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 | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 30 | 24 | 21 | 30 | 20 | 19 | 0 | 18 | 20 |
N.S. |
1 | 1.25 | 1.00 | 0.88 | 1.25 | 0.83 | 0.79 | 0.00 | 0.75 | 0.83 |
time (sec) |
N/A | 0.498 | 14.666 | 0.195 | 0.325 | 0.230 | 0.280 | 0.000 | 0.001 | 0.327 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 71 | 24 | 31 | 29 | 24 | 51 | 25 | 23 |
N.S. |
1 | 1.00 | 2.63 | 0.89 | 1.15 | 1.07 | 0.89 | 1.89 | 0.93 | 0.85 |
time (sec) |
N/A | 0.150 | 0.005 | 0.138 | 0.197 | 0.233 | 0.081 | 0.285 | 0.000 | 0.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 92 | 82 | 25 | 0 | 216 | 51 | 0 | 117 | 0 |
N.S. |
1 | 1.12 | 1.00 | 0.30 | 0.00 | 2.63 | 0.62 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.226 | 0.070 | 0.072 | 0.000 | 0.253 | 1.829 | 0.000 | 0.004 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 20 | 40 | 29 | 48 | 10 | 16 | 169 |
N.S. |
1 | 1.00 | 1.00 | 1.67 | 3.33 | 2.42 | 4.00 | 0.83 | 1.33 | 14.08 |
time (sec) |
N/A | 0.238 | 0.011 | 0.326 | 0.277 | 0.238 | 49.819 | 0.270 | 0.003 | 0.058 |
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 | 40 | 40 | 40 | 33 | 36 | 85 | 66 | 55 | 34 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.90 | 2.12 | 1.65 | 1.38 | 0.85 | 0.80 |
time (sec) |
N/A | 0.144 | 0.008 | 0.142 | 0.196 | 0.239 | 0.556 | 0.266 | 0.000 | 0.450 |
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 | 46 | 41 | 57 | 41 | 42 | 40 | 56 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.24 | 0.89 | 0.91 | 0.87 | 1.22 | 0.87 |
time (sec) |
N/A | 0.172 | 0.028 | 0.431 | 0.295 | 0.232 | 0.617 | 0.261 | 0.001 | 0.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 45 | 52 | 40 | 52 | 0 | 40 | 45 | 51 |
N.S. |
1 | 1.00 | 1.22 | 1.41 | 1.08 | 1.41 | 0.00 | 1.08 | 1.22 | 1.38 |
time (sec) |
N/A | 0.158 | 0.075 | 0.451 | 0.279 | 0.249 | 0.000 | 0.294 | 0.005 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 66 | 74 | 77 | 97 | 0 | 57 | 71 | 72 |
N.S. |
1 | 1.00 | 1.08 | 1.21 | 1.26 | 1.59 | 0.00 | 0.93 | 1.16 | 1.18 |
time (sec) |
N/A | 0.174 | 0.101 | 0.480 | 0.282 | 0.248 | 0.000 | 0.325 | 0.009 | 0.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 20 | 19 | 19 | 29 | 19 | 18 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.83 | 0.83 | 1.26 | 0.83 | 0.78 | 0.83 |
time (sec) |
N/A | 0.131 | 0.003 | 0.112 | 0.194 | 0.242 | 0.155 | 0.281 | 0.001 | 0.289 |
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 | 28 | 28 | 28 | 25 | 24 | 24 | 36 | 24 | 23 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.86 | 0.86 | 1.29 | 0.86 | 0.82 | 0.86 |
time (sec) |
N/A | 0.133 | 0.003 | 0.137 | 0.205 | 0.240 | 0.157 | 0.262 | 0.001 | 0.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 63 | 46 | 0 | 152 | 0 | 58 | 25 | 50 |
N.S. |
1 | 1.00 | 1.12 | 0.82 | 0.00 | 2.71 | 0.00 | 1.04 | 0.45 | 0.89 |
time (sec) |
N/A | 0.174 | 0.111 | 0.657 | 0.000 | 0.248 | 0.000 | 0.286 | 0.004 | 0.953 |
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 | 81 | 81 | 89 | 70 | 0 | 190 | 172 | 75 | 77 | 67 |
N.S. |
1 | 1.00 | 1.10 | 0.86 | 0.00 | 2.35 | 2.12 | 0.93 | 0.95 | 0.83 |
time (sec) |
N/A | 0.188 | 0.188 | 0.463 | 0.000 | 0.242 | 0.415 | 0.308 | 0.002 | 0.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 53 | 56 | 0 | 58 | 0 | 45 | 27 | 54 |
N.S. |
1 | 1.00 | 1.20 | 1.27 | 0.00 | 1.32 | 0.00 | 1.02 | 0.61 | 1.23 |
time (sec) |
N/A | 0.179 | 0.080 | 0.134 | 0.000 | 0.241 | 0.000 | 0.271 | 0.010 | 0.400 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 72 | 78 | 0 | 106 | 0 | 62 | 32 | 72 |
N.S. |
1 | 1.00 | 1.06 | 1.15 | 0.00 | 1.56 | 0.00 | 0.91 | 0.47 | 1.06 |
time (sec) |
N/A | 0.197 | 0.107 | 0.132 | 0.000 | 0.253 | 0.000 | 0.294 | 0.013 | 0.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 22 | 10 | 11 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.69 | 0.77 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.172 | 0.005 | 0.125 | 0.197 | 0.236 | 0.092 | 0.276 | 0.000 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 12 | 15 | 11 | 17 | 15 | 13 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.63 | 0.79 | 0.58 | 0.89 | 0.79 | 0.68 | 0.58 |
time (sec) |
N/A | 0.142 | 0.002 | 0.029 | 0.200 | 0.221 | 0.040 | 0.263 | 0.000 | 0.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 13 | 20 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.67 | 1.00 | 0.83 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.189 | 0.020 | 0.138 | 0.200 | 0.238 | 0.068 | 0.279 | 0.000 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 11 | 10 | 10 | 7 | 10 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.91 | 0.91 | 0.64 | 0.91 | 1.00 | 0.91 |
time (sec) |
N/A | 0.157 | 0.007 | 0.043 | 0.248 | 0.240 | 0.066 | 0.265 | 0.000 | 0.214 |
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 | 26 | 27 | 23 | 23 | 22 | 20 | 24 | 22 | 22 |
N.S. |
1 | 0.96 | 1.00 | 0.85 | 0.85 | 0.81 | 0.74 | 0.89 | 0.81 | 0.81 |
time (sec) |
N/A | 0.153 | 0.004 | 0.095 | 0.194 | 0.219 | 0.063 | 0.292 | 0.000 | 0.168 |
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 | 33 | 33 | 21 | 16 | 20 | 50 | 167 | 66 | 53 | 15 |
N.S. |
1 | 1.00 | 0.64 | 0.48 | 0.61 | 1.52 | 5.06 | 2.00 | 1.61 | 0.45 |
time (sec) |
N/A | 0.128 | 0.046 | 0.089 | 0.205 | 0.230 | 2.378 | 0.299 | 0.002 | 0.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 9 | 9 | 7 | 11 | 9 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 | 0.78 | 1.22 | 1.00 | 0.89 |
time (sec) |
N/A | 0.120 | 0.002 | 0.089 | 0.191 | 0.227 | 0.035 | 0.270 | 0.000 | 0.203 |
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 | 19 | 19 | 19 | 14 | 28 | 28 | 39 | 32 | 25 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 1.47 | 1.47 | 2.05 | 1.68 | 1.32 | 0.68 |
time (sec) |
N/A | 0.129 | 0.021 | 0.151 | 0.284 | 0.227 | 0.111 | 0.259 | 0.000 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 16 | 12 | 11 | 14 | 15 | 11 | 12 | 12 |
N.S. |
1 | 1.00 | 0.84 | 0.63 | 0.58 | 0.74 | 0.79 | 0.58 | 0.63 | 0.63 |
time (sec) |
N/A | 0.128 | 0.008 | 0.039 | 0.188 | 0.232 | 0.308 | 0.267 | 0.000 | 0.023 |
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 | 88 | 89 | 112 | 89 | 86 | 104 | 153 | 103 | 141 | 119 |
N.S. |
1 | 1.01 | 1.27 | 1.01 | 0.98 | 1.18 | 1.74 | 1.17 | 1.60 | 1.35 |
time (sec) |
N/A | 0.182 | 0.065 | 0.103 | 0.282 | 0.232 | 1.096 | 0.487 | 0.004 | 0.188 |
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 | 9 | 18 | 9 | 10 | 34 | 9 | 7 | 17 | 9 | 9 |
N.S. |
1 | 2.00 | 1.00 | 1.11 | 3.78 | 1.00 | 0.78 | 1.89 | 1.00 | 1.00 |
time (sec) |
N/A | 0.189 | 0.007 | 0.085 | 0.208 | 0.220 | 0.077 | 0.275 | 0.000 | 0.021 |
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 | 9 | 9 | 9 | 10 | 34 | 9 | 7 | 17 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 3.78 | 1.00 | 0.78 | 1.89 | 1.00 | 1.00 |
time (sec) |
N/A | 0.185 | 0.006 | 0.077 | 0.208 | 0.227 | 0.067 | 0.267 | 0.000 | 0.023 |
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 | 9 | 9 | 9 | 8 | 7 | 26 | 7 | 13 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 2.89 | 0.78 | 1.44 | 0.78 | 0.78 |
time (sec) |
N/A | 0.145 | 0.005 | 0.063 | 0.190 | 0.235 | 0.055 | 0.286 | 0.001 | 0.193 |
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 | 12 | 12 | 12 | 16 | 13 | 26 | 22 | 23 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.08 | 2.17 | 1.83 | 1.92 | 1.08 | 1.08 |
time (sec) |
N/A | 0.182 | 0.096 | 0.707 | 0.193 | 0.241 | 0.175 | 0.290 | 0.000 | 0.326 |
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 | 28 | 28 | 28 | 23 | 22 | 32 | 75 | 22 | 57 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.79 | 1.14 | 2.68 | 0.79 | 2.04 | 0.79 |
time (sec) |
N/A | 0.183 | 0.015 | 0.395 | 0.196 | 0.237 | 0.324 | 0.264 | 0.002 | 0.292 |
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 | 20 | 16 | 16 | 15 | 13 | 15 | 15 | 15 | 14 |
N.S. |
1 | 0.95 | 0.76 | 0.76 | 0.71 | 0.62 | 0.71 | 0.71 | 0.71 | 0.67 |
time (sec) |
N/A | 0.157 | 0.001 | 0.024 | 0.274 | 0.233 | 0.085 | 0.270 | 0.000 | 0.019 |
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 | 20 | 16 | 16 | 15 | 13 | 15 | 19 | 15 | 15 |
N.S. |
1 | 0.95 | 0.76 | 0.76 | 0.71 | 0.62 | 0.71 | 0.90 | 0.71 | 0.71 |
time (sec) |
N/A | 0.156 | 0.003 | 0.078 | 0.290 | 0.235 | 0.085 | 0.263 | 0.001 | 0.048 |
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 | 25 | 22 | 23 | 22 | 19 | 26 | 22 | 26 | 41 |
N.S. |
1 | 1.09 | 0.96 | 1.00 | 0.96 | 0.83 | 1.13 | 0.96 | 1.13 | 1.78 |
time (sec) |
N/A | 0.179 | 0.003 | 0.044 | 0.194 | 0.226 | 0.065 | 0.258 | 0.000 | 0.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 28 | 32 | 14 | 27 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 1.56 | 1.78 | 0.78 | 1.50 | 0.78 |
time (sec) |
N/A | 0.169 | 0.015 | 0.286 | 0.209 | 0.247 | 0.128 | 0.260 | 0.000 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 28 | 32 | 14 | 27 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 1.56 | 1.78 | 0.78 | 1.50 | 0.78 |
time (sec) |
N/A | 0.162 | 0.008 | 0.251 | 0.197 | 0.240 | 0.130 | 0.301 | 0.001 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 40 | 17 | 0 | 24 | 0 | 22 | 7 | 16 |
N.S. |
1 | 1.00 | 3.33 | 1.42 | 0.00 | 2.00 | 0.00 | 1.83 | 0.58 | 1.33 |
time (sec) |
N/A | 0.150 | 0.008 | 0.309 | 0.000 | 0.232 | 0.000 | 0.273 | 0.000 | 0.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 42 | 23 | 0 | 26 | 0 | 35 | 9 | 18 |
N.S. |
1 | 1.00 | 3.00 | 1.64 | 0.00 | 1.86 | 0.00 | 2.50 | 0.64 | 1.29 |
time (sec) |
N/A | 0.157 | 0.008 | 0.408 | 0.000 | 0.237 | 0.000 | 0.289 | 0.001 | 0.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 16 | 22 | 9 | 10 | 36 | 14 | 7 | 10 |
N.S. |
1 | 1.00 | 1.33 | 1.83 | 0.75 | 0.83 | 3.00 | 1.17 | 0.58 | 0.83 |
time (sec) |
N/A | 0.151 | 0.024 | 0.263 | 0.331 | 0.236 | 0.390 | 0.279 | 0.000 | 0.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 18 | 22 | 20 | 18 | 0 | 23 | 9 | 12 |
N.S. |
1 | 1.00 | 1.29 | 1.57 | 1.43 | 1.29 | 0.00 | 1.64 | 0.64 | 0.86 |
time (sec) |
N/A | 0.158 | 0.026 | 0.342 | 0.276 | 0.233 | 0.000 | 0.274 | 0.001 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 17 | 14 | 0 | 13 | 63 | 13 | 19 | 21 |
N.S. |
1 | 1.00 | 0.81 | 0.67 | 0.00 | 0.62 | 3.00 | 0.62 | 0.90 | 1.00 |
time (sec) |
N/A | 0.143 | 0.064 | 0.083 | 0.000 | 0.234 | 0.204 | 0.276 | 0.000 | 0.197 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 13 | 22 | 19 | 18 | 18 | 20 | 19 | 16 | 18 |
N.S. |
1 | 0.54 | 0.92 | 0.79 | 0.75 | 0.75 | 0.83 | 0.79 | 0.67 | 0.75 |
time (sec) |
N/A | 0.151 | 0.010 | 0.073 | 0.194 | 0.228 | 0.055 | 0.278 | 0.000 | 0.110 |
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 | 12 | 12 | 18 | 9 | 33 | 16 | 7 | 16 | 17 | 8 |
N.S. |
1 | 1.00 | 1.50 | 0.75 | 2.75 | 1.33 | 0.58 | 1.33 | 1.42 | 0.67 |
time (sec) |
N/A | 0.129 | 0.119 | 0.185 | 0.187 | 0.244 | 0.492 | 0.256 | 0.000 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 36 | 33 | 25 | 24 | 24 | 0 | 24 | 23 | 24 |
N.S. |
1 | 1.12 | 1.03 | 0.78 | 0.75 | 0.75 | 0.00 | 0.75 | 0.72 | 0.75 |
time (sec) |
N/A | 0.161 | 0.020 | 0.089 | 0.178 | 0.241 | 0.000 | 0.260 | 0.001 | 0.032 |
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 | 40 | 33 | 27 | 26 | 32 | 31 | 26 | 26 | 26 |
N.S. |
1 | 1.21 | 1.00 | 0.82 | 0.79 | 0.97 | 0.94 | 0.79 | 0.79 | 0.79 |
time (sec) |
N/A | 0.155 | 0.010 | 0.053 | 0.276 | 0.251 | 0.055 | 0.284 | 0.000 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 7 | 4 | 3 | 11 | 3 | 4 | 17 | 3 |
N.S. |
1 | 1.00 | 2.33 | 1.33 | 1.00 | 3.67 | 1.00 | 1.33 | 5.67 | 1.00 |
time (sec) |
N/A | 0.143 | 0.000 | 0.050 | 0.192 | 0.252 | 0.038 | 0.276 | 0.000 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 22 | 11 | 16 | 48 | 19 | 34 | 10 | 10 |
N.S. |
1 | 1.00 | 1.83 | 0.92 | 1.33 | 4.00 | 1.58 | 2.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.195 | 0.001 | 0.065 | 0.268 | 0.295 | 0.026 | 0.264 | 0.001 | 0.024 |
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 | 3 | 3 | 3 | 4 | 3 | 18 | 7 | 11 | 12 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.00 | 6.00 | 2.33 | 3.67 | 4.00 | 1.00 |
time (sec) |
N/A | 0.154 | 0.004 | 0.055 | 0.186 | 0.269 | 0.062 | 0.275 | 0.000 | 0.012 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 7 | 4 | 3 | 18 | 12 | 12 | 16 | 3 |
N.S. |
1 | 1.00 | 2.33 | 1.33 | 1.00 | 6.00 | 4.00 | 4.00 | 5.33 | 1.00 |
time (sec) |
N/A | 0.145 | 0.005 | 0.103 | 0.238 | 0.250 | 0.161 | 0.267 | 0.000 | 0.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 9 | 8 | 8 | 8 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.128 | 0.000 | 0.033 | 0.194 | 0.248 | 0.034 | 0.270 | 0.000 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 36 | 29 | 32 | 10 | 10 | 0 | 11 | 10 | 0 |
N.S. |
1 | 0.73 | 0.59 | 0.65 | 0.20 | 0.20 | 0.00 | 0.22 | 0.20 | 0.00 |
time (sec) |
N/A | 0.183 | 1.008 | 0.064 | 0.280 | 0.239 | 0.000 | 0.275 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 17 | 11 | 12 | 12 | 12 | 13 | 12 | 10 |
N.S. |
1 | 1.00 | 1.06 | 0.69 | 0.75 | 0.75 | 0.75 | 0.81 | 0.75 | 0.62 |
time (sec) |
N/A | 0.139 | 0.003 | 0.088 | 0.201 | 0.237 | 0.028 | 0.281 | 0.000 | 0.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 45 | 36 | 53 | 0 | 30 | 0 | 40 | 35 | 32 |
N.S. |
1 | 1.12 | 0.90 | 1.32 | 0.00 | 0.75 | 0.00 | 1.00 | 0.88 | 0.80 |
time (sec) |
N/A | 0.170 | 0.008 | 0.024 | 0.000 | 0.260 | 0.000 | 0.276 | 0.001 | 0.043 |
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 | 128 | 128 | 67 | 63 | 58 | 55 | 109 | 57 | 77 | 69 |
N.S. |
1 | 1.00 | 0.52 | 0.49 | 0.45 | 0.43 | 0.85 | 0.45 | 0.60 | 0.54 |
time (sec) |
N/A | 0.367 | 0.108 | 0.422 | 0.223 | 0.276 | 0.577 | 0.273 | 0.001 | 0.280 |
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 | 30 | 30 | 18 | 16 | 17 | 17 | 27 | 15 | 18 | 17 |
N.S. |
1 | 1.00 | 0.60 | 0.53 | 0.57 | 0.57 | 0.90 | 0.50 | 0.60 | 0.57 |
time (sec) |
N/A | 0.192 | 0.020 | 0.127 | 0.195 | 0.245 | 0.168 | 0.264 | 0.001 | 0.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 9 | 8 | 7 | 17 | 17 | 7 | 19 | 7 |
N.S. |
1 | 1.00 | 0.82 | 0.73 | 0.64 | 1.55 | 1.55 | 0.64 | 1.73 | 0.64 |
time (sec) |
N/A | 0.121 | 0.001 | 0.087 | 0.198 | 0.227 | 0.036 | 0.274 | 0.000 | 0.065 |
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 | 45 | 40 | 31 | 32 | 32 | 41 | 33 | 31 | 46 |
N.S. |
1 | 1.12 | 1.00 | 0.78 | 0.80 | 0.80 | 1.02 | 0.82 | 0.78 | 1.15 |
time (sec) |
N/A | 0.181 | 0.006 | 0.106 | 0.270 | 0.271 | 0.053 | 0.259 | 0.000 | 0.112 |
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 | 8 | 8 | 23 | 7 | 17 | 17 | 15 | 18 | 21 | 6 |
N.S. |
1 | 1.00 | 2.88 | 0.88 | 2.12 | 2.12 | 1.88 | 2.25 | 2.62 | 0.75 |
time (sec) |
N/A | 0.124 | 0.003 | 0.095 | 0.198 | 0.254 | 0.038 | 0.271 | 0.000 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 227 | 194 | 394 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.379 | 0.188 | 0.372 | 0.000 | 0.000 | 0.000 | 0.000 | 0.003 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 26 | 25 | 24 | 37 | 25 | 30 | 51 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.04 | 1.00 | 1.54 | 1.04 | 1.25 | 2.12 |
time (sec) |
N/A | 0.148 | 0.005 | 0.106 | 0.187 | 0.265 | 0.704 | 0.282 | 0.000 | 0.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 74 | 71 | 22 | 57 | 69 | 73 | 58 | 51 | 70 |
N.S. |
1 | 0.95 | 0.91 | 0.28 | 0.73 | 0.88 | 0.94 | 0.74 | 0.65 | 0.90 |
time (sec) |
N/A | 0.223 | 0.016 | 0.093 | 0.285 | 0.248 | 0.147 | 0.277 | 0.001 | 0.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 16 | 3 | 2 | 14 | 2 | 25 | 9 | 2 |
N.S. |
1 | 1.00 | 8.00 | 1.50 | 1.00 | 7.00 | 1.00 | 12.50 | 4.50 | 1.00 |
time (sec) |
N/A | 0.115 | 0.000 | 0.098 | 0.290 | 0.231 | 0.056 | 0.277 | 0.000 | 0.002 |
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 | 33 | 21 | 20 | 25 | 24 | 25 | 26 | 20 |
N.S. |
1 | 1.00 | 1.22 | 0.78 | 0.74 | 0.93 | 0.89 | 0.93 | 0.96 | 0.74 |
time (sec) |
N/A | 0.131 | 0.020 | 0.186 | 0.273 | 0.244 | 0.079 | 0.269 | 0.001 | 0.042 |
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 | 10 | 10 | 10 | 11 | 10 | 16 | 8 | 11 | 20 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.60 | 0.80 | 1.10 | 2.00 | 1.00 |
time (sec) |
N/A | 0.132 | 0.002 | 0.077 | 0.210 | 0.226 | 0.030 | 0.280 | 0.000 | 0.033 |
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 | 14 | 12 | 14 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.75 | 0.88 | 0.81 | 0.88 |
time (sec) |
N/A | 0.147 | 0.002 | 0.013 | 0.288 | 0.280 | 0.051 | 0.292 | 0.000 | 0.227 |
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 | 29 | 34 | 33 | 24 | 32 | 38 | 31 | 24 |
N.S. |
1 | 1.08 | 0.72 | 0.85 | 0.82 | 0.60 | 0.80 | 0.95 | 0.78 | 0.60 |
time (sec) |
N/A | 0.181 | 0.010 | 0.014 | 0.464 | 0.257 | 0.094 | 0.293 | 0.000 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 17 | 29 | 14 | 13 | 29 | 0 | 15 | 49 | 9 |
N.S. |
1 | 0.81 | 1.38 | 0.67 | 0.62 | 1.38 | 0.00 | 0.71 | 2.33 | 0.43 |
time (sec) |
N/A | 0.273 | 0.081 | 0.401 | 0.200 | 0.266 | 0.000 | 0.282 | 0.002 | 0.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 11 | 10 | 10 | 10 | 16 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.71 | 1.14 | 0.71 | 0.71 |
time (sec) |
N/A | 0.154 | 0.001 | 0.062 | 0.185 | 0.255 | 0.020 | 0.283 | 0.001 | 0.002 |
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 | 18 | 18 | 18 | 17 | 16 | 18 | 14 | 18 | 18 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.89 | 1.00 | 0.78 | 1.00 | 1.00 | 0.89 |
time (sec) |
N/A | 0.155 | 0.003 | 0.119 | 0.189 | 0.239 | 0.056 | 0.266 | 0.000 | 0.153 |
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 | 0.115 | 0.012 | 0.155 | 0.269 | 0.250 | 0.076 | 0.260 | 0.000 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 16 | 5 | 4 | 14 | 3 | 25 | 13 | 4 |
N.S. |
1 | 1.00 | 2.67 | 0.83 | 0.67 | 2.33 | 0.50 | 4.17 | 2.17 | 0.67 |
time (sec) |
N/A | 0.115 | 0.012 | 0.126 | 0.283 | 0.258 | 0.071 | 0.278 | 0.001 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 24 | 21 | 17 | 16 | 16 | 22 | 16 | 15 | 16 |
N.S. |
1 | 1.14 | 1.00 | 0.81 | 0.76 | 0.76 | 1.05 | 0.76 | 0.71 | 0.76 |
time (sec) |
N/A | 0.137 | 0.008 | 0.632 | 0.272 | 0.255 | 0.049 | 0.269 | 0.000 | 0.143 |
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 | 53 | 53 | 51 | 42 | 47 | 73 | 46 | 46 | 79 | 45 |
N.S. |
1 | 1.00 | 0.96 | 0.79 | 0.89 | 1.38 | 0.87 | 0.87 | 1.49 | 0.85 |
time (sec) |
N/A | 0.218 | 0.014 | 0.055 | 0.283 | 0.251 | 0.077 | 0.267 | 0.000 | 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 | 49 | 49 | 49 | 46 | 41 | 41 | 762 | 44 | 65 | 46 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.84 | 0.84 | 15.55 | 0.90 | 1.33 | 0.94 |
time (sec) |
N/A | 0.232 | 0.018 | 0.123 | 0.191 | 0.262 | 55.063 | 0.268 | 0.001 | 0.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | F | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 12 | 207 | 54 | 270 | 14 | 54 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 17.25 | 4.50 | 22.50 | 1.17 | 4.50 | 1.17 |
time (sec) |
N/A | 0.144 | 2.289 | 0.102 | 0.306 | 0.252 | 7.443 | 0.259 | 0.002 | 0.286 |
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 | 28 | 28 | 28 | 28 | 27 | 44 | 26 | 27 | 54 | 27 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.96 | 1.57 | 0.93 | 0.96 | 1.93 | 0.96 |
time (sec) |
N/A | 0.320 | 37.104 | 0.617 | 0.228 | 0.274 | 0.166 | 0.278 | 0.001 | 0.342 |
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 | 199 | 180 | 136 | 125 | 160 | 145 | 1277 | 114 | 122 | 140 |
N.S. |
1 | 0.90 | 0.68 | 0.63 | 0.80 | 0.73 | 6.42 | 0.57 | 0.61 | 0.70 |
time (sec) |
N/A | 0.384 | 0.148 | 1.576 | 0.227 | 0.281 | 151.384 | 0.271 | 0.007 | 1.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 16 | 15 | 20 | 15 | 15 | 25 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.83 | 1.11 | 0.83 | 0.83 | 1.39 | 0.83 |
time (sec) |
N/A | 0.153 | 0.007 | 0.049 | 0.193 | 0.243 | 0.154 | 0.287 | 0.000 | 0.165 |
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 | 24 | 22 | 21 | 37 | 36 | 37 | 64 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.88 | 1.54 | 1.50 | 1.54 | 2.67 | 0.88 |
time (sec) |
N/A | 0.163 | 0.006 | 0.065 | 0.205 | 0.242 | 0.213 | 0.263 | 0.000 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | F(-1) | F | B | F | F | B | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 0 | 5141 | 0 | 0 | 179 | 0 | 0 | 786 | 0 |
N.S. |
1 | 0.00 | 54.69 | 0.00 | 0.00 | 1.90 | 0.00 | 0.00 | 8.36 | 0.00 |
time (sec) |
N/A | 0.000 | 16.142 | 180.000 | 0.000 | 0.325 | 0.000 | 0.000 | 0.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | F | F | B | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 0 | 630 | 352 | 0 | 223 | 0 | 0 | 706 | 0 |
N.S. |
1 | 0.00 | 4.44 | 2.48 | 0.00 | 1.57 | 0.00 | 0.00 | 4.97 | 0.00 |
time (sec) |
N/A | 0.000 | 3.375 | 3.294 | 0.000 | 0.316 | 0.000 | 0.000 | 0.060 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 31 | 250 | 171 | 162 | 0 | 76 | 15 | 172 |
N.S. |
1 | 1.00 | 1.48 | 11.90 | 8.14 | 7.71 | 0.00 | 3.62 | 0.71 | 8.19 |
time (sec) |
N/A | 0.431 | 0.923 | 0.398 | 0.254 | 0.255 | 0.000 | 0.284 | 0.024 | 2.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4030 | 0 | 3168 | 4640 | 0 | 0 | 0 | 0 | 907 | 0 |
N.S. |
1 | 0.00 | 0.79 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.000 | 13.546 | 2.312 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 306 | 181 | 1356 | 0 | 269 | 330 | 472 | 342 | 265 |
N.S. |
1 | 0.93 | 0.55 | 4.11 | 0.00 | 0.82 | 1.00 | 1.43 | 1.04 | 0.80 |
time (sec) |
N/A | 1.035 | 0.157 | 3.702 | 0.000 | 0.261 | 6.170 | 0.289 | 0.003 | 0.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4 | 4 | 4 | 5 | 4 | 4 | 5 | 4 | 11 | 4 |
N.S. |
1 | 1.00 | 1.00 | 1.25 | 1.00 | 1.00 | 1.25 | 1.00 | 2.75 | 1.00 |
time (sec) |
N/A | 0.185 | 0.002 | 0.411 | 0.202 | 0.249 | 0.273 | 0.262 | 0.001 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 0 | 71 | 61 | 0 | 137 | 76 | 94 | 339 | 103 |
N.S. |
1 | 0.00 | 1.00 | 0.86 | 0.00 | 1.93 | 1.07 | 1.32 | 4.77 | 1.45 |
time (sec) |
N/A | 0.000 | 0.066 | 0.094 | 0.000 | 0.263 | 0.106 | 0.297 | 0.006 | 0.280 |