 | 0.163 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 39 | 34 | 71 | 34 | 119 | 39 | 28 | 30 |
N.S. |
1 | 1.00 | 0.91 | 0.79 | 1.65 | 0.79 | 2.77 | 0.91 | 0.65 | 0.70 |
time (sec) |
N/A | 0.135 | 0.034 | 0.076 | 0.035 | 0.068 | 1.634 | 0.125 | 0.158 | 0.124 |
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 | 22 | 22 | 22 | 17 | 16 | 16 | 20 | 16 | 13 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.73 | 0.73 | 0.91 | 0.73 | 0.59 | 0.73 |
time (sec) |
N/A | 0.199 | 0.009 | 0.054 | 0.038 | 0.077 | 0.104 | 0.123 | 0.153 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 18 | 8 | 11 | 33 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.38 | 0.62 | 0.85 | 2.54 | 0.85 |
time (sec) |
N/A | 0.117 | 0.002 | 0.096 | 0.024 | 0.068 | 0.243 | 0.107 | 0.159 | 0.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 16 | 18 | 19 | 6 | 6 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 2.00 | 2.25 | 2.38 | 0.75 | 0.75 | 2.00 |
time (sec) |
N/A | 0.116 | 0.091 | 0.213 | 0.103 | 0.085 | 0.486 | 0.120 | 0.152 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 11 | 25 | 25 | 8 | 25 | 29 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 1.79 | 1.79 | 0.57 | 1.79 | 2.07 | 0.71 |
time (sec) |
N/A | 0.130 | 0.012 | 0.152 | 0.022 | 0.069 | 0.442 | 0.113 | 0.151 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 26 | 14 | 0 | 22 | 0 | 22 | 26 | 18 |
N.S. |
1 | 1.00 | 1.44 | 0.78 | 0.00 | 1.22 | 0.00 | 1.22 | 1.44 | 1.00 |
time (sec) |
N/A | 0.143 | 0.042 | 0.165 | 0.000 | 0.071 | 0.000 | 0.122 | 0.149 | 0.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 29 | 23 | 17 | 55 | 0 | 0 | 19 | 32 |
N.S. |
1 | 1.00 | 0.97 | 0.77 | 0.57 | 1.83 | 0.00 | 0.00 | 0.63 | 1.07 |
time (sec) |
N/A | 0.145 | 0.094 | 0.467 | 0.108 | 0.073 | 0.000 | 0.000 | 0.145 | 0.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 15 | 14 | 17 | 0 | 35 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.82 | 1.00 | 0.00 | 2.06 | 0.76 | 0.82 |
time (sec) |
N/A | 0.121 | 0.108 | 0.112 | 0.102 | 0.068 | 0.000 | 0.126 | 0.149 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 16 | 3 | 2 | 14 | 2 | 25 | 9 | 2 |
N.S. |
1 | 1.00 | 8.00 | 1.50 | 1.00 | 7.00 | 1.00 | 12.50 | 4.50 | 1.00 |
time (sec) |
N/A | 0.108 | 0.009 | 0.099 | 0.106 | 0.068 | 0.056 | 0.123 | 0.143 | 0.074 |
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 | 30 | 15 | 14 | 14 | 17 | 0 | 11 | 14 |
N.S. |
1 | 1.00 | 1.50 | 0.75 | 0.70 | 0.70 | 0.85 | 0.00 | 0.55 | 0.70 |
time (sec) |
N/A | 0.494 | 0.009 | 0.269 | 0.024 | 0.077 | 0.186 | 0.000 | 0.151 | 0.165 |