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 | 62 | 62 | 62 | 55 | 54 | 54 | 61 | 54 | 57 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.87 | 0.87 | 0.98 | 0.87 | 0.92 | 0.87 |
time (sec) |
N/A | 0.338 | 0.012 | 0.243 | 0.027 | 0.059 | 0.020 | 0.119 | 0.214 | 0.140 |
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 | 51 | 51 | 51 | 44 | 43 | 43 | 49 | 43 | 46 | 43 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.84 | 0.84 | 0.96 | 0.84 | 0.90 | 0.84 |
time (sec) |
N/A | 0.163 | 0.001 | 0.238 | 0.034 | 0.060 | 0.024 | 0.121 | 0.251 | 0.014 |
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 | 35 | 35 | 35 | 32 | 31 | 31 | 32 | 31 | 35 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.89 | 0.89 | 0.91 | 0.89 | 1.00 | 0.89 |
time (sec) |
N/A | 0.154 | 0.001 | 0.239 | 0.033 | 0.059 | 0.022 | 0.123 | 0.210 | 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 | 25 | 25 | 25 | 22 | 21 | 21 | 22 | 21 | 24 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.84 | 0.84 | 0.88 | 0.84 | 0.96 | 0.84 |
time (sec) |
N/A | 0.138 | 0.001 | 0.242 | 0.027 | 0.063 | 0.019 | 0.122 | 0.218 | 0.036 |
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 | 0.128 | 0.000 | 0.044 | 0.027 | 0.059 | 0.016 | 0.123 | 0.222 | 0.046 |
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 | 24 | 24 | 24 | 16 | 15 | 67 | 53 | 15 | 23 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.62 | 2.79 | 2.21 | 0.62 | 0.96 | 0.67 |
time (sec) |
N/A | 0.216 | 0.007 | 0.379 | 0.110 | 0.073 | 0.061 | 0.121 | 0.269 | 0.066 |
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 | 45 | 45 | 45 | 36 | 35 | 120 | 78 | 35 | 61 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.78 | 2.67 | 1.73 | 0.78 | 1.36 | 0.73 |
time (sec) |
N/A | 0.136 | 0.017 | 0.391 | 0.113 | 0.071 | 0.128 | 0.119 | 0.240 | 0.114 |
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 | 62 | 70 | 55 | 57 | 58 | 188 | 105 | 45 | 113 | 55 |
N.S. |
1 | 1.13 | 0.89 | 0.92 | 0.94 | 3.03 | 1.69 | 0.73 | 1.82 | 0.89 |
time (sec) |
N/A | 0.149 | 0.021 | 0.389 | 0.110 | 0.072 | 0.171 | 0.119 | 0.228 | 0.066 |
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 | 79 | 95 | 66 | 78 | 80 | 254 | 129 | 56 | 162 | 77 |
N.S. |
1 | 1.20 | 0.84 | 0.99 | 1.01 | 3.22 | 1.63 | 0.71 | 2.05 | 0.97 |
time (sec) |
N/A | 0.165 | 0.022 | 0.412 | 0.111 | 0.077 | 0.205 | 0.115 | 0.293 | 0.094 |
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 | 51 | 51 | 51 | 44 | 43 | 43 | 49 | 43 | 46 | 43 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.84 | 0.84 | 0.96 | 0.84 | 0.90 | 0.84 |
time (sec) |
N/A | 0.162 | 0.001 | 0.250 | 0.036 | 0.058 | 0.031 | 0.121 | 0.249 | 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 | 36 | 36 | 36 | 33 | 32 | 32 | 32 | 32 | 35 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.89 | 0.89 | 0.89 | 0.89 | 0.97 | 0.89 |
time (sec) |
N/A | 0.153 | 0.001 | 0.244 | 0.029 | 0.060 | 0.020 | 0.125 | 0.194 | 0.024 |
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 | 25 | 25 | 25 | 22 | 21 | 21 | 22 | 21 | 24 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.84 | 0.84 | 0.88 | 0.84 | 0.96 | 0.84 |
time (sec) |
N/A | 0.141 | 0.001 | 0.241 | 0.032 | 0.054 | 0.019 | 0.119 | 0.259 | 0.017 |
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 | 13 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 1.08 | 0.83 |
time (sec) |
N/A | 0.129 | 0.000 | 0.048 | 0.029 | 0.057 | 0.016 | 0.120 | 0.232 | 0.012 |
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 | 24 | 24 | 24 | 16 | 31 | 68 | 46 | 18 | 38 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 1.29 | 2.83 | 1.92 | 0.75 | 1.58 | 0.67 |
time (sec) |
N/A | 0.123 | 0.003 | 0.355 | 0.110 | 0.066 | 0.067 | 0.124 | 0.231 | 0.156 |
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 | 46 | 46 | 47 | 37 | 52 | 126 | 71 | 39 | 102 | 34 |
N.S. |
1 | 1.00 | 1.02 | 0.80 | 1.13 | 2.74 | 1.54 | 0.85 | 2.22 | 0.74 |
time (sec) |
N/A | 0.136 | 0.011 | 0.375 | 0.109 | 0.066 | 0.119 | 0.119 | 0.238 | 0.044 |
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 | 64 | 72 | 56 | 59 | 73 | 188 | 99 | 49 | 178 | 55 |
N.S. |
1 | 1.12 | 0.88 | 0.92 | 1.14 | 2.94 | 1.55 | 0.77 | 2.78 | 0.86 |
time (sec) |
N/A | 0.150 | 0.023 | 0.370 | 0.113 | 0.075 | 0.158 | 0.124 | 0.253 | 0.080 |
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 | 82 | 98 | 67 | 81 | 97 | 260 | 122 | 60 | 254 | 78 |
N.S. |
1 | 1.20 | 0.82 | 0.99 | 1.18 | 3.17 | 1.49 | 0.73 | 3.10 | 0.95 |
time (sec) |
N/A | 0.165 | 0.022 | 0.379 | 0.105 | 0.071 | 0.223 | 0.119 | 0.223 | 0.078 |
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 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 0.86 | 0.71 | 0.86 | 0.93 | 0.93 |
time (sec) |
N/A | 0.143 | 0.000 | 0.245 | 0.034 | 0.056 | 0.018 | 0.125 | 0.241 | 0.044 |
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 | 10 | 10 | 10 | 11 | 10 | 10 | 20 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.00 | 2.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.117 | 0.002 | 0.405 | 0.105 | 0.062 | 0.046 | 0.118 | 0.201 | 0.061 |
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 | 24 | 24 | 24 | 16 | 15 | 67 | 53 | 15 | 23 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.62 | 2.79 | 2.21 | 0.62 | 0.96 | 0.67 |
time (sec) |
N/A | 0.125 | 0.002 | 0.342 | 0.109 | 0.076 | 0.076 | 0.123 | 0.264 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 27 | 23 | 23 | 34 | 20 | 25 | 41 | 17 |
N.S. |
1 | 1.00 | 1.29 | 1.10 | 1.10 | 1.62 | 0.95 | 1.19 | 1.95 | 0.81 |
time (sec) |
N/A | 0.124 | 0.007 | 0.290 | 0.025 | 0.061 | 0.044 | 0.122 | 0.238 | 0.063 |
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 | 30 | 30 | 28 | 20 | 0 | 82 | 83 | 23 | 29 | 23 |
N.S. |
1 | 1.00 | 0.93 | 0.67 | 0.00 | 2.73 | 2.77 | 0.77 | 0.97 | 0.77 |
time (sec) |
N/A | 0.139 | 0.006 | 0.467 | 0.000 | 0.069 | 0.099 | 0.119 | 0.236 | 0.141 |
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 | 37 | 37 | 44 | 33 | 0 | 102 | 87 | 33 | 45 | 29 |
N.S. |
1 | 1.00 | 1.19 | 0.89 | 0.00 | 2.76 | 2.35 | 0.89 | 1.22 | 0.78 |
time (sec) |
N/A | 0.149 | 0.009 | 0.527 | 0.000 | 0.071 | 0.137 | 0.125 | 0.259 | 0.202 |
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 | 34 | 34 | 36 | 34 | 0 | 106 | 60 | 37 | 46 | 38 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 0.00 | 3.12 | 1.76 | 1.09 | 1.35 | 1.12 |
time (sec) |
N/A | 0.139 | 0.009 | 0.515 | 0.000 | 0.068 | 0.147 | 0.119 | 0.235 | 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 | 34 | 34 | 36 | 34 | 0 | 105 | 66 | 36 | 48 | 38 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 0.00 | 3.09 | 1.94 | 1.06 | 1.41 | 1.12 |
time (sec) |
N/A | 0.132 | 0.006 | 0.509 | 0.000 | 0.072 | 0.151 | 0.118 | 0.211 | 0.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 50 | 39 | 0 | 182 | 104 | 58 | 65 | 46 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.00 | 3.64 | 2.08 | 1.16 | 1.30 | 0.92 |
time (sec) |
N/A | 0.165 | 0.012 | 0.596 | 0.000 | 0.070 | 0.168 | 0.124 | 0.310 | 0.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 23 | 7 | 17 | 17 | 15 | 15 | 17 | 6 |
N.S. |
1 | 1.00 | 3.83 | 1.17 | 2.83 | 2.83 | 2.50 | 2.50 | 2.83 | 1.00 |
time (sec) |
N/A | 0.114 | 0.002 | 0.287 | 0.024 | 0.061 | 0.075 | 0.121 | 0.247 | 0.099 |
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 | 23 | 14 | 17 | 17 | 15 | 19 | 17 | 6 |
N.S. |
1 | 1.00 | 1.10 | 0.67 | 0.81 | 0.81 | 0.71 | 0.90 | 0.81 | 0.29 |
time (sec) |
N/A | 0.136 | 0.001 | 0.361 | 0.025 | 0.061 | 0.046 | 0.121 | 0.255 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | B | A | B | F(-2) | F | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 0 | 138 | 221 | 475 | 3553 | 0 | 55 | 141 |
N.S. |
1 | 1.00 | 0.00 | 1.19 | 1.91 | 4.09 | 30.63 | 0.00 | 0.47 | 1.22 |
time (sec) |
N/A | 0.246 | 0.000 | 0.592 | 0.138 | 0.795 | 1.902 | 0.000 | 200.046 | 0.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | B | A | B | F(-2) | F | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 146 | 0 | 179 | 562 | 475 | 1093 | 0 | 79 | 141 |
N.S. |
1 | 1.26 | 0.00 | 1.54 | 4.84 | 4.09 | 9.42 | 0.00 | 0.68 | 1.22 |
time (sec) |
N/A | 0.319 | 0.000 | 0.627 | 0.175 | 0.727 | 1.433 | 0.000 | 200.059 | 0.247 |
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 | 34 | 39 | 39 | 30 | 29 | 33 | 29 | 33 | 19 | 44 |
N.S. |
1 | 1.15 | 1.15 | 0.88 | 0.85 | 0.97 | 0.85 | 0.97 | 0.56 | 1.29 |
time (sec) |
N/A | 0.149 | 0.018 | 0.329 | 0.123 | 0.068 | 0.710 | 0.126 | 0.198 | 0.123 |
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 | 34 | 36 | 36 | 28 | 32 | 33 | 75 | 25 | 19 | 26 |
N.S. |
1 | 1.06 | 1.06 | 0.82 | 0.94 | 0.97 | 2.21 | 0.74 | 0.56 | 0.76 |
time (sec) |
N/A | 0.148 | 0.019 | 0.340 | 0.106 | 0.073 | 0.586 | 0.126 | 0.221 | 0.121 |
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 | 34 | 44 | 44 | 31 | 30 | 33 | 29 | 24 | 19 | 26 |
N.S. |
1 | 1.29 | 1.29 | 0.91 | 0.88 | 0.97 | 0.85 | 0.71 | 0.56 | 0.76 |
time (sec) |
N/A | 0.148 | 0.016 | 0.349 | 0.112 | 0.069 | 0.709 | 0.132 | 0.253 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 39 | 44 | 30 | 46 | 71 | 110 | 61 | 68 | 43 |
N.S. |
1 | 1.15 | 1.29 | 0.88 | 1.35 | 2.09 | 3.24 | 1.79 | 2.00 | 1.26 |
time (sec) |
N/A | 0.136 | 0.017 | 0.377 | 0.112 | 0.074 | 0.518 | 0.135 | 0.211 | 0.181 |
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 | 34 | 36 | 44 | 24 | 56 | 71 | 70 | 51 | 68 | 43 |
N.S. |
1 | 1.06 | 1.29 | 0.71 | 1.65 | 2.09 | 2.06 | 1.50 | 2.00 | 1.26 |
time (sec) |
N/A | 0.137 | 0.009 | 0.421 | 0.117 | 0.070 | 0.512 | 0.134 | 0.255 | 0.110 |
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 | 34 | 44 | 44 | 31 | 68 | 71 | 110 | 51 | 68 | 43 |
N.S. |
1 | 1.29 | 1.29 | 0.91 | 2.00 | 2.09 | 3.24 | 1.50 | 2.00 | 1.26 |
time (sec) |
N/A | 0.135 | 0.010 | 0.416 | 0.104 | 0.074 | 0.518 | 0.125 | 0.218 | 0.070 |
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 | 84 | 90 | 71 | 59 | 58 | 146 | 97 | 63 | 80 | 37 |
N.S. |
1 | 1.07 | 0.85 | 0.70 | 0.69 | 1.74 | 1.15 | 0.75 | 0.95 | 0.44 |
time (sec) |
N/A | 0.167 | 0.096 | 0.438 | 0.029 | 0.080 | 2.579 | 0.133 | 0.235 | 0.173 |
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 | 65 | 68 | 60 | 48 | 43 | 124 | 70 | 49 | 61 | 37 |
N.S. |
1 | 1.05 | 0.92 | 0.74 | 0.66 | 1.91 | 1.08 | 0.75 | 0.94 | 0.57 |
time (sec) |
N/A | 0.149 | 0.047 | 0.412 | 0.026 | 0.081 | 1.611 | 0.131 | 0.220 | 0.080 |
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 | 46 | 46 | 48 | 36 | 28 | 94 | 41 | 37 | 40 | 35 |
N.S. |
1 | 1.00 | 1.04 | 0.78 | 0.61 | 2.04 | 0.89 | 0.80 | 0.87 | 0.76 |
time (sec) |
N/A | 0.139 | 0.028 | 0.408 | 0.028 | 0.078 | 0.974 | 0.123 | 0.222 | 0.118 |
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 | 25 | 25 | 25 | 21 | 13 | 59 | 17 | 37 | 25 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.52 | 2.36 | 0.68 | 1.48 | 1.00 | 0.80 |
time (sec) |
N/A | 0.126 | 0.004 | 0.367 | 0.030 | 0.073 | 0.580 | 0.122 | 0.205 | 0.094 |
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 | 15 | 14 | 23 | 17 | 14 | 39 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 1.44 | 1.06 | 0.88 | 2.44 | 0.88 |
time (sec) |
N/A | 0.119 | 0.023 | 0.365 | 0.032 | 0.066 | 0.458 | 0.127 | 0.244 | 0.033 |
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 | 39 | 39 | 29 | 26 | 31 | 47 | 95 | 27 | 84 | 28 |
N.S. |
1 | 1.00 | 0.74 | 0.67 | 0.79 | 1.21 | 2.44 | 0.69 | 2.15 | 0.72 |
time (sec) |
N/A | 0.132 | 0.037 | 0.375 | 0.044 | 0.071 | 0.464 | 0.130 | 0.249 | 0.082 |
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 | 58 | 66 | 40 | 37 | 46 | 69 | 413 | 41 | 127 | 44 |
N.S. |
1 | 1.14 | 0.69 | 0.64 | 0.79 | 1.19 | 7.12 | 0.71 | 2.19 | 0.76 |
time (sec) |
N/A | 0.146 | 0.048 | 0.388 | 0.031 | 0.071 | 0.796 | 0.126 | 0.205 | 0.103 |
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 | 77 | 93 | 51 | 48 | 61 | 91 | 1265 | 55 | 170 | 61 |
N.S. |
1 | 1.21 | 0.66 | 0.62 | 0.79 | 1.18 | 16.43 | 0.71 | 2.21 | 0.79 |
time (sec) |
N/A | 0.164 | 0.055 | 0.393 | 0.047 | 0.076 | 1.169 | 0.131 | 0.225 | 0.109 |
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 | 25 | 25 | 25 | 21 | 13 | 59 | 17 | 37 | 25 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.52 | 2.36 | 0.68 | 1.48 | 1.00 | 0.80 |
time (sec) |
N/A | 0.130 | 0.000 | 0.365 | 0.030 | 0.072 | 0.513 | 0.119 | 0.242 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 21 | 13 | 72 | 46 | 43 | 15 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.50 | 2.77 | 1.77 | 1.65 | 0.58 | 0.96 |
time (sec) |
N/A | 0.126 | 0.004 | 0.619 | 0.106 | 0.069 | 0.576 | 0.127 | 0.222 | 0.125 |
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 | 27 | 27 | 27 | 23 | 26 | 63 | 46 | 41 | 27 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.96 | 2.33 | 1.70 | 1.52 | 1.00 | 0.81 |
time (sec) |
N/A | 0.132 | 0.004 | 0.381 | 0.025 | 0.069 | 0.636 | 0.121 | 0.204 | 0.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 23 | 14 | 74 | 20 | 47 | 27 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.50 | 2.64 | 0.71 | 1.68 | 0.96 | 0.96 |
time (sec) |
N/A | 0.130 | 0.004 | 0.609 | 0.035 | 0.074 | 0.624 | 0.126 | 0.213 | 0.087 |
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 | 27 | 37 | 20 | 19 | 29 | 22 | 29 | 29 | 16 |
N.S. |
1 | 1.00 | 1.37 | 0.74 | 0.70 | 1.07 | 0.81 | 1.07 | 1.07 | 0.59 |
time (sec) |
N/A | 0.128 | 0.018 | 0.370 | 0.110 | 0.066 | 0.103 | 0.121 | 0.236 | 0.022 |
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 | 27 | 41 | 20 | 19 | 32 | 22 | 19 | 18 | 18 |
N.S. |
1 | 1.00 | 1.52 | 0.74 | 0.70 | 1.19 | 0.81 | 0.70 | 0.67 | 0.67 |
time (sec) |
N/A | 0.124 | 0.032 | 0.548 | 0.103 | 0.063 | 0.081 | 0.120 | 0.199 | 0.075 |
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 | 36 | 36 | 37 | 30 | 31 | 29 | 31 | 30 | 29 | 29 |
N.S. |
1 | 1.00 | 1.03 | 0.83 | 0.86 | 0.81 | 0.86 | 0.83 | 0.81 | 0.81 |
time (sec) |
N/A | 0.134 | 0.018 | 0.437 | 0.107 | 0.062 | 0.127 | 0.121 | 0.226 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | C | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 29 | 19 | 59 | 34 | 0 | 19 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.53 | 1.64 | 0.94 | 0.00 | 0.53 | 0.78 |
time (sec) |
N/A | 0.135 | 0.109 | 0.526 | 0.105 | 0.066 | 0.177 | 0.000 | 0.236 | 0.023 |
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 | 10 | 10 | 20 | 7 | 6 | 16 | 7 | 29 | 17 | 6 |
N.S. |
1 | 1.00 | 2.00 | 0.70 | 0.60 | 1.60 | 0.70 | 2.90 | 1.70 | 0.60 |
time (sec) |
N/A | 0.113 | 0.010 | 0.302 | 0.105 | 0.061 | 0.070 | 0.126 | 0.218 | 0.019 |
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 | 10 | 10 | 19 | 7 | 6 | 19 | 7 | 19 | 6 | 6 |
N.S. |
1 | 1.00 | 1.90 | 0.70 | 0.60 | 1.90 | 0.70 | 1.90 | 0.60 | 0.60 |
time (sec) |
N/A | 0.112 | 0.019 | 0.336 | 0.105 | 0.066 | 0.072 | 0.122 | 0.205 | 0.005 |
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 | 19 | 19 | 43 | 19 | 18 | 16 | 15 | 30 | 17 | 16 |
N.S. |
1 | 1.00 | 2.26 | 1.00 | 0.95 | 0.84 | 0.79 | 1.58 | 0.89 | 0.84 |
time (sec) |
N/A | 0.124 | 0.002 | 0.333 | 0.102 | 0.062 | 0.074 | 0.124 | 0.208 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | C | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 8 | 6 | 47 | 17 | 0 | 7 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.42 | 0.32 | 2.47 | 0.89 | 0.00 | 0.37 | 0.79 |
time (sec) |
N/A | 0.123 | 0.002 | 0.313 | 0.111 | 0.067 | 0.165 | 0.000 | 0.226 | 0.067 |
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 | 17 | 17 | 30 | 12 | 11 | 65 | 14 | 35 | 23 | 11 |
N.S. |
1 | 1.00 | 1.76 | 0.71 | 0.65 | 3.82 | 0.82 | 2.06 | 1.35 | 0.65 |
time (sec) |
N/A | 0.119 | 0.025 | 0.306 | 0.026 | 0.071 | 0.489 | 0.132 | 0.218 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 31 | 12 | 11 | 58 | 37 | 41 | 12 | 15 |
N.S. |
1 | 1.00 | 1.82 | 0.71 | 0.65 | 3.41 | 2.18 | 2.41 | 0.71 | 0.88 |
time (sec) |
N/A | 0.120 | 0.032 | 0.567 | 0.104 | 0.067 | 0.550 | 0.120 | 0.212 | 0.030 |
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 | 25 | 25 | 25 | 21 | 24 | 57 | 37 | 36 | 23 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.96 | 2.28 | 1.48 | 1.44 | 0.92 | 0.80 |
time (sec) |
N/A | 0.126 | 0.003 | 0.303 | 0.028 | 0.070 | 0.539 | 0.120 | 0.221 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 21 | 12 | 68 | 17 | 42 | 14 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.46 | 2.62 | 0.65 | 1.62 | 0.54 | 0.96 |
time (sec) |
N/A | 0.125 | 0.003 | 0.648 | 0.032 | 0.072 | 0.510 | 0.127 | 0.210 | 0.046 |
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 | 19 | 19 | 28 | 14 | 13 | 59 | 17 | 36 | 25 | 20 |
N.S. |
1 | 1.00 | 1.47 | 0.74 | 0.68 | 3.11 | 0.89 | 1.89 | 1.32 | 1.05 |
time (sec) |
N/A | 0.123 | 0.017 | 0.355 | 0.034 | 0.071 | 0.521 | 0.123 | 0.205 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 37 | 14 | 13 | 62 | 46 | 43 | 15 | 25 |
N.S. |
1 | 1.00 | 1.95 | 0.74 | 0.68 | 3.26 | 2.42 | 2.26 | 0.79 | 1.32 |
time (sec) |
N/A | 0.121 | 0.030 | 0.752 | 0.106 | 0.075 | 0.549 | 0.122 | 0.198 | 0.065 |
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 | 27 | 27 | 27 | 23 | 26 | 74 | 46 | 41 | 27 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.96 | 2.74 | 1.70 | 1.52 | 1.00 | 0.81 |
time (sec) |
N/A | 0.129 | 0.004 | 0.332 | 0.029 | 0.076 | 0.554 | 0.127 | 0.252 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 23 | 14 | 74 | 20 | 47 | 27 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.50 | 2.64 | 0.71 | 1.68 | 0.96 | 0.96 |
time (sec) |
N/A | 0.129 | 0.004 | 0.741 | 0.028 | 0.072 | 0.667 | 0.121 | 0.209 | 0.098 |
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 | 16 | 16 | 16 | 15 | 6 | 23 | 19 | 28 | 6 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.38 | 1.44 | 1.19 | 1.75 | 0.38 | 0.88 |
time (sec) |
N/A | 0.122 | 0.003 | 0.572 | 0.108 | 0.069 | 0.536 | 0.128 | 0.222 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 288 | 47 | 0 | 0 | 0 | 26 | 0 | 45 | 37 |
N.S. |
1 | 1.01 | 0.16 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.16 | 0.13 |
time (sec) |
N/A | 0.250 | 4.788 | 0.000 | 0.000 | 0.000 | 0.574 | 0.000 | 0.297 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 266 | 46 | 0 | 0 | 0 | 26 | 0 | 27 | 37 |
N.S. |
1 | 1.00 | 0.17 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 | 0.10 | 0.14 |
time (sec) |
N/A | 0.239 | 3.776 | 0.000 | 0.000 | 0.000 | 0.490 | 0.000 | 0.233 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 246 | 46 | 0 | 0 | 0 | 24 | 0 | 11 | 37 |
N.S. |
1 | 1.00 | 0.19 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 | 0.04 | 0.15 |
time (sec) |
N/A | 0.223 | 3.578 | 0.000 | 0.000 | 0.000 | 0.454 | 0.000 | 0.225 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 271 | 55 | 0 | 0 | 0 | 24 | 0 | 30 | 37 |
N.S. |
1 | 1.00 | 0.20 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.11 | 0.14 |
time (sec) |
N/A | 0.237 | 4.703 | 0.000 | 0.000 | 0.000 | 0.552 | 0.000 | 0.271 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 298 | 72 | 0 | 0 | 0 | 24 | 0 | 50 | 37 |
N.S. |
1 | 1.03 | 0.25 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 | 0.17 | 0.13 |
time (sec) |
N/A | 0.258 | 5.511 | 0.000 | 0.000 | 0.000 | 0.701 | 0.000 | 0.237 | 0.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 569 | 614 | 47 | 0 | 0 | 0 | 26 | 0 | 45 | 37 |
N.S. |
1 | 1.08 | 0.08 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 | 0.08 | 0.07 |
time (sec) |
N/A | 0.450 | 5.498 | 0.000 | 0.000 | 0.000 | 0.565 | 0.000 | 0.242 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 550 | 592 | 46 | 0 | 0 | 0 | 26 | 0 | 27 | 37 |
N.S. |
1 | 1.08 | 0.08 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 | 0.05 | 0.07 |
time (sec) |
N/A | 0.427 | 4.625 | 0.000 | 0.000 | 0.000 | 0.506 | 0.000 | 0.282 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 529 | 574 | 46 | 0 | 0 | 0 | 24 | 0 | 11 | 37 |
N.S. |
1 | 1.09 | 0.09 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 | 0.02 | 0.07 |
time (sec) |
N/A | 0.440 | 3.767 | 0.000 | 0.000 | 0.000 | 0.431 | 0.000 | 0.232 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 552 | 597 | 58 | 0 | 0 | 0 | 24 | 0 | 30 | 37 |
N.S. |
1 | 1.08 | 0.11 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 | 0.05 | 0.07 |
time (sec) |
N/A | 0.468 | 4.187 | 0.000 | 0.000 | 0.000 | 0.495 | 0.000 | 0.226 | 0.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 574 | 624 | 75 | 0 | 0 | 0 | 24 | 0 | 50 | 37 |
N.S. |
1 | 1.09 | 0.13 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 | 0.09 | 0.06 |
time (sec) |
N/A | 0.459 | 5.259 | 0.000 | 0.000 | 0.000 | 0.613 | 0.000 | 0.238 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 97 | 47 | 0 | 0 | 0 | 26 | 0 | 45 | 37 |
N.S. |
1 | 1.05 | 0.51 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 | 0.49 | 0.40 |
time (sec) |
N/A | 0.182 | 6.647 | 0.000 | 0.000 | 0.000 | 0.623 | 0.000 | 0.262 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 96 | 46 | 0 | 0 | 0 | 26 | 0 | 27 | 37 |
N.S. |
1 | 1.04 | 0.50 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 | 0.29 | 0.40 |
time (sec) |
N/A | 0.184 | 5.988 | 0.000 | 0.000 | 0.000 | 0.524 | 0.000 | 0.317 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 46 | 0 | 0 | 0 | 26 | 0 | 27 | 37 |
N.S. |
1 | 1.00 | 0.61 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 | 0.36 | 0.49 |
time (sec) |
N/A | 0.165 | 5.322 | 0.000 | 0.000 | 0.000 | 0.497 | 0.000 | 0.235 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 75 | 46 | 0 | 0 | 0 | 24 | 0 | 11 | 37 |
N.S. |
1 | 1.06 | 0.65 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 | 0.15 | 0.52 |
time (sec) |
N/A | 0.171 | 5.069 | 0.000 | 0.000 | 0.000 | 0.459 | 0.000 | 0.250 | 0.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 46 | 0 | 0 | 0 | 24 | 0 | 11 | 37 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 | 0.20 | 0.66 |
time (sec) |
N/A | 0.154 | 5.054 | 0.000 | 0.000 | 0.000 | 0.463 | 0.000 | 0.217 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 55 | 0 | 0 | 0 | 24 | 0 | 30 | 37 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 | 0.54 | 0.66 |
time (sec) |
N/A | 0.156 | 5.517 | 0.000 | 0.000 | 0.000 | 0.496 | 0.000 | 0.191 | 0.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 55 | 0 | 0 | 0 | 24 | 0 | 30 | 37 |
N.S. |
1 | 1.00 | 0.71 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 | 0.38 | 0.47 |
time (sec) |
N/A | 0.162 | 6.163 | 0.000 | 0.000 | 0.000 | 0.588 | 0.000 | 0.211 | 0.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 72 | 0 | 0 | 0 | 24 | 0 | 50 | 37 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 | 0.64 | 0.47 |
time (sec) |
N/A | 0.160 | 6.806 | 0.000 | 0.000 | 0.000 | 0.745 | 0.000 | 0.210 | 0.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 101 | 48 | 0 | 0 | 0 | 27 | 0 | 48 | 38 |
N.S. |
1 | 1.05 | 0.50 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 | 0.50 | 0.40 |
time (sec) |
N/A | 0.179 | 6.775 | 0.000 | 0.000 | 0.000 | 0.642 | 0.000 | 0.245 | 0.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 47 | 0 | 0 | 0 | 27 | 0 | 29 | 38 |
N.S. |
1 | 1.00 | 0.60 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 | 0.37 | 0.49 |
time (sec) |
N/A | 0.170 | 6.094 | 0.000 | 0.000 | 0.000 | 0.558 | 0.000 | 0.260 | 0.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 47 | 0 | 0 | 0 | 27 | 0 | 29 | 38 |
N.S. |
1 | 1.00 | 0.60 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 | 0.37 | 0.49 |
time (sec) |
N/A | 0.164 | 5.460 | 0.000 | 0.000 | 0.000 | 0.523 | 0.000 | 0.212 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 47 | 0 | 0 | 0 | 26 | 0 | 12 | 38 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 | 0.21 | 0.66 |
time (sec) |
N/A | 0.153 | 5.237 | 0.000 | 0.000 | 0.000 | 0.596 | 0.000 | 0.208 | 0.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 47 | 0 | 0 | 0 | 26 | 0 | 12 | 38 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 | 0.21 | 0.66 |
time (sec) |
N/A | 0.150 | 5.145 | 0.000 | 0.000 | 0.000 | 0.524 | 0.000 | 0.218 | 0.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 56 | 0 | 0 | 0 | 26 | 0 | 33 | 38 |
N.S. |
1 | 1.00 | 0.73 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 | 0.43 | 0.49 |
time (sec) |
N/A | 0.162 | 5.699 | 0.000 | 0.000 | 0.000 | 0.510 | 0.000 | 0.251 | 0.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 56 | 0 | 0 | 0 | 26 | 0 | 33 | 38 |
N.S. |
1 | 1.00 | 0.69 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 | 0.41 | 0.47 |
time (sec) |
N/A | 0.162 | 6.414 | 0.000 | 0.000 | 0.000 | 0.616 | 0.000 | 0.219 | 0.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 105 | 74 | 0 | 0 | 0 | 26 | 0 | 53 | 38 |
N.S. |
1 | 1.04 | 0.73 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 | 0.52 | 0.38 |
time (sec) |
N/A | 0.175 | 6.923 | 0.000 | 0.000 | 0.000 | 0.747 | 0.000 | 0.188 | 0.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 23 | 20 | 0 | 0 | 24 | 0 | 26 | 18 |
N.S. |
1 | 1.00 | 0.70 | 0.61 | 0.00 | 0.00 | 0.73 | 0.00 | 0.79 | 0.55 |
time (sec) |
N/A | 0.143 | 10.009 | 0.472 | 0.000 | 0.000 | 0.580 | 0.000 | 0.239 | 0.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 29 | 19 | 0 | 0 | 26 | 0 | 28 | 17 |
N.S. |
1 | 1.00 | 0.88 | 0.58 | 0.00 | 0.00 | 0.79 | 0.00 | 0.85 | 0.52 |
time (sec) |
N/A | 0.145 | 10.008 | 0.395 | 0.000 | 0.000 | 0.617 | 0.000 | 0.228 | 0.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 47 | 0 | 0 | 0 | 26 | 0 | 31 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 | 0.66 | 0.79 |
time (sec) |
N/A | 0.150 | 7.723 | 0.000 | 0.000 | 0.000 | 0.828 | 0.000 | 0.212 | 0.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 0 | 0 | 0 | 26 | 0 | 11 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 | 0.24 | 0.80 |
time (sec) |
N/A | 0.151 | 7.244 | 0.000 | 0.000 | 0.000 | 0.625 | 0.000 | 0.217 | 0.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 0 | 0 | 0 | 26 | 0 | 11 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 | 0.24 | 0.80 |
time (sec) |
N/A | 0.148 | 6.799 | 0.000 | 0.000 | 0.000 | 0.514 | 0.000 | 0.246 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 0 | 0 | 0 | 26 | 0 | 11 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 | 0.24 | 0.80 |
time (sec) |
N/A | 0.145 | 6.247 | 0.000 | 0.000 | 0.000 | 0.506 | 0.000 | 0.222 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 0 | 0 | 0 | 24 | 0 | 11 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 | 0.24 | 0.80 |
time (sec) |
N/A | 0.148 | 6.173 | 0.000 | 0.000 | 0.000 | 0.449 | 0.000 | 0.196 | 0.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 0 | 0 | 0 | 24 | 0 | 11 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 | 0.24 | 0.80 |
time (sec) |
N/A | 0.146 | 6.300 | 0.000 | 0.000 | 0.000 | 0.470 | 0.000 | 0.200 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 0 | 0 | 0 | 24 | 0 | 11 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 | 0.24 | 0.80 |
time (sec) |
N/A | 0.151 | 6.155 | 0.000 | 0.000 | 0.000 | 0.474 | 0.000 | 0.234 | 0.135 |