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 | Mupad | |
grade |
N/A | A | C | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 22 | 11 | 16 | 48 | 19 | 34 | 10 |
N.S. |
1 | 1.00 | 1.83 | 0.92 | 1.33 | 4.00 | 1.58 | 2.83 | 0.83 |
time (sec) |
N/A | 0.183 | 0.001 | 0.058 | 0.271 | 0.243 | 0.025 | 0.266 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 15 | 19 | 14 | 15 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.15 | 1.46 | 1.08 | 1.15 | 0.92 |
time (sec) |
N/A | 0.124 | 0.006 | 0.136 | 0.277 | 0.231 | 0.045 | 0.256 | 0.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 14 | 11 | 11 | 14 | 15 | 11 | 10 |
N.S. |
1 | 1.00 | 0.74 | 0.58 | 0.58 | 0.74 | 0.79 | 0.58 | 0.53 |
time (sec) |
N/A | 0.122 | 0.012 | 0.073 | 0.198 | 0.242 | 0.074 | 0.277 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 2 | 3 | 2 | 2 | 2 | 2 | 2 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.128 | 0.001 | 0.030 | 0.208 | 0.245 | 0.032 | 0.261 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.67 | 0.67 | 0.56 | 0.67 | 0.67 |
time (sec) |
N/A | 0.129 | 0.001 | 0.032 | 0.204 | 0.235 | 0.029 | 0.260 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 |
time (sec) |
N/A | 0.155 | 0.007 | 0.155 | 0.193 | 0.261 | 0.020 | 0.288 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 10 | 9 | 9 | 22 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 0.69 | 1.69 | 0.69 | 0.69 |
time (sec) |
N/A | 0.117 | 0.002 | 0.103 | 0.195 | 0.231 | 0.068 | 0.292 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 14 | 12 | 11 | 13 | 15 | 11 | 11 |
N.S. |
1 | 1.00 | 0.74 | 0.63 | 0.58 | 0.68 | 0.79 | 0.58 | 0.58 |
time (sec) |
N/A | 0.146 | 0.010 | 0.085 | 0.201 | 0.237 | 0.098 | 0.280 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 14 | 8 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 1.75 | 1.00 | 0.75 | 0.75 |
time (sec) |
N/A | 0.157 | 0.007 | 0.157 | 0.196 | 0.232 | 0.022 | 0.285 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 4 | 4 | 4 | 4 | 15 | 3 | 3 | 3 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 3.75 | 0.75 | 0.75 | 0.75 | 0.00 |
time (sec) |
N/A | 0.177 | 0.018 | 0.147 | 0.235 | 0.242 | 0.281 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 2 | 3 | 13 | 2 | 2 | 2 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 6.50 | 1.00 | 1.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.145 | 0.019 | 0.081 | 0.231 | 0.254 | 0.389 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 8 | 7 | 7 | 5 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.88 | 0.88 | 0.62 | 0.88 | 0.88 |
time (sec) |
N/A | 0.119 | 0.010 | 0.104 | 0.193 | 0.241 | 0.032 | 0.298 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.86 | 0.86 | 0.71 | 0.86 | 0.86 |
time (sec) |
N/A | 0.134 | 0.036 | 0.043 | 0.201 | 0.236 | 0.035 | 0.309 | 0.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 26 | 21 | 19 | 19 | 20 | 19 | 21 |
N.S. |
1 | 1.00 | 0.93 | 0.75 | 0.68 | 0.68 | 0.71 | 0.68 | 0.75 |
time (sec) |
N/A | 0.180 | 0.044 | 0.036 | 0.191 | 0.237 | 0.039 | 0.273 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 17 | 16 | 16 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.73 | 0.73 | 0.68 | 0.73 | 0.73 |
time (sec) |
N/A | 0.134 | 0.013 | 0.031 | 0.188 | 0.235 | 0.037 | 0.279 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.62 | 0.75 | 0.75 |
time (sec) |
N/A | 0.143 | 0.001 | 0.049 | 0.188 | 0.260 | 0.034 | 0.283 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.67 | 0.67 | 0.56 | 0.67 | 0.67 |
time (sec) |
N/A | 0.130 | 0.000 | 0.033 | 0.191 | 0.249 | 0.029 | 0.272 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 10 | 9 | 9 | 22 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 0.69 | 1.69 | 0.69 | 0.69 |
time (sec) |
N/A | 0.119 | 0.001 | 0.104 | 0.180 | 0.256 | 0.070 | 0.272 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 6 | 6 | 5 | 5 | 5 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.144 | 0.013 | 0.029 | 0.182 | 0.242 | 0.030 | 0.299 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 6 | 5 | 5 | 7 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.56 | 0.56 | 0.78 | 0.56 | 0.56 |
time (sec) |
N/A | 0.110 | 0.001 | 0.037 | 0.183 | 0.237 | 0.032 | 0.281 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 9 | 8 | 8 | 7 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 0.70 | 0.80 | 0.80 |
time (sec) |
N/A | 0.142 | 0.008 | 0.076 | 0.184 | 0.240 | 0.045 | 0.263 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 8 | 7 | 7 | 7 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.130 | 0.001 | 0.032 | 0.190 | 0.226 | 0.046 | 0.251 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 9 | 19 | 8 | 7 | 7 | 8 | 7 | 7 |
N.S. |
1 | 0.90 | 1.90 | 0.80 | 0.70 | 0.70 | 0.80 | 0.70 | 0.70 |
time (sec) |
N/A | 0.187 | 0.029 | 0.150 | 0.201 | 0.259 | 0.285 | 0.261 | 0.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 18 | 13 | 15 | 15 | 34 | 15 | 12 |
N.S. |
1 | 1.00 | 0.78 | 0.57 | 0.65 | 0.65 | 1.48 | 0.65 | 0.52 |
time (sec) |
N/A | 0.138 | 0.016 | 0.109 | 0.191 | 0.230 | 0.555 | 0.289 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 25 | 10 | 17 | 17 | 17 | 19 | 9 |
N.S. |
1 | 1.00 | 1.92 | 0.77 | 1.31 | 1.31 | 1.31 | 1.46 | 0.69 |
time (sec) |
N/A | 0.129 | 0.004 | 0.127 | 0.275 | 0.253 | 0.063 | 0.268 | 0.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 14 | 13 | 13 | 15 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.72 | 0.72 | 0.83 | 0.72 | 0.72 |
time (sec) |
N/A | 0.157 | 0.038 | 0.049 | 0.283 | 0.251 | 0.062 | 0.264 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 20 | 19 | 76 | 22 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.65 | 0.61 | 2.45 | 0.71 | 0.61 | 0.61 |
time (sec) |
N/A | 0.176 | 0.039 | 0.087 | 0.294 | 0.245 | 0.078 | 0.270 | 0.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 9 | 8 | 11 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 1.00 | 1.38 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.176 | 0.016 | 0.041 | 0.182 | 0.258 | 0.040 | 0.289 | 0.211 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 15 | 14 | 14 | 10 | 13 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.25 | 1.17 | 1.17 | 0.83 | 1.08 | 1.00 |
time (sec) |
N/A | 0.137 | 0.004 | 0.054 | 0.186 | 0.233 | 0.033 | 0.266 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 18 | 20 | 17 | 16 | 16 | 15 | 16 | 16 |
N.S. |
1 | 0.90 | 1.00 | 0.85 | 0.80 | 0.80 | 0.75 | 0.80 | 0.80 |
time (sec) |
N/A | 0.218 | 0.001 | 0.144 | 0.186 | 0.245 | 0.122 | 0.267 | 0.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 55 | 260 | 41 | 40 | 40 | 46 | 40 | 52 |
N.S. |
1 | 1.12 | 5.31 | 0.84 | 0.82 | 0.82 | 0.94 | 0.82 | 1.06 |
time (sec) |
N/A | 0.195 | 0.118 | 0.146 | 0.280 | 0.239 | 0.078 | 0.275 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 142 | 41 | 0 | 0 | 54 | 0 | 0 |
N.S. |
1 | 1.00 | 1.23 | 0.36 | 0.00 | 0.00 | 0.47 | 0.00 | 0.00 |
time (sec) |
N/A | 0.243 | 0.306 | 0.385 | 0.000 | 0.000 | 1.501 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 22 | 17 | 16 | 16 | 20 | 16 | 16 |
N.S. |
1 | 0.95 | 1.00 | 0.77 | 0.73 | 0.73 | 0.91 | 0.73 | 0.73 |
time (sec) |
N/A | 0.210 | 0.018 | 0.075 | 0.192 | 0.250 | 0.096 | 0.277 | 0.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 18 | 13 | 15 | 15 | 34 | 15 | 12 |
N.S. |
1 | 1.00 | 0.78 | 0.57 | 0.65 | 0.65 | 1.48 | 0.65 | 0.52 |
time (sec) |
N/A | 0.134 | 0.002 | 0.105 | 0.198 | 0.228 | 0.559 | 0.282 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 36 | 33 | 25 | 24 | 24 | 0 | 24 | 24 |
N.S. |
1 | 1.12 | 1.03 | 0.78 | 0.75 | 0.75 | 0.00 | 0.75 | 0.75 |
time (sec) |
N/A | 0.161 | 0.006 | 0.093 | 0.188 | 0.240 | 0.000 | 0.284 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 75 | 75 | 80 | 55 | 0 | 61 | 57 |
N.S. |
1 | 1.00 | 1.70 | 1.70 | 1.82 | 1.25 | 0.00 | 1.39 | 1.30 |
time (sec) |
N/A | 0.154 | 0.141 | 0.191 | 0.284 | 0.250 | 0.000 | 0.290 | 0.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 44 | 30 | 44 | 63 | 105 | 29 | 91 |
N.S. |
1 | 1.00 | 1.26 | 0.86 | 1.26 | 1.80 | 3.00 | 0.83 | 2.60 |
time (sec) |
N/A | 0.141 | 0.106 | 0.257 | 0.273 | 0.250 | 0.398 | 0.279 | 0.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 85 | 52 | 44 | 113 | 44 | 190 | 90 | 0 |
N.S. |
1 | 1.13 | 0.69 | 0.59 | 1.51 | 0.59 | 2.53 | 1.20 | 0.00 |
time (sec) |
N/A | 0.158 | 0.091 | 0.120 | 0.177 | 0.241 | 18.654 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 44 | 30 | 44 | 63 | 105 | 29 | 91 |
N.S. |
1 | 1.00 | 1.26 | 0.86 | 1.26 | 1.80 | 3.00 | 0.83 | 2.60 |
time (sec) |
N/A | 0.139 | 0.005 | 0.165 | 0.276 | 0.235 | 0.391 | 0.272 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 78 | 90 | 114 | 129 | 0 | 295 | 0 |
N.S. |
1 | 1.00 | 1.53 | 1.76 | 2.24 | 2.53 | 0.00 | 5.78 | 0.00 |
time (sec) |
N/A | 0.182 | 1.540 | 0.566 | 0.272 | 0.262 | 0.000 | 0.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 11 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.145 | 0.002 | 0.061 | 0.191 | 0.256 | 0.018 | 0.269 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 57 | 99 | 149 | 116 | 244 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 2.02 | 3.04 | 2.37 | 4.98 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.264 | 0.166 | 1.128 | 0.274 | 0.321 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 6 | 5 | 9 | 9 | 3 | 30 | 4 |
N.S. |
1 | 1.00 | 0.67 | 0.56 | 1.00 | 1.00 | 0.33 | 3.33 | 0.44 |
time (sec) |
N/A | 0.158 | 0.003 | 0.054 | 0.189 | 0.249 | 0.098 | 0.285 | 0.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 7 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 1.00 | 0.64 | 0.64 | 0.55 | 0.55 | 0.45 | 0.55 | 0.55 |
time (sec) |
N/A | 0.150 | 0.001 | 0.026 | 0.185 | 0.236 | 0.028 | 0.267 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 9 | 8 | 8 | 5 | 30 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.89 | 0.89 | 0.56 | 3.33 | 0.89 |
time (sec) |
N/A | 0.151 | 0.070 | 0.100 | 0.188 | 0.232 | 0.033 | 0.287 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.86 | 0.86 | 0.71 | 0.86 | 0.86 |
time (sec) |
N/A | 0.169 | 0.002 | 0.040 | 0.187 | 0.239 | 0.032 | 0.285 | 0.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 8 | 9 | 7 | 8 | 9 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.82 | 0.64 | 0.73 | 0.82 | 0.64 |
time (sec) |
N/A | 0.127 | 0.001 | 0.018 | 0.185 | 0.235 | 0.081 | 0.274 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 2 | 8 | 2 | 2 | 2 | 2 | 2 |
N.S. |
1 | 1.00 | 1.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.130 | 0.001 | 0.033 | 0.221 | 0.237 | 0.366 | 0.269 | 0.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 45 | 40 | 33 | 34 | 34 | 41 | 35 | 46 |
N.S. |
1 | 1.10 | 0.98 | 0.80 | 0.83 | 0.83 | 1.00 | 0.85 | 1.12 |
time (sec) |
N/A | 0.183 | 0.010 | 0.116 | 0.263 | 0.240 | 0.061 | 0.270 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 79 | 75 | 66 | 65 | 65 | 83 | 67 | 88 |
N.S. |
1 | 1.68 | 1.60 | 1.40 | 1.38 | 1.38 | 1.77 | 1.43 | 1.87 |
time (sec) |
N/A | 0.220 | 0.014 | 0.112 | 0.260 | 0.240 | 0.127 | 0.285 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 30 | 39 | 27 | 70 | 41 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.43 | 1.86 | 1.29 | 3.33 | 1.95 | 1.00 |
time (sec) |
N/A | 0.134 | 0.005 | 0.189 | 0.195 | 0.237 | 0.151 | 0.270 | 0.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.53 |
time (sec) |
N/A | 0.135 | 0.000 | 0.019 | 0.179 | 0.243 | 0.031 | 0.275 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 43 | 29 | 34 | 33 | 24 | 32 | 38 | 24 |
N.S. |
1 | 1.08 | 0.72 | 0.85 | 0.82 | 0.60 | 0.80 | 0.95 | 0.60 |
time (sec) |
N/A | 0.201 | 0.009 | 0.012 | 0.265 | 0.243 | 0.093 | 0.277 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 7 | 8 | 7 | 7 | 5 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.00 | 1.00 | 0.71 | 1.00 | 1.00 |
time (sec) |
N/A | 0.122 | 0.001 | 0.122 | 0.206 | 0.238 | 0.026 | 0.265 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 9 | 8 | 8 | 5 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 1.00 | 1.00 | 0.62 | 1.00 | 1.00 |
time (sec) |
N/A | 0.176 | 0.016 | 0.119 | 0.179 | 0.231 | 0.035 | 0.275 | 0.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 3 | 4 | 3 | 3 | 15 | 3 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.00 | 1.00 | 5.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.145 | 0.028 | 0.095 | 0.264 | 0.242 | 0.069 | 0.259 | 0.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 2 | 9 | 3 | 2 | 2 | 3 | 2 |
N.S. |
1 | 1.00 | 1.00 | 4.50 | 1.50 | 1.00 | 1.00 | 1.50 | 1.00 |
time (sec) |
N/A | 0.124 | 0.001 | 0.015 | 0.200 | 0.237 | 0.173 | 0.261 | 0.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 14 | 14 | 15 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.00 | 1.07 | 1.00 | 1.00 |
time (sec) |
N/A | 0.158 | 0.006 | 0.194 | 0.188 | 0.261 | 0.069 | 0.267 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 13 | 13 | 11 | 14 | 8 | 11 | 15 |
N.S. |
1 | 1.00 | 0.76 | 0.76 | 0.65 | 0.82 | 0.47 | 0.65 | 0.88 |
time (sec) |
N/A | 0.194 | 0.006 | 0.030 | 0.186 | 0.250 | 0.044 | 0.268 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 29 | 25 | 24 | 24 | 26 | 24 | 28 |
N.S. |
1 | 1.00 | 0.76 | 0.66 | 0.63 | 0.63 | 0.68 | 0.63 | 0.74 |
time (sec) |
N/A | 0.179 | 0.055 | 0.037 | 0.189 | 0.240 | 0.042 | 0.276 | 0.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 7 | 8 | 7 | 7 | 7 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.176 | 0.003 | 0.082 | 0.215 | 0.233 | 0.070 | 0.279 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 22 | 17 | 16 | 16 | 20 | 16 | 16 |
N.S. |
1 | 0.95 | 1.00 | 0.77 | 0.73 | 0.73 | 0.91 | 0.73 | 0.73 |
time (sec) |
N/A | 0.208 | 0.006 | 0.066 | 0.192 | 0.245 | 0.107 | 0.279 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 7 | 8 | 7 | 7 | 7 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.180 | 0.002 | 0.055 | 0.180 | 0.250 | 0.061 | 0.274 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 23 | 17 | 22 | 22 | 22 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.61 | 0.79 | 0.79 | 0.79 | 0.61 |
time (sec) |
N/A | 0.158 | 0.001 | 0.024 | 0.180 | 0.231 | 0.040 | 0.278 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 10 | 9 | 15 | 8 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.82 | 1.36 | 0.73 | 0.82 | 0.82 |
time (sec) |
N/A | 0.170 | 0.004 | 0.190 | 0.183 | 0.240 | 0.121 | 0.278 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 3 | 4 | 3 | 3 | 15 | 3 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.00 | 1.00 | 5.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.141 | 0.003 | 0.083 | 0.283 | 0.245 | 0.091 | 0.282 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 3 | 4 | 0 | 3 | 3 | 3 | 43 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 0.00 | 1.00 | 1.00 | 1.00 | 14.33 |
time (sec) |
N/A | 0.189 | 0.103 | 0.118 | 0.000 | 0.251 | 0.133 | 0.288 | 2.835 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 20 | 53 | 15 | 12 | 21 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.25 | 3.31 | 0.94 | 0.75 | 1.31 | 0.81 |
time (sec) |
N/A | 0.229 | 0.053 | 0.257 | 0.316 | 0.246 | 0.055 | 0.304 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 73 | 89 | 115 | 128 | 0 | 295 | 0 |
N.S. |
1 | 1.00 | 1.38 | 1.68 | 2.17 | 2.42 | 0.00 | 5.57 | 0.00 |
time (sec) |
N/A | 0.215 | 0.194 | 0.273 | 0.291 | 0.257 | 0.000 | 0.354 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 46 | 35 | 71 | 69 | 67 | 202 | 83 | 360 |
N.S. |
1 | 2.88 | 2.19 | 4.44 | 4.31 | 4.19 | 12.62 | 5.19 | 22.50 |
time (sec) |
N/A | 0.275 | 0.268 | 0.625 | 0.265 | 0.265 | 106.059 | 0.287 | 0.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | C | B | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 44 | 35 | 70 | 68 | 26 | 422 | 82 | 352 |
N.S. |
1 | 2.75 | 2.19 | 4.38 | 4.25 | 1.62 | 26.38 | 5.12 | 22.00 |
time (sec) |
N/A | 0.299 | 0.022 | 0.178 | 0.277 | 0.255 | 0.991 | 0.284 | 0.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | C | B | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 44 | 35 | 40 | 65 | 26 | 422 | 79 | 352 |
N.S. |
1 | 2.75 | 2.19 | 2.50 | 4.06 | 1.62 | 26.38 | 4.94 | 22.00 |
time (sec) |
N/A | 0.159 | 0.016 | 0.210 | 0.263 | 0.253 | 1.009 | 0.274 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 44 | 30 | 44 | 63 | 105 | 29 | 91 |
N.S. |
1 | 1.00 | 1.26 | 0.86 | 1.26 | 1.80 | 3.00 | 0.83 | 2.60 |
time (sec) |
N/A | 0.144 | 0.016 | 0.204 | 0.282 | 0.241 | 0.382 | 0.277 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 13 | 12 | 26 | 19 | 12 | 12 |
N.S. |
1 | 1.00 | 1.14 | 0.93 | 0.86 | 1.86 | 1.36 | 0.86 | 0.86 |
time (sec) |
N/A | 0.194 | 0.007 | 0.197 | 0.279 | 0.244 | 0.022 | 0.283 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 11 | 8 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 0.62 | 0.85 | 0.85 |
time (sec) |
N/A | 0.133 | 0.005 | 0.132 | 0.267 | 0.229 | 0.032 | 0.265 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.86 | 0.86 | 0.71 | 0.86 | 0.86 |
time (sec) |
N/A | 0.163 | 0.002 | 0.039 | 0.188 | 0.240 | 0.032 | 0.276 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 19 | 24 | 23 | 23 | 20 | 30 | 24 |
N.S. |
1 | 1.00 | 0.79 | 1.00 | 0.96 | 0.96 | 0.83 | 1.25 | 1.00 |
time (sec) |
N/A | 0.442 | 0.379 | 0.128 | 0.301 | 0.239 | 0.048 | 0.278 | 0.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 9 | 8 | 8 | 7 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.89 | 0.89 | 0.78 | 0.89 | 0.89 |
time (sec) |
N/A | 0.135 | 0.015 | 0.026 | 0.182 | 0.236 | 0.029 | 0.255 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 20 | 24 | 19 | 19 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.96 | 0.76 | 0.76 | 0.76 | 0.76 |
time (sec) |
N/A | 0.192 | 0.004 | 0.037 | 0.185 | 0.244 | 0.039 | 0.257 | 0.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.62 | 0.75 | 0.75 |
time (sec) |
N/A | 0.127 | 0.004 | 0.124 | 0.266 | 0.236 | 0.038 | 0.271 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 14 | 16 | 13 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 0.88 | 1.00 | 0.81 | 0.75 | 0.75 | 0.62 | 0.75 | 0.75 |
time (sec) |
N/A | 0.134 | 0.006 | 0.133 | 0.273 | 0.227 | 0.040 | 0.252 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 11 | 16 | 20 | 36 | 16 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 1.14 | 1.43 | 2.57 | 1.14 | 0.71 |
time (sec) |
N/A | 0.191 | 0.003 | 0.055 | 0.298 | 0.238 | 0.178 | 0.262 | 0.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 44 | 30 | 44 | 63 | 105 | 29 | 91 |
N.S. |
1 | 1.00 | 1.26 | 0.86 | 1.26 | 1.80 | 3.00 | 0.83 | 2.60 |
time (sec) |
N/A | 0.147 | 0.001 | 0.176 | 0.295 | 0.242 | 0.391 | 0.269 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 35 | 16 | 15 | 45 | 34 | 21 | 37 |
N.S. |
1 | 1.00 | 2.06 | 0.94 | 0.88 | 2.65 | 2.00 | 1.24 | 2.18 |
time (sec) |
N/A | 0.134 | 0.074 | 0.191 | 0.276 | 0.255 | 0.180 | 0.277 | 0.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 14 | 12 | 11 | 13 | 15 | 11 | 11 |
N.S. |
1 | 1.00 | 0.74 | 0.63 | 0.58 | 0.68 | 0.79 | 0.58 | 0.58 |
time (sec) |
N/A | 0.146 | 0.007 | 0.074 | 0.177 | 0.254 | 0.088 | 0.253 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 1.00 | 1.00 | 1.00 | 1.50 | 1.00 |
time (sec) |
N/A | 0.113 | 0.000 | 0.010 | 0.178 | 0.234 | 0.033 | 0.262 | 0.007 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 40 | 73 | 31 | 256 | 71 | 0 | 33 | 32 |
N.S. |
1 | 0.89 | 1.62 | 0.69 | 5.69 | 1.58 | 0.00 | 0.73 | 0.71 |
time (sec) |
N/A | 0.276 | 0.713 | 1.533 | 0.357 | 0.279 | 0.000 | 0.283 | 0.707 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 11 | 10 | 10 | 10 | 16 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.71 | 1.14 | 0.71 |
time (sec) |
N/A | 0.148 | 0.002 | 0.054 | 0.179 | 0.237 | 0.023 | 0.269 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 14 | 11 | 11 | 10 | 14 | 11 | 10 |
N.S. |
1 | 1.00 | 0.82 | 0.65 | 0.65 | 0.59 | 0.82 | 0.65 | 0.59 |
time (sec) |
N/A | 0.131 | 0.013 | 0.040 | 0.182 | 0.234 | 0.077 | 0.254 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 25 | 31 | 20 | 19 | 27 | 19 | 27 | 27 |
N.S. |
1 | 1.09 | 1.35 | 0.87 | 0.83 | 1.17 | 0.83 | 1.17 | 1.17 |
time (sec) |
N/A | 0.161 | 0.069 | 0.378 | 0.271 | 0.239 | 0.255 | 0.306 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 10 | 5 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 1.25 | 0.62 | 0.75 | 0.75 |
time (sec) |
N/A | 0.158 | 0.002 | 0.079 | 0.176 | 0.265 | 0.034 | 0.264 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 6 | 6 | 5 | 5 | 5 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.140 | 0.001 | 0.023 | 0.184 | 0.242 | 0.032 | 0.254 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 0.83 |
time (sec) |
N/A | 0.160 | 0.002 | 0.033 | 0.191 | 0.238 | 0.037 | 0.280 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 8 | 9 | 10 | 10 | 7 | 8 | 6 |
N.S. |
1 | 1.00 | 0.67 | 0.75 | 0.83 | 0.83 | 0.58 | 0.67 | 0.50 |
time (sec) |
N/A | 0.157 | 0.006 | 0.069 | 0.179 | 0.247 | 0.163 | 0.270 | 0.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 |
time (sec) |
N/A | 0.152 | 0.002 | 0.142 | 0.172 | 0.239 | 0.021 | 0.261 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.53 |
time (sec) |
N/A | 0.136 | 0.000 | 0.019 | 0.181 | 0.234 | 0.038 | 0.269 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.62 | 0.75 | 0.75 |
time (sec) |
N/A | 0.149 | 0.001 | 0.036 | 0.196 | 0.236 | 0.032 | 0.264 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 28 | 47 | 21 | 22 | 32 | 15 | 20 | 20 |
N.S. |
1 | 1.17 | 1.96 | 0.88 | 0.92 | 1.33 | 0.62 | 0.83 | 0.83 |
time (sec) |
N/A | 0.153 | 0.063 | 0.408 | 0.265 | 0.250 | 0.348 | 0.278 | 0.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 14 | 13 | 19 | 15 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.70 | 0.65 | 0.95 | 0.75 | 0.65 | 0.65 |
time (sec) |
N/A | 0.158 | 0.006 | 0.046 | 0.267 | 0.232 | 0.049 | 0.263 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 44 | 30 | 44 | 63 | 105 | 29 | 91 |
N.S. |
1 | 1.00 | 1.26 | 0.86 | 1.26 | 1.80 | 3.00 | 0.83 | 2.60 |
time (sec) |
N/A | 0.140 | 0.013 | 0.180 | 0.299 | 0.248 | 0.403 | 0.282 | 0.002 |