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 | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 102 | 107 | 120 | 120 | 143 | 137 | 106 | 113 |
N.S. |
1 | 1.00 | 2.27 | 2.38 | 2.67 | 2.67 | 3.18 | 3.04 | 2.36 | 2.51 |
time (sec) |
N/A | 0.248 | 0.019 | 0.434 | 0.033 | 0.077 | 0.031 | 0.137 | 0.176 | 0.037 |
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 | 45 | 45 | 66 | 46 | 97 | 97 | 114 | 73 | 83 | 93 |
N.S. |
1 | 1.00 | 1.47 | 1.02 | 2.16 | 2.16 | 2.53 | 1.62 | 1.84 | 2.07 |
time (sec) |
N/A | 0.240 | 0.013 | 0.432 | 0.031 | 0.072 | 0.027 | 0.110 | 0.210 | 5.549 |
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 | 45 | 45 | 64 | 61 | 71 | 71 | 85 | 79 | 60 | 69 |
N.S. |
1 | 1.00 | 1.42 | 1.36 | 1.58 | 1.58 | 1.89 | 1.76 | 1.33 | 1.53 |
time (sec) |
N/A | 0.224 | 0.013 | 0.430 | 0.039 | 0.067 | 0.025 | 0.121 | 0.184 | 5.570 |
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 | 17 | 17 | 22 | 16 | 15 | 36 | 39 | 32 | 33 | 36 |
N.S. |
1 | 1.00 | 1.29 | 0.94 | 0.88 | 2.12 | 2.29 | 1.88 | 1.94 | 2.12 |
time (sec) |
N/A | 0.151 | 0.005 | 0.146 | 0.028 | 0.070 | 0.020 | 0.127 | 0.195 | 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 | 48 | 48 | 37 | 42 | 41 | 39 | 37 | 47 | 45 | 44 |
N.S. |
1 | 1.00 | 0.77 | 0.88 | 0.85 | 0.81 | 0.77 | 0.98 | 0.94 | 0.92 |
time (sec) |
N/A | 0.208 | 0.011 | 0.508 | 0.027 | 0.091 | 0.108 | 0.126 | 0.193 | 0.038 |
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 | 38 | 38 | 41 | 25 | 40 | 43 | 36 | 170 | 24 | 36 |
N.S. |
1 | 1.00 | 1.08 | 0.66 | 1.05 | 1.13 | 0.95 | 4.47 | 0.63 | 0.95 |
time (sec) |
N/A | 0.197 | 0.011 | 0.499 | 0.027 | 0.074 | 0.109 | 0.129 | 0.234 | 5.438 |
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 | 44 | 44 | 37 | 41 | 60 | 70 | 60 | 41 | 74 | 42 |
N.S. |
1 | 1.00 | 0.84 | 0.93 | 1.36 | 1.59 | 1.36 | 0.93 | 1.68 | 0.95 |
time (sec) |
N/A | 0.207 | 0.016 | 0.487 | 0.042 | 0.077 | 0.196 | 0.110 | 0.197 | 0.041 |
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 | 45 | 38 | 38 | 71 | 71 | 75 | 37 | 67 | 71 |
N.S. |
1 | 1.00 | 0.84 | 0.84 | 1.58 | 1.58 | 1.67 | 0.82 | 1.49 | 1.58 |
time (sec) |
N/A | 0.206 | 0.020 | 0.487 | 0.028 | 0.077 | 0.204 | 0.125 | 0.215 | 5.487 |
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 | 37 | 37 | 38 | 38 | 85 | 85 | 90 | 60 | 72 | 85 |
N.S. |
1 | 1.00 | 1.03 | 1.03 | 2.30 | 2.30 | 2.43 | 1.62 | 1.95 | 2.30 |
time (sec) |
N/A | 0.166 | 0.013 | 0.487 | 0.030 | 0.090 | 0.298 | 0.163 | 0.233 | 5.498 |
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 | 45 | 45 | 43 | 38 | 99 | 99 | 105 | 37 | 83 | 99 |
N.S. |
1 | 1.00 | 0.96 | 0.84 | 2.20 | 2.20 | 2.33 | 0.82 | 1.84 | 2.20 |
time (sec) |
N/A | 0.208 | 0.017 | 0.490 | 0.035 | 0.081 | 0.310 | 0.123 | 0.240 | 0.045 |
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 | 45 | 45 | 43 | 38 | 113 | 113 | 121 | 37 | 94 | 113 |
N.S. |
1 | 1.00 | 0.96 | 0.84 | 2.51 | 2.51 | 2.69 | 0.82 | 2.09 | 2.51 |
time (sec) |
N/A | 0.208 | 0.016 | 0.496 | 0.036 | 0.072 | 0.430 | 0.112 | 0.206 | 0.054 |
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 | 45 | 45 | 39 | 38 | 127 | 127 | 136 | 37 | 105 | 127 |
N.S. |
1 | 1.00 | 0.87 | 0.84 | 2.82 | 2.82 | 3.02 | 0.82 | 2.33 | 2.82 |
time (sec) |
N/A | 0.207 | 0.014 | 0.497 | 0.048 | 0.073 | 0.436 | 0.118 | 0.207 | 5.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 168 | 227 | 237 | 237 | 291 | 286 | 226 | 224 |
N.S. |
1 | 1.00 | 2.30 | 3.11 | 3.25 | 3.25 | 3.99 | 3.92 | 3.10 | 3.07 |
time (sec) |
N/A | 0.358 | 0.048 | 0.786 | 0.031 | 0.082 | 0.043 | 0.127 | 0.209 | 5.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 179 | 190 | 201 | 201 | 248 | 240 | 189 | 190 |
N.S. |
1 | 1.00 | 2.45 | 2.60 | 2.75 | 2.75 | 3.40 | 3.29 | 2.59 | 2.60 |
time (sec) |
N/A | 0.310 | 0.021 | 0.766 | 0.041 | 0.090 | 0.037 | 0.139 | 0.249 | 0.049 |
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 | 55 | 55 | 97 | 46 | 161 | 161 | 194 | 124 | 151 | 152 |
N.S. |
1 | 1.00 | 1.76 | 0.84 | 2.93 | 2.93 | 3.53 | 2.25 | 2.75 | 2.76 |
time (sec) |
N/A | 0.203 | 0.020 | 0.754 | 0.042 | 0.080 | 0.034 | 0.105 | 0.224 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 111 | 116 | 127 | 127 | 156 | 148 | 115 | 120 |
N.S. |
1 | 1.00 | 1.52 | 1.59 | 1.74 | 1.74 | 2.14 | 2.03 | 1.58 | 1.64 |
time (sec) |
N/A | 0.282 | 0.015 | 0.767 | 0.034 | 0.138 | 0.029 | 0.105 | 0.191 | 0.031 |
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 | 17 | 17 | 37 | 16 | 15 | 73 | 80 | 52 | 74 | 67 |
N.S. |
1 | 1.00 | 2.18 | 0.94 | 0.88 | 4.29 | 4.71 | 3.06 | 4.35 | 3.94 |
time (sec) |
N/A | 0.153 | 0.009 | 0.707 | 0.029 | 0.090 | 0.027 | 0.128 | 0.192 | 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 | 72 | 72 | 61 | 67 | 89 | 88 | 78 | 116 | 101 | 133 |
N.S. |
1 | 1.00 | 0.85 | 0.93 | 1.24 | 1.22 | 1.08 | 1.61 | 1.40 | 1.85 |
time (sec) |
N/A | 0.261 | 0.024 | 0.846 | 0.033 | 0.125 | 0.164 | 0.131 | 0.229 | 5.514 |
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 | 72 | 72 | 59 | 45 | 77 | 85 | 82 | 134 | 42 | 96 |
N.S. |
1 | 1.00 | 0.82 | 0.62 | 1.07 | 1.18 | 1.14 | 1.86 | 0.58 | 1.33 |
time (sec) |
N/A | 0.245 | 0.041 | 0.839 | 0.038 | 0.074 | 0.183 | 0.128 | 0.207 | 0.038 |
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 | 79 | 79 | 61 | 74 | 96 | 147 | 102 | 88 | 165 | 106 |
N.S. |
1 | 1.00 | 0.77 | 0.94 | 1.22 | 1.86 | 1.29 | 1.11 | 2.09 | 1.34 |
time (sec) |
N/A | 0.262 | 0.041 | 0.826 | 0.036 | 0.085 | 0.402 | 0.148 | 0.200 | 5.632 |
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 | 66 | 66 | 53 | 67 | 116 | 125 | 117 | 82 | 92 | 67 |
N.S. |
1 | 1.00 | 0.80 | 1.02 | 1.76 | 1.89 | 1.77 | 1.24 | 1.39 | 1.02 |
time (sec) |
N/A | 0.241 | 0.042 | 0.819 | 0.050 | 0.071 | 0.438 | 0.141 | 0.230 | 5.617 |
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 | 72 | 72 | 59 | 73 | 136 | 168 | 139 | 146 | 180 | 135 |
N.S. |
1 | 1.00 | 0.82 | 1.01 | 1.89 | 2.33 | 1.93 | 2.03 | 2.50 | 1.88 |
time (sec) |
N/A | 0.244 | 0.029 | 0.822 | 0.035 | 0.080 | 0.749 | 0.120 | 0.216 | 0.068 |
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 | 73 | 73 | 59 | 74 | 149 | 149 | 158 | 87 | 142 | 141 |
N.S. |
1 | 1.00 | 0.81 | 1.01 | 2.04 | 2.04 | 2.16 | 1.19 | 1.95 | 1.93 |
time (sec) |
N/A | 0.241 | 0.025 | 0.826 | 0.052 | 0.073 | 0.648 | 0.132 | 0.205 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 65 | 74 | 164 | 164 | 173 | 87 | 144 | 157 |
N.S. |
1 | 1.00 | 1.76 | 2.00 | 4.43 | 4.43 | 4.68 | 2.35 | 3.89 | 4.24 |
time (sec) |
N/A | 0.177 | 0.022 | 0.829 | 0.040 | 0.078 | 1.153 | 0.156 | 0.201 | 5.579 |
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 | 73 | 73 | 59 | 74 | 176 | 176 | 189 | 87 | 155 | 168 |
N.S. |
1 | 1.00 | 0.81 | 1.01 | 2.41 | 2.41 | 2.59 | 1.19 | 2.12 | 2.30 |
time (sec) |
N/A | 0.241 | 0.027 | 0.826 | 0.039 | 0.086 | 0.948 | 0.111 | 0.224 | 5.522 |
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 | 73 | 73 | 59 | 74 | 192 | 192 | 204 | 87 | 166 | 185 |
N.S. |
1 | 1.00 | 0.81 | 1.01 | 2.63 | 2.63 | 2.79 | 1.19 | 2.27 | 2.53 |
time (sec) |
N/A | 0.243 | 0.021 | 0.836 | 0.048 | 0.080 | 1.671 | 0.113 | 0.220 | 5.272 |
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 | 73 | 73 | 59 | 74 | 206 | 206 | 219 | 87 | 177 | 199 |
N.S. |
1 | 1.00 | 0.81 | 1.01 | 2.82 | 2.82 | 3.00 | 1.19 | 2.42 | 2.73 |
time (sec) |
N/A | 0.244 | 0.032 | 0.827 | 0.061 | 0.085 | 1.293 | 0.131 | 0.184 | 5.336 |
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 | 73 | 73 | 59 | 74 | 220 | 220 | 235 | 87 | 188 | 213 |
N.S. |
1 | 1.00 | 0.81 | 1.01 | 3.01 | 3.01 | 3.22 | 1.19 | 2.58 | 2.92 |
time (sec) |
N/A | 0.253 | 0.025 | 0.822 | 0.046 | 0.085 | 2.324 | 0.105 | 0.196 | 0.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 224 | 338 | 342 | 342 | 428 | 424 | 337 | 326 |
N.S. |
1 | 1.00 | 2.22 | 3.35 | 3.39 | 3.39 | 4.24 | 4.20 | 3.34 | 3.23 |
time (sec) |
N/A | 0.440 | 0.083 | 0.774 | 0.038 | 0.075 | 0.051 | 0.120 | 0.216 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 259 | 287 | 290 | 290 | 371 | 361 | 286 | 274 |
N.S. |
1 | 1.00 | 2.56 | 2.84 | 2.87 | 2.87 | 3.67 | 3.57 | 2.83 | 2.71 |
time (sec) |
N/A | 0.386 | 0.033 | 0.761 | 0.029 | 0.079 | 0.047 | 0.131 | 0.205 | 5.628 |
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 | 55 | 55 | 132 | 46 | 243 | 243 | 299 | 171 | 235 | 229 |
N.S. |
1 | 1.00 | 2.40 | 0.84 | 4.42 | 4.42 | 5.44 | 3.11 | 4.27 | 4.16 |
time (sec) |
N/A | 0.201 | 0.026 | 0.770 | 0.032 | 0.074 | 0.041 | 0.127 | 0.209 | 5.594 |
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 | 101 | 101 | 179 | 185 | 198 | 198 | 246 | 235 | 184 | 188 |
N.S. |
1 | 1.00 | 1.77 | 1.83 | 1.96 | 1.96 | 2.44 | 2.33 | 1.82 | 1.86 |
time (sec) |
N/A | 0.344 | 0.022 | 0.779 | 0.041 | 0.068 | 0.038 | 0.124 | 0.199 | 5.105 |
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 | 17 | 17 | 52 | 16 | 15 | 129 | 144 | 73 | 129 | 119 |
N.S. |
1 | 1.00 | 3.06 | 0.94 | 0.88 | 7.59 | 8.47 | 4.29 | 7.59 | 7.00 |
time (sec) |
N/A | 0.151 | 0.013 | 0.706 | 0.039 | 0.073 | 0.032 | 0.128 | 0.231 | 0.035 |
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 | 100 | 100 | 111 | 169 | 163 | 162 | 156 | 213 | 187 | 304 |
N.S. |
1 | 1.00 | 1.11 | 1.69 | 1.63 | 1.62 | 1.56 | 2.13 | 1.87 | 3.04 |
time (sec) |
N/A | 0.316 | 0.034 | 0.817 | 0.035 | 0.078 | 0.266 | 0.128 | 0.236 | 0.043 |
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 | 94 | 94 | 101 | 75 | 138 | 138 | 160 | 221 | 73 | 293 |
N.S. |
1 | 1.00 | 1.07 | 0.80 | 1.47 | 1.47 | 1.70 | 2.35 | 0.78 | 3.12 |
time (sec) |
N/A | 0.295 | 0.065 | 0.826 | 0.026 | 0.076 | 0.323 | 0.139 | 0.185 | 5.142 |
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 | 100 | 100 | 90 | 114 | 147 | 252 | 156 | 148 | 287 | 223 |
N.S. |
1 | 1.00 | 0.90 | 1.14 | 1.47 | 2.52 | 1.56 | 1.48 | 2.87 | 2.23 |
time (sec) |
N/A | 0.306 | 0.075 | 0.836 | 0.035 | 0.079 | 0.639 | 0.166 | 0.189 | 5.154 |
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 | 103 | 103 | 81 | 116 | 175 | 198 | 192 | 164 | 131 | 194 |
N.S. |
1 | 1.00 | 0.79 | 1.13 | 1.70 | 1.92 | 1.86 | 1.59 | 1.27 | 1.88 |
time (sec) |
N/A | 0.296 | 0.044 | 0.832 | 0.062 | 0.073 | 0.698 | 0.151 | 0.238 | 5.184 |
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 | 107 | 107 | 80 | 121 | 194 | 291 | 209 | 262 | 333 | 202 |
N.S. |
1 | 1.00 | 0.75 | 1.13 | 1.81 | 2.72 | 1.95 | 2.45 | 3.11 | 1.89 |
time (sec) |
N/A | 0.302 | 0.053 | 0.836 | 0.040 | 0.084 | 1.535 | 0.121 | 0.196 | 5.211 |
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 | 94 | 94 | 72 | 114 | 218 | 227 | 223 | 160 | 212 | 129 |
N.S. |
1 | 1.00 | 0.77 | 1.21 | 2.32 | 2.41 | 2.37 | 1.70 | 2.26 | 1.37 |
time (sec) |
N/A | 0.278 | 0.082 | 0.830 | 0.054 | 0.082 | 1.435 | 0.157 | 0.182 | 5.190 |
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 | 100 | 100 | 78 | 120 | 238 | 292 | 245 | 163 | 316 | 229 |
N.S. |
1 | 1.00 | 0.78 | 1.20 | 2.38 | 2.92 | 2.45 | 1.63 | 3.16 | 2.29 |
time (sec) |
N/A | 0.282 | 0.074 | 0.852 | 0.053 | 0.083 | 2.880 | 0.136 | 0.275 | 0.101 |
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 | 101 | 101 | 79 | 121 | 248 | 248 | 267 | 165 | 245 | 233 |
N.S. |
1 | 1.00 | 0.78 | 1.20 | 2.46 | 2.46 | 2.64 | 1.63 | 2.43 | 2.31 |
time (sec) |
N/A | 0.284 | 0.037 | 0.828 | 0.040 | 0.078 | 2.180 | 0.128 | 0.286 | 5.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 96 | 121 | 266 | 266 | 282 | 165 | 244 | 254 |
N.S. |
1 | 1.00 | 2.59 | 3.27 | 7.19 | 7.19 | 7.62 | 4.46 | 6.59 | 6.86 |
time (sec) |
N/A | 0.171 | 0.067 | 0.834 | 0.047 | 0.082 | 5.023 | 0.125 | 0.280 | 5.413 |
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 | 101 | 101 | 79 | 121 | 280 | 280 | 298 | 165 | 255 | 268 |
N.S. |
1 | 1.00 | 0.78 | 1.20 | 2.77 | 2.77 | 2.95 | 1.63 | 2.52 | 2.65 |
time (sec) |
N/A | 0.279 | 0.041 | 0.832 | 0.059 | 0.086 | 3.275 | 0.146 | 0.214 | 5.527 |
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 | 101 | 101 | 79 | 121 | 294 | 294 | 313 | 165 | 266 | 282 |
N.S. |
1 | 1.00 | 0.78 | 1.20 | 2.91 | 2.91 | 3.10 | 1.63 | 2.63 | 2.79 |
time (sec) |
N/A | 0.285 | 0.044 | 0.842 | 0.048 | 0.083 | 9.694 | 0.117 | 0.202 | 5.647 |
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 | 101 | 101 | 79 | 121 | 306 | 306 | 328 | 165 | 277 | 292 |
N.S. |
1 | 1.00 | 0.78 | 1.20 | 3.03 | 3.03 | 3.25 | 1.63 | 2.74 | 2.89 |
time (sec) |
N/A | 0.286 | 0.050 | 0.849 | 0.050 | 0.097 | 4.583 | 0.155 | 0.260 | 5.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 115 | 188 | 246 | 0 | 536 | 502 | 313 | 330 | 761 |
N.S. |
1 | 0.94 | 1.54 | 2.02 | 0.00 | 4.39 | 4.11 | 2.57 | 2.70 | 6.24 |
time (sec) |
N/A | 0.327 | 0.092 | 0.965 | 0.000 | 0.089 | 0.532 | 0.152 | 0.191 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 79 | 110 | 167 | 181 | 181 | 185 | 219 | 200 | 418 |
N.S. |
1 | 0.92 | 1.28 | 1.94 | 2.10 | 2.10 | 2.15 | 2.55 | 2.33 | 4.86 |
time (sec) |
N/A | 0.265 | 0.041 | 0.852 | 0.027 | 0.087 | 0.468 | 0.114 | 0.196 | 5.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 93 | 120 | 154 | 0 | 356 | 337 | 197 | 206 | 296 |
N.S. |
1 | 0.96 | 1.24 | 1.59 | 0.00 | 3.67 | 3.47 | 2.03 | 2.12 | 3.05 |
time (sec) |
N/A | 0.278 | 0.056 | 0.865 | 0.000 | 0.093 | 0.382 | 0.132 | 0.185 | 5.527 |
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 | 61 | 57 | 54 | 89 | 99 | 99 | 99 | 118 | 109 | 139 |
N.S. |
1 | 0.93 | 0.89 | 1.46 | 1.62 | 1.62 | 1.62 | 1.93 | 1.79 | 2.28 |
time (sec) |
N/A | 0.221 | 0.018 | 0.904 | 0.031 | 0.081 | 0.324 | 0.108 | 0.216 | 0.041 |
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 | 72 | 71 | 72 | 90 | 0 | 208 | 204 | 115 | 110 | 133 |
N.S. |
1 | 0.99 | 1.00 | 1.25 | 0.00 | 2.89 | 2.83 | 1.60 | 1.53 | 1.85 |
time (sec) |
N/A | 0.236 | 0.030 | 0.867 | 0.000 | 0.081 | 0.255 | 0.130 | 0.188 | 5.555 |
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 | 33 | 39 | 43 | 43 | 44 | 50 | 48 | 47 |
N.S. |
1 | 1.00 | 0.92 | 1.08 | 1.19 | 1.19 | 1.22 | 1.39 | 1.33 | 1.31 |
time (sec) |
N/A | 0.190 | 0.010 | 0.856 | 0.032 | 0.102 | 0.206 | 0.106 | 0.193 | 0.039 |
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 | 49 | 49 | 47 | 52 | 0 | 132 | 99 | 57 | 44 | 81 |
N.S. |
1 | 1.00 | 0.96 | 1.06 | 0.00 | 2.69 | 2.02 | 1.16 | 0.90 | 1.65 |
time (sec) |
N/A | 0.203 | 0.018 | 0.866 | 0.000 | 0.106 | 0.151 | 0.136 | 0.183 | 5.393 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 12 | 14 | 13 | 13 | 12 | 21 | 13 | 13 |
N.S. |
1 | 1.00 | 0.92 | 1.08 | 1.00 | 1.00 | 0.92 | 1.62 | 1.00 | 1.00 |
time (sec) |
N/A | 0.151 | 0.003 | 0.799 | 0.039 | 0.080 | 0.092 | 0.116 | 0.211 | 5.108 |
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 | 34 | 41 | 48 | 35 | 42 | 57 | 39 | 47 |
N.S. |
1 | 1.00 | 0.71 | 0.85 | 1.00 | 0.73 | 0.88 | 1.19 | 0.81 | 0.98 |
time (sec) |
N/A | 0.200 | 0.022 | 0.960 | 0.042 | 0.076 | 0.381 | 0.114 | 0.204 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 63 | 62 | 0 | 256 | 240 | 117 | 145 | 115 |
N.S. |
1 | 1.00 | 1.03 | 1.02 | 0.00 | 4.20 | 3.93 | 1.92 | 2.38 | 1.89 |
time (sec) |
N/A | 0.219 | 0.038 | 0.994 | 0.000 | 0.082 | 0.468 | 0.129 | 0.186 | 5.367 |
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 | 70 | 79 | 65 | 73 | 129 | 156 | 119 | 111 | 186 | 151 |
N.S. |
1 | 1.13 | 0.93 | 1.04 | 1.84 | 2.23 | 1.70 | 1.59 | 2.66 | 2.16 |
time (sec) |
N/A | 0.238 | 0.031 | 0.961 | 0.037 | 0.089 | 0.830 | 0.118 | 0.207 | 5.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 95 | 83 | 84 | 0 | 627 | 442 | 128 | 402 | 219 |
N.S. |
1 | 1.10 | 0.97 | 0.98 | 0.00 | 7.29 | 5.14 | 1.49 | 4.67 | 2.55 |
time (sec) |
N/A | 0.251 | 0.039 | 1.013 | 0.000 | 0.097 | 0.878 | 0.132 | 0.217 | 5.788 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 119 | 155 | 240 | 0 | 753 | 476 | 308 | 589 | 508 |
N.S. |
1 | 0.94 | 1.23 | 1.90 | 0.00 | 5.98 | 3.78 | 2.44 | 4.67 | 4.03 |
time (sec) |
N/A | 0.308 | 0.055 | 0.887 | 0.000 | 0.099 | 1.247 | 0.148 | 0.208 | 5.589 |
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 | 89 | 83 | 103 | 138 | 155 | 283 | 160 | 181 | 315 | 234 |
N.S. |
1 | 0.93 | 1.16 | 1.55 | 1.74 | 3.18 | 1.80 | 2.03 | 3.54 | 2.63 |
time (sec) |
N/A | 0.251 | 0.058 | 0.939 | 0.033 | 0.084 | 1.316 | 0.159 | 0.212 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 97 | 108 | 151 | 0 | 504 | 313 | 197 | 373 | 230 |
N.S. |
1 | 0.97 | 1.08 | 1.51 | 0.00 | 5.04 | 3.13 | 1.97 | 3.73 | 2.30 |
time (sec) |
N/A | 0.271 | 0.048 | 0.887 | 0.000 | 0.087 | 0.814 | 0.137 | 0.211 | 0.050 |
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 | 65 | 61 | 64 | 78 | 86 | 165 | 90 | 100 | 181 | 97 |
N.S. |
1 | 0.94 | 0.98 | 1.20 | 1.32 | 2.54 | 1.38 | 1.54 | 2.78 | 1.49 |
time (sec) |
N/A | 0.219 | 0.027 | 0.858 | 0.039 | 0.076 | 0.873 | 0.138 | 0.199 | 5.643 |
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 | 76 | 75 | 77 | 84 | 0 | 297 | 173 | 112 | 186 | 143 |
N.S. |
1 | 0.99 | 1.01 | 1.11 | 0.00 | 3.91 | 2.28 | 1.47 | 2.45 | 1.88 |
time (sec) |
N/A | 0.234 | 0.044 | 0.871 | 0.000 | 0.090 | 0.530 | 0.132 | 0.224 | 0.062 |
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 | 43 | 43 | 42 | 43 | 43 | 64 | 42 | 101 | 76 | 47 |
N.S. |
1 | 1.00 | 0.98 | 1.00 | 1.00 | 1.49 | 0.98 | 2.35 | 1.77 | 1.09 |
time (sec) |
N/A | 0.191 | 0.017 | 0.844 | 0.028 | 0.102 | 0.443 | 0.129 | 0.194 | 6.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 65 | 62 | 0 | 309 | 211 | 66 | 208 | 88 |
N.S. |
1 | 1.00 | 1.05 | 1.00 | 0.00 | 4.98 | 3.40 | 1.06 | 3.35 | 1.42 |
time (sec) |
N/A | 0.203 | 0.026 | 0.855 | 0.000 | 0.087 | 0.309 | 0.105 | 0.229 | 0.039 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 14 | 16 | 15 | 15 | 12 | 22 | 15 | 15 |
N.S. |
1 | 1.00 | 0.93 | 1.07 | 1.00 | 1.00 | 0.80 | 1.47 | 1.00 | 1.00 |
time (sec) |
N/A | 0.152 | 0.004 | 0.795 | 0.031 | 0.079 | 0.205 | 0.134 | 0.206 | 5.683 |
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 | 78 | 86 | 59 | 78 | 121 | 141 | 102 | 108 | 181 | 125 |
N.S. |
1 | 1.10 | 0.76 | 1.00 | 1.55 | 1.81 | 1.31 | 1.38 | 2.32 | 1.60 |
time (sec) |
N/A | 0.236 | 0.039 | 0.976 | 0.042 | 0.086 | 0.800 | 0.132 | 0.190 | 5.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 107 | 84 | 98 | 0 | 644 | 459 | 220 | 448 | 232 |
N.S. |
1 | 1.09 | 0.86 | 1.00 | 0.00 | 6.57 | 4.68 | 2.24 | 4.57 | 2.37 |
time (sec) |
N/A | 0.257 | 0.100 | 1.016 | 0.000 | 0.104 | 0.930 | 0.130 | 0.196 | 5.766 |
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 | 110 | 125 | 79 | 100 | 296 | 409 | 304 | 203 | 528 | 278 |
N.S. |
1 | 1.14 | 0.72 | 0.91 | 2.69 | 3.72 | 2.76 | 1.85 | 4.80 | 2.53 |
time (sec) |
N/A | 0.294 | 0.064 | 0.958 | 0.055 | 0.086 | 1.576 | 0.142 | 0.227 | 5.851 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 147 | 192 | 351 | 0 | 1185 | 660 | 460 | 1013 | 695 |
N.S. |
1 | 0.92 | 1.20 | 2.19 | 0.00 | 7.41 | 4.12 | 2.88 | 6.33 | 4.34 |
time (sec) |
N/A | 0.354 | 0.077 | 0.934 | 0.000 | 0.098 | 3.677 | 0.137 | 0.206 | 0.122 |
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 | 123 | 111 | 131 | 228 | 278 | 490 | 320 | 299 | 588 | 385 |
N.S. |
1 | 0.90 | 1.07 | 1.85 | 2.26 | 3.98 | 2.60 | 2.43 | 4.78 | 3.13 |
time (sec) |
N/A | 0.307 | 0.039 | 0.938 | 0.039 | 0.086 | 5.367 | 0.144 | 0.206 | 5.999 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 125 | 142 | 236 | 0 | 868 | 469 | 315 | 713 | 368 |
N.S. |
1 | 0.93 | 1.06 | 1.76 | 0.00 | 6.48 | 3.50 | 2.35 | 5.32 | 2.75 |
time (sec) |
N/A | 0.327 | 0.059 | 0.928 | 0.000 | 0.099 | 2.493 | 0.142 | 0.203 | 0.091 |
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 | 97 | 89 | 92 | 144 | 189 | 346 | 219 | 191 | 403 | 214 |
N.S. |
1 | 0.92 | 0.95 | 1.48 | 1.95 | 3.57 | 2.26 | 1.97 | 4.15 | 2.21 |
time (sec) |
N/A | 0.258 | 0.027 | 0.892 | 0.044 | 0.086 | 3.185 | 0.151 | 0.224 | 5.869 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 103 | 113 | 151 | 0 | 571 | 299 | 196 | 421 | 254 |
N.S. |
1 | 0.95 | 1.05 | 1.40 | 0.00 | 5.29 | 2.77 | 1.81 | 3.90 | 2.35 |
time (sec) |
N/A | 0.275 | 0.048 | 0.895 | 0.000 | 0.088 | 1.612 | 0.152 | 0.201 | 5.815 |
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 | 73 | 71 | 65 | 89 | 124 | 182 | 141 | 110 | 222 | 136 |
N.S. |
1 | 0.97 | 0.89 | 1.22 | 1.70 | 2.49 | 1.93 | 1.51 | 3.04 | 1.86 |
time (sec) |
N/A | 0.221 | 0.032 | 0.954 | 0.035 | 0.076 | 1.708 | 0.131 | 0.205 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 90 | 89 | 96 | 0 | 625 | 304 | 114 | 471 | 166 |
N.S. |
1 | 0.98 | 0.97 | 1.04 | 0.00 | 6.79 | 3.30 | 1.24 | 5.12 | 1.80 |
time (sec) |
N/A | 0.240 | 0.051 | 0.878 | 0.000 | 0.092 | 0.956 | 0.111 | 0.198 | 5.598 |
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 | 37 | 37 | 38 | 39 | 71 | 71 | 80 | 50 | 70 | 74 |
N.S. |
1 | 1.00 | 1.03 | 1.05 | 1.92 | 1.92 | 2.16 | 1.35 | 1.89 | 2.00 |
time (sec) |
N/A | 0.172 | 0.021 | 0.868 | 0.034 | 0.097 | 0.826 | 0.133 | 0.221 | 5.788 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 97 | 98 | 148 | 0 | 713 | 430 | 134 | 521 | 233 |
N.S. |
1 | 0.97 | 0.98 | 1.48 | 0.00 | 7.13 | 4.30 | 1.34 | 5.21 | 2.33 |
time (sec) |
N/A | 0.249 | 0.064 | 0.888 | 0.000 | 0.088 | 0.671 | 0.120 | 0.199 | 0.118 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 16 | 16 | 15 | 40 | 44 | 22 | 46 | 44 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.88 | 2.35 | 2.59 | 1.29 | 2.71 | 2.59 |
time (sec) |
N/A | 0.152 | 0.005 | 0.819 | 0.039 | 0.074 | 0.453 | 0.130 | 0.202 | 0.033 |
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 | 112 | 126 | 87 | 128 | 266 | 386 | 246 | 188 | 503 | 239 |
N.S. |
1 | 1.12 | 0.78 | 1.14 | 2.38 | 3.45 | 2.20 | 1.68 | 4.49 | 2.13 |
time (sec) |
N/A | 0.293 | 0.072 | 0.997 | 0.044 | 0.085 | 1.441 | 0.114 | 0.192 | 5.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 155 | 119 | 139 | 0 | 1170 | 804 | 302 | 893 | 494 |
N.S. |
1 | 1.11 | 0.85 | 0.99 | 0.00 | 8.36 | 5.74 | 2.16 | 6.38 | 3.53 |
time (sec) |
N/A | 0.318 | 0.101 | 1.069 | 0.000 | 0.096 | 1.613 | 0.114 | 0.222 | 5.568 |
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 | 154 | 173 | 111 | 152 | 553 | 809 | 600 | 302 | 1062 | 522 |
N.S. |
1 | 1.12 | 0.72 | 0.99 | 3.59 | 5.25 | 3.90 | 1.96 | 6.90 | 3.39 |
time (sec) |
N/A | 0.348 | 0.139 | 1.029 | 0.067 | 0.103 | 2.383 | 0.131 | 0.210 | 5.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 189 | 140 | 165 | 0 | 2077 | 1238 | 311 | 1605 | 827 |
N.S. |
1 | 1.12 | 0.83 | 0.98 | 0.00 | 12.36 | 7.37 | 1.85 | 9.55 | 4.92 |
time (sec) |
N/A | 0.375 | 0.328 | 1.101 | 0.000 | 0.128 | 2.487 | 0.140 | 0.204 | 5.808 |
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 | 8 | 10 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 | 0.89 | 1.11 | 1.00 | 1.00 |
time (sec) |
N/A | 0.150 | 0.003 | 0.676 | 0.035 | 0.084 | 0.033 | 0.122 | 0.205 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 14 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.88 | 0.88 | 0.75 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.154 | 0.006 | 1.244 | 0.031 | 0.073 | 0.045 | 0.117 | 0.229 | 0.017 |
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 | 55 | 55 | 45 | 46 | 46 | 122 | 289 | 567 | 104 | 39 |
N.S. |
1 | 1.00 | 0.82 | 0.84 | 0.84 | 2.22 | 5.25 | 10.31 | 1.89 | 0.71 |
time (sec) |
N/A | 0.205 | 0.052 | 0.585 | 0.036 | 0.077 | 0.374 | 0.131 | 0.195 | 0.035 |
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 | 55 | 55 | 45 | 46 | 46 | 87 | 73 | 376 | 79 | 39 |
N.S. |
1 | 1.00 | 0.82 | 0.84 | 0.84 | 1.58 | 1.33 | 6.84 | 1.44 | 0.71 |
time (sec) |
N/A | 0.197 | 0.044 | 0.578 | 0.046 | 0.084 | 0.694 | 0.138 | 0.206 | 5.239 |
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 | 55 | 55 | 42 | 45 | 46 | 58 | 73 | 228 | 55 | 39 |
N.S. |
1 | 1.00 | 0.76 | 0.82 | 0.84 | 1.05 | 1.33 | 4.15 | 1.00 | 0.71 |
time (sec) |
N/A | 0.198 | 0.037 | 0.533 | 0.034 | 0.076 | 0.635 | 0.149 | 0.185 | 5.917 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 43 | 41 | 116 | 40 | 146 | 116 | 38 | 37 |
N.S. |
1 | 1.00 | 0.78 | 0.75 | 2.11 | 0.73 | 2.65 | 2.11 | 0.69 | 0.67 |
time (sec) |
N/A | 0.197 | 0.037 | 0.540 | 0.033 | 0.083 | 0.464 | 0.130 | 0.211 | 5.321 |
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 | 55 | 55 | 43 | 39 | 51 | 52 | 73 | 47 | 38 | 37 |
N.S. |
1 | 1.00 | 0.78 | 0.71 | 0.93 | 0.95 | 1.33 | 0.85 | 0.69 | 0.67 |
time (sec) |
N/A | 0.194 | 0.036 | 0.547 | 0.033 | 0.083 | 0.711 | 0.125 | 0.214 | 0.027 |
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 | 55 | 40 | 45 | 51 | 68 | 235 | 47 | 48 | 37 |
N.S. |
1 | 1.00 | 0.73 | 0.82 | 0.93 | 1.24 | 4.27 | 0.85 | 0.87 | 0.67 |
time (sec) |
N/A | 0.198 | 0.039 | 0.552 | 0.034 | 0.083 | 0.267 | 0.163 | 0.188 | 5.358 |
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 | 55 | 40 | 43 | 45 | 81 | 298 | 47 | 61 | 37 |
N.S. |
1 | 1.00 | 0.73 | 0.78 | 0.82 | 1.47 | 5.42 | 0.85 | 1.11 | 0.67 |
time (sec) |
N/A | 0.193 | 0.041 | 0.519 | 0.053 | 0.082 | 0.391 | 0.129 | 0.197 | 0.023 |
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 | 55 | 55 | 42 | 44 | 46 | 96 | 360 | 48 | 72 | 39 |
N.S. |
1 | 1.00 | 0.76 | 0.80 | 0.84 | 1.75 | 6.55 | 0.87 | 1.31 | 0.71 |
time (sec) |
N/A | 0.196 | 0.048 | 0.523 | 0.033 | 0.082 | 0.602 | 0.109 | 0.278 | 5.340 |
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 | 88 | 88 | 78 | 83 | 81 | 164 | 144 | 867 | 158 | 99 |
N.S. |
1 | 1.00 | 0.89 | 0.94 | 0.92 | 1.86 | 1.64 | 9.85 | 1.80 | 1.12 |
time (sec) |
N/A | 0.246 | 0.067 | 0.914 | 0.048 | 0.091 | 0.899 | 0.120 | 0.286 | 0.048 |
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 | 88 | 88 | 78 | 83 | 81 | 121 | 144 | 580 | 120 | 99 |
N.S. |
1 | 1.00 | 0.89 | 0.94 | 0.92 | 1.38 | 1.64 | 6.59 | 1.36 | 1.12 |
time (sec) |
N/A | 0.235 | 0.071 | 0.871 | 0.039 | 0.092 | 0.838 | 0.115 | 0.295 | 5.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 78 | 82 | 351 | 92 | 144 | 349 | 90 | 99 |
N.S. |
1 | 1.00 | 0.89 | 0.93 | 3.99 | 1.05 | 1.64 | 3.97 | 1.02 | 1.12 |
time (sec) |
N/A | 0.230 | 0.068 | 0.863 | 0.043 | 0.098 | 0.780 | 0.122 | 0.210 | 5.220 |
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 | 78 | 91 | 89 | 105 | 134 | 109 | 91 | 99 |
N.S. |
1 | 1.00 | 0.89 | 1.03 | 1.01 | 1.19 | 1.52 | 1.24 | 1.03 | 1.12 |
time (sec) |
N/A | 0.224 | 0.058 | 0.881 | 0.027 | 0.084 | 1.231 | 0.140 | 0.198 | 5.179 |
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 | 78 | 95 | 90 | 120 | 134 | 109 | 100 | 99 |
N.S. |
1 | 1.00 | 0.89 | 1.08 | 1.02 | 1.36 | 1.52 | 1.24 | 1.14 | 1.12 |
time (sec) |
N/A | 0.220 | 0.067 | 0.885 | 0.037 | 0.093 | 1.242 | 0.141 | 0.223 | 5.215 |
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 | 88 | 88 | 78 | 84 | 93 | 134 | 688 | 99 | 111 | 92 |
N.S. |
1 | 1.00 | 0.89 | 0.95 | 1.06 | 1.52 | 7.82 | 1.12 | 1.26 | 1.05 |
time (sec) |
N/A | 0.226 | 0.077 | 0.907 | 0.040 | 0.082 | 0.448 | 0.113 | 0.212 | 5.231 |
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 | 88 | 88 | 78 | 82 | 92 | 149 | 826 | 100 | 122 | 92 |
N.S. |
1 | 1.00 | 0.89 | 0.93 | 1.05 | 1.69 | 9.39 | 1.14 | 1.39 | 1.05 |
time (sec) |
N/A | 0.221 | 0.067 | 0.899 | 0.028 | 0.094 | 0.652 | 0.116 | 0.196 | 5.201 |
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 | 88 | 88 | 78 | 84 | 81 | 162 | 966 | 99 | 133 | 67 |
N.S. |
1 | 1.00 | 0.89 | 0.95 | 0.92 | 1.84 | 10.98 | 1.12 | 1.51 | 0.76 |
time (sec) |
N/A | 0.224 | 0.069 | 0.915 | 0.045 | 0.088 | 0.940 | 0.115 | 0.205 | 5.180 |