Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 51 | 0 | 22 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.34 | 0.00 | 0.58 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.651 | 0.026 | 0.135 | 0.000 | 0.079 | 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 | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 63 | 56 | 84 | 0 | 86 | 0 | 0 | 98 | 0 |
N.S. |
1 | 0.69 | 0.62 | 0.92 | 0.00 | 0.95 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.756 | 0.059 | 0.139 | 0.000 | 0.109 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 93 | 83 | 169 | 0 | 136 | 0 | 0 | 250 | 0 |
N.S. |
1 | 0.51 | 0.45 | 0.92 | 0.00 | 0.74 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.824 | 0.071 | 0.154 | 0.000 | 0.087 | 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(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 121 | 101 | 241 | 0 | 191 | 0 | 0 | 393 | 0 |
N.S. |
1 | 0.44 | 0.36 | 0.87 | 0.00 | 0.69 | 0.00 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.858 | 0.104 | 0.142 | 0.000 | 0.090 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 198 | 167 | 138 | 192 | 329 | 714 | 164 | 198 | 0 |
N.S. |
1 | 1.17 | 0.99 | 0.82 | 1.14 | 1.95 | 4.22 | 0.97 | 1.17 | 0.00 |
time (sec) |
N/A | 0.814 | 0.216 | 0.181 | 0.123 | 0.126 | 3.430 | 0.143 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 172 | 151 | 122 | 173 | 286 | 614 | 141 | 160 | 0 |
N.S. |
1 | 1.18 | 1.03 | 0.84 | 1.18 | 1.96 | 4.21 | 0.97 | 1.10 | 0.00 |
time (sec) |
N/A | 0.751 | 0.227 | 0.185 | 0.125 | 0.118 | 3.094 | 0.136 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 146 | 135 | 106 | 154 | 241 | 314 | 116 | 122 | 0 |
N.S. |
1 | 1.19 | 1.10 | 0.86 | 1.25 | 1.96 | 2.55 | 0.94 | 0.99 | 0.00 |
time (sec) |
N/A | 0.694 | 0.161 | 0.182 | 0.114 | 0.094 | 2.592 | 0.139 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 120 | 117 | 90 | 131 | 180 | 250 | 85 | 82 | 0 |
N.S. |
1 | 1.20 | 1.17 | 0.90 | 1.31 | 1.80 | 2.50 | 0.85 | 0.82 | 0.00 |
time (sec) |
N/A | 0.643 | 0.134 | 0.178 | 0.116 | 0.099 | 2.309 | 0.145 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 95 | 76 | 69 | 47 | 134 | 0 | 62 | 42 | 0 |
N.S. |
1 | 1.23 | 0.99 | 0.90 | 0.61 | 1.74 | 0.00 | 0.81 | 0.55 | 0.00 |
time (sec) |
N/A | 0.607 | 0.075 | 0.177 | 0.111 | 0.109 | 0.000 | 0.127 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 66 | 82 | 79 | 40 | 153 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.12 | 1.39 | 1.34 | 0.68 | 2.59 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.575 | 0.055 | 0.177 | 0.110 | 0.106 | 0.000 | 0.000 | 0.156 | 0.000 |
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 | 51 | 57 | 64 | 31 | 61 | 47 | 0 | 148 | 54 | 33 |
N.S. |
1 | 1.12 | 1.25 | 0.61 | 1.20 | 0.92 | 0.00 | 2.90 | 1.06 | 0.65 |
time (sec) |
N/A | 0.563 | 0.065 | 0.178 | 0.032 | 0.111 | 0.000 | 0.159 | 0.161 | 13.358 |
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 | 74 | 88 | 53 | 47 | 80 | 75 | 0 | 0 | 104 | 56 |
N.S. |
1 | 1.19 | 0.72 | 0.64 | 1.08 | 1.01 | 0.00 | 0.00 | 1.41 | 0.76 |
time (sec) |
N/A | 0.597 | 0.051 | 0.183 | 0.036 | 0.111 | 0.000 | 0.000 | 0.152 | 13.232 |
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 | 97 | 119 | 96 | 64 | 99 | 124 | 0 | 0 | 150 | 134 |
N.S. |
1 | 1.23 | 0.99 | 0.66 | 1.02 | 1.28 | 0.00 | 0.00 | 1.55 | 1.38 |
time (sec) |
N/A | 0.645 | 0.064 | 0.184 | 0.037 | 0.203 | 0.000 | 0.000 | 0.168 | 13.265 |
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 | 120 | 150 | 112 | 80 | 118 | 152 | 0 | 0 | 247 | 177 |
N.S. |
1 | 1.25 | 0.93 | 0.67 | 0.98 | 1.27 | 0.00 | 0.00 | 2.06 | 1.48 |
time (sec) |
N/A | 0.665 | 0.080 | 0.188 | 0.037 | 0.386 | 0.000 | 0.000 | 0.158 | 13.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 94 | 71 | 100 | 204 | 95 | 0 | 0 | 73 | 0 |
N.S. |
1 | 0.51 | 0.38 | 0.54 | 1.10 | 0.51 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.818 | 0.074 | 0.146 | 0.053 | 0.074 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 79 | 63 | 100 | 172 | 95 | 0 | 0 | 73 | 0 |
N.S. |
1 | 0.57 | 0.45 | 0.72 | 1.24 | 0.68 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.801 | 0.062 | 0.148 | 0.048 | 0.077 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 66 | 55 | 84 | 140 | 73 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.71 | 0.59 | 0.90 | 1.51 | 0.78 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.744 | 0.050 | 0.142 | 0.051 | 0.084 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 58 | 48 | 97 | 42 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.26 | 1.04 | 2.11 | 0.91 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.687 | 0.039 | 0.145 | 0.050 | 0.077 | 0.000 | 0.000 | 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 | 113 | 61 | 59 | 67 | 0 | 33 | 0 | 76 | 32 | 0 |
N.S. |
1 | 0.54 | 0.52 | 0.59 | 0.00 | 0.29 | 0.00 | 0.67 | 0.28 | 0.00 |
time (sec) |
N/A | 0.677 | 0.038 | 0.144 | 0.000 | 0.100 | 0.000 | 0.138 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 57 | 49 | 64 | 0 | 39 | 0 | 0 | 41 | 0 |
N.S. |
1 | 0.72 | 0.62 | 0.81 | 0.00 | 0.49 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.739 | 0.045 | 0.145 | 0.000 | 0.075 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 51 | 39 | 0 | 39 | 0 | 0 | 26 | 90 |
N.S. |
1 | 1.00 | 1.09 | 0.83 | 0.00 | 0.83 | 0.00 | 0.00 | 0.55 | 1.91 |
time (sec) |
N/A | 0.690 | 0.096 | 0.145 | 0.000 | 0.087 | 0.000 | 0.000 | 0.149 | 13.364 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 93 | 71 | 169 | 0 | 139 | 0 | 0 | 242 | 0 |
N.S. |
1 | 0.50 | 0.38 | 0.91 | 0.00 | 0.75 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.792 | 0.074 | 0.152 | 0.000 | 0.088 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 123 | 99 | 241 | 0 | 190 | 0 | 0 | 394 | 0 |
N.S. |
1 | 0.44 | 0.36 | 0.87 | 0.00 | 0.68 | 0.00 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.859 | 0.104 | 0.148 | 0.000 | 0.092 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 111 | 79 | 113 | 0 | 117 | 0 | 185 | 89 | 0 |
N.S. |
1 | 0.47 | 0.34 | 0.48 | 0.00 | 0.50 | 0.00 | 0.79 | 0.38 | 0.00 |
time (sec) |
N/A | 0.837 | 0.084 | 0.143 | 0.000 | 0.073 | 0.000 | 0.128 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 95 | 71 | 97 | 0 | 95 | 0 | 151 | 73 | 0 |
N.S. |
1 | 0.51 | 0.38 | 0.52 | 0.00 | 0.51 | 0.00 | 0.81 | 0.39 | 0.00 |
time (sec) |
N/A | 0.805 | 0.064 | 0.148 | 0.000 | 0.074 | 0.000 | 0.122 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 81 | 63 | 81 | 0 | 73 | 0 | 117 | 57 | 0 |
N.S. |
1 | 0.58 | 0.45 | 0.58 | 0.00 | 0.53 | 0.00 | 0.84 | 0.41 | 0.00 |
time (sec) |
N/A | 0.759 | 0.051 | 0.142 | 0.000 | 0.069 | 0.000 | 0.120 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 67 | 53 | 63 | 0 | 43 | 0 | 73 | 39 | 0 |
N.S. |
1 | 0.71 | 0.56 | 0.66 | 0.00 | 0.45 | 0.00 | 0.77 | 0.41 | 0.00 |
time (sec) |
N/A | 0.728 | 0.041 | 0.154 | 0.000 | 0.069 | 0.000 | 0.113 | 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 | 47 | 47 | 41 | 44 | 0 | 22 | 0 | 39 | 22 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.94 | 0.00 | 0.47 | 0.00 | 0.83 | 0.47 | 0.00 |
time (sec) |
N/A | 0.616 | 0.026 | 0.135 | 0.000 | 0.086 | 0.000 | 0.149 | 0.167 | 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 | 37 | 37 | 37 | 51 | 0 | 22 | 0 | 22 | 35 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.38 | 0.00 | 0.59 | 0.00 | 0.59 | 0.95 | 0.00 |
time (sec) |
N/A | 0.633 | 0.033 | 0.137 | 0.000 | 0.069 | 0.000 | 0.147 | 0.159 | 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 | 90 | 63 | 54 | 84 | 0 | 83 | 0 | 58 | 99 | 0 |
N.S. |
1 | 0.70 | 0.60 | 0.93 | 0.00 | 0.92 | 0.00 | 0.64 | 1.10 | 0.00 |
time (sec) |
N/A | 0.728 | 0.057 | 0.140 | 0.000 | 0.120 | 0.000 | 0.143 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 91 | 81 | 169 | 0 | 137 | 0 | 80 | 249 | 0 |
N.S. |
1 | 0.50 | 0.44 | 0.92 | 0.00 | 0.75 | 0.00 | 0.44 | 1.36 | 0.00 |
time (sec) |
N/A | 0.769 | 0.084 | 0.142 | 0.000 | 0.100 | 0.000 | 0.161 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 121 | 99 | 241 | 0 | 186 | 0 | 96 | 392 | 0 |
N.S. |
1 | 0.44 | 0.36 | 0.87 | 0.00 | 0.67 | 0.00 | 0.35 | 1.42 | 0.00 |
time (sec) |
N/A | 0.841 | 0.114 | 0.142 | 0.000 | 0.105 | 0.000 | 0.156 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 147 | 136 | 106 | 154 | 241 | 314 | 117 | 122 | 0 |
N.S. |
1 | 1.20 | 1.11 | 0.86 | 1.25 | 1.96 | 2.55 | 0.95 | 0.99 | 0.00 |
time (sec) |
N/A | 0.694 | 0.194 | 0.188 | 0.121 | 0.114 | 2.644 | 0.136 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 121 | 117 | 90 | 130 | 180 | 248 | 85 | 82 | 0 |
N.S. |
1 | 1.21 | 1.17 | 0.90 | 1.30 | 1.80 | 2.48 | 0.85 | 0.82 | 0.00 |
time (sec) |
N/A | 0.652 | 0.123 | 0.179 | 0.114 | 0.104 | 2.292 | 0.129 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 95 | 100 | 69 | 47 | 134 | 0 | 62 | 42 | 0 |
N.S. |
1 | 1.23 | 1.30 | 0.90 | 0.61 | 1.74 | 0.00 | 0.81 | 0.55 | 0.00 |
time (sec) |
N/A | 0.620 | 0.073 | 0.185 | 0.109 | 0.103 | 0.000 | 0.123 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 67 | 100 | 73 | 39 | 151 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.05 | 1.56 | 1.14 | 0.61 | 2.36 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.599 | 0.118 | 0.178 | 0.111 | 0.098 | 0.000 | 0.000 | 0.164 | 0.000 |
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 | 65 | 58 | 63 | 31 | 60 | 47 | 0 | 148 | 56 | 33 |
N.S. |
1 | 0.89 | 0.97 | 0.48 | 0.92 | 0.72 | 0.00 | 2.28 | 0.86 | 0.51 |
time (sec) |
N/A | 0.609 | 0.053 | 0.177 | 0.031 | 0.084 | 0.000 | 0.169 | 0.150 | 13.157 |
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 | 88 | 89 | 79 | 47 | 79 | 75 | 0 | 0 | 107 | 56 |
N.S. |
1 | 1.01 | 0.90 | 0.53 | 0.90 | 0.85 | 0.00 | 0.00 | 1.22 | 0.64 |
time (sec) |
N/A | 0.590 | 0.085 | 0.178 | 0.037 | 0.156 | 0.000 | 0.000 | 0.152 | 13.232 |
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 | 111 | 120 | 96 | 64 | 98 | 124 | 0 | 0 | 150 | 134 |
N.S. |
1 | 1.08 | 0.86 | 0.58 | 0.88 | 1.12 | 0.00 | 0.00 | 1.35 | 1.21 |
time (sec) |
N/A | 0.631 | 0.105 | 0.181 | 0.037 | 0.190 | 0.000 | 0.000 | 0.158 | 13.272 |
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 | 134 | 151 | 112 | 80 | 117 | 152 | 0 | 0 | 247 | 177 |
N.S. |
1 | 1.13 | 0.84 | 0.60 | 0.87 | 1.13 | 0.00 | 0.00 | 1.84 | 1.32 |
time (sec) |
N/A | 0.653 | 0.125 | 0.181 | 0.038 | 0.365 | 0.000 | 0.000 | 0.159 | 13.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 97 | 71 | 100 | 204 | 95 | 0 | 151 | 73 | 0 |
N.S. |
1 | 0.51 | 0.38 | 0.53 | 1.08 | 0.50 | 0.00 | 0.80 | 0.39 | 0.00 |
time (sec) |
N/A | 0.835 | 0.088 | 0.145 | 0.051 | 0.066 | 0.000 | 0.137 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 83 | 63 | 100 | 172 | 95 | 0 | 151 | 73 | 0 |
N.S. |
1 | 0.58 | 0.44 | 0.70 | 1.21 | 0.67 | 0.00 | 1.06 | 0.51 | 0.00 |
time (sec) |
N/A | 0.792 | 0.081 | 0.142 | 0.048 | 0.065 | 0.000 | 0.116 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 67 | 55 | 84 | 140 | 73 | 0 | 117 | 57 | 0 |
N.S. |
1 | 0.71 | 0.58 | 0.88 | 1.47 | 0.77 | 0.00 | 1.23 | 0.60 | 0.00 |
time (sec) |
N/A | 0.758 | 0.063 | 0.138 | 0.048 | 0.079 | 0.000 | 0.113 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 58 | 48 | 97 | 42 | 0 | 72 | 38 | 0 |
N.S. |
1 | 1.00 | 1.23 | 1.02 | 2.06 | 0.89 | 0.00 | 1.53 | 0.81 | 0.00 |
time (sec) |
N/A | 0.680 | 0.051 | 0.138 | 0.047 | 0.077 | 0.000 | 0.121 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 59 | 58 | 67 | 0 | 33 | 0 | 56 | 30 | 0 |
N.S. |
1 | 0.53 | 0.52 | 0.60 | 0.00 | 0.29 | 0.00 | 0.50 | 0.27 | 0.00 |
time (sec) |
N/A | 0.664 | 0.046 | 0.139 | 0.000 | 0.103 | 0.000 | 0.118 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 57 | 47 | 62 | 0 | 38 | 0 | 0 | 77 | 0 |
N.S. |
1 | 0.74 | 0.61 | 0.81 | 0.00 | 0.49 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.739 | 0.055 | 0.136 | 0.000 | 0.075 | 0.000 | 0.000 | 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 | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 51 | 39 | 0 | 39 | 0 | 26 | 26 | 58 |
N.S. |
1 | 1.00 | 1.11 | 0.85 | 0.00 | 0.85 | 0.00 | 0.57 | 0.57 | 1.26 |
time (sec) |
N/A | 0.685 | 0.129 | 0.132 | 0.000 | 0.088 | 0.000 | 0.147 | 0.147 | 13.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 91 | 71 | 169 | 0 | 136 | 0 | 98 | 250 | 0 |
N.S. |
1 | 0.50 | 0.39 | 0.93 | 0.00 | 0.75 | 0.00 | 0.54 | 1.37 | 0.00 |
time (sec) |
N/A | 0.822 | 0.107 | 0.139 | 0.000 | 0.091 | 0.000 | 0.174 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 119 | 99 | 241 | 0 | 193 | 0 | 133 | 394 | 0 |
N.S. |
1 | 0.43 | 0.36 | 0.88 | 0.00 | 0.70 | 0.00 | 0.48 | 1.43 | 0.00 |
time (sec) |
N/A | 0.849 | 0.145 | 0.139 | 0.000 | 0.097 | 0.000 | 0.182 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 52 | 45 | 47 | 0 | 25 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.68 | 0.59 | 0.62 | 0.00 | 0.33 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.785 | 0.034 | 0.136 | 0.000 | 0.078 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 52 | 43 | 47 | 0 | 25 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.70 | 0.58 | 0.64 | 0.00 | 0.34 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.717 | 0.034 | 0.134 | 0.000 | 0.072 | 0.000 | 0.000 | 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 | 46 | 46 | 41 | 44 | 0 | 22 | 0 | 36 | 22 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.96 | 0.00 | 0.48 | 0.00 | 0.78 | 0.48 | 0.00 |
time (sec) |
N/A | 0.582 | 0.014 | 0.132 | 0.000 | 0.077 | 0.000 | 0.116 | 0.139 | 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 | 69 | 42 | 41 | 44 | 0 | 18 | 0 | 31 | 34 | 0 |
N.S. |
1 | 0.61 | 0.59 | 0.64 | 0.00 | 0.26 | 0.00 | 0.45 | 0.49 | 0.00 |
time (sec) |
N/A | 0.635 | 0.031 | 0.135 | 0.000 | 0.108 | 0.000 | 0.149 | 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 | 73 | 46 | 44 | 48 | 0 | 22 | 0 | 25 | 41 | 0 |
N.S. |
1 | 0.63 | 0.60 | 0.66 | 0.00 | 0.30 | 0.00 | 0.34 | 0.56 | 0.00 |
time (sec) |
N/A | 0.751 | 0.033 | 0.135 | 0.000 | 0.095 | 0.000 | 0.132 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 192 | 96 | 97 | 117 | 184 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.25 | 0.62 | 0.63 | 0.76 | 1.19 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 1.057 | 0.222 | 0.211 | 0.126 | 0.104 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 161 | 88 | 89 | 93 | 168 | 0 | 84 | 81 | 0 |
N.S. |
1 | 1.25 | 0.68 | 0.69 | 0.72 | 1.30 | 0.00 | 0.65 | 0.63 | 0.00 |
time (sec) |
N/A | 0.974 | 0.160 | 0.195 | 0.119 | 0.122 | 0.000 | 0.166 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 120 | 79 | 80 | 70 | 150 | 0 | 72 | 61 | 0 |
N.S. |
1 | 1.21 | 0.80 | 0.81 | 0.71 | 1.52 | 0.00 | 0.73 | 0.62 | 0.00 |
time (sec) |
N/A | 0.821 | 0.148 | 0.190 | 0.119 | 0.094 | 0.000 | 0.126 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 95 | 76 | 69 | 47 | 134 | 0 | 62 | 42 | 0 |
N.S. |
1 | 1.23 | 0.99 | 0.90 | 0.61 | 1.74 | 0.00 | 0.81 | 0.55 | 0.00 |
time (sec) |
N/A | 0.613 | 0.049 | 0.171 | 0.108 | 0.090 | 0.000 | 0.136 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 84 | 97 | 129 | 90 | 181 | 0 | 95 | 32 | 0 |
N.S. |
1 | 1.12 | 1.29 | 1.72 | 1.20 | 2.41 | 0.00 | 1.27 | 0.43 | 0.00 |
time (sec) |
N/A | 0.900 | 0.217 | 0.178 | 0.118 | 0.088 | 0.000 | 0.132 | 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 | 82 | 89 | 104 | 102 | 0 | 199 | 0 | 134 | 38 | 0 |
N.S. |
1 | 1.09 | 1.27 | 1.24 | 0.00 | 2.43 | 0.00 | 1.63 | 0.46 | 0.00 |
time (sec) |
N/A | 0.894 | 0.188 | 0.201 | 0.000 | 0.108 | 0.000 | 0.155 | 0.155 | 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 | 78 | 88 | 76 | 78 | 0 | 138 | 0 | 200 | 50 | 0 |
N.S. |
1 | 1.13 | 0.97 | 1.00 | 0.00 | 1.77 | 0.00 | 2.56 | 0.64 | 0.00 |
time (sec) |
N/A | 0.860 | 0.232 | 0.217 | 0.000 | 0.107 | 0.000 | 0.123 | 0.151 | 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 | 99 | 114 | 82 | 86 | 0 | 154 | 0 | 250 | 69 | 0 |
N.S. |
1 | 1.15 | 0.83 | 0.87 | 0.00 | 1.56 | 0.00 | 2.53 | 0.70 | 0.00 |
time (sec) |
N/A | 0.915 | 0.244 | 0.225 | 0.000 | 0.104 | 0.000 | 0.137 | 0.154 | 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 | 130 | 150 | 95 | 95 | 0 | 170 | 0 | 324 | 90 | 0 |
N.S. |
1 | 1.15 | 0.73 | 0.73 | 0.00 | 1.31 | 0.00 | 2.49 | 0.69 | 0.00 |
time (sec) |
N/A | 0.997 | 0.278 | 0.266 | 0.000 | 0.135 | 0.000 | 0.150 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 89 | 87 | 92 | 0 | 58 | 0 | 0 | 56 | 0 |
N.S. |
1 | 0.39 | 0.38 | 0.40 | 0.00 | 0.25 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.872 | 0.084 | 0.140 | 0.000 | 0.090 | 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 | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 77 | 74 | 83 | 0 | 49 | 0 | 123 | 48 | 0 |
N.S. |
1 | 0.41 | 0.40 | 0.45 | 0.00 | 0.26 | 0.00 | 0.66 | 0.26 | 0.00 |
time (sec) |
N/A | 0.926 | 0.069 | 0.138 | 0.000 | 0.085 | 0.000 | 0.161 | 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 | 152 | 71 | 66 | 76 | 0 | 42 | 0 | 93 | 40 | 0 |
N.S. |
1 | 0.47 | 0.43 | 0.50 | 0.00 | 0.28 | 0.00 | 0.61 | 0.26 | 0.00 |
time (sec) |
N/A | 0.830 | 0.078 | 0.142 | 0.000 | 0.084 | 0.000 | 0.137 | 0.145 | 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 | 113 | 61 | 59 | 67 | 0 | 33 | 0 | 76 | 32 | 0 |
N.S. |
1 | 0.54 | 0.52 | 0.59 | 0.00 | 0.29 | 0.00 | 0.67 | 0.28 | 0.00 |
time (sec) |
N/A | 0.682 | 0.018 | 0.139 | 0.000 | 0.124 | 0.000 | 0.134 | 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 | 114 | 53 | 54 | 59 | 0 | 28 | 0 | 49 | 40 | 0 |
N.S. |
1 | 0.46 | 0.47 | 0.52 | 0.00 | 0.25 | 0.00 | 0.43 | 0.35 | 0.00 |
time (sec) |
N/A | 0.715 | 0.046 | 0.141 | 0.000 | 0.115 | 0.000 | 0.149 | 0.153 | 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 | 114 | 58 | 54 | 64 | 0 | 33 | 0 | 34 | 52 | 0 |
N.S. |
1 | 0.51 | 0.47 | 0.56 | 0.00 | 0.29 | 0.00 | 0.30 | 0.46 | 0.00 |
time (sec) |
N/A | 0.823 | 0.041 | 0.149 | 0.000 | 0.107 | 0.000 | 0.141 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 70 | 64 | 77 | 0 | 90 | 0 | 46 | 74 | 0 |
N.S. |
1 | 0.46 | 0.42 | 0.50 | 0.00 | 0.59 | 0.00 | 0.30 | 0.48 | 0.00 |
time (sec) |
N/A | 0.841 | 0.054 | 0.145 | 0.000 | 0.106 | 0.000 | 0.136 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 80 | 76 | 85 | 0 | 98 | 0 | 54 | 82 | 0 |
N.S. |
1 | 0.41 | 0.39 | 0.44 | 0.00 | 0.51 | 0.00 | 0.28 | 0.42 | 0.00 |
time (sec) |
N/A | 0.842 | 0.077 | 0.145 | 0.000 | 0.097 | 0.000 | 0.144 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 86 | 80 | 93 | 0 | 106 | 0 | 62 | 90 | 0 |
N.S. |
1 | 0.38 | 0.35 | 0.41 | 0.00 | 0.46 | 0.00 | 0.27 | 0.39 | 0.00 |
time (sec) |
N/A | 0.839 | 0.075 | 0.145 | 0.000 | 0.078 | 0.000 | 0.153 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 94 | 83 | 106 | 0 | 76 | 0 | 0 | 118 | 0 |
N.S. |
1 | 0.45 | 0.39 | 0.50 | 0.00 | 0.36 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.827 | 0.111 | 0.144 | 0.000 | 0.127 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 84 | 74 | 98 | 0 | 69 | 0 | 0 | 112 | 0 |
N.S. |
1 | 0.49 | 0.43 | 0.57 | 0.00 | 0.40 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.776 | 0.082 | 0.144 | 0.000 | 0.094 | 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 | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 79 | 62 | 86 | 0 | 56 | 0 | 0 | 98 | 0 |
N.S. |
1 | 0.61 | 0.48 | 0.66 | 0.00 | 0.43 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.875 | 0.064 | 0.146 | 0.000 | 0.116 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 63 | 52 | 84 | 0 | 86 | 0 | 0 | 100 | 0 |
N.S. |
1 | 0.72 | 0.60 | 0.97 | 0.00 | 0.99 | 0.00 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.791 | 0.055 | 0.146 | 0.000 | 0.114 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 63 | 56 | 84 | 0 | 86 | 0 | 0 | 98 | 0 |
N.S. |
1 | 0.69 | 0.62 | 0.92 | 0.00 | 0.95 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.736 | 0.030 | 0.139 | 0.000 | 0.083 | 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 | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 72 | 68 | 93 | 0 | 63 | 0 | 0 | 149 | 0 |
N.S. |
1 | 0.41 | 0.38 | 0.53 | 0.00 | 0.36 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.828 | 0.070 | 0.145 | 0.000 | 0.116 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 82 | 79 | 118 | 0 | 92 | 0 | 0 | 194 | 0 |
N.S. |
1 | 0.38 | 0.37 | 0.55 | 0.00 | 0.43 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.864 | 0.077 | 0.148 | 0.000 | 0.130 | 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 | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 99 | 94 | 138 | 0 | 113 | 0 | 0 | 222 | 0 |
N.S. |
1 | 0.39 | 0.37 | 0.55 | 0.00 | 0.45 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.893 | 0.104 | 0.145 | 0.000 | 0.102 | 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 | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 113 | 100 | 185 | 0 | 138 | 0 | 0 | 258 | 0 |
N.S. |
1 | 0.43 | 0.38 | 0.71 | 0.00 | 0.53 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.827 | 0.133 | 0.150 | 0.000 | 0.106 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 109 | 84 | 169 | 0 | 122 | 0 | 0 | 250 | 0 |
N.S. |
1 | 0.50 | 0.39 | 0.78 | 0.00 | 0.56 | 0.00 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.918 | 0.112 | 0.149 | 0.000 | 0.118 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 93 | 72 | 169 | 0 | 136 | 0 | 0 | 250 | 0 |
N.S. |
1 | 0.53 | 0.41 | 0.96 | 0.00 | 0.77 | 0.00 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.901 | 0.117 | 0.152 | 0.000 | 0.104 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 93 | 85 | 164 | 0 | 134 | 0 | 0 | 243 | 0 |
N.S. |
1 | 0.51 | 0.46 | 0.89 | 0.00 | 0.73 | 0.00 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.895 | 0.071 | 0.148 | 0.000 | 0.096 | 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(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 78 | 62 | 164 | 0 | 134 | 0 | 0 | 242 | 0 |
N.S. |
1 | 0.57 | 0.45 | 1.20 | 0.00 | 0.98 | 0.00 | 0.00 | 1.77 | 0.00 |
time (sec) |
N/A | 0.809 | 0.071 | 0.150 | 0.000 | 0.122 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 93 | 83 | 169 | 0 | 136 | 0 | 0 | 250 | 0 |
N.S. |
1 | 0.51 | 0.45 | 0.92 | 0.00 | 0.74 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.777 | 0.032 | 0.142 | 0.000 | 0.093 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 96 | 88 | 196 | 0 | 145 | 0 | 0 | 371 | 0 |
N.S. |
1 | 0.35 | 0.32 | 0.72 | 0.00 | 0.54 | 0.00 | 0.00 | 1.37 | 0.00 |
time (sec) |
N/A | 0.891 | 0.127 | 0.151 | 0.000 | 0.106 | 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 | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 108 | 99 | 225 | 0 | 174 | 0 | 0 | 412 | 0 |
N.S. |
1 | 0.35 | 0.32 | 0.73 | 0.00 | 0.57 | 0.00 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.940 | 0.103 | 0.148 | 0.000 | 0.092 | 0.000 | 0.000 | 0.155 | 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 | 76 | 53 | 45 | 47 | 0 | 25 | 0 | 42 | 26 | 0 |
N.S. |
1 | 0.70 | 0.59 | 0.62 | 0.00 | 0.33 | 0.00 | 0.55 | 0.34 | 0.00 |
time (sec) |
N/A | 0.792 | 0.034 | 0.136 | 0.000 | 0.075 | 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 | 74 | 53 | 43 | 47 | 0 | 25 | 0 | 42 | 26 | 0 |
N.S. |
1 | 0.72 | 0.58 | 0.64 | 0.00 | 0.34 | 0.00 | 0.57 | 0.35 | 0.00 |
time (sec) |
N/A | 0.740 | 0.028 | 0.138 | 0.000 | 0.076 | 0.000 | 0.144 | 0.153 | 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 | 47 | 47 | 41 | 44 | 0 | 22 | 0 | 39 | 22 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.94 | 0.00 | 0.47 | 0.00 | 0.83 | 0.47 | 0.00 |
time (sec) |
N/A | 0.602 | 0.015 | 0.135 | 0.000 | 0.090 | 0.000 | 0.107 | 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 | 70 | 44 | 42 | 46 | 0 | 20 | 0 | 27 | 14 | 0 |
N.S. |
1 | 0.63 | 0.60 | 0.66 | 0.00 | 0.29 | 0.00 | 0.39 | 0.20 | 0.00 |
time (sec) |
N/A | 0.658 | 0.033 | 0.135 | 0.000 | 0.123 | 0.000 | 0.141 | 0.163 | 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 | 48 | 43 | 48 | 0 | 22 | 0 | 28 | 20 | 0 |
N.S. |
1 | 0.67 | 0.60 | 0.67 | 0.00 | 0.31 | 0.00 | 0.39 | 0.28 | 0.00 |
time (sec) |
N/A | 0.822 | 0.030 | 0.135 | 0.000 | 0.086 | 0.000 | 0.121 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 193 | 96 | 97 | 117 | 184 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.38 | 0.69 | 0.69 | 0.84 | 1.31 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 1.036 | 0.210 | 0.223 | 0.118 | 0.088 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 161 | 88 | 89 | 93 | 168 | 0 | 84 | 81 | 0 |
N.S. |
1 | 1.25 | 0.68 | 0.69 | 0.72 | 1.30 | 0.00 | 0.65 | 0.63 | 0.00 |
time (sec) |
N/A | 0.987 | 0.174 | 0.198 | 0.118 | 0.121 | 0.000 | 0.120 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 121 | 79 | 79 | 70 | 150 | 0 | 73 | 61 | 0 |
N.S. |
1 | 1.22 | 0.80 | 0.80 | 0.71 | 1.52 | 0.00 | 0.74 | 0.62 | 0.00 |
time (sec) |
N/A | 0.829 | 0.140 | 0.194 | 0.108 | 0.121 | 0.000 | 0.156 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 95 | 100 | 69 | 47 | 134 | 0 | 62 | 42 | 0 |
N.S. |
1 | 1.23 | 1.30 | 0.90 | 0.61 | 1.74 | 0.00 | 0.81 | 0.55 | 0.00 |
time (sec) |
N/A | 0.606 | 0.059 | 0.178 | 0.116 | 0.112 | 0.000 | 0.132 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 84 | 97 | 121 | 86 | 181 | 0 | 95 | 32 | 0 |
N.S. |
1 | 1.12 | 1.29 | 1.61 | 1.15 | 2.41 | 0.00 | 1.27 | 0.43 | 0.00 |
time (sec) |
N/A | 0.883 | 0.173 | 0.191 | 0.123 | 0.086 | 0.000 | 0.149 | 0.157 | 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 | 82 | 91 | 104 | 102 | 0 | 198 | 0 | 134 | 38 | 0 |
N.S. |
1 | 1.11 | 1.27 | 1.24 | 0.00 | 2.41 | 0.00 | 1.63 | 0.46 | 0.00 |
time (sec) |
N/A | 0.888 | 0.157 | 0.220 | 0.000 | 0.119 | 0.000 | 0.128 | 0.153 | 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 | 78 | 88 | 76 | 79 | 0 | 137 | 0 | 200 | 50 | 0 |
N.S. |
1 | 1.13 | 0.97 | 1.01 | 0.00 | 1.76 | 0.00 | 2.56 | 0.64 | 0.00 |
time (sec) |
N/A | 0.865 | 0.202 | 0.226 | 0.000 | 0.092 | 0.000 | 0.146 | 0.156 | 0.000 |