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 | 11 | 11 | 11 | 11 | 10 | 10 | 8 | 10 | 14 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.91 | 0.91 | 0.73 | 0.91 | 1.27 | 0.91 |
time (sec) |
N/A | 0.164 | 0.011 | 0.044 | 0.033 | 0.089 | 0.040 | 0.111 | 0.238 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 16 | 18 | 19 | 16 | 14 | 16 | 17 | 17 |
N.S. |
1 | 0.00 | 0.55 | 0.62 | 0.66 | 0.55 | 0.48 | 0.55 | 0.59 | 0.59 |
time (sec) |
N/A | 0.000 | 0.105 | 0.438 | 0.162 | 0.094 | 0.108 | 0.130 | 0.214 | 2.645 |
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 | 7 | 7 | 8 | 7 | 10 | 3 | 7 | 11 | 7 |
N.S. |
1 | 0.33 | 0.33 | 0.38 | 0.33 | 0.48 | 0.14 | 0.33 | 0.52 | 0.33 |
time (sec) |
N/A | 0.219 | 0.001 | 0.024 | 0.031 | 0.069 | 0.025 | 0.111 | 0.205 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 26 | 21 | 18 | 23 | 42 | 17 | 23 | 29 | 17 |
N.S. |
1 | 1.08 | 0.88 | 0.75 | 0.96 | 1.75 | 0.71 | 0.96 | 1.21 | 0.71 |
time (sec) |
N/A | 0.352 | 0.022 | 0.257 | 0.038 | 0.086 | 0.138 | 0.113 | 0.222 | 0.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 49 | 18 | 15 | 117 | 37 | 0 | 37 | 16 | 42 |
N.S. |
1 | 2.72 | 1.00 | 0.83 | 6.50 | 2.06 | 0.00 | 2.06 | 0.89 | 2.33 |
time (sec) |
N/A | 0.410 | 0.023 | 1.088 | 0.300 | 0.077 | 0.000 | 0.138 | 0.216 | 2.638 |
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 | 19 | 19 | 19 | 19 | 19 | 17 | 19 | 18 | 19 |
N.S. |
1 | 0.70 | 0.70 | 0.70 | 0.70 | 0.70 | 0.63 | 0.70 | 0.67 | 0.70 |
time (sec) |
N/A | 0.262 | 0.000 | 0.027 | 0.026 | 0.070 | 0.019 | 0.118 | 0.222 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 31 | 31 | 31 | 21 | 50 | 22 | 26 | 48 | 41 |
N.S. |
1 | 0.97 | 0.97 | 0.97 | 0.66 | 1.56 | 0.69 | 0.81 | 1.50 | 1.28 |
time (sec) |
N/A | 0.490 | 0.049 | 0.337 | 0.035 | 0.083 | 0.065 | 0.113 | 0.207 | 0.194 |
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 | 19 | 18 | 23 | 19 | 23 | 28 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.05 | 0.86 | 1.05 | 1.27 | 0.86 |
time (sec) |
N/A | 0.325 | 0.008 | 0.243 | 0.033 | 0.104 | 0.059 | 0.107 | 0.273 | 2.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 298 | 206 | 185 | 184 | 186 | 224 | 187 | 213 | 43 |
N.S. |
1 | 9.93 | 6.87 | 6.17 | 6.13 | 6.20 | 7.47 | 6.23 | 7.10 | 1.43 |
time (sec) |
N/A | 1.298 | 4.603 | 6.194 | 0.116 | 0.104 | 0.216 | 0.118 | 0.242 | 2.766 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 47 | 21 | 17 | 30 | 16 | 29 | 16 | 31 | 16 |
N.S. |
1 | 2.24 | 1.00 | 0.81 | 1.43 | 0.76 | 1.38 | 0.76 | 1.48 | 0.76 |
time (sec) |
N/A | 0.323 | 0.040 | 0.076 | 0.034 | 0.075 | 0.095 | 0.113 | 0.228 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 19 | 23 | 18 | 0 | 23 | 15 | 45 | 29 | 18 |
N.S. |
1 | 0.83 | 1.00 | 0.78 | 0.00 | 1.00 | 0.65 | 1.96 | 1.26 | 0.78 |
time (sec) |
N/A | 0.670 | 0.497 | 0.767 | 0.000 | 0.100 | 5.535 | 0.117 | 0.260 | 2.707 |
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 | 29 | 19 | 21 | 28 | 24 | 29 | 24 | 27 | 31 | 21 |
N.S. |
1 | 0.66 | 0.72 | 0.97 | 0.83 | 1.00 | 0.83 | 0.93 | 1.07 | 0.72 |
time (sec) |
N/A | 0.218 | 0.008 | 0.086 | 0.028 | 0.076 | 0.048 | 0.115 | 0.246 | 0.059 |
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 | 20 | 15 | 18 | 14 | 13 | 13 | 14 | 14 | 13 | 13 |
N.S. |
1 | 0.75 | 0.90 | 0.70 | 0.65 | 0.65 | 0.70 | 0.70 | 0.65 | 0.65 |
time (sec) |
N/A | 0.160 | 0.006 | 0.051 | 0.036 | 0.070 | 0.032 | 0.107 | 0.243 | 2.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 90 | 16 | 20 | 29 | 19 | 15 | 19 | 19 | 16 |
N.S. |
1 | 5.00 | 0.89 | 1.11 | 1.61 | 1.06 | 0.83 | 1.06 | 1.06 | 0.89 |
time (sec) |
N/A | 1.249 | 0.121 | 0.163 | 0.086 | 0.072 | 0.055 | 0.120 | 0.235 | 0.137 |
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 | 25 | 29 | 27 | 28 | 30 | 22 | 33 | 34 | 25 |
N.S. |
1 | 1.04 | 1.21 | 1.12 | 1.17 | 1.25 | 0.92 | 1.38 | 1.42 | 1.04 |
time (sec) |
N/A | 0.196 | 0.006 | 0.111 | 0.033 | 0.091 | 0.110 | 0.120 | 0.241 | 2.473 |
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 | 31 | 31 | 32 | 31 | 31 | 31 | 31 | 28 | 27 |
N.S. |
1 | 1.29 | 1.29 | 1.33 | 1.29 | 1.29 | 1.29 | 1.29 | 1.17 | 1.12 |
time (sec) |
N/A | 0.161 | 0.003 | 0.140 | 0.039 | 0.080 | 0.048 | 0.116 | 0.239 | 2.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 60 | 14 | 14 | 14 | 16 | 8 | 16 | 16 | 13 |
N.S. |
1 | 3.16 | 0.74 | 0.74 | 0.74 | 0.84 | 0.42 | 0.84 | 0.84 | 0.68 |
time (sec) |
N/A | 0.508 | 0.141 | 0.070 | 0.044 | 0.082 | 0.047 | 0.110 | 0.201 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 84 | 94 | 76 | 69 | 107 | 82 | 68 | 92 | 106 |
N.S. |
1 | 2.55 | 2.85 | 2.30 | 2.09 | 3.24 | 2.48 | 2.06 | 2.79 | 3.21 |
time (sec) |
N/A | 0.395 | 0.048 | 0.305 | 0.032 | 0.085 | 0.331 | 0.113 | 0.222 | 2.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 26 | 16 | 15 | 21 | 17 | 21 | 22 | 15 |
N.S. |
1 | 0.00 | 1.37 | 0.84 | 0.79 | 1.11 | 0.89 | 1.11 | 1.16 | 0.79 |
time (sec) |
N/A | 0.000 | 0.246 | 0.059 | 0.068 | 0.087 | 0.085 | 0.113 | 0.249 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 71 | 25 | 39 | 26 | 34 | 31 | 39 | 37 | 0 |
N.S. |
1 | 2.73 | 0.96 | 1.50 | 1.00 | 1.31 | 1.19 | 1.50 | 1.42 | 0.00 |
time (sec) |
N/A | 12.537 | 0.051 | 26.316 | 0.188 | 0.078 | 0.258 | 0.325 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 49 | 58 | 40 | 50 | 50 | 88 | 50 | 48 | 102 |
N.S. |
1 | 2.04 | 2.42 | 1.67 | 2.08 | 2.08 | 3.67 | 2.08 | 2.00 | 4.25 |
time (sec) |
N/A | 0.286 | 0.005 | 0.112 | 0.031 | 0.077 | 0.025 | 0.109 | 0.203 | 2.341 |
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 | 18 | 21 | 16 | 15 | 15 | 15 | 15 | 16 | 17 |
N.S. |
1 | 0.72 | 0.84 | 0.64 | 0.60 | 0.60 | 0.60 | 0.60 | 0.64 | 0.68 |
time (sec) |
N/A | 0.255 | 0.002 | 0.035 | 0.035 | 0.062 | 0.020 | 0.113 | 0.212 | 0.064 |
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 | 26 | 25 | 18 | 26 | 20 | 24 | 22 | 25 | 17 |
N.S. |
1 | 1.18 | 1.14 | 0.82 | 1.18 | 0.91 | 1.09 | 1.00 | 1.14 | 0.77 |
time (sec) |
N/A | 1.095 | 0.043 | 1.238 | 0.099 | 0.097 | 0.187 | 0.129 | 0.241 | 3.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 0 | 83 | 89 | 113 | 113 | 110 | 131 | 133 | 0 |
N.S. |
1 | 0.00 | 2.13 | 2.28 | 2.90 | 2.90 | 2.82 | 3.36 | 3.41 | 0.00 |
time (sec) |
N/A | 0.000 | 6.836 | 1.263 | 0.279 | 0.097 | 0.430 | 3.244 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 29 | 26 | 23 | 0 | 24 | 22 | 27 | 162 | 29 |
N.S. |
1 | 0.81 | 0.72 | 0.64 | 0.00 | 0.67 | 0.61 | 0.75 | 4.50 | 0.81 |
time (sec) |
N/A | 8.915 | 0.658 | 9.753 | 0.000 | 0.085 | 9.155 | 1.019 | 200.038 | 2.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 17 | 16 | 16 | 20 | 16 | 23 | 110 |
N.S. |
1 | 0.00 | 1.00 | 0.85 | 0.80 | 0.80 | 1.00 | 0.80 | 1.15 | 5.50 |
time (sec) |
N/A | 0.000 | 0.134 | 0.298 | 0.078 | 0.081 | 0.115 | 0.131 | 0.247 | 2.831 |
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 | 48 | 37 | 38 | 58 | 39 | 29 | 40 | 45 | 38 |
N.S. |
1 | 1.37 | 1.06 | 1.09 | 1.66 | 1.11 | 0.83 | 1.14 | 1.29 | 1.09 |
time (sec) |
N/A | 1.578 | 0.084 | 1.487 | 0.094 | 0.080 | 0.263 | 0.118 | 0.240 | 2.616 |
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 | 13 | 13 | 11 | 10 | 10 | 7 | 10 | 12 | 10 |
N.S. |
1 | 0.39 | 0.39 | 0.33 | 0.30 | 0.30 | 0.21 | 0.30 | 0.36 | 0.30 |
time (sec) |
N/A | 0.191 | 0.005 | 0.034 | 0.037 | 0.090 | 0.038 | 0.114 | 0.272 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 81 | 35 | 31 | 65 | 28 | 29 | 33 | 38 | 35 |
N.S. |
1 | 2.79 | 1.21 | 1.07 | 2.24 | 0.97 | 1.00 | 1.14 | 1.31 | 1.21 |
time (sec) |
N/A | 1.678 | 0.093 | 0.709 | 0.087 | 0.083 | 0.114 | 0.113 | 0.245 | 2.485 |
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 | 24 | 27 | 23 | 27 | 20 | 26 | 28 | 24 |
N.S. |
1 | 0.89 | 0.89 | 1.00 | 0.85 | 1.00 | 0.74 | 0.96 | 1.04 | 0.89 |
time (sec) |
N/A | 0.190 | 0.005 | 0.053 | 0.033 | 0.073 | 0.034 | 0.112 | 0.229 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 37 | 20 | 18 | 35 | 36 | 34 | 35 | 29 | 29 |
N.S. |
1 | 2.06 | 1.11 | 1.00 | 1.94 | 2.00 | 1.89 | 1.94 | 1.61 | 1.61 |
time (sec) |
N/A | 0.171 | 0.002 | 0.078 | 0.031 | 0.067 | 0.022 | 0.112 | 0.253 | 2.392 |
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 | 8 | 8 | 9 | 8 | 8 | 5 | 8 | 8 | 8 |
N.S. |
1 | 0.30 | 0.30 | 0.33 | 0.30 | 0.30 | 0.19 | 0.30 | 0.30 | 0.30 |
time (sec) |
N/A | 0.140 | 0.000 | 0.025 | 0.032 | 0.063 | 0.015 | 0.107 | 0.241 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 23 | 248 | 213 | 179 | 182 | 685 | 352 | 248 |
N.S. |
1 | 0.00 | 1.10 | 11.81 | 10.14 | 8.52 | 8.67 | 32.62 | 16.76 | 11.81 |
time (sec) |
N/A | 0.000 | 0.874 | 0.010 | 50.506 | 0.094 | 1.024 | 0.371 | 200.031 | 3.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 81 | 33 | 114 | 68 | 76 | 133 | 384 | 0 |
N.S. |
1 | 0.00 | 2.89 | 1.18 | 4.07 | 2.43 | 2.71 | 4.75 | 13.71 | 0.00 |
time (sec) |
N/A | 0.000 | 0.217 | 3.451 | 0.726 | 0.082 | 0.322 | 0.656 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 25 | 30 | 30 | 26 | 30 | 35 | 31 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.20 | 1.20 | 1.04 | 1.20 | 1.40 | 1.24 |
time (sec) |
N/A | 0.000 | 0.066 | 7.911 | 0.214 | 0.083 | 0.235 | 0.189 | 0.252 | 0.367 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 25 | 27 | 25 | 0 | 0 | 35 | 30 |
N.S. |
1 | 0.00 | 1.00 | 0.93 | 1.00 | 0.93 | 0.00 | 0.00 | 1.30 | 1.11 |
time (sec) |
N/A | 0.000 | 2.554 | 0.033 | 0.224 | 0.081 | 0.000 | 0.000 | 0.238 | 0.236 |
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 | 13 | 13 | 12 | 11 | 20 | 8 | 11 | 13 | 11 |
N.S. |
1 | 0.59 | 0.59 | 0.55 | 0.50 | 0.91 | 0.36 | 0.50 | 0.59 | 0.50 |
time (sec) |
N/A | 0.154 | 0.006 | 0.028 | 0.039 | 0.083 | 0.066 | 0.112 | 0.198 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | F(-2) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 54 | 60 | 56 | 69 | 0 | 68 | 68 | 27623 |
N.S. |
1 | 0.00 | 1.54 | 1.71 | 1.60 | 1.97 | 0.00 | 1.94 | 1.94 | 789.23 |
time (sec) |
N/A | 0.000 | 2.299 | 0.806 | 0.160 | 0.114 | 0.000 | 0.166 | 0.213 | 6.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 43 | 36 | 43 | 44 | 39 | 39 | 42 | 34 |
N.S. |
1 | 0.00 | 1.30 | 1.09 | 1.30 | 1.33 | 1.18 | 1.18 | 1.27 | 1.03 |
time (sec) |
N/A | 0.000 | 0.090 | 33.966 | 0.100 | 0.087 | 1.029 | 0.145 | 1.656 | 2.917 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | C | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 70 | 32 | 62 | 66 | 71 | 79 | 69 |
N.S. |
1 | 0.00 | 0.95 | 3.18 | 1.45 | 2.82 | 3.00 | 3.23 | 3.59 | 3.14 |
time (sec) |
N/A | 0.000 | 0.229 | 1.501 | 0.174 | 0.078 | 0.509 | 0.184 | 0.238 | 3.152 |
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 | 24 | 24 | 22 | 21 | 57 | 31 | 20 | 28 | 31 | 28 |
N.S. |
1 | 1.00 | 0.92 | 0.88 | 2.38 | 1.29 | 0.83 | 1.17 | 1.29 | 1.17 |
time (sec) |
N/A | 0.912 | 0.108 | 1.909 | 0.584 | 0.079 | 0.192 | 0.126 | 0.196 | 2.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 0 | 15 | 30 | 29 | 27 | 14 | 27 | 196 | 14 |
N.S. |
1 | 0.00 | 1.00 | 2.00 | 1.93 | 1.80 | 0.93 | 1.80 | 13.07 | 0.93 |
time (sec) |
N/A | 0.000 | 0.035 | 3.392 | 0.105 | 0.090 | 0.573 | 0.406 | 0.217 | 2.485 |
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 | 29 | 25 | 26 | 25 | 24 | 24 | 19 | 24 | 36 | 25 |
N.S. |
1 | 0.86 | 0.90 | 0.86 | 0.83 | 0.83 | 0.66 | 0.83 | 1.24 | 0.86 |
time (sec) |
N/A | 0.695 | 2.244 | 0.652 | 0.091 | 0.080 | 0.086 | 0.190 | 0.184 | 14.217 |
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 | 31 | 30 | 34 | 35 | 43 | 27 | 35 | 43 | 35 |
N.S. |
1 | 1.24 | 1.20 | 1.36 | 1.40 | 1.72 | 1.08 | 1.40 | 1.72 | 1.40 |
time (sec) |
N/A | 0.322 | 0.022 | 0.102 | 0.032 | 0.070 | 0.188 | 0.113 | 0.196 | 0.109 |
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 | 24 | 21 | 21 | 20 | 75 | 19 | 17 | 19 | 19 | 19 |
N.S. |
1 | 0.88 | 0.88 | 0.83 | 3.12 | 0.79 | 0.71 | 0.79 | 0.79 | 0.79 |
time (sec) |
N/A | 0.345 | 0.037 | 0.280 | 0.031 | 0.089 | 0.072 | 0.117 | 0.207 | 2.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 214 | 31 | 30 | 115 | 29 | 42 | 29 | 92 | 29 |
N.S. |
1 | 6.90 | 1.00 | 0.97 | 3.71 | 0.94 | 1.35 | 0.94 | 2.97 | 0.94 |
time (sec) |
N/A | 3.209 | 0.240 | 0.700 | 0.667 | 0.081 | 0.165 | 0.119 | 0.221 | 2.665 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 53 | 53 | 45 | 55 | 49 | 0 | 49 | 174 | 50 |
N.S. |
1 | 1.83 | 1.83 | 1.55 | 1.90 | 1.69 | 0.00 | 1.69 | 6.00 | 1.72 |
time (sec) |
N/A | 8.779 | 0.194 | 26.124 | 0.195 | 0.099 | 0.000 | 0.675 | 200.013 | 2.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 58 | 68 | 63 | 69 | 71 | 0 | 124 | 76 |
N.S. |
1 | 0.00 | 1.81 | 2.12 | 1.97 | 2.16 | 2.22 | 0.00 | 3.88 | 2.38 |
time (sec) |
N/A | 0.000 | 0.124 | 0.312 | 0.464 | 0.086 | 0.623 | 0.000 | 200.039 | 2.591 |
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 | 42 | 37 | 33 | 31 | 31 | 39 | 31 | 37 | 34 |
N.S. |
1 | 1.56 | 1.37 | 1.22 | 1.15 | 1.15 | 1.44 | 1.15 | 1.37 | 1.26 |
time (sec) |
N/A | 0.281 | 0.003 | 0.074 | 0.040 | 0.071 | 0.049 | 0.117 | 0.194 | 2.368 |
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 | 19 | 17 | 22 | 17 | 23 | 20 | 23 | 24 | 17 |
N.S. |
1 | 0.70 | 0.63 | 0.81 | 0.63 | 0.85 | 0.74 | 0.85 | 0.89 | 0.63 |
time (sec) |
N/A | 0.480 | 0.052 | 0.247 | 0.096 | 0.080 | 0.146 | 0.116 | 0.878 | 2.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | F(-1) | B | B | B | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 0 | 61 | 0 | 60 | 58 | 221 | 128 | 229 |
N.S. |
1 | 0.00 | 0.00 | 3.05 | 0.00 | 3.00 | 2.90 | 11.05 | 6.40 | 11.45 |
time (sec) |
N/A | 0.000 | 0.000 | 0.007 | 0.000 | 0.068 | 0.368 | 0.134 | 200.032 | 2.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 30 | 29 | 29 | 28 | 27 | 28 | 30 | 28 |
N.S. |
1 | 0.00 | 1.25 | 1.21 | 1.21 | 1.17 | 1.12 | 1.17 | 1.25 | 1.17 |
time (sec) |
N/A | 0.000 | 0.623 | 0.201 | 0.165 | 0.089 | 0.285 | 0.118 | 0.197 | 2.590 |
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 | 24 | 22 | 23 | 38 | 38 | 20 | 41 | 36 | 44 |
N.S. |
1 | 1.00 | 0.92 | 0.96 | 1.58 | 1.58 | 0.83 | 1.71 | 1.50 | 1.83 |
time (sec) |
N/A | 0.819 | 0.018 | 0.471 | 0.081 | 0.081 | 0.537 | 0.124 | 0.211 | 2.789 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 17 | 17 | 13 | 12 | 32 | 14 | 0 | 15 | 12 |
N.S. |
1 | 0.85 | 0.85 | 0.65 | 0.60 | 1.60 | 0.70 | 0.00 | 0.75 | 0.60 |
time (sec) |
N/A | 0.259 | 0.108 | 0.131 | 0.035 | 0.081 | 0.231 | 0.000 | 0.182 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 58 | 16 | 15 | 22 | 14 | 14 | 22 | 14 | 14 |
N.S. |
1 | 4.14 | 1.14 | 1.07 | 1.57 | 1.00 | 1.00 | 1.57 | 1.00 | 1.00 |
time (sec) |
N/A | 0.756 | 0.095 | 0.145 | 0.150 | 0.071 | 0.127 | 0.117 | 0.201 | 2.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 36 | 66 | 35 | 29 | 70 | 28 | 69 |
N.S. |
1 | 0.00 | 0.93 | 1.29 | 2.36 | 1.25 | 1.04 | 2.50 | 1.00 | 2.46 |
time (sec) |
N/A | 0.000 | 0.079 | 0.418 | 0.189 | 0.086 | 0.501 | 0.621 | 0.224 | 0.301 |
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 | 20 | 13 | 13 | 13 | 12 | 12 | 12 | 12 | 13 | 12 |
N.S. |
1 | 0.65 | 0.65 | 0.65 | 0.60 | 0.60 | 0.60 | 0.60 | 0.65 | 0.60 |
time (sec) |
N/A | 0.177 | 0.003 | 0.077 | 0.034 | 0.074 | 0.125 | 0.111 | 0.199 | 2.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 117 | 28 | 83 | 81 | 81 | 80 | 81 | 95 | 25 |
N.S. |
1 | 3.90 | 0.93 | 2.77 | 2.70 | 2.70 | 2.67 | 2.70 | 3.17 | 0.83 |
time (sec) |
N/A | 0.572 | 2.422 | 1.337 | 0.033 | 0.085 | 0.189 | 0.116 | 0.203 | 2.413 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 26 | 31 | 25 | 26 | 121 | 28 | 64 |
N.S. |
1 | 0.00 | 1.00 | 0.87 | 1.03 | 0.83 | 0.87 | 4.03 | 0.93 | 2.13 |
time (sec) |
N/A | 0.000 | 0.046 | 4.768 | 0.178 | 0.077 | 0.325 | 0.369 | 0.178 | 2.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 33 | 27 | 28 | 33 | 32 | 0 | 33 | 29 |
N.S. |
1 | 0.00 | 1.22 | 1.00 | 1.04 | 1.22 | 1.19 | 0.00 | 1.22 | 1.07 |
time (sec) |
N/A | 0.000 | 0.137 | 0.220 | 0.089 | 0.078 | 0.145 | 0.000 | 0.217 | 2.464 |
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 | 20 | 30 | 26 | 19 | 21 | 18 | 20 | 24 | 16 | 16 |
N.S. |
1 | 1.50 | 1.30 | 0.95 | 1.05 | 0.90 | 1.00 | 1.20 | 0.80 | 0.80 |
time (sec) |
N/A | 0.750 | 0.019 | 0.565 | 0.193 | 0.087 | 0.322 | 0.111 | 0.193 | 2.566 |
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 | 6 | 6 | 6 | 8 | 7 | 10 | 8 | 10 | 6 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.17 | 1.67 | 1.33 | 1.67 | 1.00 | 1.17 |
time (sec) |
N/A | 0.212 | 0.000 | 0.023 | 0.035 | 0.072 | 0.042 | 0.107 | 0.174 | 0.036 |
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 | 42 | 43 | 40 | 48 | 41 | 37 | 44 | 46 | 40 |
N.S. |
1 | 1.56 | 1.59 | 1.48 | 1.78 | 1.52 | 1.37 | 1.63 | 1.70 | 1.48 |
time (sec) |
N/A | 0.495 | 0.048 | 0.513 | 0.094 | 0.095 | 0.189 | 0.114 | 0.184 | 0.112 |
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 | 13 | 13 | 14 | 13 | 13 | 12 | 13 | 11 | 11 |
N.S. |
1 | 0.76 | 0.76 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.65 | 0.65 |
time (sec) |
N/A | 0.245 | 0.001 | 0.049 | 0.031 | 0.085 | 0.076 | 0.114 | 0.182 | 2.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 32 | 28 | 31 | 34 | 30 | 0 | 32 | 32 | 30 |
N.S. |
1 | 1.39 | 1.22 | 1.35 | 1.48 | 1.30 | 0.00 | 1.39 | 1.39 | 1.30 |
time (sec) |
N/A | 1.030 | 0.145 | 1.281 | 0.173 | 0.096 | 0.000 | 0.125 | 0.174 | 2.703 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 25 | 24 | 24 | 22 | 24 | 24 | 24 |
N.S. |
1 | 0.00 | 0.00 | 1.14 | 1.09 | 1.09 | 1.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.000 | 0.000 | 0.521 | 0.183 | 0.108 | 0.482 | 0.153 | 0.180 | 2.791 |
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 | 20 | 20 | 18 | 18 | 17 | 17 | 18 | 18 | 17 |
N.S. |
1 | 0.91 | 0.91 | 0.82 | 0.82 | 0.77 | 0.77 | 0.82 | 0.82 | 0.77 |
time (sec) |
N/A | 0.367 | 0.113 | 11.523 | 0.128 | 0.110 | 0.647 | 0.126 | 0.180 | 4.268 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 22 | 50 | 42 | 60 | 51 | 66 | 57 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 2.08 | 1.75 | 2.50 | 2.12 | 2.75 | 2.38 |
time (sec) |
N/A | 0.000 | 0.114 | 0.435 | 0.098 | 0.097 | 0.259 | 0.127 | 0.186 | 2.794 |
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 | 28 | 20 | 20 | 24 | 22 | 21 | 22 | 68 | 75 | 20 |
N.S. |
1 | 0.71 | 0.71 | 0.86 | 0.79 | 0.75 | 0.79 | 2.43 | 2.68 | 0.71 |
time (sec) |
N/A | 0.441 | 0.022 | 0.513 | 0.173 | 0.092 | 0.371 | 0.118 | 0.181 | 3.792 |
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 | 35 | 35 | 32 | 33 | 33 | 32 | 35 | 44 | 31 |
N.S. |
1 | 0.97 | 0.97 | 0.89 | 0.92 | 0.92 | 0.89 | 0.97 | 1.22 | 0.86 |
time (sec) |
N/A | 0.281 | 0.008 | 0.061 | 0.040 | 0.080 | 0.178 | 0.114 | 0.191 | 2.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 21 | 25 | 41 | 41 | 20 | 24 | 49 | 28 |
N.S. |
1 | 0.00 | 0.91 | 1.09 | 1.78 | 1.78 | 0.87 | 1.04 | 2.13 | 1.22 |
time (sec) |
N/A | 0.000 | 0.112 | 0.793 | 0.072 | 0.088 | 0.147 | 0.117 | 0.195 | 2.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 34 | 27 | 25 | 29 | 20 | 27 | 24 | 27 | 24 |
N.S. |
1 | 2.00 | 1.59 | 1.47 | 1.71 | 1.18 | 1.59 | 1.41 | 1.59 | 1.41 |
time (sec) |
N/A | 0.212 | 0.007 | 0.131 | 0.040 | 0.109 | 0.209 | 0.108 | 0.206 | 2.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 19 | 0 | 19 | 19 | 32 | 25 | 18 |
N.S. |
1 | 0.00 | 0.96 | 0.79 | 0.00 | 0.79 | 0.79 | 1.33 | 1.04 | 0.75 |
time (sec) |
N/A | 0.000 | 0.068 | 0.178 | 0.000 | 0.114 | 0.267 | 0.110 | 0.202 | 2.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 16 | 16 | 20 | 15 | 20 | 24 | 16 | 15 |
N.S. |
1 | 0.00 | 0.80 | 0.80 | 1.00 | 0.75 | 1.00 | 1.20 | 0.80 | 0.75 |
time (sec) |
N/A | 0.000 | 0.442 | 0.079 | 0.087 | 0.098 | 0.149 | 0.120 | 0.204 | 2.379 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | C | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 48 | 62 | 57 | 71 | 55 | 61 | 77 | 59 | 62 |
N.S. |
1 | 1.66 | 2.14 | 1.97 | 2.45 | 1.90 | 2.10 | 2.66 | 2.03 | 2.14 |
time (sec) |
N/A | 0.723 | 0.044 | 0.602 | 0.071 | 0.101 | 0.177 | 0.118 | 0.215 | 2.450 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 40 | 28 | 27 | 27 | 26 | 27 | 27 | 107 |
N.S. |
1 | 0.00 | 1.60 | 1.12 | 1.08 | 1.08 | 1.04 | 1.08 | 1.08 | 4.28 |
time (sec) |
N/A | 0.000 | 5.039 | 0.853 | 0.175 | 0.110 | 1.046 | 0.135 | 0.195 | 3.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 38 | 30 | 19 | 18 | 18 | 17 | 19 | 18 | 18 |
N.S. |
1 | 2.11 | 1.67 | 1.06 | 1.00 | 1.00 | 0.94 | 1.06 | 1.00 | 1.00 |
time (sec) |
N/A | 0.239 | 0.009 | 0.113 | 0.033 | 0.104 | 0.165 | 0.111 | 0.196 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 44 | 20 | 38 | 0 | 27 | 34 | 30 | 28 | 18 |
N.S. |
1 | 1.76 | 0.80 | 1.52 | 0.00 | 1.08 | 1.36 | 1.20 | 1.12 | 0.72 |
time (sec) |
N/A | 0.307 | 0.095 | 6.759 | 0.000 | 0.100 | 0.463 | 0.137 | 0.192 | 2.467 |
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 | 14 | 13 | 13 | 12 | 13 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.93 | 0.93 | 0.86 | 0.93 | 1.00 | 0.93 |
time (sec) |
N/A | 0.136 | 0.000 | 0.082 | 0.031 | 0.080 | 0.049 | 0.113 | 0.199 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 122 | 116 | 71 | 841 | 60 | 75 | 0 | 75 | 88 |
N.S. |
1 | 4.69 | 4.46 | 2.73 | 32.35 | 2.31 | 2.88 | 0.00 | 2.88 | 3.38 |
time (sec) |
N/A | 1.446 | 0.126 | 25.289 | 0.186 | 0.088 | 4.792 | 0.000 | 0.208 | 3.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 48 | 23 | 18 | 22 | 21 | 15 | 25 | 24 | 17 |
N.S. |
1 | 2.67 | 1.28 | 1.00 | 1.22 | 1.17 | 0.83 | 1.39 | 1.33 | 0.94 |
time (sec) |
N/A | 0.911 | 0.258 | 0.250 | 0.087 | 0.089 | 0.200 | 0.112 | 0.193 | 2.408 |
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 | 16 | 15 | 15 | 10 | 15 | 13 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.23 | 1.15 | 1.15 | 0.77 | 1.15 | 1.00 | 0.92 |
time (sec) |
N/A | 0.564 | 0.016 | 0.083 | 0.145 | 0.077 | 0.159 | 0.115 | 0.182 | 2.499 |
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 | 12 | 12 | 11 | 10 | 17 | 10 | 10 | 17 | 12 |
N.S. |
1 | 0.75 | 0.75 | 0.69 | 0.62 | 1.06 | 0.62 | 0.62 | 1.06 | 0.75 |
time (sec) |
N/A | 0.234 | 0.001 | 0.033 | 0.028 | 0.069 | 0.078 | 0.115 | 0.191 | 0.025 |
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 | 22 | 22 | 20 | 16 | 15 | 30 | 17 | 0 | 22 | 15 |
N.S. |
1 | 1.00 | 0.91 | 0.73 | 0.68 | 1.36 | 0.77 | 0.00 | 1.00 | 0.68 |
time (sec) |
N/A | 0.475 | 0.016 | 0.979 | 1.015 | 0.102 | 1.675 | 0.000 | 0.186 | 2.399 |
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 | 36 | 25 | 20 | 29 | 29 | 24 | 29 | 26 | 24 |
N.S. |
1 | 1.57 | 1.09 | 0.87 | 1.26 | 1.26 | 1.04 | 1.26 | 1.13 | 1.04 |
time (sec) |
N/A | 0.279 | 0.004 | 0.050 | 0.041 | 0.075 | 0.029 | 0.106 | 0.195 | 2.336 |
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 | 11 | 9 | 10 | 9 | 9 | 8 | 10 | 9 | 9 |
N.S. |
1 | 0.65 | 0.53 | 0.59 | 0.53 | 0.53 | 0.47 | 0.59 | 0.53 | 0.53 |
time (sec) |
N/A | 0.256 | 0.003 | 0.036 | 0.040 | 0.067 | 0.047 | 0.118 | 0.181 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 0 | 27 | 168 | 49 | 48 | 169 | 48 | 429 |
N.S. |
1 | 0.00 | 0.00 | 1.35 | 8.40 | 2.45 | 2.40 | 8.45 | 2.40 | 21.45 |
time (sec) |
N/A | 0.000 | 0.000 | 3.447 | 0.524 | 0.086 | 1.138 | 1.350 | 0.200 | 2.882 |
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 | 17 | 17 | 18 | 18 | 21 | 17 | 19 | 21 | 18 |
N.S. |
1 | 0.81 | 0.81 | 0.86 | 0.86 | 1.00 | 0.81 | 0.90 | 1.00 | 0.86 |
time (sec) |
N/A | 0.372 | 0.005 | 0.160 | 0.039 | 0.077 | 0.528 | 0.112 | 0.191 | 0.067 |
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 | 40 | 43 | 31 | 29 | 28 | 28 | 26 | 28 | 29 | 28 |
N.S. |
1 | 1.08 | 0.78 | 0.72 | 0.70 | 0.70 | 0.65 | 0.70 | 0.72 | 0.70 |
time (sec) |
N/A | 2.019 | 0.120 | 0.308 | 0.076 | 0.079 | 0.165 | 0.122 | 0.197 | 2.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 27 | 25 | 24 | 26 | 34 | 0 | 26 | 31 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.96 | 1.04 | 1.36 | 0.00 | 1.04 | 1.24 | 0.00 |
time (sec) |
N/A | 0.763 | 0.033 | 0.770 | 0.188 | 0.081 | 0.000 | 0.138 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 11 | 13 | 14 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 0.00 | 0.65 | 0.76 | 0.82 | 0.71 | 0.71 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.000 | 0.044 | 0.138 | 0.152 | 0.082 | 0.115 | 0.111 | 0.191 | 2.419 |
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 | 3 | 3 | 4 | 3 | 3 | 2 | 3 | 3 | 3 |
N.S. |
1 | 0.33 | 0.33 | 0.44 | 0.33 | 0.33 | 0.22 | 0.33 | 0.33 | 0.33 |
time (sec) |
N/A | 0.129 | 0.000 | 0.014 | 0.035 | 0.058 | 0.030 | 0.107 | 0.199 | 0.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 65 | 30 | 34 | 32 | 30 | 34 | 34 | 31 | 28 |
N.S. |
1 | 2.17 | 1.00 | 1.13 | 1.07 | 1.00 | 1.13 | 1.13 | 1.03 | 0.93 |
time (sec) |
N/A | 0.370 | 0.020 | 0.300 | 0.037 | 0.078 | 1.201 | 0.114 | 0.198 | 2.556 |
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 | 24 | 23 | 21 | 20 | 29 | 27 | 20 | 33 | 20 |
N.S. |
1 | 0.96 | 0.92 | 0.84 | 0.80 | 1.16 | 1.08 | 0.80 | 1.32 | 0.80 |
time (sec) |
N/A | 0.180 | 0.009 | 0.135 | 0.035 | 0.084 | 0.077 | 0.110 | 0.195 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | B | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 174 | 95 | 80 | 131 | 85 | 88 | 100 | 109 | 81 |
N.S. |
1 | 5.80 | 3.17 | 2.67 | 4.37 | 2.83 | 2.93 | 3.33 | 3.63 | 2.70 |
time (sec) |
N/A | 0.560 | 0.091 | 2.670 | 0.085 | 0.098 | 0.197 | 0.115 | 0.193 | 2.538 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | F(-2) | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 0 | 47 | 57 | 41 | 0 | 48 | 51 | 46 |
N.S. |
1 | 0.00 | 0.00 | 2.24 | 2.71 | 1.95 | 0.00 | 2.29 | 2.43 | 2.19 |
time (sec) |
N/A | 0.000 | 0.000 | 3.941 | 0.190 | 0.096 | 0.000 | 1.405 | 0.205 | 3.027 |
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 | 34 | 40 | 28 | 35 | 35 | 32 | 36 | 39 | 35 |
N.S. |
1 | 1.03 | 1.21 | 0.85 | 1.06 | 1.06 | 0.97 | 1.09 | 1.18 | 1.06 |
time (sec) |
N/A | 0.350 | 0.016 | 0.102 | 0.035 | 0.066 | 0.510 | 0.112 | 0.190 | 2.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | C | A | A | B | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 19 | 567 | 74 | 27 | 20 | 76 | 28 | 18 |
N.S. |
1 | 0.00 | 0.90 | 27.00 | 3.52 | 1.29 | 0.95 | 3.62 | 1.33 | 0.86 |
time (sec) |
N/A | 0.000 | 0.045 | 1.060 | 0.204 | 0.089 | 1.563 | 0.223 | 0.193 | 2.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 28 | 21 | 20 | 120 | 20 | 14 | 81 | 48 | 29 |
N.S. |
1 | 1.04 | 0.78 | 0.74 | 4.44 | 0.74 | 0.52 | 3.00 | 1.78 | 1.07 |
time (sec) |
N/A | 2.465 | 0.190 | 0.505 | 0.045 | 0.079 | 0.261 | 1.597 | 0.208 | 2.725 |
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 | 47 | 17 | 21 | 23 | 23 | 20 | 23 | 21 | 24 |
N.S. |
1 | 1.74 | 0.63 | 0.78 | 0.85 | 0.85 | 0.74 | 0.85 | 0.78 | 0.89 |
time (sec) |
N/A | 0.342 | 0.047 | 0.138 | 0.030 | 0.073 | 0.162 | 0.118 | 0.249 | 0.062 |