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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 65 | 0 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.240 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 63 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.230 | 0.016 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 59 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.232 | 0.008 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 33 | 0 | 59 | 175 | 0 | 36 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.00 | 1.51 | 4.49 | 0.00 | 0.92 | 0.95 |
time (sec) |
N/A | 0.224 | 0.016 | 1.618 | 0.000 | 0.085 | 8.333 | 0.000 | 0.146 | 14.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 82 | 51 | 46 | 0 | 129 | 1103 | 0 | 87 | 100 |
N.S. |
1 | 0.98 | 0.61 | 0.55 | 0.00 | 1.54 | 13.13 | 0.00 | 1.04 | 1.19 |
time (sec) |
N/A | 0.260 | 0.034 | 4.871 | 0.000 | 0.106 | 43.865 | 0.000 | 0.152 | 14.279 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 126 | 74 | 68 | 0 | 229 | 3526 | 0 | 183 | 167 |
N.S. |
1 | 0.93 | 0.55 | 0.50 | 0.00 | 1.70 | 26.12 | 0.00 | 1.36 | 1.24 |
time (sec) |
N/A | 0.296 | 0.050 | 13.333 | 0.000 | 0.105 | 148.096 | 0.000 | 0.154 | 14.295 |
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 | 83 | 94 | 50 | 64 | 69 | 69 | 100 | 57 | 66 | 82 |
N.S. |
1 | 1.13 | 0.60 | 0.77 | 0.83 | 0.83 | 1.20 | 0.69 | 0.80 | 0.99 |
time (sec) |
N/A | 0.289 | 0.061 | 0.217 | 0.116 | 0.078 | 0.715 | 0.131 | 0.154 | 14.157 |
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 | 45 | 48 | 32 | 28 | 58 | 39 | 66 | 47 | 35 | 36 |
N.S. |
1 | 1.07 | 0.71 | 0.62 | 1.29 | 0.87 | 1.47 | 1.04 | 0.78 | 0.80 |
time (sec) |
N/A | 0.263 | 0.017 | 0.167 | 0.110 | 0.093 | 0.248 | 0.115 | 0.147 | 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 | 58 | 62 | 40 | 63 | 48 | 60 | 90 | 45 | 45 | 61 |
N.S. |
1 | 1.07 | 0.69 | 1.09 | 0.83 | 1.03 | 1.55 | 0.78 | 0.78 | 1.05 |
time (sec) |
N/A | 0.255 | 0.046 | 0.200 | 0.110 | 0.087 | 0.686 | 0.149 | 0.149 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 37 | 29 | 42 | 18 | 26 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 1.68 | 1.32 | 1.91 | 0.82 | 1.18 | 0.82 |
time (sec) |
N/A | 0.211 | 0.009 | 0.158 | 0.109 | 0.088 | 0.203 | 0.115 | 0.146 | 0.018 |
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 | 33 | 33 | 30 | 45 | 27 | 47 | 80 | 30 | 25 | 37 |
N.S. |
1 | 1.00 | 0.91 | 1.36 | 0.82 | 1.42 | 2.42 | 0.91 | 0.76 | 1.12 |
time (sec) |
N/A | 0.204 | 0.010 | 0.193 | 0.112 | 0.171 | 0.699 | 0.120 | 0.146 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 39 | 57 | 32 | 44 | 36 | 73 | 53 | 23 | 31 |
N.S. |
1 | 1.11 | 1.63 | 0.91 | 1.26 | 1.03 | 2.09 | 1.51 | 0.66 | 0.89 |
time (sec) |
N/A | 0.240 | 0.083 | 0.180 | 0.111 | 0.081 | 3.708 | 0.113 | 0.146 | 13.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 28 | 28 | 27 | 47 | 87 | 74 | 25 | 38 |
N.S. |
1 | 1.00 | 0.97 | 0.97 | 0.93 | 1.62 | 3.00 | 2.55 | 0.86 | 1.31 |
time (sec) |
N/A | 0.235 | 0.025 | 0.188 | 0.114 | 0.078 | 1.065 | 0.111 | 0.157 | 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 | 46 | 44 | 67 | 40 | 51 | 47 | 87 | 64 | 33 | 38 |
N.S. |
1 | 0.96 | 1.46 | 0.87 | 1.11 | 1.02 | 1.89 | 1.39 | 0.72 | 0.83 |
time (sec) |
N/A | 0.245 | 0.017 | 0.208 | 0.113 | 0.079 | 3.476 | 0.128 | 0.147 | 14.290 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 40 | 29 | 133 | 124 | 26 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 1.82 | 1.32 | 6.05 | 5.64 | 1.18 | 0.82 |
time (sec) |
N/A | 0.222 | 0.008 | 0.171 | 0.109 | 0.097 | 1.361 | 0.119 | 0.152 | 14.541 |
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 | 140 | 153 | 89 | 102 | 141 | 104 | 163 | 92 | 120 | 154 |
N.S. |
1 | 1.09 | 0.64 | 0.73 | 1.01 | 0.74 | 1.16 | 0.66 | 0.86 | 1.10 |
time (sec) |
N/A | 0.375 | 0.112 | 0.244 | 0.117 | 0.097 | 0.737 | 0.124 | 0.153 | 14.271 |
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 | 112 | 121 | 75 | 94 | 118 | 92 | 151 | 81 | 101 | 131 |
N.S. |
1 | 1.08 | 0.67 | 0.84 | 1.05 | 0.82 | 1.35 | 0.72 | 0.90 | 1.17 |
time (sec) |
N/A | 0.338 | 0.078 | 0.243 | 0.114 | 0.103 | 0.725 | 0.141 | 0.154 | 0.021 |
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 | 89 | 86 | 67 | 86 | 95 | 82 | 136 | 69 | 82 | 108 |
N.S. |
1 | 0.97 | 0.75 | 0.97 | 1.07 | 0.92 | 1.53 | 0.78 | 0.92 | 1.21 |
time (sec) |
N/A | 0.284 | 0.096 | 0.222 | 0.117 | 0.090 | 0.808 | 0.126 | 0.150 | 0.019 |
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 | 61 | 56 | 59 | 75 | 72 | 70 | 129 | 54 | 63 | 82 |
N.S. |
1 | 0.92 | 0.97 | 1.23 | 1.18 | 1.15 | 2.11 | 0.89 | 1.03 | 1.34 |
time (sec) |
N/A | 0.234 | 0.079 | 0.214 | 0.115 | 0.093 | 0.787 | 0.125 | 0.152 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 57 | 125 | 114 | 76 | 76 | 182 | 84 | 51 | 77 |
N.S. |
1 | 0.97 | 2.12 | 1.93 | 1.29 | 1.29 | 3.08 | 1.42 | 0.86 | 1.31 |
time (sec) |
N/A | 0.304 | 0.069 | 0.217 | 0.112 | 0.082 | 4.186 | 0.131 | 0.145 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 53 | 84 | 83 | 80 | 91 | 151 | 140 | 80 | 87 |
N.S. |
1 | 0.91 | 1.45 | 1.43 | 1.38 | 1.57 | 2.60 | 2.41 | 1.38 | 1.50 |
time (sec) |
N/A | 0.311 | 0.175 | 0.233 | 0.125 | 0.100 | 1.741 | 0.131 | 0.146 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 63 | 147 | 87 | 86 | 95 | 223 | 192 | 65 | 90 |
N.S. |
1 | 0.94 | 2.19 | 1.30 | 1.28 | 1.42 | 3.33 | 2.87 | 0.97 | 1.34 |
time (sec) |
N/A | 0.312 | 0.088 | 0.237 | 0.114 | 0.187 | 2.616 | 0.132 | 0.144 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 70 | 91 | 73 | 99 | 73 | 269 | 233 | 72 | 90 |
N.S. |
1 | 0.93 | 1.21 | 0.97 | 1.32 | 0.97 | 3.59 | 3.11 | 0.96 | 1.20 |
time (sec) |
N/A | 0.294 | 0.025 | 0.251 | 0.111 | 0.088 | 2.965 | 0.128 | 0.149 | 14.270 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 97 | 99 | 81 | 122 | 84 | 413 | 240 | 91 | 113 |
N.S. |
1 | 0.95 | 0.97 | 0.79 | 1.20 | 0.82 | 4.05 | 2.35 | 0.89 | 1.11 |
time (sec) |
N/A | 0.317 | 0.024 | 0.261 | 0.114 | 0.079 | 4.529 | 0.130 | 0.150 | 14.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 124 | 107 | 89 | 145 | 95 | 520 | 297 | 110 | 136 |
N.S. |
1 | 0.96 | 0.83 | 0.69 | 1.12 | 0.74 | 4.03 | 2.30 | 0.85 | 1.05 |
time (sec) |
N/A | 0.354 | 0.025 | 0.280 | 0.111 | 0.094 | 4.909 | 0.132 | 0.154 | 14.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 151 | 115 | 97 | 168 | 106 | 644 | 424 | 129 | 159 |
N.S. |
1 | 0.97 | 0.74 | 0.62 | 1.08 | 0.68 | 4.13 | 2.72 | 0.83 | 1.02 |
time (sec) |
N/A | 0.388 | 0.026 | 0.282 | 0.116 | 0.107 | 10.544 | 0.133 | 0.149 | 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 | 164 | 177 | 91 | 110 | 164 | 114 | 182 | 104 | 139 | 177 |
N.S. |
1 | 1.08 | 0.55 | 0.67 | 1.00 | 0.70 | 1.11 | 0.63 | 0.85 | 1.08 |
time (sec) |
N/A | 0.430 | 0.093 | 0.253 | 0.114 | 0.103 | 0.754 | 0.158 | 0.149 | 0.025 |
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 | 136 | 147 | 83 | 102 | 141 | 104 | 172 | 92 | 120 | 154 |
N.S. |
1 | 1.08 | 0.61 | 0.75 | 1.04 | 0.76 | 1.26 | 0.68 | 0.88 | 1.13 |
time (sec) |
N/A | 0.388 | 0.088 | 0.257 | 0.113 | 0.102 | 0.744 | 0.130 | 0.147 | 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 | 113 | 115 | 75 | 94 | 118 | 92 | 155 | 81 | 101 | 108 |
N.S. |
1 | 1.02 | 0.66 | 0.83 | 1.04 | 0.81 | 1.37 | 0.72 | 0.89 | 0.96 |
time (sec) |
N/A | 0.328 | 0.104 | 0.239 | 0.115 | 0.077 | 0.741 | 0.130 | 0.150 | 14.208 |
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 | 88 | 67 | 83 | 95 | 82 | 146 | 66 | 82 | 105 |
N.S. |
1 | 1.06 | 0.81 | 1.00 | 1.14 | 0.99 | 1.76 | 0.80 | 0.99 | 1.27 |
time (sec) |
N/A | 0.259 | 0.099 | 0.234 | 0.125 | 0.085 | 0.755 | 0.135 | 0.146 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 67 | 135 | 144 | 100 | 88 | 209 | 95 | 69 | 110 |
N.S. |
1 | 0.89 | 1.80 | 1.92 | 1.33 | 1.17 | 2.79 | 1.27 | 0.92 | 1.47 |
time (sec) |
N/A | 0.349 | 0.096 | 0.220 | 0.119 | 0.086 | 4.136 | 0.130 | 0.156 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 77 | 143 | 107 | 102 | 104 | 182 | 152 | 79 | 108 |
N.S. |
1 | 0.93 | 1.72 | 1.29 | 1.23 | 1.25 | 2.19 | 1.83 | 0.95 | 1.30 |
time (sec) |
N/A | 0.365 | 0.096 | 0.244 | 0.126 | 0.152 | 1.835 | 0.142 | 0.147 | 14.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 80 | 155 | 106 | 107 | 118 | 224 | 212 | 92 | 111 |
N.S. |
1 | 0.87 | 1.68 | 1.15 | 1.16 | 1.28 | 2.43 | 2.30 | 1.00 | 1.21 |
time (sec) |
N/A | 0.341 | 0.120 | 0.234 | 0.114 | 0.108 | 2.197 | 0.129 | 0.149 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 84 | 156 | 104 | 110 | 105 | 275 | 250 | 112 | 114 |
N.S. |
1 | 0.95 | 1.77 | 1.18 | 1.25 | 1.19 | 3.12 | 2.84 | 1.27 | 1.30 |
time (sec) |
N/A | 0.343 | 0.127 | 0.256 | 0.111 | 0.102 | 2.735 | 0.128 | 0.148 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 97 | 99 | 81 | 122 | 84 | 347 | 300 | 91 | 113 |
N.S. |
1 | 0.95 | 0.97 | 0.79 | 1.20 | 0.82 | 3.40 | 2.94 | 0.89 | 1.11 |
time (sec) |
N/A | 0.322 | 0.028 | 0.257 | 0.111 | 0.105 | 4.082 | 0.131 | 0.150 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 124 | 107 | 89 | 145 | 95 | 474 | 297 | 110 | 136 |
N.S. |
1 | 0.96 | 0.83 | 0.69 | 1.12 | 0.74 | 3.67 | 2.30 | 0.85 | 1.05 |
time (sec) |
N/A | 0.358 | 0.026 | 0.287 | 0.109 | 0.104 | 4.808 | 0.131 | 0.151 | 0.026 |
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 | 189 | 215 | 99 | 118 | 187 | 126 | 228 | 117 | 158 | 200 |
N.S. |
1 | 1.14 | 0.52 | 0.62 | 0.99 | 0.67 | 1.21 | 0.62 | 0.84 | 1.06 |
time (sec) |
N/A | 0.570 | 0.112 | 0.308 | 0.115 | 0.086 | 0.791 | 0.146 | 0.154 | 13.976 |
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 | 161 | 179 | 91 | 110 | 164 | 114 | 211 | 104 | 139 | 177 |
N.S. |
1 | 1.11 | 0.57 | 0.68 | 1.02 | 0.71 | 1.31 | 0.65 | 0.86 | 1.10 |
time (sec) |
N/A | 0.523 | 0.099 | 0.318 | 0.118 | 0.079 | 0.779 | 0.140 | 0.148 | 0.025 |
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 | 138 | 151 | 83 | 102 | 141 | 104 | 194 | 94 | 120 | 154 |
N.S. |
1 | 1.09 | 0.60 | 0.74 | 1.02 | 0.75 | 1.41 | 0.68 | 0.87 | 1.12 |
time (sec) |
N/A | 0.431 | 0.156 | 0.266 | 0.112 | 0.082 | 0.766 | 0.133 | 0.148 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 122 | 75 | 91 | 118 | 92 | 189 | 78 | 101 | 128 |
N.S. |
1 | 1.13 | 0.69 | 0.84 | 1.09 | 0.85 | 1.75 | 0.72 | 0.94 | 1.19 |
time (sec) |
N/A | 0.291 | 0.106 | 0.284 | 0.111 | 0.080 | 0.793 | 0.132 | 0.145 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 109 | 142 | 239 | 105 | 95 | 343 | 100 | 75 | 110 |
N.S. |
1 | 0.95 | 1.23 | 2.08 | 0.91 | 0.83 | 2.98 | 0.87 | 0.65 | 0.96 |
time (sec) |
N/A | 0.458 | 0.075 | 0.256 | 0.113 | 0.078 | 5.299 | 0.126 | 0.148 | 14.092 |
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 | 123 | 99 | 152 | 134 | 125 | 116 | 289 | 164 | 99 | 131 |
N.S. |
1 | 0.80 | 1.24 | 1.09 | 1.02 | 0.94 | 2.35 | 1.33 | 0.80 | 1.07 |
time (sec) |
N/A | 0.437 | 0.097 | 0.292 | 0.108 | 0.083 | 2.022 | 0.133 | 0.150 | 13.964 |
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 | 136 | 98 | 106 | 132 | 129 | 125 | 337 | 224 | 111 | 133 |
N.S. |
1 | 0.72 | 0.78 | 0.97 | 0.95 | 0.92 | 2.48 | 1.65 | 0.82 | 0.98 |
time (sec) |
N/A | 0.450 | 0.191 | 0.294 | 0.112 | 0.103 | 2.893 | 0.128 | 0.154 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 106 | 164 | 122 | 131 | 129 | 355 | 270 | 131 | 135 |
N.S. |
1 | 0.78 | 1.21 | 0.90 | 0.96 | 0.95 | 2.61 | 1.99 | 0.96 | 0.99 |
time (sec) |
N/A | 0.449 | 0.106 | 0.314 | 0.112 | 0.083 | 3.241 | 0.130 | 0.149 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 114 | 125 | 104 | 109 | 106 | 502 | 316 | 84 | 113 |
N.S. |
1 | 1.04 | 1.14 | 0.95 | 0.99 | 0.96 | 4.56 | 2.87 | 0.76 | 1.03 |
time (sec) |
N/A | 0.444 | 0.193 | 0.303 | 0.111 | 0.138 | 5.438 | 0.153 | 0.150 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 126 | 107 | 89 | 145 | 95 | 605 | 354 | 110 | 136 |
N.S. |
1 | 0.98 | 0.83 | 0.69 | 1.12 | 0.74 | 4.69 | 2.74 | 0.85 | 1.05 |
time (sec) |
N/A | 0.422 | 0.032 | 0.342 | 0.109 | 0.079 | 5.743 | 0.132 | 0.149 | 14.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 153 | 115 | 97 | 168 | 106 | 799 | 424 | 129 | 159 |
N.S. |
1 | 0.98 | 0.74 | 0.62 | 1.08 | 0.68 | 5.12 | 2.72 | 0.83 | 1.02 |
time (sec) |
N/A | 0.466 | 0.029 | 0.322 | 0.113 | 0.092 | 12.028 | 0.133 | 0.151 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 160 | 81 | 130 | 129 | 95 | 0 | 0 | 180 | 163 |
N.S. |
1 | 1.12 | 0.57 | 0.91 | 0.90 | 0.66 | 0.00 | 0.00 | 1.26 | 1.14 |
time (sec) |
N/A | 0.572 | 0.064 | 0.257 | 0.117 | 0.094 | 0.000 | 0.000 | 0.148 | 0.041 |
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 | 111 | 126 | 72 | 121 | 105 | 86 | 0 | 101 | 152 | 158 |
N.S. |
1 | 1.14 | 0.65 | 1.09 | 0.95 | 0.77 | 0.00 | 0.91 | 1.37 | 1.42 |
time (sec) |
N/A | 0.471 | 0.048 | 0.234 | 0.125 | 0.083 | 0.000 | 0.123 | 0.152 | 14.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 90 | 64 | 113 | 83 | 78 | 0 | 0 | 125 | 129 |
N.S. |
1 | 0.98 | 0.70 | 1.23 | 0.90 | 0.85 | 0.00 | 0.00 | 1.36 | 1.40 |
time (sec) |
N/A | 0.380 | 0.038 | 0.228 | 0.117 | 0.078 | 0.000 | 0.000 | 0.146 | 0.034 |
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 | 64 | 66 | 53 | 95 | 61 | 69 | 0 | 78 | 96 | 90 |
N.S. |
1 | 1.03 | 0.83 | 1.48 | 0.95 | 1.08 | 0.00 | 1.22 | 1.50 | 1.41 |
time (sec) |
N/A | 0.279 | 0.031 | 0.217 | 0.114 | 0.081 | 0.000 | 0.129 | 0.145 | 14.172 |
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 | 43 | 41 | 46 | 74 | 40 | 62 | 0 | 53 | 45 | 71 |
N.S. |
1 | 0.95 | 1.07 | 1.72 | 0.93 | 1.44 | 0.00 | 1.23 | 1.05 | 1.65 |
time (sec) |
N/A | 0.237 | 0.019 | 0.203 | 0.108 | 0.089 | 0.000 | 0.134 | 0.149 | 14.210 |
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 | 48 | 46 | 55 | 61 | 0 | 56 | 0 | 80 | 51 | 68 |
N.S. |
1 | 0.96 | 1.15 | 1.27 | 0.00 | 1.17 | 0.00 | 1.67 | 1.06 | 1.42 |
time (sec) |
N/A | 0.292 | 0.018 | 0.214 | 0.000 | 0.082 | 0.000 | 0.137 | 0.148 | 14.295 |
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 | 72 | 67 | 68 | 77 | 0 | 80 | 0 | 159 | 84 | 91 |
N.S. |
1 | 0.93 | 0.94 | 1.07 | 0.00 | 1.11 | 0.00 | 2.21 | 1.17 | 1.26 |
time (sec) |
N/A | 0.327 | 0.016 | 0.230 | 0.000 | 0.091 | 0.000 | 0.124 | 0.147 | 14.055 |
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 | 103 | 96 | 83 | 99 | 0 | 99 | 0 | 224 | 108 | 117 |
N.S. |
1 | 0.93 | 0.81 | 0.96 | 0.00 | 0.96 | 0.00 | 2.17 | 1.05 | 1.14 |
time (sec) |
N/A | 0.432 | 0.027 | 0.250 | 0.000 | 0.106 | 0.000 | 0.144 | 0.154 | 0.041 |
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 | 128 | 125 | 91 | 116 | 0 | 107 | 0 | 283 | 130 | 140 |
N.S. |
1 | 0.98 | 0.71 | 0.91 | 0.00 | 0.84 | 0.00 | 2.21 | 1.02 | 1.09 |
time (sec) |
N/A | 0.542 | 0.029 | 0.262 | 0.000 | 0.086 | 0.000 | 0.127 | 0.148 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 155 | 80 | 162 | 153 | 125 | 0 | 0 | 235 | 189 |
N.S. |
1 | 1.05 | 0.54 | 1.09 | 1.03 | 0.84 | 0.00 | 0.00 | 1.59 | 1.28 |
time (sec) |
N/A | 0.623 | 0.094 | 0.266 | 0.123 | 0.099 | 0.000 | 0.000 | 0.148 | 14.036 |
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 | 124 | 113 | 72 | 153 | 130 | 117 | 0 | 176 | 208 | 166 |
N.S. |
1 | 0.91 | 0.58 | 1.23 | 1.05 | 0.94 | 0.00 | 1.42 | 1.68 | 1.34 |
time (sec) |
N/A | 0.470 | 0.082 | 0.250 | 0.120 | 0.107 | 0.000 | 0.134 | 0.154 | 14.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 105 | 64 | 147 | 109 | 109 | 0 | 0 | 181 | 143 |
N.S. |
1 | 1.12 | 0.68 | 1.56 | 1.16 | 1.16 | 0.00 | 0.00 | 1.93 | 1.52 |
time (sec) |
N/A | 0.343 | 0.065 | 0.238 | 0.117 | 0.114 | 0.000 | 0.000 | 0.146 | 14.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 76 | 57 | 161 | 88 | 102 | 0 | 0 | 112 | 108 |
N.S. |
1 | 1.03 | 0.77 | 2.18 | 1.19 | 1.38 | 0.00 | 0.00 | 1.51 | 1.46 |
time (sec) |
N/A | 0.289 | 0.020 | 0.214 | 0.118 | 0.088 | 0.000 | 0.000 | 0.149 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 29 | 33 | 73 | 60 | 0 | 66 | 71 | 32 |
N.S. |
1 | 1.00 | 0.91 | 1.03 | 2.28 | 1.88 | 0.00 | 2.06 | 2.22 | 1.00 |
time (sec) |
N/A | 0.219 | 0.006 | 0.218 | 0.107 | 0.072 | 0.000 | 0.128 | 0.155 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 71 | 78 | 147 | 0 | 93 | 0 | 245 | 125 | 119 |
N.S. |
1 | 0.90 | 0.99 | 1.86 | 0.00 | 1.18 | 0.00 | 3.10 | 1.58 | 1.51 |
time (sec) |
N/A | 0.353 | 0.031 | 0.232 | 0.000 | 0.105 | 0.000 | 0.143 | 0.150 | 14.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 96 | 91 | 118 | 0 | 118 | 0 | 307 | 166 | 146 |
N.S. |
1 | 0.83 | 0.78 | 1.02 | 0.00 | 1.02 | 0.00 | 2.65 | 1.43 | 1.26 |
time (sec) |
N/A | 0.453 | 0.032 | 0.250 | 0.000 | 0.106 | 0.000 | 0.138 | 0.150 | 13.988 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 127 | 103 | 181 | 0 | 136 | 0 | 332 | 192 | 169 |
N.S. |
1 | 0.82 | 0.66 | 1.17 | 0.00 | 0.88 | 0.00 | 2.14 | 1.24 | 1.09 |
time (sec) |
N/A | 0.557 | 0.040 | 0.273 | 0.000 | 0.233 | 0.000 | 0.146 | 0.157 | 14.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 156 | 111 | 202 | 0 | 144 | 0 | 372 | 212 | 192 |
N.S. |
1 | 0.83 | 0.59 | 1.07 | 0.00 | 0.77 | 0.00 | 1.98 | 1.13 | 1.02 |
time (sec) |
N/A | 0.714 | 0.041 | 0.365 | 0.000 | 0.090 | 0.000 | 0.155 | 0.154 | 14.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 150 | 122 | 195 | 185 | 153 | 0 | 0 | 295 | 302 |
N.S. |
1 | 0.96 | 0.78 | 1.25 | 1.19 | 0.98 | 0.00 | 0.00 | 1.89 | 1.94 |
time (sec) |
N/A | 0.653 | 0.096 | 0.292 | 0.117 | 0.127 | 0.000 | 0.000 | 0.150 | 14.016 |
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 | 129 | 131 | 72 | 190 | 163 | 145 | 0 | 186 | 268 | 234 |
N.S. |
1 | 1.02 | 0.56 | 1.47 | 1.26 | 1.12 | 0.00 | 1.44 | 2.08 | 1.81 |
time (sec) |
N/A | 0.495 | 0.069 | 0.260 | 0.123 | 0.096 | 0.000 | 0.132 | 0.158 | 13.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 99 | 77 | 292 | 144 | 138 | 0 | 0 | 241 | 259 |
N.S. |
1 | 0.93 | 0.72 | 2.73 | 1.35 | 1.29 | 0.00 | 0.00 | 2.25 | 2.42 |
time (sec) |
N/A | 0.366 | 0.026 | 0.238 | 0.113 | 0.091 | 0.000 | 0.000 | 0.149 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 63 | 35 | 41 | 132 | 91 | 0 | 121 | 96 | 143 |
N.S. |
1 | 0.97 | 0.54 | 0.63 | 2.03 | 1.40 | 0.00 | 1.86 | 1.48 | 2.20 |
time (sec) |
N/A | 0.276 | 0.015 | 0.236 | 0.109 | 0.085 | 0.000 | 0.125 | 0.151 | 14.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 63 | 35 | 40 | 126 | 89 | 0 | 145 | 142 | 183 |
N.S. |
1 | 0.97 | 0.54 | 0.62 | 1.94 | 1.37 | 0.00 | 2.23 | 2.18 | 2.82 |
time (sec) |
N/A | 0.255 | 0.013 | 0.245 | 0.110 | 0.104 | 0.000 | 0.130 | 0.150 | 13.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 89 | 71 | 275 | 0 | 130 | 0 | 189 | 232 | 209 |
N.S. |
1 | 0.82 | 0.66 | 2.55 | 0.00 | 1.20 | 0.00 | 1.75 | 2.15 | 1.94 |
time (sec) |
N/A | 0.457 | 0.030 | 0.253 | 0.000 | 0.084 | 0.000 | 0.129 | 0.147 | 14.081 |
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 | 148 | 126 | 101 | 248 | 0 | 155 | 0 | 269 | 308 | 234 |
N.S. |
1 | 0.85 | 0.68 | 1.68 | 0.00 | 1.05 | 0.00 | 1.82 | 2.08 | 1.58 |
time (sec) |
N/A | 0.584 | 0.047 | 0.303 | 0.000 | 0.113 | 0.000 | 0.131 | 0.152 | 0.038 |
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 | 187 | 159 | 113 | 223 | 0 | 173 | 0 | 338 | 293 | 257 |
N.S. |
1 | 0.85 | 0.60 | 1.19 | 0.00 | 0.93 | 0.00 | 1.81 | 1.57 | 1.37 |
time (sec) |
N/A | 0.721 | 0.051 | 0.325 | 0.000 | 0.118 | 0.000 | 0.137 | 0.157 | 14.002 |
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 | 220 | 176 | 121 | 331 | 0 | 181 | 0 | 393 | 370 | 328 |
N.S. |
1 | 0.80 | 0.55 | 1.50 | 0.00 | 0.82 | 0.00 | 1.79 | 1.68 | 1.49 |
time (sec) |
N/A | 0.843 | 0.053 | 0.352 | 0.000 | 0.105 | 0.000 | 0.126 | 0.158 | 14.045 |
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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 183 | 126 | 235 | 250 | 187 | 0 | 252 | 424 | 323 |
N.S. |
1 | 0.97 | 0.67 | 1.25 | 1.33 | 0.99 | 0.00 | 1.34 | 2.26 | 1.72 |
time (sec) |
N/A | 0.850 | 0.163 | 0.309 | 0.125 | 0.110 | 0.000 | 0.131 | 0.157 | 14.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 160 | 95 | 229 | 229 | 179 | 0 | 0 | 405 | 350 |
N.S. |
1 | 0.99 | 0.59 | 1.42 | 1.42 | 1.11 | 0.00 | 0.00 | 2.52 | 2.17 |
time (sec) |
N/A | 0.559 | 0.066 | 0.296 | 0.115 | 0.114 | 0.000 | 0.000 | 0.161 | 14.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 127 | 94 | 466 | 208 | 172 | 0 | 220 | 386 | 281 |
N.S. |
1 | 0.92 | 0.68 | 3.38 | 1.51 | 1.25 | 0.00 | 1.59 | 2.80 | 2.04 |
time (sec) |
N/A | 0.436 | 0.103 | 0.253 | 0.129 | 0.091 | 0.000 | 0.130 | 0.150 | 0.038 |
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 | 97 | 129 | 43 | 49 | 197 | 118 | 0 | 0 | 72 | 347 |
N.S. |
1 | 1.33 | 0.44 | 0.51 | 2.03 | 1.22 | 0.00 | 0.00 | 0.74 | 3.58 |
time (sec) |
N/A | 0.369 | 0.024 | 0.264 | 0.114 | 0.097 | 0.000 | 0.000 | 0.150 | 0.036 |
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 | 97 | 100 | 42 | 48 | 197 | 116 | 0 | 148 | 72 | 295 |
N.S. |
1 | 1.03 | 0.43 | 0.49 | 2.03 | 1.20 | 0.00 | 1.53 | 0.74 | 3.04 |
time (sec) |
N/A | 0.314 | 0.019 | 0.266 | 0.113 | 0.090 | 0.000 | 0.127 | 0.162 | 13.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 43 | 49 | 189 | 116 | 0 | 199 | 72 | 49 |
N.S. |
1 | 1.00 | 0.44 | 0.51 | 1.95 | 1.20 | 0.00 | 2.05 | 0.74 | 0.51 |
time (sec) |
N/A | 0.279 | 0.022 | 0.265 | 0.109 | 0.079 | 0.000 | 0.131 | 0.145 | 14.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 129 | 79 | 451 | 0 | 163 | 0 | 243 | 32 | 327 |
N.S. |
1 | 0.94 | 0.58 | 3.29 | 0.00 | 1.19 | 0.00 | 1.77 | 0.23 | 2.39 |
time (sec) |
N/A | 0.517 | 0.052 | 0.289 | 0.000 | 0.085 | 0.000 | 0.135 | 200.018 | 14.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 156 | 109 | 423 | 0 | 188 | 0 | 323 | 337 | 352 |
N.S. |
1 | 0.87 | 0.61 | 2.35 | 0.00 | 1.04 | 0.00 | 1.79 | 1.87 | 1.96 |
time (sec) |
N/A | 0.737 | 0.057 | 0.341 | 0.000 | 0.112 | 0.000 | 0.131 | 0.158 | 14.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 191 | 121 | 397 | 0 | 206 | 0 | 392 | 32 | 375 |
N.S. |
1 | 0.87 | 0.55 | 1.81 | 0.00 | 0.94 | 0.00 | 1.79 | 0.15 | 1.71 |
time (sec) |
N/A | 0.890 | 0.055 | 0.359 | 0.000 | 0.090 | 0.000 | 0.132 | 200.018 | 14.001 |
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 | 50 | 66 | 42 | 28 | 40 | 38 | 37 | 21 | 38 | 22 |
N.S. |
1 | 1.32 | 0.84 | 0.56 | 0.80 | 0.76 | 0.74 | 0.42 | 0.76 | 0.44 |
time (sec) |
N/A | 0.232 | 0.028 | 0.203 | 0.104 | 0.086 | 0.115 | 0.120 | 0.157 | 0.021 |
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 | 41 | 37 | 25 | 28 | 33 | 27 | 19 | 27 | 21 |
N.S. |
1 | 1.14 | 1.03 | 0.69 | 0.78 | 0.92 | 0.75 | 0.53 | 0.75 | 0.58 |
time (sec) |
N/A | 0.215 | 0.018 | 0.194 | 0.107 | 0.075 | 0.089 | 0.117 | 0.149 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 91 | 51 | 37 | 56 | 45 | 54 | 28 | 53 | 29 |
N.S. |
1 | 1.40 | 0.78 | 0.57 | 0.86 | 0.69 | 0.83 | 0.43 | 0.82 | 0.45 |
time (sec) |
N/A | 0.258 | 0.031 | 0.208 | 0.107 | 0.084 | 0.160 | 0.138 | 0.148 | 14.001 |
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 | 56 | 66 | 44 | 32 | 42 | 40 | 44 | 25 | 40 | 26 |
N.S. |
1 | 1.18 | 0.79 | 0.57 | 0.75 | 0.71 | 0.79 | 0.45 | 0.71 | 0.46 |
time (sec) |
N/A | 0.223 | 0.030 | 0.199 | 0.107 | 0.088 | 0.109 | 0.119 | 0.152 | 0.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 18 | 13 | 12 | 11 | 11 | 8 | 11 | 10 | 11 |
N.S. |
1 | 1.38 | 1.00 | 0.92 | 0.85 | 0.85 | 0.62 | 0.85 | 0.77 | 0.85 |
time (sec) |
N/A | 0.208 | 0.004 | 0.165 | 0.025 | 0.081 | 0.056 | 0.146 | 0.146 | 14.134 |
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 | 2 | 2 | 2 | 3 | 2 | 18 | 2 | 17 | 2 | 2 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 1.00 | 9.00 | 1.00 | 8.50 | 1.00 | 1.00 |
time (sec) |
N/A | 0.196 | 0.002 | 0.176 | 0.105 | 0.088 | 0.058 | 0.117 | 0.145 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 18 | 18 | 44 | 0 | 24 | 28 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.90 | 2.20 | 0.00 | 1.20 | 1.40 | 0.90 |
time (sec) |
N/A | 0.217 | 0.010 | 0.197 | 0.106 | 0.109 | 0.000 | 0.121 | 0.143 | 0.021 |
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 | 18 | 18 | 18 | 14 | 16 | 19 | 0 | 21 | 16 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.89 | 1.06 | 0.00 | 1.17 | 0.89 | 0.72 |
time (sec) |
N/A | 0.202 | 0.004 | 0.191 | 0.106 | 0.097 | 0.000 | 0.120 | 0.147 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 111 | 51 | 48 | 106 | 58 | 0 | 0 | 35 | 53 |
N.S. |
1 | 1.10 | 0.50 | 0.48 | 1.05 | 0.57 | 0.00 | 0.00 | 0.35 | 0.52 |
time (sec) |
N/A | 0.389 | 0.027 | 0.189 | 0.046 | 0.084 | 0.000 | 0.000 | 0.158 | 14.242 |
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 | 69 | 68 | 43 | 40 | 83 | 49 | 0 | 54 | 26 | 46 |
N.S. |
1 | 0.99 | 0.62 | 0.58 | 1.20 | 0.71 | 0.00 | 0.78 | 0.38 | 0.67 |
time (sec) |
N/A | 0.294 | 0.016 | 0.187 | 0.047 | 0.077 | 0.000 | 0.124 | 0.152 | 14.142 |
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 | 35 | 35 | 37 | 34 | 58 | 39 | 0 | 34 | 18 | 37 |
N.S. |
1 | 1.00 | 1.06 | 0.97 | 1.66 | 1.11 | 0.00 | 0.97 | 0.51 | 1.06 |
time (sec) |
N/A | 0.233 | 0.010 | 0.187 | 0.047 | 0.083 | 0.000 | 0.114 | 0.235 | 0.001 |
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 | 68 | 69 | 46 | 71 | 0 | 179 | 0 | 83 | 46 | 0 |
N.S. |
1 | 1.01 | 0.68 | 1.04 | 0.00 | 2.63 | 0.00 | 1.22 | 0.68 | 0.00 |
time (sec) |
N/A | 0.342 | 0.019 | 0.188 | 0.000 | 0.117 | 0.000 | 0.142 | 0.215 | 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 | 72 | 73 | 57 | 78 | 0 | 203 | 0 | 97 | 55 | 0 |
N.S. |
1 | 1.01 | 0.79 | 1.08 | 0.00 | 2.82 | 0.00 | 1.35 | 0.76 | 0.00 |
time (sec) |
N/A | 0.343 | 0.024 | 0.204 | 0.000 | 0.079 | 0.000 | 0.131 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 106 | 48 | 45 | 74 | 44 | 136 | 189 | 44 | 83 |
N.S. |
1 | 1.05 | 0.48 | 0.45 | 0.73 | 0.44 | 1.35 | 1.87 | 0.44 | 0.82 |
time (sec) |
N/A | 0.369 | 0.021 | 0.252 | 0.035 | 0.092 | 4.434 | 0.120 | 0.150 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 85 | 40 | 37 | 60 | 36 | 110 | 142 | 36 | 66 |
N.S. |
1 | 1.06 | 0.50 | 0.46 | 0.75 | 0.45 | 1.38 | 1.78 | 0.45 | 0.82 |
time (sec) |
N/A | 0.348 | 0.017 | 0.243 | 0.029 | 0.073 | 3.880 | 0.118 | 0.146 | 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 | 57 | 62 | 31 | 28 | 44 | 27 | 82 | 92 | 28 | 46 |
N.S. |
1 | 1.09 | 0.54 | 0.49 | 0.77 | 0.47 | 1.44 | 1.61 | 0.49 | 0.81 |
time (sec) |
N/A | 0.303 | 0.013 | 0.242 | 0.035 | 0.089 | 3.851 | 0.116 | 0.148 | 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 | 38 | 43 | 23 | 20 | 30 | 19 | 54 | 44 | 20 | 32 |
N.S. |
1 | 1.13 | 0.61 | 0.53 | 0.79 | 0.50 | 1.42 | 1.16 | 0.53 | 0.84 |
time (sec) |
N/A | 0.255 | 0.009 | 0.213 | 0.030 | 0.082 | 2.583 | 0.110 | 0.147 | 0.001 |