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 | B | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 56 | 49 | 266 | 120 | 98 | 0 | 75 | 64 | 229 |
N.S. |
1 | 1.27 | 1.11 | 6.05 | 2.73 | 2.23 | 0.00 | 1.70 | 1.45 | 5.20 |
time (sec) |
N/A | 0.314 | 0.066 | 0.506 | 0.150 | 0.087 | 0.000 | 0.145 | 0.158 | 16.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 12 | 36 | 65 | 37 | 0 | 49 | 27 | 26 |
N.S. |
1 | 1.00 | 0.44 | 1.33 | 2.41 | 1.37 | 0.00 | 1.81 | 1.00 | 0.96 |
time (sec) |
N/A | 0.244 | 0.009 | 0.526 | 0.126 | 0.217 | 0.000 | 0.139 | 0.155 | 0.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 118 | 228 | 0 | 316 | 0 | 130 | 158 | 0 |
N.S. |
1 | 1.00 | 1.27 | 2.45 | 0.00 | 3.40 | 0.00 | 1.40 | 1.70 | 0.00 |
time (sec) |
N/A | 0.350 | 0.144 | 0.556 | 0.000 | 0.101 | 0.000 | 0.160 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 149 | 188 | 0 | 459 | 0 | 627 | 1078 | 0 |
N.S. |
1 | 1.00 | 0.99 | 1.25 | 0.00 | 3.06 | 0.00 | 4.18 | 7.19 | 0.00 |
time (sec) |
N/A | 0.412 | 0.175 | 0.777 | 0.000 | 0.119 | 0.000 | 0.149 | 0.158 | 0.000 |
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 | 127 | 128 | 107 | 123 | 210 | 136 | 286 | 127 | 177 | 118 |
N.S. |
1 | 1.01 | 0.84 | 0.97 | 1.65 | 1.07 | 2.25 | 1.00 | 1.39 | 0.93 |
time (sec) |
N/A | 0.308 | 0.167 | 0.352 | 0.109 | 0.099 | 0.862 | 0.155 | 0.157 | 0.048 |
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 | 105 | 104 | 91 | 107 | 164 | 115 | 235 | 103 | 139 | 100 |
N.S. |
1 | 0.99 | 0.87 | 1.02 | 1.56 | 1.10 | 2.24 | 0.98 | 1.32 | 0.95 |
time (sec) |
N/A | 0.282 | 0.133 | 0.300 | 0.112 | 0.095 | 0.848 | 0.155 | 0.151 | 0.034 |
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 | 83 | 80 | 75 | 91 | 118 | 92 | 184 | 78 | 101 | 82 |
N.S. |
1 | 0.96 | 0.90 | 1.10 | 1.42 | 1.11 | 2.22 | 0.94 | 1.22 | 0.99 |
time (sec) |
N/A | 0.264 | 0.107 | 0.260 | 0.111 | 0.108 | 0.916 | 0.166 | 0.156 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 54 | 57 | 71 | 64 | 63 | 114 | 46 | 61 | 80 |
N.S. |
1 | 0.98 | 1.04 | 1.29 | 1.16 | 1.15 | 2.07 | 0.84 | 1.11 | 1.45 |
time (sec) |
N/A | 0.231 | 0.080 | 0.211 | 0.108 | 0.102 | 0.698 | 0.132 | 0.158 | 16.775 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 122 | 74 | 121 | 204 | 86 | 0 | 102 | 152 | 140 |
N.S. |
1 | 1.09 | 0.66 | 1.08 | 1.82 | 0.77 | 0.00 | 0.91 | 1.36 | 1.25 |
time (sec) |
N/A | 0.476 | 0.027 | 0.258 | 0.202 | 0.082 | 0.000 | 0.144 | 0.152 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 86 | 65 | 112 | 178 | 77 | 0 | 0 | 123 | 128 |
N.S. |
1 | 0.99 | 0.75 | 1.29 | 2.05 | 0.89 | 0.00 | 0.00 | 1.41 | 1.47 |
time (sec) |
N/A | 0.376 | 0.023 | 0.248 | 0.174 | 0.095 | 0.000 | 0.000 | 0.155 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 61 | 54 | 93 | 157 | 69 | 0 | 78 | 94 | 93 |
N.S. |
1 | 1.02 | 0.90 | 1.55 | 2.62 | 1.15 | 0.00 | 1.30 | 1.57 | 1.55 |
time (sec) |
N/A | 0.310 | 0.014 | 0.243 | 0.148 | 0.124 | 0.000 | 0.148 | 0.153 | 15.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 37 | 45 | 76 | 137 | 64 | 0 | 59 | 45 | 64 |
N.S. |
1 | 0.95 | 1.15 | 1.95 | 3.51 | 1.64 | 0.00 | 1.51 | 1.15 | 1.64 |
time (sec) |
N/A | 0.269 | 0.014 | 0.224 | 0.134 | 0.083 | 0.000 | 0.149 | 0.150 | 15.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 26 | 25 | 125 | 33 | 0 | 37 | 26 | 47 |
N.S. |
1 | 1.00 | 2.00 | 1.92 | 9.62 | 2.54 | 0.00 | 2.85 | 2.00 | 3.62 |
time (sec) |
N/A | 0.213 | 0.007 | 0.226 | 0.114 | 0.082 | 0.000 | 0.127 | 0.153 | 0.022 |
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 | 44 | 42 | 53 | 60 | 0 | 55 | 0 | 80 | 51 | 67 |
N.S. |
1 | 0.95 | 1.20 | 1.36 | 0.00 | 1.25 | 0.00 | 1.82 | 1.16 | 1.52 |
time (sec) |
N/A | 0.305 | 0.017 | 0.236 | 0.000 | 0.093 | 0.000 | 0.133 | 0.158 | 14.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 63 | 67 | 75 | 104 | 78 | 0 | 159 | 84 | 90 |
N.S. |
1 | 0.93 | 0.99 | 1.10 | 1.53 | 1.15 | 0.00 | 2.34 | 1.24 | 1.32 |
time (sec) |
N/A | 0.331 | 0.019 | 0.252 | 0.039 | 0.072 | 0.000 | 0.138 | 0.164 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 92 | 83 | 97 | 0 | 99 | 0 | 224 | 151 | 117 |
N.S. |
1 | 0.93 | 0.84 | 0.98 | 0.00 | 1.00 | 0.00 | 2.26 | 1.53 | 1.18 |
time (sec) |
N/A | 0.421 | 0.031 | 0.270 | 0.000 | 0.097 | 0.000 | 0.134 | 0.155 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 121 | 91 | 117 | 148 | 107 | 0 | 283 | 130 | 140 |
N.S. |
1 | 0.95 | 0.71 | 0.91 | 1.16 | 0.84 | 0.00 | 2.21 | 1.02 | 1.09 |
time (sec) |
N/A | 0.545 | 0.029 | 0.272 | 0.040 | 0.101 | 0.000 | 0.133 | 0.157 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 154 | 93 | 198 | 0 | 159 | 0 | 0 | 129 | 241 |
N.S. |
1 | 0.95 | 0.57 | 1.22 | 0.00 | 0.98 | 0.00 | 0.00 | 0.80 | 1.49 |
time (sec) |
N/A | 0.593 | 0.036 | 0.289 | 0.000 | 0.108 | 0.000 | 0.000 | 0.153 | 14.464 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 122 | 86 | 189 | 0 | 152 | 0 | 0 | 120 | 218 |
N.S. |
1 | 0.88 | 0.62 | 1.37 | 0.00 | 1.10 | 0.00 | 0.00 | 0.87 | 1.58 |
time (sec) |
N/A | 0.489 | 0.032 | 0.277 | 0.000 | 0.091 | 0.000 | 0.000 | 0.168 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 94 | 78 | 183 | 0 | 144 | 0 | 0 | 114 | 196 |
N.S. |
1 | 0.85 | 0.71 | 1.66 | 0.00 | 1.31 | 0.00 | 0.00 | 1.04 | 1.78 |
time (sec) |
N/A | 0.398 | 0.029 | 0.263 | 0.000 | 0.091 | 0.000 | 0.000 | 0.168 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 70 | 69 | 196 | 0 | 137 | 0 | 0 | 105 | 176 |
N.S. |
1 | 0.80 | 0.78 | 2.23 | 0.00 | 1.56 | 0.00 | 0.00 | 1.19 | 2.00 |
time (sec) |
N/A | 0.360 | 0.024 | 0.237 | 0.000 | 0.095 | 0.000 | 0.000 | 0.150 | 14.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 45 | 41 | 0 | 91 | 0 | 0 | 70 | 102 |
N.S. |
1 | 1.00 | 0.79 | 0.72 | 0.00 | 1.60 | 0.00 | 0.00 | 1.23 | 1.79 |
time (sec) |
N/A | 0.299 | 0.011 | 0.238 | 0.000 | 0.108 | 0.000 | 0.000 | 0.153 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 53 | 44 | 41 | 0 | 89 | 0 | 0 | 68 | 63 |
N.S. |
1 | 0.96 | 0.80 | 0.75 | 0.00 | 1.62 | 0.00 | 0.00 | 1.24 | 1.15 |
time (sec) |
N/A | 0.270 | 0.010 | 0.244 | 0.000 | 0.084 | 0.000 | 0.000 | 0.164 | 14.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 50 | 45 | 42 | 0 | 89 | 0 | 0 | 70 | 48 |
N.S. |
1 | 0.96 | 0.87 | 0.81 | 0.00 | 1.71 | 0.00 | 0.00 | 1.35 | 0.92 |
time (sec) |
N/A | 0.234 | 0.013 | 0.247 | 0.000 | 0.102 | 0.000 | 0.000 | 0.157 | 14.498 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 71 | 77 | 182 | 0 | 127 | 0 | 0 | 109 | 173 |
N.S. |
1 | 0.96 | 1.04 | 2.46 | 0.00 | 1.72 | 0.00 | 0.00 | 1.47 | 2.34 |
time (sec) |
N/A | 0.350 | 0.031 | 0.316 | 0.000 | 0.087 | 0.000 | 0.000 | 0.159 | 14.365 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 96 | 91 | 150 | 144 | 153 | 0 | 0 | 134 | 198 |
N.S. |
1 | 0.83 | 0.79 | 1.30 | 1.25 | 1.33 | 0.00 | 0.00 | 1.17 | 1.72 |
time (sec) |
N/A | 0.465 | 0.033 | 0.274 | 0.043 | 0.080 | 0.000 | 0.000 | 0.153 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 127 | 103 | 214 | 0 | 171 | 0 | 0 | 293 | 221 |
N.S. |
1 | 0.84 | 0.68 | 1.42 | 0.00 | 1.13 | 0.00 | 0.00 | 1.94 | 1.46 |
time (sec) |
N/A | 0.564 | 0.036 | 0.293 | 0.000 | 0.081 | 0.000 | 0.000 | 0.150 | 14.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 157 | 110 | 236 | 191 | 178 | 0 | 0 | 158 | 244 |
N.S. |
1 | 0.87 | 0.61 | 1.31 | 1.06 | 0.99 | 0.00 | 0.00 | 0.88 | 1.36 |
time (sec) |
N/A | 0.726 | 0.037 | 0.299 | 0.045 | 0.074 | 0.000 | 0.000 | 0.159 | 14.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 153 | 116 | 265 | 0 | 221 | 0 | 0 | 238 | 352 |
N.S. |
1 | 0.83 | 0.63 | 1.44 | 0.00 | 1.20 | 0.00 | 0.00 | 1.29 | 1.91 |
time (sec) |
N/A | 0.629 | 0.055 | 0.328 | 0.000 | 0.102 | 0.000 | 0.000 | 0.159 | 14.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 125 | 108 | 259 | 0 | 213 | 0 | 0 | 230 | 379 |
N.S. |
1 | 0.80 | 0.69 | 1.65 | 0.00 | 1.36 | 0.00 | 0.00 | 1.46 | 2.41 |
time (sec) |
N/A | 0.501 | 0.047 | 0.309 | 0.000 | 0.108 | 0.000 | 0.000 | 0.152 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 101 | 100 | 399 | 0 | 206 | 0 | 0 | 222 | 312 |
N.S. |
1 | 0.74 | 0.73 | 2.91 | 0.00 | 1.50 | 0.00 | 0.00 | 1.62 | 2.28 |
time (sec) |
N/A | 0.465 | 0.039 | 0.279 | 0.000 | 0.116 | 0.000 | 0.000 | 0.161 | 14.380 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 86 | 68 | 58 | 0 | 146 | 0 | 0 | 140 | 335 |
N.S. |
1 | 1.06 | 0.84 | 0.72 | 0.00 | 1.80 | 0.00 | 0.00 | 1.73 | 4.14 |
time (sec) |
N/A | 0.396 | 0.016 | 0.274 | 0.000 | 0.075 | 0.000 | 0.000 | 0.153 | 14.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 82 | 68 | 58 | 0 | 145 | 0 | 0 | 140 | 287 |
N.S. |
1 | 1.11 | 0.92 | 0.78 | 0.00 | 1.96 | 0.00 | 0.00 | 1.89 | 3.88 |
time (sec) |
N/A | 0.365 | 0.015 | 0.280 | 0.000 | 0.100 | 0.000 | 0.000 | 0.153 | 14.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 68 | 58 | 0 | 146 | 0 | 0 | 140 | 329 |
N.S. |
1 | 1.00 | 0.81 | 0.69 | 0.00 | 1.74 | 0.00 | 0.00 | 1.67 | 3.92 |
time (sec) |
N/A | 0.320 | 0.015 | 0.278 | 0.000 | 0.078 | 0.000 | 0.000 | 0.155 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 77 | 68 | 58 | 0 | 145 | 0 | 0 | 140 | 271 |
N.S. |
1 | 0.96 | 0.85 | 0.72 | 0.00 | 1.81 | 0.00 | 0.00 | 1.75 | 3.39 |
time (sec) |
N/A | 0.289 | 0.014 | 0.283 | 0.000 | 0.083 | 0.000 | 0.000 | 0.153 | 14.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 59 | 58 | 0 | 144 | 0 | 0 | 140 | 279 |
N.S. |
1 | 1.00 | 0.80 | 0.78 | 0.00 | 1.95 | 0.00 | 0.00 | 1.89 | 3.77 |
time (sec) |
N/A | 0.266 | 0.021 | 0.290 | 0.000 | 0.114 | 0.000 | 0.000 | 0.151 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 100 | 108 | 384 | 0 | 198 | 0 | 0 | 235 | 306 |
N.S. |
1 | 0.99 | 1.07 | 3.80 | 0.00 | 1.96 | 0.00 | 0.00 | 2.33 | 3.03 |
time (sec) |
N/A | 0.383 | 0.045 | 0.302 | 0.000 | 0.093 | 0.000 | 0.000 | 0.170 | 14.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 121 | 121 | 314 | 178 | 223 | 0 | 0 | 258 | 335 |
N.S. |
1 | 0.75 | 0.75 | 1.94 | 1.10 | 1.38 | 0.00 | 0.00 | 1.59 | 2.07 |
time (sec) |
N/A | 0.573 | 0.051 | 0.355 | 0.051 | 0.119 | 0.000 | 0.000 | 0.153 | 14.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 154 | 133 | 326 | 0 | 241 | 0 | 0 | 434 | 357 |
N.S. |
1 | 0.77 | 0.66 | 1.63 | 0.00 | 1.20 | 0.00 | 0.00 | 2.17 | 1.78 |
time (sec) |
N/A | 0.693 | 0.054 | 0.371 | 0.000 | 0.097 | 0.000 | 0.000 | 0.161 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 98 | 75 | 74 | 0 | 198 | 0 | 0 | 209 | 477 |
N.S. |
1 | 1.02 | 0.78 | 0.77 | 0.00 | 2.06 | 0.00 | 0.00 | 2.18 | 4.97 |
time (sec) |
N/A | 0.269 | 0.034 | 0.316 | 0.000 | 0.101 | 0.000 | 0.000 | 0.152 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 122 | 91 | 90 | 0 | 252 | 0 | 0 | 280 | 783 |
N.S. |
1 | 1.03 | 0.77 | 0.76 | 0.00 | 2.14 | 0.00 | 0.00 | 2.37 | 6.64 |
time (sec) |
N/A | 0.291 | 0.031 | 0.421 | 0.000 | 0.157 | 0.000 | 0.000 | 0.153 | 14.312 |
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 | 49 | 49 | 49 | 42 | 43 | 42 | 39 | 44 | 42 | 42 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.88 | 0.86 | 0.80 | 0.90 | 0.86 | 0.86 |
time (sec) |
N/A | 0.331 | 0.004 | 0.174 | 0.031 | 0.064 | 0.051 | 0.119 | 0.161 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 34 | 35 | 34 | 31 | 36 | 34 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.90 | 0.87 | 0.79 | 0.92 | 0.87 | 0.87 |
time (sec) |
N/A | 0.312 | 0.003 | 0.168 | 0.026 | 0.067 | 0.052 | 0.119 | 0.151 | 0.023 |
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 | 29 | 29 | 26 | 26 | 25 | 22 | 27 | 26 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.90 | 0.86 | 0.76 | 0.93 | 0.90 | 0.79 |
time (sec) |
N/A | 0.302 | 0.003 | 0.167 | 0.029 | 0.061 | 0.052 | 0.123 | 0.144 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 16 | 18 | 15 | 14 | 19 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.95 | 0.79 | 0.74 | 1.00 | 0.89 | 0.79 |
time (sec) |
N/A | 0.255 | 0.003 | 0.159 | 0.027 | 0.067 | 0.049 | 0.116 | 0.147 | 14.042 |
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 | 12 | 12 | 12 | 12 | 11 | 11 | 8 | 12 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.92 | 0.92 | 0.67 | 1.00 | 0.92 | 0.92 |
time (sec) |
N/A | 0.222 | 0.002 | 0.386 | 0.029 | 0.072 | 0.027 | 0.329 | 0.151 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 12 | 11 | 11 | 8 | 13 | 11 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.92 | 0.92 | 0.67 | 1.08 | 0.92 | 0.75 |
time (sec) |
N/A | 0.265 | 0.003 | 0.167 | 0.025 | 0.062 | 0.064 | 0.121 | 0.147 | 13.992 |
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 | 20 | 20 | 20 | 19 | 22 | 15 | 21 | 21 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.95 | 1.10 | 0.75 | 1.05 | 1.05 | 0.80 |
time (sec) |
N/A | 0.292 | 0.003 | 0.171 | 0.030 | 0.073 | 0.081 | 0.117 | 0.148 | 14.105 |
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 | 32 | 32 | 32 | 29 | 29 | 35 | 26 | 31 | 35 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.91 | 1.09 | 0.81 | 0.97 | 1.09 | 0.72 |
time (sec) |
N/A | 0.308 | 0.004 | 0.175 | 0.029 | 0.072 | 0.091 | 0.122 | 0.159 | 0.028 |
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 | 42 | 42 | 42 | 37 | 37 | 43 | 34 | 39 | 43 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.88 | 1.02 | 0.81 | 0.93 | 1.02 | 0.74 |
time (sec) |
N/A | 0.314 | 0.004 | 0.179 | 0.031 | 0.066 | 0.106 | 0.126 | 0.153 | 0.028 |
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 | 58 | 58 | 45 | 48 | 52 | 62 | 48 | 56 | 68 | 54 |
N.S. |
1 | 1.00 | 0.78 | 0.83 | 0.90 | 1.07 | 0.83 | 0.97 | 1.17 | 0.93 |
time (sec) |
N/A | 0.339 | 0.025 | 0.169 | 0.025 | 0.075 | 0.141 | 0.116 | 0.155 | 14.116 |
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 | 48 | 48 | 39 | 41 | 43 | 55 | 39 | 42 | 59 | 46 |
N.S. |
1 | 1.00 | 0.81 | 0.85 | 0.90 | 1.15 | 0.81 | 0.88 | 1.23 | 0.96 |
time (sec) |
N/A | 0.332 | 0.014 | 0.168 | 0.026 | 0.064 | 0.132 | 0.131 | 0.151 | 0.034 |
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 | 43 | 43 | 33 | 36 | 38 | 42 | 34 | 37 | 52 | 39 |
N.S. |
1 | 1.00 | 0.77 | 0.84 | 0.88 | 0.98 | 0.79 | 0.86 | 1.21 | 0.91 |
time (sec) |
N/A | 0.317 | 0.009 | 0.166 | 0.032 | 0.070 | 0.119 | 0.114 | 0.163 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 22 | 36 | 38 | 42 | 32 | 37 | 50 | 22 |
N.S. |
1 | 1.00 | 0.81 | 1.33 | 1.41 | 1.56 | 1.19 | 1.37 | 1.85 | 0.81 |
time (sec) |
N/A | 0.285 | 0.007 | 0.166 | 0.030 | 0.068 | 0.091 | 0.108 | 0.149 | 13.957 |
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 | 20 | 36 | 36 | 40 | 29 | 37 | 50 | 22 |
N.S. |
1 | 1.00 | 0.74 | 1.33 | 1.33 | 1.48 | 1.07 | 1.37 | 1.85 | 0.81 |
time (sec) |
N/A | 0.262 | 0.006 | 0.163 | 0.028 | 0.069 | 0.096 | 0.125 | 0.161 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 32 | 29 | 28 | 45 | 29 | 31 | 58 | 30 |
N.S. |
1 | 1.00 | 0.89 | 0.81 | 0.78 | 1.25 | 0.81 | 0.86 | 1.61 | 0.83 |
time (sec) |
N/A | 0.315 | 0.017 | 0.175 | 0.031 | 0.090 | 0.134 | 0.128 | 0.152 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 39 | 42 | 75 | 42 | 44 | 85 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.91 | 1.63 | 0.91 | 0.96 | 1.85 | 0.87 |
time (sec) |
N/A | 0.319 | 0.019 | 0.178 | 0.027 | 0.070 | 0.212 | 0.110 | 0.151 | 14.010 |
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 | 63 | 63 | 59 | 54 | 59 | 96 | 58 | 59 | 101 | 58 |
N.S. |
1 | 1.00 | 0.94 | 0.86 | 0.94 | 1.52 | 0.92 | 0.94 | 1.60 | 0.92 |
time (sec) |
N/A | 0.343 | 0.023 | 0.184 | 0.032 | 0.070 | 0.219 | 0.109 | 0.159 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 67 | 62 | 67 | 105 | 66 | 67 | 110 | 66 |
N.S. |
1 | 1.00 | 0.92 | 0.85 | 0.92 | 1.44 | 0.90 | 0.92 | 1.51 | 0.90 |
time (sec) |
N/A | 0.349 | 0.025 | 0.187 | 0.031 | 0.075 | 0.238 | 0.117 | 0.148 | 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 | 88 | 88 | 65 | 73 | 80 | 125 | 82 | 77 | 150 | 82 |
N.S. |
1 | 1.00 | 0.74 | 0.83 | 0.91 | 1.42 | 0.93 | 0.88 | 1.70 | 0.93 |
time (sec) |
N/A | 0.367 | 0.052 | 0.178 | 0.026 | 0.084 | 0.246 | 0.127 | 0.160 | 0.045 |
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 | 76 | 76 | 55 | 65 | 72 | 117 | 71 | 64 | 142 | 73 |
N.S. |
1 | 1.00 | 0.72 | 0.86 | 0.95 | 1.54 | 0.93 | 0.84 | 1.87 | 0.96 |
time (sec) |
N/A | 0.360 | 0.045 | 0.174 | 0.026 | 0.068 | 0.250 | 0.118 | 0.149 | 13.994 |
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 | 72 | 72 | 55 | 60 | 66 | 101 | 68 | 58 | 134 | 67 |
N.S. |
1 | 1.00 | 0.76 | 0.83 | 0.92 | 1.40 | 0.94 | 0.81 | 1.86 | 0.93 |
time (sec) |
N/A | 0.345 | 0.034 | 0.170 | 0.026 | 0.081 | 0.232 | 0.116 | 0.147 | 14.047 |
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 | 56 | 56 | 53 | 56 | 66 | 101 | 66 | 58 | 134 | 53 |
N.S. |
1 | 1.00 | 0.95 | 1.00 | 1.18 | 1.80 | 1.18 | 1.04 | 2.39 | 0.95 |
time (sec) |
N/A | 0.336 | 0.011 | 0.174 | 0.030 | 0.068 | 0.184 | 0.118 | 0.156 | 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 | 56 | 56 | 52 | 54 | 65 | 100 | 63 | 57 | 129 | 54 |
N.S. |
1 | 1.00 | 0.93 | 0.96 | 1.16 | 1.79 | 1.12 | 1.02 | 2.30 | 0.96 |
time (sec) |
N/A | 0.332 | 0.009 | 0.173 | 0.027 | 0.075 | 0.187 | 0.119 | 0.155 | 13.988 |
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 | 41 | 41 | 28 | 48 | 65 | 100 | 61 | 57 | 129 | 51 |
N.S. |
1 | 1.00 | 0.68 | 1.17 | 1.59 | 2.44 | 1.49 | 1.39 | 3.15 | 1.24 |
time (sec) |
N/A | 0.291 | 0.012 | 0.176 | 0.027 | 0.076 | 0.205 | 0.112 | 0.147 | 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 | 56 | 56 | 53 | 59 | 64 | 99 | 65 | 58 | 134 | 49 |
N.S. |
1 | 1.00 | 0.95 | 1.05 | 1.14 | 1.77 | 1.16 | 1.04 | 2.39 | 0.88 |
time (sec) |
N/A | 0.287 | 0.007 | 0.172 | 0.033 | 0.078 | 0.289 | 0.113 | 0.154 | 0.033 |
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 | 59 | 59 | 54 | 47 | 57 | 122 | 60 | 51 | 161 | 57 |
N.S. |
1 | 1.00 | 0.92 | 0.80 | 0.97 | 2.07 | 1.02 | 0.86 | 2.73 | 0.97 |
time (sec) |
N/A | 0.341 | 0.021 | 0.181 | 0.031 | 0.079 | 0.308 | 0.122 | 0.157 | 14.134 |
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 | 71 | 71 | 65 | 59 | 72 | 150 | 78 | 67 | 190 | 71 |
N.S. |
1 | 1.00 | 0.92 | 0.83 | 1.01 | 2.11 | 1.10 | 0.94 | 2.68 | 1.00 |
time (sec) |
N/A | 0.350 | 0.029 | 0.207 | 0.032 | 0.084 | 0.316 | 0.127 | 0.152 | 0.043 |
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 | 89 | 89 | 83 | 78 | 89 | 172 | 95 | 82 | 210 | 89 |
N.S. |
1 | 1.00 | 0.93 | 0.88 | 1.00 | 1.93 | 1.07 | 0.92 | 2.36 | 1.00 |
time (sec) |
N/A | 0.369 | 0.036 | 0.198 | 0.031 | 0.084 | 0.345 | 0.134 | 0.151 | 14.052 |
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 | 102 | 102 | 91 | 86 | 97 | 180 | 104 | 90 | 218 | 97 |
N.S. |
1 | 1.00 | 0.89 | 0.84 | 0.95 | 1.76 | 1.02 | 0.88 | 2.14 | 0.95 |
time (sec) |
N/A | 0.388 | 0.043 | 0.197 | 0.029 | 0.077 | 0.461 | 0.126 | 0.152 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 46 | 42 | 37 | 0 | 50 | 0 | 17 | 13 | 38 |
N.S. |
1 | 0.62 | 0.57 | 0.50 | 0.00 | 0.68 | 0.00 | 0.23 | 0.18 | 0.51 |
time (sec) |
N/A | 0.482 | 0.018 | 0.273 | 0.000 | 0.082 | 0.000 | 0.110 | 0.161 | 14.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 46 | 42 | 37 | 0 | 50 | 0 | 17 | 13 | 38 |
N.S. |
1 | 0.62 | 0.57 | 0.50 | 0.00 | 0.68 | 0.00 | 0.23 | 0.18 | 0.51 |
time (sec) |
N/A | 0.398 | 0.013 | 0.210 | 0.000 | 0.074 | 0.000 | 0.111 | 0.164 | 14.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 40 | 34 | 0 | 47 | 0 | 14 | 10 | 34 |
N.S. |
1 | 1.00 | 0.93 | 0.79 | 0.00 | 1.09 | 0.00 | 0.33 | 0.23 | 0.79 |
time (sec) |
N/A | 0.312 | 0.013 | 0.207 | 0.000 | 0.079 | 0.000 | 0.114 | 0.159 | 14.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 36 | 36 | 34 | 56 | 263 | 0 | 11 | 9 | 0 |
N.S. |
1 | 0.55 | 0.55 | 0.52 | 0.86 | 4.05 | 0.00 | 0.17 | 0.14 | 0.00 |
time (sec) |
N/A | 0.425 | 0.015 | 0.215 | 0.043 | 0.101 | 0.000 | 0.119 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 40 | 40 | 38 | 60 | 265 | 0 | 15 | 13 | 0 |
N.S. |
1 | 0.59 | 0.59 | 0.56 | 0.88 | 3.90 | 0.00 | 0.22 | 0.19 | 0.00 |
time (sec) |
N/A | 0.435 | 0.013 | 0.211 | 0.042 | 0.098 | 0.000 | 0.111 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 60 | 57 | 53 | 66 | 68 | 0 | 0 | 28 | 55 |
N.S. |
1 | 0.67 | 0.64 | 0.60 | 0.74 | 0.76 | 0.00 | 0.00 | 0.31 | 0.62 |
time (sec) |
N/A | 0.359 | 0.022 | 0.209 | 0.043 | 0.071 | 0.000 | 0.000 | 0.148 | 14.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 73 | 60 | 71 | 111 | 98 | 0 | 0 | 46 | 85 |
N.S. |
1 | 0.54 | 0.44 | 0.52 | 0.82 | 0.72 | 0.00 | 0.00 | 0.34 | 0.62 |
time (sec) |
N/A | 0.371 | 0.027 | 0.214 | 0.046 | 0.076 | 0.000 | 0.000 | 0.142 | 14.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 88 | 68 | 87 | 154 | 120 | 0 | 0 | 62 | 107 |
N.S. |
1 | 0.48 | 0.37 | 0.48 | 0.84 | 0.66 | 0.00 | 0.00 | 0.34 | 0.58 |
time (sec) |
N/A | 0.401 | 0.034 | 0.217 | 0.046 | 0.077 | 0.000 | 0.000 | 0.152 | 14.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 79 | 71 | 72 | 0 | 387 | 0 | 63 | 47 | 0 |
N.S. |
1 | 0.41 | 0.37 | 0.37 | 0.00 | 1.99 | 0.00 | 0.32 | 0.24 | 0.00 |
time (sec) |
N/A | 0.505 | 0.030 | 0.207 | 0.000 | 0.107 | 0.000 | 0.109 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 69 | 63 | 64 | 0 | 371 | 0 | 46 | 39 | 0 |
N.S. |
1 | 0.45 | 0.41 | 0.41 | 0.00 | 2.39 | 0.00 | 0.30 | 0.25 | 0.00 |
time (sec) |
N/A | 0.474 | 0.024 | 0.207 | 0.000 | 0.114 | 0.000 | 0.116 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 59 | 54 | 55 | 0 | 352 | 0 | 40 | 31 | 0 |
N.S. |
1 | 0.51 | 0.47 | 0.47 | 0.00 | 3.03 | 0.00 | 0.34 | 0.27 | 0.00 |
time (sec) |
N/A | 0.452 | 0.019 | 0.207 | 0.000 | 0.097 | 0.000 | 0.112 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 49 | 45 | 47 | 0 | 331 | 0 | 26 | 20 | 0 |
N.S. |
1 | 0.64 | 0.58 | 0.61 | 0.00 | 4.30 | 0.00 | 0.34 | 0.26 | 0.00 |
time (sec) |
N/A | 0.398 | 0.018 | 0.205 | 0.000 | 0.099 | 0.000 | 0.118 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 41 | 0 | 227 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 5.54 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.316 | 0.009 | 0.204 | 0.000 | 0.097 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 42 | 42 | 42 | 0 | 302 | 0 | 1 | 17 | 0 |
N.S. |
1 | 0.59 | 0.59 | 0.59 | 0.00 | 4.25 | 0.00 | 0.01 | 0.24 | 0.00 |
time (sec) |
N/A | 0.412 | 0.011 | 0.207 | 0.000 | 0.105 | 0.000 | 0.117 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 50 | 50 | 51 | 0 | 416 | 0 | 31 | 26 | 0 |
N.S. |
1 | 0.47 | 0.47 | 0.48 | 0.00 | 3.89 | 0.00 | 0.29 | 0.24 | 0.00 |
time (sec) |
N/A | 0.437 | 0.016 | 0.208 | 0.000 | 0.114 | 0.000 | 0.118 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 62 | 62 | 65 | 0 | 453 | 0 | 40 | 40 | 0 |
N.S. |
1 | 0.42 | 0.42 | 0.44 | 0.00 | 3.06 | 0.00 | 0.27 | 0.27 | 0.00 |
time (sec) |
N/A | 0.459 | 0.026 | 0.210 | 0.000 | 0.134 | 0.000 | 0.115 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 72 | 72 | 73 | 0 | 482 | 0 | 49 | 48 | 0 |
N.S. |
1 | 0.39 | 0.39 | 0.39 | 0.00 | 2.58 | 0.00 | 0.26 | 0.26 | 0.00 |
time (sec) |
N/A | 0.466 | 0.025 | 0.204 | 0.000 | 0.115 | 0.000 | 0.130 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 102 | 87 | 108 | 0 | 0 | 0 | 86 | 82 | 0 |
N.S. |
1 | 0.39 | 0.33 | 0.41 | 0.00 | 0.00 | 0.00 | 0.33 | 0.31 | 0.00 |
time (sec) |
N/A | 0.511 | 0.046 | 0.214 | 0.000 | 0.000 | 0.000 | 0.110 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 91 | 77 | 99 | 0 | 0 | 0 | 74 | 73 | 0 |
N.S. |
1 | 0.42 | 0.35 | 0.45 | 0.00 | 0.00 | 0.00 | 0.34 | 0.33 | 0.00 |
time (sec) |
N/A | 0.515 | 0.047 | 0.213 | 0.000 | 0.000 | 0.000 | 0.112 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 81 | 71 | 91 | 0 | 0 | 0 | 54 | 64 | 0 |
N.S. |
1 | 0.46 | 0.40 | 0.52 | 0.00 | 0.00 | 0.00 | 0.31 | 0.36 | 0.00 |
time (sec) |
N/A | 0.505 | 0.034 | 0.211 | 0.000 | 0.000 | 0.000 | 0.119 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 76 | 76 | 79 | 0 | 0 | 0 | 46 | 57 | 0 |
N.S. |
1 | 0.55 | 0.55 | 0.57 | 0.00 | 0.00 | 0.00 | 0.33 | 0.41 | 0.00 |
time (sec) |
N/A | 0.510 | 0.025 | 0.216 | 0.000 | 0.000 | 0.000 | 0.108 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 60 | 60 | 77 | 0 | 348 | 0 | 46 | 55 | 0 |
N.S. |
1 | 0.66 | 0.66 | 0.85 | 0.00 | 3.82 | 0.00 | 0.51 | 0.60 | 0.00 |
time (sec) |
N/A | 0.441 | 0.021 | 0.210 | 0.000 | 0.103 | 0.000 | 0.113 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 60 | 60 | 77 | 0 | 343 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.66 | 0.66 | 0.85 | 0.00 | 3.77 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.377 | 0.020 | 0.210 | 0.000 | 0.094 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 69 | 65 | 86 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 0.42 | 0.39 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.487 | 0.034 | 0.218 | 0.000 | 0.000 | 0.000 | 0.000 | 0.142 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 79 | 76 | 111 | 0 | 0 | 0 | 0 | 90 | 0 |
N.S. |
1 | 0.38 | 0.37 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.495 | 0.041 | 0.214 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 96 | 91 | 131 | 0 | 0 | 0 | 0 | 106 | 0 |
N.S. |
1 | 0.38 | 0.36 | 0.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.511 | 0.052 | 0.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 106 | 99 | 140 | 0 | 0 | 0 | 0 | 115 | 0 |
N.S. |
1 | 0.36 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.526 | 0.059 | 0.242 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 312 | 121 | 97 | 179 | 0 | 0 | 0 | 118 | 155 | 0 |
N.S. |
1 | 0.39 | 0.31 | 0.57 | 0.00 | 0.00 | 0.00 | 0.38 | 0.50 | 0.00 |
time (sec) |
N/A | 0.539 | 0.107 | 0.336 | 0.000 | 0.000 | 0.000 | 0.177 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 109 | 87 | 171 | 0 | 0 | 0 | 0 | 147 | 0 |
N.S. |
1 | 0.41 | 0.32 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.524 | 0.084 | 0.906 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 105 | 87 | 155 | 0 | 0 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.45 | 0.38 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.529 | 0.075 | 0.966 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |