Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 178 | 112 | 265 | 169 | 204 | 0 | 0 | 268 | 137 |
N.S. |
1 | 0.95 | 0.60 | 1.41 | 0.90 | 1.09 | 0.00 | 0.00 | 1.43 | 0.73 |
time (sec) |
N/A | 1.346 | 0.117 | 0.144 | 0.030 | 0.137 | 0.000 | 0.000 | 0.168 | 13.582 |
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 | 48 | 57 | 47 | 57 | 67 | 63 | 58 | 51 | 51 |
N.S. |
1 | 0.79 | 0.93 | 0.77 | 0.93 | 1.10 | 1.03 | 0.95 | 0.84 | 0.84 |
time (sec) |
N/A | 0.733 | 0.100 | 0.180 | 0.030 | 0.111 | 0.141 | 0.116 | 0.171 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 34 | 41 | 32 | 37 | 43 | 39 | 38 | 35 | 35 |
N.S. |
1 | 0.85 | 1.02 | 0.80 | 0.92 | 1.08 | 0.98 | 0.95 | 0.88 | 0.88 |
time (sec) |
N/A | 0.710 | 0.067 | 0.177 | 0.025 | 0.082 | 0.095 | 0.113 | 0.162 | 13.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 32 | 38 | 31 | 37 | 45 | 37 | 38 | 35 | 35 |
N.S. |
1 | 0.82 | 0.97 | 0.79 | 0.95 | 1.15 | 0.95 | 0.97 | 0.90 | 0.90 |
time (sec) |
N/A | 0.705 | 0.059 | 0.156 | 0.031 | 0.116 | 0.084 | 0.134 | 0.159 | 13.833 |
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 | 20 | 16 | 17 | 16 | 21 | 15 | 16 | 19 | 19 |
N.S. |
1 | 1.25 | 1.00 | 1.06 | 1.00 | 1.31 | 0.94 | 1.00 | 1.19 | 1.19 |
time (sec) |
N/A | 0.680 | 0.049 | 0.152 | 0.024 | 0.126 | 0.042 | 0.127 | 0.163 | 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 | 11 | 11 | 11 | 12 | 11 | 13 | 10 | 12 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.18 | 0.91 | 1.09 | 1.00 | 1.00 |
time (sec) |
N/A | 0.592 | 0.036 | 0.132 | 0.025 | 0.104 | 0.039 | 0.125 | 0.173 | 0.018 |
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 | 37 | 36 | 30 | 35 | 35 | 40 | 26 | 36 | 44 | 34 |
N.S. |
1 | 0.97 | 0.81 | 0.95 | 0.95 | 1.08 | 0.70 | 0.97 | 1.19 | 0.92 |
time (sec) |
N/A | 0.696 | 0.039 | 0.128 | 0.026 | 0.080 | 0.092 | 0.119 | 0.169 | 13.719 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 52 | 52 | 47 | 55 | 70 | 49 | 42 | 71 | 54 |
N.S. |
1 | 0.98 | 0.98 | 0.89 | 1.04 | 1.32 | 0.92 | 0.79 | 1.34 | 1.02 |
time (sec) |
N/A | 0.760 | 0.078 | 0.138 | 0.027 | 0.086 | 0.136 | 0.119 | 0.171 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 68 | 63 | 56 | 75 | 100 | 73 | 50 | 99 | 71 |
N.S. |
1 | 0.93 | 0.86 | 0.77 | 1.03 | 1.37 | 1.00 | 0.68 | 1.36 | 0.97 |
time (sec) |
N/A | 0.776 | 0.082 | 0.132 | 0.028 | 0.094 | 0.190 | 0.120 | 0.176 | 13.669 |
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 | 87 | 81 | 71 | 67 | 93 | 126 | 94 | 58 | 129 | 90 |
N.S. |
1 | 0.93 | 0.82 | 0.77 | 1.07 | 1.45 | 1.08 | 0.67 | 1.48 | 1.03 |
time (sec) |
N/A | 0.800 | 0.099 | 0.133 | 0.025 | 0.091 | 0.256 | 0.131 | 0.179 | 13.650 |
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 | 103 | 102 | 175 | 157 | 223 | 156 | 0 | 248 | 155 | 183 |
N.S. |
1 | 0.99 | 1.70 | 1.52 | 2.17 | 1.51 | 0.00 | 2.41 | 1.50 | 1.78 |
time (sec) |
N/A | 0.602 | 0.292 | 0.092 | 0.115 | 0.123 | 0.000 | 0.147 | 0.197 | 0.070 |
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 | 61 | 63 | 51 | 105 | 151 | 85 | 0 | 69 | 91 | 119 |
N.S. |
1 | 1.03 | 0.84 | 1.72 | 2.48 | 1.39 | 0.00 | 1.13 | 1.49 | 1.95 |
time (sec) |
N/A | 0.433 | 0.094 | 0.080 | 0.108 | 0.114 | 0.000 | 0.131 | 0.172 | 13.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 67 | 154 | 131 | 125 | 114 | 0 | 138 | 105 | 90 |
N.S. |
1 | 1.06 | 2.44 | 2.08 | 1.98 | 1.81 | 0.00 | 2.19 | 1.67 | 1.43 |
time (sec) |
N/A | 0.586 | 0.204 | 0.080 | 0.110 | 0.116 | 0.000 | 0.148 | 0.172 | 13.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 55 | 73 | 145 | 114 | 88 | 0 | 91 | 74 | 82 |
N.S. |
1 | 1.12 | 1.49 | 2.96 | 2.33 | 1.80 | 0.00 | 1.86 | 1.51 | 1.67 |
time (sec) |
N/A | 0.566 | 0.143 | 0.087 | 0.116 | 0.098 | 0.000 | 0.149 | 0.166 | 13.550 |
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 | 116 | 109 | 70 | 183 | 133 | 128 | 0 | 63 | 130 | 100 |
N.S. |
1 | 0.94 | 0.60 | 1.58 | 1.15 | 1.10 | 0.00 | 0.54 | 1.12 | 0.86 |
time (sec) |
N/A | 0.834 | 0.206 | 0.116 | 0.033 | 0.100 | 0.000 | 0.151 | 0.179 | 0.056 |
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 | 149 | 143 | 104 | 225 | 153 | 170 | 0 | 63 | 199 | 120 |
N.S. |
1 | 0.96 | 0.70 | 1.51 | 1.03 | 1.14 | 0.00 | 0.42 | 1.34 | 0.81 |
time (sec) |
N/A | 1.083 | 0.100 | 0.128 | 0.030 | 0.086 | 0.000 | 0.156 | 0.186 | 13.653 |
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 | 182 | 158 | 112 | 265 | 169 | 204 | 0 | 0 | 268 | 137 |
N.S. |
1 | 0.87 | 0.62 | 1.46 | 0.93 | 1.12 | 0.00 | 0.00 | 1.47 | 0.75 |
time (sec) |
N/A | 1.322 | 0.102 | 0.136 | 0.039 | 0.115 | 0.000 | 0.000 | 0.177 | 0.058 |
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 | 215 | 213 | 120 | 305 | 185 | 240 | 0 | 63 | 337 | 153 |
N.S. |
1 | 0.99 | 0.56 | 1.42 | 0.86 | 1.12 | 0.00 | 0.29 | 1.57 | 0.71 |
time (sec) |
N/A | 1.612 | 0.119 | 0.149 | 0.037 | 0.118 | 0.000 | 0.218 | 0.180 | 13.738 |
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 | 64 | 51 | 51 | 48 | 59 | 67 | 63 | 123 | 51 | 51 |
N.S. |
1 | 0.80 | 0.80 | 0.75 | 0.92 | 1.05 | 0.98 | 1.92 | 0.80 | 0.80 |
time (sec) |
N/A | 0.704 | 0.092 | 0.234 | 0.032 | 0.129 | 0.150 | 0.127 | 0.154 | 0.036 |
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 | 30 | 28 | 28 | 27 | 31 | 36 | 31 | 59 | 29 | 27 |
N.S. |
1 | 0.93 | 0.93 | 0.90 | 1.03 | 1.20 | 1.03 | 1.97 | 0.97 | 0.90 |
time (sec) |
N/A | 0.686 | 0.064 | 0.199 | 0.024 | 0.089 | 0.087 | 0.117 | 0.163 | 13.844 |
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 | 35 | 38 | 30 | 34 | 43 | 37 | 98 | 35 | 31 |
N.S. |
1 | 0.92 | 1.00 | 0.79 | 0.89 | 1.13 | 0.97 | 2.58 | 0.92 | 0.82 |
time (sec) |
N/A | 0.689 | 0.064 | 0.191 | 0.041 | 0.106 | 0.088 | 0.137 | 0.175 | 0.026 |
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 | 27 | 23 | 23 | 24 | 27 | 32 | 26 | 94 | 25 | 25 |
N.S. |
1 | 0.85 | 0.85 | 0.89 | 1.00 | 1.19 | 0.96 | 3.48 | 0.93 | 0.93 |
time (sec) |
N/A | 0.672 | 0.050 | 0.174 | 0.029 | 0.184 | 0.058 | 0.115 | 0.169 | 0.024 |
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 | 25 | 22 | 22 | 22 | 24 | 23 | 17 | 55 | 21 | 24 |
N.S. |
1 | 0.88 | 0.88 | 0.88 | 0.96 | 0.92 | 0.68 | 2.20 | 0.84 | 0.96 |
time (sec) |
N/A | 0.615 | 0.043 | 0.165 | 0.024 | 0.107 | 0.116 | 0.112 | 0.171 | 13.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 51 | 51 | 43 | 49 | 64 | 41 | 74 | 73 | 48 |
N.S. |
1 | 0.96 | 0.96 | 0.81 | 0.92 | 1.21 | 0.77 | 1.40 | 1.38 | 0.91 |
time (sec) |
N/A | 0.725 | 0.040 | 0.150 | 0.031 | 0.081 | 0.136 | 0.127 | 0.169 | 0.035 |
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 | 71 | 66 | 63 | 56 | 75 | 100 | 73 | 94 | 99 | 71 |
N.S. |
1 | 0.93 | 0.89 | 0.79 | 1.06 | 1.41 | 1.03 | 1.32 | 1.39 | 1.00 |
time (sec) |
N/A | 0.794 | 0.075 | 0.154 | 0.033 | 0.089 | 0.197 | 0.135 | 0.166 | 13.780 |
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 | 82 | 71 | 67 | 93 | 126 | 94 | 109 | 129 | 90 |
N.S. |
1 | 0.92 | 0.80 | 0.75 | 1.04 | 1.42 | 1.06 | 1.22 | 1.45 | 1.01 |
time (sec) |
N/A | 0.789 | 0.099 | 0.163 | 0.028 | 0.077 | 0.307 | 0.123 | 0.169 | 0.047 |
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 | 105 | 94 | 79 | 78 | 113 | 154 | 114 | 124 | 159 | 109 |
N.S. |
1 | 0.90 | 0.75 | 0.74 | 1.08 | 1.47 | 1.09 | 1.18 | 1.51 | 1.04 |
time (sec) |
N/A | 0.811 | 0.112 | 0.155 | 0.027 | 0.088 | 0.373 | 0.111 | 0.165 | 13.670 |
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 | 130 | 142 | 175 | 157 | 223 | 156 | 0 | 265 | 163 | 185 |
N.S. |
1 | 1.09 | 1.35 | 1.21 | 1.72 | 1.20 | 0.00 | 2.04 | 1.25 | 1.42 |
time (sec) |
N/A | 1.183 | 0.185 | 0.121 | 0.115 | 0.127 | 0.000 | 0.166 | 0.174 | 13.657 |
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 | 106 | 107 | 167 | 149 | 201 | 143 | 0 | 232 | 134 | 163 |
N.S. |
1 | 1.01 | 1.58 | 1.41 | 1.90 | 1.35 | 0.00 | 2.19 | 1.26 | 1.54 |
time (sec) |
N/A | 0.965 | 0.168 | 0.116 | 0.128 | 0.128 | 0.000 | 0.133 | 0.172 | 0.064 |
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 | 77 | 80 | 55 | 134 | 126 | 113 | 0 | 130 | 105 | 90 |
N.S. |
1 | 1.04 | 0.71 | 1.74 | 1.64 | 1.47 | 0.00 | 1.69 | 1.36 | 1.17 |
time (sec) |
N/A | 0.780 | 0.229 | 0.115 | 0.112 | 0.115 | 0.000 | 0.136 | 0.173 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 55 | 73 | 137 | 114 | 88 | 0 | 85 | 74 | 82 |
N.S. |
1 | 1.12 | 1.49 | 2.80 | 2.33 | 1.80 | 0.00 | 1.73 | 1.51 | 1.67 |
time (sec) |
N/A | 0.525 | 0.157 | 0.096 | 0.107 | 0.098 | 0.000 | 0.151 | 0.168 | 13.479 |
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 | 19 | 19 | 19 | 28 | 44 | 27 | 0 | 24 | 19 | 39 |
N.S. |
1 | 1.00 | 1.00 | 1.47 | 2.32 | 1.42 | 0.00 | 1.26 | 1.00 | 2.05 |
time (sec) |
N/A | 0.384 | 0.113 | 0.096 | 0.033 | 0.091 | 0.000 | 0.114 | 0.171 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 74 | 69 | 144 | 120 | 97 | 0 | 0 | 70 | 62 |
N.S. |
1 | 1.06 | 0.99 | 2.06 | 1.71 | 1.39 | 0.00 | 0.00 | 1.00 | 0.89 |
time (sec) |
N/A | 0.564 | 0.051 | 0.129 | 0.032 | 0.139 | 0.000 | 0.000 | 0.160 | 13.484 |
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 | 110 | 100 | 94 | 185 | 137 | 134 | 0 | 0 | 130 | 105 |
N.S. |
1 | 0.91 | 0.85 | 1.68 | 1.25 | 1.22 | 0.00 | 0.00 | 1.18 | 0.95 |
time (sec) |
N/A | 0.802 | 0.082 | 0.145 | 0.035 | 0.108 | 0.000 | 0.000 | 0.178 | 0.056 |
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 | 143 | 129 | 104 | 225 | 153 | 170 | 0 | 59 | 199 | 121 |
N.S. |
1 | 0.90 | 0.73 | 1.57 | 1.07 | 1.19 | 0.00 | 0.41 | 1.39 | 0.85 |
time (sec) |
N/A | 1.057 | 0.091 | 0.168 | 0.045 | 0.089 | 0.000 | 0.152 | 0.174 | 13.528 |
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 | 54 | 54 | 51 | 60 | 71 | 56 | 62 | 57 | 61 |
N.S. |
1 | 0.83 | 0.83 | 0.78 | 0.92 | 1.09 | 0.86 | 0.95 | 0.88 | 0.94 |
time (sec) |
N/A | 0.748 | 0.085 | 0.201 | 0.029 | 0.100 | 0.257 | 0.117 | 0.170 | 0.053 |
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 | 54 | 44 | 46 | 43 | 51 | 62 | 42 | 53 | 49 | 51 |
N.S. |
1 | 0.81 | 0.85 | 0.80 | 0.94 | 1.15 | 0.78 | 0.98 | 0.91 | 0.94 |
time (sec) |
N/A | 0.719 | 0.076 | 0.181 | 0.028 | 0.107 | 0.200 | 0.144 | 0.188 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 34 | 34 | 31 | 40 | 43 | 31 | 42 | 35 | 40 |
N.S. |
1 | 0.85 | 0.85 | 0.78 | 1.00 | 1.08 | 0.78 | 1.05 | 0.88 | 1.00 |
time (sec) |
N/A | 0.689 | 0.061 | 0.165 | 0.032 | 0.079 | 0.158 | 0.113 | 0.164 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 19 | 23 | 20 | 23 | 22 | 17 | 25 | 19 | 23 |
N.S. |
1 | 0.83 | 1.00 | 0.87 | 1.00 | 0.96 | 0.74 | 1.09 | 0.83 | 1.00 |
time (sec) |
N/A | 0.601 | 0.042 | 0.148 | 0.033 | 0.086 | 0.122 | 0.126 | 0.168 | 13.526 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 22 | 22 | 20 | 20 | 19 | 17 | 21 | 19 | 19 |
N.S. |
1 | 1.10 | 1.10 | 1.00 | 1.00 | 0.95 | 0.85 | 1.05 | 0.95 | 0.95 |
time (sec) |
N/A | 0.650 | 0.025 | 0.124 | 0.030 | 0.089 | 0.052 | 0.116 | 0.174 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 23 | 18 | 28 | 34 | 27 | 34 | 36 | 33 | 17 |
N.S. |
1 | 1.28 | 1.00 | 1.56 | 1.89 | 1.50 | 1.89 | 2.00 | 1.83 | 0.94 |
time (sec) |
N/A | 0.650 | 0.047 | 0.144 | 0.034 | 0.094 | 0.091 | 0.143 | 0.183 | 0.037 |
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 | 55 | 57 | 48 | 53 | 59 | 56 | 51 | 62 | 52 |
N.S. |
1 | 0.96 | 1.00 | 0.84 | 0.93 | 1.04 | 0.98 | 0.89 | 1.09 | 0.91 |
time (sec) |
N/A | 0.733 | 0.076 | 0.141 | 0.032 | 0.106 | 0.173 | 0.113 | 0.180 | 13.781 |
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 | 75 | 72 | 72 | 60 | 69 | 93 | 73 | 57 | 105 | 68 |
N.S. |
1 | 0.96 | 0.96 | 0.80 | 0.92 | 1.24 | 0.97 | 0.76 | 1.40 | 0.91 |
time (sec) |
N/A | 0.765 | 0.098 | 0.145 | 0.026 | 0.115 | 0.227 | 0.117 | 0.175 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | F | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 173 | 567 | 191 | 246 | 157 | 0 | 0 | 271 | 211 |
N.S. |
1 | 1.09 | 3.57 | 1.20 | 1.55 | 0.99 | 0.00 | 0.00 | 1.70 | 1.33 |
time (sec) |
N/A | 1.479 | 1.385 | 0.136 | 0.117 | 0.097 | 0.000 | 0.000 | 0.193 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | F | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 138 | 663 | 181 | 225 | 146 | 0 | 0 | 251 | 190 |
N.S. |
1 | 1.02 | 4.91 | 1.34 | 1.67 | 1.08 | 0.00 | 0.00 | 1.86 | 1.41 |
time (sec) |
N/A | 1.226 | 0.537 | 0.137 | 0.108 | 0.100 | 0.000 | 0.000 | 0.174 | 13.509 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | F | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 111 | 424 | 169 | 149 | 120 | 0 | 0 | 212 | 117 |
N.S. |
1 | 1.06 | 4.04 | 1.61 | 1.42 | 1.14 | 0.00 | 0.00 | 2.02 | 1.11 |
time (sec) |
N/A | 0.964 | 0.450 | 0.133 | 0.121 | 0.101 | 0.000 | 0.000 | 0.168 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F | F | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 87 | 234 | 376 | 135 | 92 | 0 | 0 | 165 | 107 |
N.S. |
1 | 1.16 | 3.12 | 5.01 | 1.80 | 1.23 | 0.00 | 0.00 | 2.20 | 1.43 |
time (sec) |
N/A | 0.732 | 0.563 | 0.096 | 0.123 | 0.136 | 0.000 | 0.000 | 0.169 | 13.555 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 70 | 61 | 137 | 120 | 69 | 0 | 0 | 95 | 87 |
N.S. |
1 | 0.97 | 0.85 | 1.90 | 1.67 | 0.96 | 0.00 | 0.00 | 1.32 | 1.21 |
time (sec) |
N/A | 0.552 | 0.172 | 0.108 | 0.033 | 0.110 | 0.000 | 0.000 | 0.172 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 68 | 69 | 138 | 125 | 67 | 0 | 0 | 95 | 90 |
N.S. |
1 | 0.96 | 0.97 | 1.94 | 1.76 | 0.94 | 0.00 | 0.00 | 1.34 | 1.27 |
time (sec) |
N/A | 0.529 | 0.050 | 0.129 | 0.034 | 0.095 | 0.000 | 0.000 | 0.150 | 13.643 |
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 | 41 | 45 | 33 | 41 | 92 | 42 | 0 | 42 | 37 | 41 |
N.S. |
1 | 1.10 | 0.80 | 1.00 | 2.24 | 1.02 | 0.00 | 1.02 | 0.90 | 1.00 |
time (sec) |
N/A | 0.402 | 0.029 | 0.121 | 0.031 | 0.090 | 0.000 | 0.138 | 0.167 | 13.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 105 | 94 | 218 | 160 | 134 | 0 | 0 | 156 | 128 |
N.S. |
1 | 0.95 | 0.85 | 1.98 | 1.45 | 1.22 | 0.00 | 0.00 | 1.42 | 1.16 |
time (sec) |
N/A | 0.614 | 0.080 | 0.155 | 0.046 | 0.084 | 0.000 | 0.000 | 0.162 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 132 | 104 | 259 | 176 | 170 | 0 | 0 | 268 | 144 |
N.S. |
1 | 0.92 | 0.73 | 1.81 | 1.23 | 1.19 | 0.00 | 0.00 | 1.87 | 1.01 |
time (sec) |
N/A | 1.034 | 0.106 | 0.170 | 0.034 | 0.083 | 0.000 | 0.000 | 0.163 | 13.459 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 183 | 109 | 166 | 0 | 437 | 0 | 0 | 123 | 0 |
N.S. |
1 | 0.78 | 0.46 | 0.71 | 0.00 | 1.86 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.697 | 0.142 | 0.104 | 0.000 | 0.122 | 0.000 | 0.000 | 0.179 | 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 | 196 | 150 | 101 | 149 | 0 | 415 | 0 | 0 | 105 | 0 |
N.S. |
1 | 0.77 | 0.52 | 0.76 | 0.00 | 2.12 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.635 | 0.090 | 0.098 | 0.000 | 0.127 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 115 | 89 | 132 | 0 | 381 | 0 | 0 | 87 | 0 |
N.S. |
1 | 0.73 | 0.57 | 0.84 | 0.00 | 2.43 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.589 | 0.082 | 0.088 | 0.000 | 0.154 | 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 | 117 | 122 | 70 | 106 | 0 | 313 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.04 | 0.60 | 0.91 | 0.00 | 2.68 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.667 | 0.061 | 0.105 | 0.000 | 0.140 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 82 | 66 | 87 | 0 | 295 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.05 | 0.85 | 1.12 | 0.00 | 3.78 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.560 | 0.048 | 0.083 | 0.000 | 0.120 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 103 | 95 | 151 | 0 | 517 | 0 | 0 | 118 | 0 |
N.S. |
1 | 0.77 | 0.71 | 1.13 | 0.00 | 3.86 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.601 | 0.090 | 0.181 | 0.000 | 0.155 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 137 | 122 | 259 | 0 | 594 | 0 | 0 | 252 | 0 |
N.S. |
1 | 0.81 | 0.72 | 1.52 | 0.00 | 3.49 | 0.00 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.644 | 0.108 | 0.193 | 0.000 | 0.204 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 175 | 135 | 328 | 0 | 668 | 0 | 0 | 420 | 0 |
N.S. |
1 | 0.82 | 0.63 | 1.54 | 0.00 | 3.14 | 0.00 | 0.00 | 1.97 | 0.00 |
time (sec) |
N/A | 0.711 | 0.142 | 0.197 | 0.000 | 0.149 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 146 | 91 | 155 | 0 | 243 | 2222 | 0 | 123 | 0 |
N.S. |
1 | 1.02 | 0.64 | 1.08 | 0.00 | 1.70 | 15.54 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.816 | 0.167 | 0.174 | 0.000 | 0.126 | 20.493 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 124 | 83 | 144 | 0 | 221 | 740 | 0 | 105 | 0 |
N.S. |
1 | 1.05 | 0.70 | 1.22 | 0.00 | 1.87 | 6.27 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.815 | 0.130 | 0.170 | 0.000 | 0.086 | 6.914 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 103 | 75 | 108 | 0 | 191 | 144 | 0 | 87 | 0 |
N.S. |
1 | 1.08 | 0.79 | 1.14 | 0.00 | 2.01 | 1.52 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.741 | 0.092 | 0.168 | 0.000 | 0.112 | 13.704 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 80 | 55 | 103 | 0 | 146 | 173 | 0 | 59 | 0 |
N.S. |
1 | 1.14 | 0.79 | 1.47 | 0.00 | 2.09 | 2.47 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.715 | 0.072 | 0.154 | 0.000 | 0.091 | 21.563 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 58 | 50 | 98 | 0 | 133 | 0 | 96 | 33 | 0 |
N.S. |
1 | 1.16 | 1.00 | 1.96 | 0.00 | 2.66 | 0.00 | 1.92 | 0.66 | 0.00 |
time (sec) |
N/A | 0.679 | 0.038 | 0.150 | 0.000 | 0.086 | 0.000 | 0.138 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 83 | 43 | 150 | 0 | 185 | 0 | 170 | 62 | 0 |
N.S. |
1 | 1.19 | 0.61 | 2.14 | 0.00 | 2.64 | 0.00 | 2.43 | 0.89 | 0.00 |
time (sec) |
N/A | 0.701 | 0.039 | 0.181 | 0.000 | 0.105 | 0.000 | 0.159 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 110 | 55 | 201 | 0 | 247 | 0 | 245 | 114 | 0 |
N.S. |
1 | 1.16 | 0.58 | 2.12 | 0.00 | 2.60 | 0.00 | 2.58 | 1.20 | 0.00 |
time (sec) |
N/A | 0.769 | 0.040 | 0.169 | 0.000 | 0.101 | 0.000 | 0.180 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 137 | 58 | 247 | 0 | 303 | 0 | 316 | 175 | 0 |
N.S. |
1 | 1.16 | 0.49 | 2.09 | 0.00 | 2.57 | 0.00 | 2.68 | 1.48 | 0.00 |
time (sec) |
N/A | 0.806 | 0.039 | 0.177 | 0.000 | 0.088 | 0.000 | 0.238 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 164 | 46 | 291 | 0 | 355 | 0 | 391 | 236 | 0 |
N.S. |
1 | 1.13 | 0.32 | 2.01 | 0.00 | 2.45 | 0.00 | 2.70 | 1.63 | 0.00 |
time (sec) |
N/A | 0.829 | 0.049 | 0.184 | 0.000 | 0.122 | 0.000 | 0.338 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 168 | 109 | 178 | 0 | 437 | 0 | 0 | 123 | 0 |
N.S. |
1 | 0.71 | 0.46 | 0.76 | 0.00 | 1.86 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.665 | 0.121 | 0.094 | 0.000 | 0.121 | 0.000 | 0.000 | 0.169 | 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 | 195 | 132 | 101 | 161 | 0 | 415 | 0 | 0 | 105 | 0 |
N.S. |
1 | 0.68 | 0.52 | 0.83 | 0.00 | 2.13 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.612 | 0.094 | 0.089 | 0.000 | 0.140 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 162 | 89 | 144 | 0 | 381 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.04 | 0.57 | 0.92 | 0.00 | 2.44 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.772 | 0.074 | 0.092 | 0.000 | 0.151 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 123 | 66 | 118 | 0 | 315 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.04 | 0.56 | 1.00 | 0.00 | 2.67 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.660 | 0.052 | 0.074 | 0.000 | 0.155 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 104 | 95 | 160 | 0 | 512 | 0 | 0 | 117 | 0 |
N.S. |
1 | 0.77 | 0.70 | 1.19 | 0.00 | 3.79 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.588 | 0.062 | 0.184 | 0.000 | 0.167 | 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 | 170 | 135 | 115 | 259 | 0 | 581 | 0 | 0 | 252 | 0 |
N.S. |
1 | 0.79 | 0.68 | 1.52 | 0.00 | 3.42 | 0.00 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.657 | 0.115 | 0.191 | 0.000 | 0.185 | 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) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 172 | 135 | 326 | 0 | 668 | 0 | 0 | 420 | 0 |
N.S. |
1 | 0.83 | 0.65 | 1.57 | 0.00 | 3.21 | 0.00 | 0.00 | 2.02 | 0.00 |
time (sec) |
N/A | 0.727 | 0.144 | 0.194 | 0.000 | 0.142 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 210 | 143 | 376 | 0 | 736 | 0 | 0 | 583 | 0 |
N.S. |
1 | 0.84 | 0.57 | 1.51 | 0.00 | 2.96 | 0.00 | 0.00 | 2.34 | 0.00 |
time (sec) |
N/A | 0.781 | 0.176 | 0.198 | 0.000 | 0.170 | 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 | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 148 | 101 | 161 | 0 | 415 | 0 | 0 | 105 | 0 |
N.S. |
1 | 0.76 | 0.52 | 0.82 | 0.00 | 2.12 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.654 | 0.112 | 0.115 | 0.000 | 0.116 | 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) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 113 | 89 | 144 | 0 | 381 | 0 | 0 | 87 | 0 |
N.S. |
1 | 0.72 | 0.57 | 0.92 | 0.00 | 2.43 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.591 | 0.076 | 0.114 | 0.000 | 0.162 | 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 | 116 | 93 | 70 | 118 | 0 | 315 | 0 | 0 | 59 | 0 |
N.S. |
1 | 0.80 | 0.60 | 1.02 | 0.00 | 2.72 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.574 | 0.057 | 0.112 | 0.000 | 0.156 | 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 | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 87 | 65 | 101 | 0 | 297 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.10 | 0.82 | 1.28 | 0.00 | 3.76 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.575 | 0.046 | 0.102 | 0.000 | 0.118 | 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 | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 84 | 65 | 102 | 0 | 299 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.08 | 0.83 | 1.31 | 0.00 | 3.83 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.568 | 0.053 | 0.097 | 0.000 | 0.135 | 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 | B | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 112 | 91 | 162 | 0 | 522 | 0 | 0 | 120 | 0 |
N.S. |
1 | 0.82 | 0.67 | 1.19 | 0.00 | 3.84 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.588 | 0.075 | 0.188 | 0.000 | 0.150 | 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 | 179 | 140 | 123 | 264 | 0 | 596 | 0 | 0 | 252 | 0 |
N.S. |
1 | 0.78 | 0.69 | 1.47 | 0.00 | 3.33 | 0.00 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 0.656 | 0.112 | 0.223 | 0.000 | 0.195 | 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 | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 175 | 135 | 316 | 0 | 668 | 0 | 0 | 420 | 0 |
N.S. |
1 | 0.81 | 0.62 | 1.46 | 0.00 | 3.09 | 0.00 | 0.00 | 1.94 | 0.00 |
time (sec) |
N/A | 0.735 | 0.160 | 0.224 | 0.000 | 0.143 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 172 | 125 | 223 | 0 | 340 | 0 | 0 | 197 | 0 |
N.S. |
1 | 1.06 | 0.77 | 1.37 | 0.00 | 2.09 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.941 | 0.271 | 0.225 | 0.000 | 0.143 | 0.000 | 0.000 | 0.163 | 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 | 138 | 150 | 116 | 213 | 0 | 302 | 0 | 0 | 179 | 0 |
N.S. |
1 | 1.09 | 0.84 | 1.54 | 0.00 | 2.19 | 0.00 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 0.905 | 0.124 | 0.214 | 0.000 | 0.118 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 128 | 95 | 193 | 0 | 252 | 0 | 0 | 139 | 0 |
N.S. |
1 | 1.13 | 0.84 | 1.71 | 0.00 | 2.23 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.866 | 0.093 | 0.194 | 0.000 | 0.117 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 108 | 92 | 168 | 0 | 236 | 0 | 0 | 107 | 0 |
N.S. |
1 | 1.17 | 1.00 | 1.83 | 0.00 | 2.57 | 0.00 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 0.777 | 0.056 | 0.183 | 0.000 | 0.092 | 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 | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 105 | 95 | 136 | 0 | 235 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.11 | 1.00 | 1.43 | 0.00 | 2.47 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.794 | 0.057 | 0.183 | 0.000 | 0.095 | 0.000 | 0.000 | 0.163 | 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 | 94 | 116 | 94 | 136 | 0 | 232 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.23 | 1.00 | 1.45 | 0.00 | 2.47 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.852 | 0.070 | 0.203 | 0.000 | 0.103 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 132 | 70 | 227 | 0 | 304 | 0 | 0 | 152 | 0 |
N.S. |
1 | 1.14 | 0.60 | 1.96 | 0.00 | 2.62 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.858 | 0.069 | 0.226 | 0.000 | 0.112 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 162 | 79 | 271 | 0 | 376 | 0 | 0 | 304 | 0 |
N.S. |
1 | 1.10 | 0.54 | 1.84 | 0.00 | 2.56 | 0.00 | 0.00 | 2.07 | 0.00 |
time (sec) |
N/A | 0.894 | 0.072 | 0.227 | 0.000 | 0.094 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 192 | 82 | 315 | 0 | 448 | 0 | 0 | 475 | 0 |
N.S. |
1 | 1.12 | 0.48 | 1.83 | 0.00 | 2.60 | 0.00 | 0.00 | 2.76 | 0.00 |
time (sec) |
N/A | 0.978 | 0.075 | 0.237 | 0.000 | 0.100 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 177 | 132 | 212 | 0 | 415 | 0 | 0 | 113 | 0 |
N.S. |
1 | 0.76 | 0.57 | 0.91 | 0.00 | 1.79 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.675 | 0.133 | 0.144 | 0.000 | 0.153 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 144 | 124 | 195 | 0 | 381 | 0 | 0 | 101 | 0 |
N.S. |
1 | 0.75 | 0.64 | 1.01 | 0.00 | 1.97 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.637 | 0.123 | 0.124 | 0.000 | 0.136 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 109 | 71 | 169 | 0 | 315 | 0 | 0 | 77 | 0 |
N.S. |
1 | 0.72 | 0.47 | 1.11 | 0.00 | 2.07 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.577 | 0.088 | 0.136 | 0.000 | 0.119 | 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 | 115 | 92 | 67 | 146 | 0 | 299 | 0 | 0 | 59 | 0 |
N.S. |
1 | 0.80 | 0.58 | 1.27 | 0.00 | 2.60 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.568 | 0.067 | 0.113 | 0.000 | 0.140 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 125 | 69 | 149 | 0 | 303 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.06 | 0.58 | 1.26 | 0.00 | 2.57 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.677 | 0.068 | 0.114 | 0.000 | 0.110 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 121 | 64 | 149 | 0 | 311 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.03 | 0.55 | 1.27 | 0.00 | 2.66 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.654 | 0.059 | 0.112 | 0.000 | 0.194 | 0.000 | 0.000 | 0.147 | 0.000 |