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 | C | F(-2) | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 156 | 125 | 32 | 0 | 1961 | 76 | 141 | 151 | 127 |
N.S. |
1 | 0.97 | 0.78 | 0.20 | 0.00 | 12.18 | 0.47 | 0.88 | 0.94 | 0.79 |
time (sec) |
N/A | 0.559 | 0.042 | 0.092 | 0.000 | 0.868 | 0.394 | 0.131 | 0.152 | 5.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 179 | 200 | 43 | 192 | 5014 | 156 | 175 | 217 | 357 |
N.S. |
1 | 0.96 | 1.08 | 0.23 | 1.03 | 26.96 | 0.84 | 0.94 | 1.17 | 1.92 |
time (sec) |
N/A | 0.745 | 0.061 | 0.093 | 0.112 | 0.953 | 0.594 | 0.128 | 0.152 | 5.990 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 222 | 214 | 66 | 240 | 7245 | 245 | 214 | 321 | 370 |
N.S. |
1 | 1.00 | 0.96 | 0.30 | 1.08 | 32.64 | 1.10 | 0.96 | 1.45 | 1.67 |
time (sec) |
N/A | 0.803 | 0.126 | 0.093 | 0.126 | 1.350 | 2.492 | 0.124 | 0.153 | 0.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 280 | 277 | 90 | 303 | 8787 | 325 | 294 | 420 | 513 |
N.S. |
1 | 1.00 | 0.99 | 0.32 | 1.08 | 31.38 | 1.16 | 1.05 | 1.50 | 1.83 |
time (sec) |
N/A | 0.997 | 0.172 | 0.105 | 0.122 | 4.525 | 26.154 | 0.144 | 0.153 | 6.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 191 | 180 | 65 | 169 | 2088 | 105 | 174 | 351 | 169 |
N.S. |
1 | 1.01 | 0.95 | 0.34 | 0.89 | 11.05 | 0.56 | 0.92 | 1.86 | 0.89 |
time (sec) |
N/A | 0.731 | 0.125 | 0.111 | 0.108 | 0.913 | 0.578 | 0.128 | 0.159 | 0.276 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 86 | 72 | 87 | 71 | 103 | 238 | 72 | 177 | 97 |
N.S. |
1 | 1.09 | 0.91 | 1.10 | 0.90 | 1.30 | 3.01 | 0.91 | 2.24 | 1.23 |
time (sec) |
N/A | 0.476 | 0.042 | 0.102 | 0.107 | 0.112 | 0.371 | 0.117 | 0.147 | 5.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 225 | 205 | 86 | 203 | 2215 | 146 | 194 | 564 | 206 |
N.S. |
1 | 1.05 | 0.95 | 0.40 | 0.94 | 10.30 | 0.68 | 0.90 | 2.62 | 0.96 |
time (sec) |
N/A | 0.808 | 0.110 | 0.121 | 0.110 | 0.897 | 0.715 | 0.131 | 0.154 | 0.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 258 | 229 | 110 | 238 | 2308 | 185 | 218 | 775 | 241 |
N.S. |
1 | 1.08 | 0.95 | 0.46 | 0.99 | 9.62 | 0.77 | 0.91 | 3.23 | 1.00 |
time (sec) |
N/A | 0.907 | 0.142 | 0.115 | 0.126 | 0.907 | 0.862 | 0.126 | 0.156 | 5.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 154 | 125 | 34 | 0 | 1905 | 78 | 136 | 150 | 124 |
N.S. |
1 | 0.96 | 0.78 | 0.21 | 0.00 | 11.83 | 0.48 | 0.84 | 0.93 | 0.77 |
time (sec) |
N/A | 0.563 | 0.039 | 0.112 | 0.000 | 0.877 | 0.394 | 0.126 | 0.148 | 5.873 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 17 | 16 | 16 | 26 | 16 | 15 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.84 | 0.84 | 1.37 | 0.84 | 0.79 | 0.84 |
time (sec) |
N/A | 0.264 | 0.008 | 0.085 | 0.105 | 0.095 | 0.056 | 0.124 | 0.146 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 17 | 16 | 16 | 26 | 16 | 15 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.84 | 0.84 | 1.37 | 0.84 | 0.79 | 0.84 |
time (sec) |
N/A | 0.261 | 0.004 | 0.085 | 0.160 | 0.082 | 0.054 | 0.115 | 0.151 | 5.704 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 34 | 28 | 54 | 28 | 25 | 28 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.17 | 0.97 | 1.86 | 0.97 | 0.86 | 0.97 |
time (sec) |
N/A | 0.283 | 0.009 | 0.133 | 0.110 | 0.124 | 0.095 | 0.118 | 0.148 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 29 | 33 | 26 | 53 | 26 | 25 | 28 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.14 | 0.90 | 1.83 | 0.90 | 0.86 | 0.97 |
time (sec) |
N/A | 0.285 | 0.008 | 0.102 | 0.108 | 0.105 | 0.090 | 0.126 | 0.149 | 0.049 |
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 | 22 | 22 | 22 | 17 | 16 | 16 | 17 | 17 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.73 | 0.73 | 0.77 | 0.77 | 0.73 | 0.73 |
time (sec) |
N/A | 0.276 | 0.005 | 0.096 | 0.108 | 0.098 | 0.049 | 0.123 | 0.150 | 0.067 |
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 | 22 | 22 | 22 | 19 | 18 | 18 | 17 | 19 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 0.82 | 0.77 | 0.86 | 0.82 | 0.82 |
time (sec) |
N/A | 0.273 | 0.005 | 0.086 | 0.109 | 0.078 | 0.045 | 0.109 | 0.146 | 0.124 |
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 | 44 | 35 | 41 | 35 | 34 | 42 | 34 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.93 | 0.80 | 0.77 | 0.95 | 0.77 | 0.84 |
time (sec) |
N/A | 0.320 | 0.007 | 0.107 | 0.032 | 0.086 | 0.142 | 0.124 | 0.149 | 5.705 |
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 | 44 | 37 | 40 | 34 | 34 | 41 | 36 | 36 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.91 | 0.77 | 0.77 | 0.93 | 0.82 | 0.82 |
time (sec) |
N/A | 0.313 | 0.007 | 0.095 | 0.026 | 0.102 | 0.153 | 0.137 | 0.154 | 5.631 |
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 | 41 | 42 | 41 | 33 | 32 | 32 | 44 | 33 | 31 | 46 |
N.S. |
1 | 1.02 | 1.00 | 0.80 | 0.78 | 0.78 | 1.07 | 0.80 | 0.76 | 1.12 |
time (sec) |
N/A | 0.346 | 0.008 | 0.105 | 0.104 | 0.095 | 0.078 | 0.119 | 0.149 | 0.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 34 | 28 | 54 | 28 | 25 | 28 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.17 | 0.97 | 1.86 | 0.97 | 0.86 | 0.97 |
time (sec) |
N/A | 0.278 | 0.010 | 0.118 | 0.118 | 0.087 | 0.103 | 0.119 | 0.147 | 5.551 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 29 | 33 | 26 | 53 | 26 | 25 | 28 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.14 | 0.90 | 1.83 | 0.90 | 0.86 | 0.97 |
time (sec) |
N/A | 0.270 | 0.007 | 0.096 | 0.108 | 0.087 | 0.089 | 0.121 | 0.151 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 35 | 35 | 195 | 163 | 107 | 88 | 48 | 27 | 49 |
N.S. |
1 | 0.90 | 0.90 | 5.00 | 4.18 | 2.74 | 2.26 | 1.23 | 0.69 | 1.26 |
time (sec) |
N/A | 0.288 | 0.013 | 0.222 | 0.107 | 0.110 | 0.142 | 0.143 | 0.148 | 0.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 37 | 129 | 202 | 174 | 114 | 105 | 57 | 27 | 49 |
N.S. |
1 | 0.90 | 3.15 | 4.93 | 4.24 | 2.78 | 2.56 | 1.39 | 0.66 | 1.20 |
time (sec) |
N/A | 0.308 | 0.037 | 0.235 | 0.136 | 0.117 | 0.175 | 0.142 | 0.150 | 5.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 270 | 269 | 85 | 0 | 12827 | 0 | 282 | 451 | 769 |
N.S. |
1 | 1.00 | 1.00 | 0.31 | 0.00 | 47.51 | 0.00 | 1.04 | 1.67 | 2.85 |
time (sec) |
N/A | 1.034 | 0.202 | 0.213 | 0.000 | 1.422 | 0.000 | 0.128 | 0.152 | 6.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 416 | 416 | 439 | 181 | 0 | 29479 | 0 | 462 | 855 | 1700 |
N.S. |
1 | 1.00 | 1.06 | 0.44 | 0.00 | 70.86 | 0.00 | 1.11 | 2.06 | 4.09 |
time (sec) |
N/A | 1.360 | 0.289 | 0.191 | 0.000 | 7.855 | 0.000 | 0.135 | 0.150 | 5.866 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 643 | 643 | 678 | 350 | 0 | 47284 | 0 | 773 | 1391 | 2971 |
N.S. |
1 | 1.00 | 1.05 | 0.54 | 0.00 | 73.54 | 0.00 | 1.20 | 2.16 | 4.62 |
time (sec) |
N/A | 2.084 | 0.234 | 0.192 | 0.000 | 77.466 | 0.000 | 0.134 | 0.156 | 5.773 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 90 | 47 | 159 | 310 | 26 | 103 | 65 | 98 |
N.S. |
1 | 1.00 | 0.76 | 0.40 | 1.35 | 2.63 | 0.22 | 0.87 | 0.55 | 0.83 |
time (sec) |
N/A | 0.511 | 0.014 | 0.112 | 0.116 | 0.122 | 0.092 | 0.131 | 0.151 | 0.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 90 | 49 | 159 | 305 | 22 | 115 | 67 | 96 |
N.S. |
1 | 1.00 | 0.76 | 0.42 | 1.35 | 2.58 | 0.19 | 0.97 | 0.57 | 0.81 |
time (sec) |
N/A | 0.461 | 0.010 | 0.104 | 0.118 | 0.101 | 0.095 | 0.131 | 0.149 | 6.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 124 | 52 | 188 | 1961 | 76 | 147 | 145 | 127 |
N.S. |
1 | 1.00 | 0.77 | 0.32 | 1.17 | 12.18 | 0.47 | 0.91 | 0.90 | 0.79 |
time (sec) |
N/A | 0.570 | 0.031 | 0.102 | 0.113 | 0.867 | 0.529 | 0.134 | 0.146 | 5.894 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | C | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 135 | 122 | 36 | 0 | 1344 | 75 | 118 | 121 | 158 |
N.S. |
1 | 1.02 | 0.92 | 0.27 | 0.00 | 10.11 | 0.56 | 0.89 | 0.91 | 1.19 |
time (sec) |
N/A | 0.634 | 0.020 | 0.101 | 0.000 | 0.870 | 0.219 | 0.128 | 0.150 | 5.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 130 | 123 | 36 | 0 | 1040 | 70 | 124 | 126 | 178 |
N.S. |
1 | 0.97 | 0.92 | 0.27 | 0.00 | 7.76 | 0.52 | 0.93 | 0.94 | 1.33 |
time (sec) |
N/A | 0.544 | 0.025 | 0.100 | 0.000 | 0.869 | 0.290 | 0.127 | 0.149 | 0.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 72 | 42 | 42 | 36 | 60 | 37 | 33 | 84 |
N.S. |
1 | 1.00 | 1.95 | 1.14 | 1.14 | 0.97 | 1.62 | 1.00 | 0.89 | 2.27 |
time (sec) |
N/A | 0.362 | 0.019 | 0.119 | 0.115 | 0.118 | 0.172 | 0.125 | 0.147 | 5.815 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 71 | 38 | 44 | 36 | 60 | 38 | 34 | 86 |
N.S. |
1 | 1.00 | 1.82 | 0.97 | 1.13 | 0.92 | 1.54 | 0.97 | 0.87 | 2.21 |
time (sec) |
N/A | 0.338 | 0.020 | 0.116 | 0.117 | 0.117 | 0.208 | 0.122 | 0.151 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 76 | 115 | 47 | 134 | 58 | 115 | 34 | 147 |
N.S. |
1 | 1.00 | 1.58 | 2.40 | 0.98 | 2.79 | 1.21 | 2.40 | 0.71 | 3.06 |
time (sec) |
N/A | 0.330 | 0.017 | 0.147 | 0.116 | 0.107 | 0.205 | 0.321 | 0.148 | 6.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 43 | 72 | 96 | 36 | 40 | 85 | 76 | 34 | 145 |
N.S. |
1 | 0.91 | 1.53 | 2.04 | 0.77 | 0.85 | 1.81 | 1.62 | 0.72 | 3.09 |
time (sec) |
N/A | 0.332 | 0.020 | 0.115 | 0.113 | 0.121 | 0.171 | 0.135 | 0.148 | 6.058 |
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 | 46 | 50 | 32 | 31 | 31 | 42 | 32 | 30 | 46 |
N.S. |
1 | 1.15 | 1.25 | 0.80 | 0.78 | 0.78 | 1.05 | 0.80 | 0.75 | 1.15 |
time (sec) |
N/A | 0.366 | 0.009 | 0.092 | 0.113 | 0.115 | 0.082 | 0.127 | 0.150 | 0.159 |
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 | 12 | 12 | 12 | 12 | 7 | 13 | 11 | 12 |
N.S. |
1 | 1.00 | 1.09 | 1.09 | 1.09 | 1.09 | 0.64 | 1.18 | 1.00 | 1.09 |
time (sec) |
N/A | 0.258 | 0.001 | 0.109 | 0.034 | 0.075 | 0.050 | 0.140 | 0.155 | 5.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 18 | 210 | 17 | 20 | 16 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 10.00 | 0.81 | 0.95 | 0.76 | 0.71 | 0.71 |
time (sec) |
N/A | 0.264 | 0.002 | 0.174 | 0.126 | 0.099 | 0.094 | 0.130 | 0.148 | 5.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 31 | 28 | 26 | 26 | 24 | 27 | 35 | 35 |
N.S. |
1 | 1.00 | 0.97 | 0.88 | 0.81 | 0.81 | 0.75 | 0.84 | 1.09 | 1.09 |
time (sec) |
N/A | 0.318 | 0.013 | 0.100 | 0.114 | 0.088 | 0.294 | 0.123 | 0.154 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 60 | 62 | 55 | 47 | 47 | 323 | 52 | 84 | 87 |
N.S. |
1 | 1.09 | 1.13 | 1.00 | 0.85 | 0.85 | 5.87 | 0.95 | 1.53 | 1.58 |
time (sec) |
N/A | 0.411 | 0.028 | 0.132 | 0.114 | 0.109 | 0.640 | 0.120 | 0.151 | 5.627 |
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 | 8 | 8 | 8 | 7 | 6 | 6 | 5 | 7 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.62 | 0.88 | 0.75 | 0.75 |
time (sec) |
N/A | 0.233 | 0.001 | 0.071 | 0.025 | 0.072 | 0.031 | 0.117 | 0.147 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 31 | 32 | 32 | 5 | 33 | 31 | 63 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.07 | 1.07 | 0.17 | 1.10 | 1.03 | 2.10 |
time (sec) |
N/A | 0.346 | 0.008 | 0.097 | 0.108 | 0.087 | 0.085 | 0.129 | 0.152 | 5.716 |
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 | 18 | 18 | 18 | 17 | 16 | 16 | 15 | 17 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.89 | 0.89 | 0.83 | 0.94 | 0.89 | 0.89 |
time (sec) |
N/A | 0.276 | 0.005 | 0.083 | 0.108 | 0.074 | 0.063 | 0.122 | 0.145 | 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 | 44 | 44 | 44 | 38 | 37 | 37 | 48 | 38 | 36 | 49 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.84 | 0.84 | 1.09 | 0.86 | 0.82 | 1.11 |
time (sec) |
N/A | 0.351 | 0.008 | 0.099 | 0.126 | 0.085 | 0.098 | 0.123 | 0.208 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 113 | 98 | 97 | 97 | 117 | 97 | 99 | 97 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.86 | 0.86 | 1.04 | 0.86 | 0.88 | 0.86 |
time (sec) |
N/A | 0.512 | 0.004 | 0.126 | 0.031 | 0.083 | 0.033 | 0.119 | 0.169 | 5.669 |
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 | 88 | 88 | 88 | 75 | 74 | 74 | 90 | 74 | 75 | 74 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.84 | 0.84 | 1.02 | 0.84 | 0.85 | 0.84 |
time (sec) |
N/A | 0.426 | 0.003 | 0.120 | 0.032 | 0.076 | 0.029 | 0.123 | 0.152 | 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 | 60 | 60 | 60 | 51 | 50 | 50 | 58 | 50 | 51 | 50 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.83 | 0.83 | 0.97 | 0.83 | 0.85 | 0.83 |
time (sec) |
N/A | 0.374 | 0.002 | 0.105 | 0.033 | 0.074 | 0.025 | 0.122 | 0.154 | 0.030 |
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 | 14 | 14 | 12 | 11 | 10 | 10 | 8 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 0.86 | 0.79 | 0.71 | 0.71 | 0.57 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.253 | 0.001 | 0.093 | 0.033 | 0.076 | 0.038 | 0.125 | 0.149 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 156 | 124 | 32 | 135 | 1931 | 76 | 141 | 151 | 127 |
N.S. |
1 | 0.97 | 0.77 | 0.20 | 0.84 | 11.99 | 0.47 | 0.88 | 0.94 | 0.79 |
time (sec) |
N/A | 0.600 | 0.040 | 0.102 | 0.110 | 0.844 | 0.490 | 0.128 | 0.152 | 5.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 191 | 180 | 65 | 169 | 2088 | 105 | 174 | 351 | 169 |
N.S. |
1 | 1.01 | 0.95 | 0.34 | 0.89 | 11.05 | 0.56 | 0.92 | 1.86 | 0.89 |
time (sec) |
N/A | 0.709 | 0.113 | 0.105 | 0.130 | 0.877 | 0.679 | 0.139 | 0.156 | 5.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 54 | 38 | 37 | 37 | 44 | 38 | 36 | 49 |
N.S. |
1 | 1.00 | 1.26 | 0.88 | 0.86 | 0.86 | 1.02 | 0.88 | 0.84 | 1.14 |
time (sec) |
N/A | 0.449 | 0.011 | 0.092 | 0.111 | 0.084 | 0.094 | 0.119 | 0.153 | 5.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 54 | 36 | 37 | 37 | 46 | 38 | 36 | 51 |
N.S. |
1 | 1.00 | 1.17 | 0.78 | 0.80 | 0.80 | 1.00 | 0.83 | 0.78 | 1.11 |
time (sec) |
N/A | 0.435 | 0.009 | 0.087 | 0.116 | 0.098 | 0.127 | 0.121 | 0.149 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 585 | 594 | 78 | 786 | 0 | 117 | 265 | 0 | 152 | 0 |
N.S. |
1 | 1.02 | 0.13 | 1.34 | 0.00 | 0.20 | 0.45 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.338 | 7.489 | 0.671 | 0.000 | 0.099 | 4.193 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 556 | 562 | 76 | 762 | 0 | 93 | 170 | 0 | 112 | 0 |
N.S. |
1 | 1.01 | 0.14 | 1.37 | 0.00 | 0.17 | 0.31 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 1.159 | 6.789 | 0.664 | 0.000 | 0.102 | 2.830 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 525 | 530 | 75 | 744 | 0 | 69 | 163 | 0 | 76 | 0 |
N.S. |
1 | 1.01 | 0.14 | 1.42 | 0.00 | 0.13 | 0.31 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.015 | 5.413 | 0.632 | 0.000 | 0.098 | 2.233 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 490 | 495 | 75 | 720 | 0 | 43 | 78 | 0 | 46 | 0 |
N.S. |
1 | 1.01 | 0.15 | 1.47 | 0.00 | 0.09 | 0.16 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.877 | 10.031 | 0.539 | 0.000 | 0.104 | 2.441 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 522 | 527 | 96 | 765 | 0 | 94 | 163 | 0 | 68 | 0 |
N.S. |
1 | 1.01 | 0.18 | 1.47 | 0.00 | 0.18 | 0.31 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.988 | 10.046 | 0.565 | 0.000 | 0.144 | 5.094 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 554 | 565 | 123 | 809 | 0 | 155 | 163 | 0 | 90 | 0 |
N.S. |
1 | 1.02 | 0.22 | 1.46 | 0.00 | 0.28 | 0.29 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.134 | 10.076 | 0.574 | 0.000 | 0.096 | 16.500 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 581 | 600 | 138 | 853 | 0 | 214 | 163 | 0 | 112 | 0 |
N.S. |
1 | 1.03 | 0.24 | 1.47 | 0.00 | 0.37 | 0.28 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 1.260 | 10.089 | 0.576 | 0.000 | 0.100 | 49.480 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 590 | 594 | 135 | 785 | 0 | 87 | 187 | 0 | 141 | 0 |
N.S. |
1 | 1.01 | 0.23 | 1.33 | 0.00 | 0.15 | 0.32 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 1.487 | 10.102 | 0.730 | 0.000 | 0.128 | 2.293 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 575 | 589 | 130 | 821 | 0 | 153 | 189 | 0 | 360 | 0 |
N.S. |
1 | 1.02 | 0.23 | 1.43 | 0.00 | 0.27 | 0.33 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 1.306 | 10.093 | 0.562 | 0.000 | 0.100 | 7.406 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 624 | 632 | 170 | 861 | 0 | 261 | 209 | 0 | 677 | 0 |
N.S. |
1 | 1.01 | 0.27 | 1.38 | 0.00 | 0.42 | 0.33 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 1.387 | 10.139 | 0.612 | 0.000 | 0.101 | 60.202 | 0.000 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 672 | 684 | 196 | 921 | 0 | 373 | 0 | 0 | 1082 | 0 |
N.S. |
1 | 1.02 | 0.29 | 1.37 | 0.00 | 0.56 | 0.00 | 0.00 | 1.61 | 0.00 |
time (sec) |
N/A | 1.590 | 10.202 | 0.638 | 0.000 | 0.120 | 0.000 | 0.000 | 0.405 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 230 | 47 | 47 | 0 | 21 | 92 | 0 | 53 | 312 |
N.S. |
1 | 1.00 | 0.20 | 0.20 | 0.00 | 0.09 | 0.40 | 0.00 | 0.23 | 1.36 |
time (sec) |
N/A | 0.537 | 10.026 | 0.296 | 0.000 | 0.088 | 0.957 | 0.000 | 0.157 | 0.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 43 | 41 | 0 | 23 | 97 | 0 | 62 | 342 |
N.S. |
1 | 1.00 | 0.17 | 0.16 | 0.00 | 0.09 | 0.38 | 0.00 | 0.24 | 1.33 |
time (sec) |
N/A | 0.574 | 10.035 | 0.306 | 0.000 | 0.110 | 1.377 | 0.000 | 0.154 | 5.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 63 | 95 | 0 | 21 | 82 | 0 | 55 | 326 |
N.S. |
1 | 1.00 | 0.44 | 0.66 | 0.00 | 0.15 | 0.57 | 0.00 | 0.38 | 2.26 |
time (sec) |
N/A | 0.386 | 10.027 | 0.268 | 0.000 | 0.155 | 1.392 | 0.000 | 0.156 | 5.790 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 67 | 52 | 0 | 23 | 99 | 0 | 56 | 360 |
N.S. |
1 | 1.00 | 0.50 | 0.39 | 0.00 | 0.17 | 0.73 | 0.00 | 0.41 | 2.67 |
time (sec) |
N/A | 0.378 | 10.034 | 0.278 | 0.000 | 0.102 | 1.199 | 0.000 | 0.155 | 5.903 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 468 | 468 | 90 | 1003 | 0 | 49 | 122 | 0 | 76 | 0 |
N.S. |
1 | 1.00 | 0.19 | 2.14 | 0.00 | 0.10 | 0.26 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.812 | 10.051 | 0.760 | 0.000 | 0.099 | 2.093 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 481 | 481 | 91 | 949 | 0 | 55 | 128 | 0 | 83 | 0 |
N.S. |
1 | 1.00 | 0.19 | 1.97 | 0.00 | 0.11 | 0.27 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.847 | 10.056 | 1.086 | 0.000 | 0.111 | 3.019 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 271 | 92 | 952 | 0 | 48 | 112 | 0 | 87 | 0 |
N.S. |
1 | 1.00 | 0.34 | 3.51 | 0.00 | 0.18 | 0.41 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.515 | 10.038 | 0.713 | 0.000 | 0.091 | 3.195 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 266 | 93 | 1012 | 0 | 56 | 129 | 0 | 79 | 0 |
N.S. |
1 | 1.00 | 0.35 | 3.80 | 0.00 | 0.21 | 0.48 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.515 | 10.046 | 0.657 | 0.000 | 0.094 | 2.262 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 520 | 516 | 89 | 1004 | 0 | 53 | 124 | 0 | 80 | 0 |
N.S. |
1 | 0.99 | 0.17 | 1.93 | 0.00 | 0.10 | 0.24 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.903 | 10.051 | 0.562 | 0.000 | 0.126 | 1.505 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 533 | 529 | 89 | 950 | 0 | 56 | 129 | 0 | 87 | 0 |
N.S. |
1 | 0.99 | 0.17 | 1.78 | 0.00 | 0.11 | 0.24 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.936 | 10.044 | 0.641 | 0.000 | 0.114 | 1.781 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 256 | 90 | 953 | 0 | 52 | 114 | 0 | 91 | 0 |
N.S. |
1 | 1.00 | 0.35 | 3.72 | 0.00 | 0.20 | 0.45 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.537 | 10.059 | 0.483 | 0.000 | 0.091 | 1.941 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 251 | 92 | 1013 | 0 | 57 | 131 | 0 | 82 | 0 |
N.S. |
1 | 1.00 | 0.37 | 4.04 | 0.00 | 0.23 | 0.52 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.540 | 10.033 | 0.494 | 0.000 | 0.098 | 1.559 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 49 | 48 | 0 | 21 | 92 | 0 | 54 | 313 |
N.S. |
1 | 1.00 | 0.39 | 0.38 | 0.00 | 0.17 | 0.72 | 0.00 | 0.43 | 2.46 |
time (sec) |
N/A | 0.396 | 10.024 | 0.241 | 0.000 | 0.097 | 1.032 | 0.000 | 0.196 | 0.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 142 | 45 | 42 | 0 | 23 | 97 | 0 | 61 | 343 |
N.S. |
1 | 1.00 | 0.32 | 0.30 | 0.00 | 0.16 | 0.68 | 0.00 | 0.43 | 2.42 |
time (sec) |
N/A | 0.384 | 10.020 | 0.223 | 0.000 | 0.101 | 1.463 | 0.000 | 0.200 | 5.690 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 264 | 63 | 96 | 0 | 21 | 82 | 0 | 56 | 327 |
N.S. |
1 | 1.00 | 0.24 | 0.36 | 0.00 | 0.08 | 0.31 | 0.00 | 0.21 | 1.24 |
time (sec) |
N/A | 0.592 | 10.026 | 0.204 | 0.000 | 0.125 | 1.534 | 0.000 | 0.159 | 5.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 247 | 67 | 52 | 0 | 23 | 97 | 0 | 59 | 361 |
N.S. |
1 | 1.00 | 0.27 | 0.21 | 0.00 | 0.09 | 0.39 | 0.00 | 0.24 | 1.46 |
time (sec) |
N/A | 0.558 | 10.024 | 0.210 | 0.000 | 0.106 | 1.133 | 0.000 | 0.159 | 5.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 47 | 48 | 0 | 21 | 92 | 0 | 57 | 312 |
N.S. |
1 | 1.00 | 0.37 | 0.38 | 0.00 | 0.17 | 0.73 | 0.00 | 0.45 | 2.48 |
time (sec) |
N/A | 0.371 | 10.028 | 0.219 | 0.000 | 0.111 | 1.437 | 0.000 | 0.155 | 5.563 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 43 | 42 | 0 | 23 | 97 | 0 | 62 | 342 |
N.S. |
1 | 1.00 | 0.30 | 0.29 | 0.00 | 0.16 | 0.68 | 0.00 | 0.43 | 2.39 |
time (sec) |
N/A | 0.382 | 10.015 | 0.210 | 0.000 | 0.093 | 1.356 | 0.000 | 0.158 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 263 | 63 | 96 | 0 | 21 | 82 | 0 | 55 | 326 |
N.S. |
1 | 1.00 | 0.24 | 0.37 | 0.00 | 0.08 | 0.31 | 0.00 | 0.21 | 1.24 |
time (sec) |
N/A | 0.549 | 10.019 | 0.175 | 0.000 | 0.118 | 1.046 | 0.000 | 0.158 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 248 | 67 | 52 | 0 | 23 | 97 | 0 | 56 | 360 |
N.S. |
1 | 1.00 | 0.27 | 0.21 | 0.00 | 0.09 | 0.39 | 0.00 | 0.23 | 1.45 |
time (sec) |
N/A | 0.572 | 10.019 | 0.211 | 0.000 | 0.102 | 1.437 | 0.000 | 0.155 | 5.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 256 | 90 | 1003 | 0 | 48 | 122 | 0 | 77 | 0 |
N.S. |
1 | 1.00 | 0.35 | 3.92 | 0.00 | 0.19 | 0.48 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.466 | 10.061 | 0.743 | 0.000 | 0.091 | 2.370 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 263 | 90 | 949 | 0 | 56 | 128 | 0 | 84 | 0 |
N.S. |
1 | 1.00 | 0.34 | 3.61 | 0.00 | 0.21 | 0.49 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.505 | 10.082 | 0.780 | 0.000 | 0.096 | 3.020 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 497 | 497 | 91 | 952 | 0 | 49 | 112 | 0 | 86 | 0 |
N.S. |
1 | 1.00 | 0.18 | 1.92 | 0.00 | 0.10 | 0.23 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.907 | 10.052 | 0.646 | 0.000 | 0.136 | 3.142 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 488 | 488 | 93 | 1012 | 0 | 55 | 128 | 0 | 80 | 0 |
N.S. |
1 | 1.00 | 0.19 | 2.07 | 0.00 | 0.11 | 0.26 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.868 | 10.058 | 0.686 | 0.000 | 0.096 | 2.533 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 241 | 89 | 1004 | 0 | 52 | 124 | 0 | 81 | 0 |
N.S. |
1 | 1.00 | 0.37 | 4.17 | 0.00 | 0.22 | 0.51 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.560 | 10.043 | 0.585 | 0.000 | 0.084 | 1.443 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 248 | 89 | 950 | 0 | 57 | 129 | 0 | 88 | 0 |
N.S. |
1 | 1.00 | 0.36 | 3.83 | 0.00 | 0.23 | 0.52 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.527 | 10.043 | 0.617 | 0.000 | 0.081 | 1.619 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 549 | 545 | 90 | 953 | 0 | 53 | 114 | 0 | 90 | 0 |
N.S. |
1 | 0.99 | 0.16 | 1.74 | 0.00 | 0.10 | 0.21 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.954 | 10.039 | 0.506 | 0.000 | 0.087 | 1.543 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 540 | 536 | 92 | 1013 | 0 | 56 | 129 | 0 | 83 | 0 |
N.S. |
1 | 0.99 | 0.17 | 1.88 | 0.00 | 0.10 | 0.24 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.928 | 10.033 | 0.516 | 0.000 | 0.085 | 1.460 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 490 | 495 | 75 | 720 | 0 | 43 | 78 | 0 | 46 | 0 |
N.S. |
1 | 1.01 | 0.15 | 1.47 | 0.00 | 0.09 | 0.16 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.842 | 0.014 | 0.222 | 0.000 | 0.101 | 0.995 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 503 | 508 | 75 | 681 | 0 | 47 | 82 | 0 | 50 | 0 |
N.S. |
1 | 1.01 | 0.15 | 1.35 | 0.00 | 0.09 | 0.16 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.832 | 10.027 | 0.257 | 0.000 | 0.085 | 1.073 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 515 | 522 | 76 | 683 | 0 | 43 | 73 | 0 | 54 | 0 |
N.S. |
1 | 1.01 | 0.15 | 1.33 | 0.00 | 0.08 | 0.14 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.907 | 10.024 | 0.249 | 0.000 | 0.083 | 1.110 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 508 | 513 | 78 | 726 | 0 | 47 | 83 | 0 | 49 | 0 |
N.S. |
1 | 1.01 | 0.15 | 1.43 | 0.00 | 0.09 | 0.16 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.887 | 10.024 | 0.234 | 0.000 | 0.088 | 1.096 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 247 | 42 | 33 | 0 | 18 | 61 | 0 | 38 | 373 |
N.S. |
1 | 1.00 | 0.17 | 0.13 | 0.00 | 0.07 | 0.25 | 0.00 | 0.15 | 1.52 |
time (sec) |
N/A | 0.569 | 10.021 | 0.207 | 0.000 | 0.083 | 0.766 | 0.000 | 0.154 | 0.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 272 | 38 | 29 | 0 | 18 | 65 | 0 | 44 | 406 |
N.S. |
1 | 1.00 | 0.14 | 0.11 | 0.00 | 0.07 | 0.24 | 0.00 | 0.16 | 1.50 |
time (sec) |
N/A | 0.587 | 10.023 | 0.204 | 0.000 | 0.106 | 0.879 | 0.000 | 0.153 | 5.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 278 | 58 | 65 | 0 | 18 | 56 | 0 | 38 | 374 |
N.S. |
1 | 1.01 | 0.21 | 0.24 | 0.00 | 0.07 | 0.20 | 0.00 | 0.14 | 1.36 |
time (sec) |
N/A | 0.591 | 10.034 | 0.214 | 0.000 | 0.112 | 0.820 | 0.000 | 0.154 | 5.625 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 262 | 62 | 36 | 0 | 18 | 66 | 0 | 41 | 405 |
N.S. |
1 | 1.00 | 0.24 | 0.14 | 0.00 | 0.07 | 0.25 | 0.00 | 0.16 | 1.55 |
time (sec) |
N/A | 0.584 | 10.056 | 0.211 | 0.000 | 0.100 | 0.889 | 0.000 | 0.155 | 5.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 189 | 100 | 0 | 0 | 0 | 124 | 0 | 120 | 0 |
N.S. |
1 | 0.98 | 0.52 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.732 | 6.589 | 0.000 | 0.000 | 0.000 | 1.908 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 220 | 300 | 0 | 0 | 0 | 119 | 0 | 46 | 0 |
N.S. |
1 | 1.35 | 1.84 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.530 | 10.385 | 0.000 | 0.000 | 0.000 | 1.742 | 0.000 | 0.176 | 0.000 |