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 | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 0 | 37 | 0 | 26 | 3753 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 0.00 | 1.54 | 0.00 | 1.08 | 156.38 | 1.08 |
time (sec) |
N/A | 0.305 | 36.293 | 1.848 | 0.000 | 0.100 | 0.000 | 0.161 | 0.727 | 25.845 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 35 | 20 | 26 | 69 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.46 | 0.83 | 1.08 | 2.88 | 1.08 |
time (sec) |
N/A | 0.310 | 0.283 | 0.265 | 0.136 | 0.072 | 14.146 | 0.120 | 0.154 | 25.953 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 24 | 24 | 19 | 24 | 41 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.86 | 1.09 | 1.86 | 1.09 |
time (sec) |
N/A | 0.291 | 0.227 | 0.083 | 0.134 | 0.079 | 5.816 | 0.117 | 0.145 | 25.985 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 26 | 20 | 26 | 36 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.83 | 1.08 | 1.50 | 1.08 |
time (sec) |
N/A | 0.312 | 8.631 | 0.899 | 0.101 | 0.085 | 103.270 | 0.117 | 0.157 | 25.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 37 | 0 | 26 | 59 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.54 | 0.00 | 1.08 | 2.46 | 1.08 |
time (sec) |
N/A | 0.308 | 11.939 | 0.908 | 0.108 | 0.078 | 0.000 | 0.120 | 0.180 | 26.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 152 | 35 | 22 | 26 | 69 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 6.33 | 1.46 | 0.92 | 1.08 | 2.88 | 1.08 |
time (sec) |
N/A | 0.304 | 0.660 | 0.091 | 0.155 | 0.093 | 21.703 | 0.120 | 0.156 | 26.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 104 | 24 | 20 | 24 | 41 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 4.73 | 1.09 | 0.91 | 1.09 | 1.86 | 1.09 |
time (sec) |
N/A | 0.284 | 0.386 | 0.006 | 0.157 | 0.084 | 8.762 | 0.114 | 0.164 | 26.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 159 | 26 | 22 | 26 | 40 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 6.62 | 1.08 | 0.92 | 1.08 | 1.67 | 1.08 |
time (sec) |
N/A | 0.309 | 10.743 | 0.007 | 0.113 | 0.072 | 140.391 | 0.124 | 0.156 | 26.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 215 | 37 | 0 | 26 | 65 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 8.96 | 1.54 | 0.00 | 1.08 | 2.71 | 1.08 |
time (sec) |
N/A | 0.307 | 12.824 | 0.089 | 0.112 | 0.081 | 0.000 | 0.130 | 0.251 | 25.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 146 | 170 | 140 | 132 | 152 | 0 | 399 | 164 | 127 |
N.S. |
1 | 1.03 | 1.20 | 0.99 | 0.93 | 1.07 | 0.00 | 2.81 | 1.15 | 0.89 |
time (sec) |
N/A | 0.658 | 0.056 | 3.322 | 0.032 | 0.080 | 0.000 | 0.131 | 0.165 | 26.029 |
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 | 119 | 124 | 140 | 117 | 108 | 128 | 156 | 269 | 138 | 103 |
N.S. |
1 | 1.04 | 1.18 | 0.98 | 0.91 | 1.08 | 1.31 | 2.26 | 1.16 | 0.87 |
time (sec) |
N/A | 0.596 | 0.035 | 2.252 | 0.032 | 0.073 | 63.909 | 0.130 | 0.144 | 25.942 |
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 | 94 | 97 | 98 | 127 | 99 | 99 | 126 | 143 | 112 | 78 |
N.S. |
1 | 1.03 | 1.04 | 1.35 | 1.05 | 1.05 | 1.34 | 1.52 | 1.19 | 0.83 |
time (sec) |
N/A | 0.462 | 0.036 | 1.990 | 0.028 | 0.075 | 16.937 | 0.121 | 0.154 | 25.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 75 | 80 | 157 | 0 | 0 | 0 | 0 | 105 | 0 |
N.S. |
1 | 0.91 | 0.98 | 1.91 | 0.00 | 0.00 | 0.00 | 0.00 | 1.28 | 0.00 |
time (sec) |
N/A | 0.497 | 0.025 | 0.813 | 0.000 | 0.000 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 89 | 92 | 155 | 0 | 0 | 0 | 0 | 181 | 0 |
N.S. |
1 | 0.96 | 0.99 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 1.95 | 0.00 |
time (sec) |
N/A | 0.525 | 0.032 | 1.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 100 | 105 | 88 | 77 | 97 | 167 | 209 | 120 | 85 |
N.S. |
1 | 1.08 | 1.13 | 0.95 | 0.83 | 1.04 | 1.80 | 2.25 | 1.29 | 0.91 |
time (sec) |
N/A | 0.597 | 0.044 | 1.157 | 0.036 | 0.090 | 78.228 | 0.125 | 0.172 | 26.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 118 | 134 | 108 | 104 | 129 | 0 | 316 | 149 | 113 |
N.S. |
1 | 0.94 | 1.07 | 0.86 | 0.83 | 1.03 | 0.00 | 2.53 | 1.19 | 0.90 |
time (sec) |
N/A | 0.582 | 0.069 | 1.809 | 0.030 | 0.092 | 0.000 | 0.122 | 0.254 | 26.322 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 143 | 162 | 131 | 132 | 155 | 0 | 379 | 175 | 134 |
N.S. |
1 | 0.97 | 1.09 | 0.89 | 0.89 | 1.05 | 0.00 | 2.56 | 1.18 | 0.91 |
time (sec) |
N/A | 0.638 | 0.108 | 3.219 | 0.029 | 0.086 | 0.000 | 0.126 | 0.171 | 26.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 154 | 118 | 118 | 0 | 300 | 320 | 121 | 142 | 126 |
N.S. |
1 | 1.00 | 0.77 | 0.77 | 0.00 | 1.95 | 2.08 | 0.79 | 0.92 | 0.82 |
time (sec) |
N/A | 0.531 | 0.065 | 2.533 | 0.000 | 0.106 | 32.765 | 0.121 | 0.145 | 26.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 117 | 89 | 0 | 220 | 260 | 94 | 113 | 97 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.00 | 1.88 | 2.22 | 0.80 | 0.97 | 0.83 |
time (sec) |
N/A | 0.446 | 0.031 | 0.881 | 0.000 | 0.092 | 8.479 | 0.128 | 0.144 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 93 | 62 | 73 | 0 | 199 | 204 | 68 | 100 | 83 |
N.S. |
1 | 1.29 | 0.86 | 1.01 | 0.00 | 2.76 | 2.83 | 0.94 | 1.39 | 1.15 |
time (sec) |
N/A | 0.431 | 0.055 | 1.454 | 0.000 | 0.124 | 16.414 | 0.120 | 0.153 | 26.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 96 | 77 | 0 | 191 | 901 | 88 | 105 | 65 |
N.S. |
1 | 1.00 | 0.89 | 0.71 | 0.00 | 1.77 | 8.34 | 0.81 | 0.97 | 0.60 |
time (sec) |
N/A | 0.471 | 0.043 | 1.211 | 0.000 | 0.125 | 39.139 | 0.119 | 0.160 | 26.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 101 | 96 | 0 | 259 | 1134 | 117 | 132 | 88 |
N.S. |
1 | 1.00 | 0.72 | 0.69 | 0.00 | 1.85 | 8.10 | 0.84 | 0.94 | 0.63 |
time (sec) |
N/A | 0.496 | 0.012 | 2.404 | 0.000 | 0.093 | 156.924 | 0.123 | 0.158 | 26.358 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 250 | 205 | 253 | 223 | 262 | 0 | 753 | 296 | 224 |
N.S. |
1 | 1.00 | 0.82 | 1.01 | 0.89 | 1.04 | 0.00 | 3.00 | 1.18 | 0.89 |
time (sec) |
N/A | 0.933 | 0.197 | 6.712 | 0.032 | 0.086 | 0.000 | 0.144 | 0.173 | 26.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 209 | 257 | 211 | 185 | 224 | 0 | 544 | 252 | 184 |
N.S. |
1 | 1.00 | 1.22 | 1.00 | 0.88 | 1.07 | 0.00 | 2.59 | 1.20 | 0.88 |
time (sec) |
N/A | 0.838 | 0.091 | 4.329 | 0.034 | 0.111 | 0.000 | 0.134 | 0.149 | 25.773 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 123 | 135 | 206 | 152 | 180 | 235 | 340 | 208 | 142 |
N.S. |
1 | 0.99 | 1.09 | 1.66 | 1.23 | 1.45 | 1.90 | 2.74 | 1.68 | 1.15 |
time (sec) |
N/A | 0.547 | 0.114 | 3.073 | 0.033 | 0.075 | 62.820 | 0.128 | 0.148 | 25.860 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 152 | 121 | 209 | 0 | 0 | 0 | 0 | 194 | 0 |
N.S. |
1 | 0.99 | 0.79 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.661 | 0.089 | 1.568 | 0.000 | 0.000 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 134 | 133 | 211 | 0 | 0 | 0 | 0 | 250 | 0 |
N.S. |
1 | 0.99 | 0.99 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 | 1.85 | 0.00 |
time (sec) |
N/A | 0.645 | 0.082 | 2.741 | 0.000 | 0.000 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 174 | 152 | 208 | 0 | 0 | 0 | 0 | 206 | 0 |
N.S. |
1 | 1.01 | 0.88 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.726 | 0.122 | 2.839 | 0.000 | 0.000 | 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 | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 134 | 141 | 159 | 137 | 183 | 0 | 464 | 225 | 151 |
N.S. |
1 | 1.03 | 1.08 | 1.22 | 1.05 | 1.41 | 0.00 | 3.57 | 1.73 | 1.16 |
time (sec) |
N/A | 0.663 | 0.126 | 2.193 | 0.036 | 0.083 | 0.000 | 0.137 | 0.161 | 25.783 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 208 | 184 | 193 | 183 | 230 | 0 | 604 | 271 | 190 |
N.S. |
1 | 0.96 | 0.85 | 0.89 | 0.85 | 1.06 | 0.00 | 2.80 | 1.25 | 0.88 |
time (sec) |
N/A | 0.831 | 0.169 | 3.527 | 0.033 | 0.112 | 0.000 | 0.135 | 0.146 | 25.795 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 244 | 215 | 230 | 223 | 268 | 0 | 699 | 315 | 225 |
N.S. |
1 | 0.96 | 0.85 | 0.91 | 0.88 | 1.06 | 0.00 | 2.76 | 1.25 | 0.89 |
time (sec) |
N/A | 0.912 | 0.201 | 5.785 | 0.034 | 0.096 | 0.000 | 0.134 | 0.146 | 25.835 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 278 | 188 | 211 | 0 | 492 | 559 | 215 | 259 | 235 |
N.S. |
1 | 1.00 | 0.68 | 0.76 | 0.00 | 1.77 | 2.01 | 0.77 | 0.93 | 0.85 |
time (sec) |
N/A | 0.774 | 0.155 | 5.363 | 0.000 | 0.090 | 125.207 | 0.127 | 0.148 | 25.796 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 221 | 151 | 167 | 0 | 404 | 478 | 174 | 212 | 193 |
N.S. |
1 | 1.00 | 0.68 | 0.76 | 0.00 | 1.83 | 2.16 | 0.79 | 0.96 | 0.87 |
time (sec) |
N/A | 0.619 | 0.066 | 2.328 | 0.000 | 0.092 | 33.368 | 0.122 | 0.166 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 112 | 127 | 0 | 366 | 400 | 136 | 194 | 180 |
N.S. |
1 | 1.00 | 0.63 | 0.71 | 0.00 | 2.06 | 2.25 | 0.76 | 1.09 | 1.01 |
time (sec) |
N/A | 0.589 | 0.149 | 3.434 | 0.000 | 0.089 | 61.974 | 0.127 | 0.228 | 25.712 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 113 | 125 | 0 | 350 | 381 | 135 | 188 | 108 |
N.S. |
1 | 1.00 | 0.67 | 0.74 | 0.00 | 2.07 | 2.25 | 0.80 | 1.11 | 0.64 |
time (sec) |
N/A | 0.591 | 0.134 | 3.800 | 0.000 | 0.116 | 76.240 | 0.123 | 0.156 | 25.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 156 | 134 | 0 | 351 | 1603 | 163 | 194 | 115 |
N.S. |
1 | 1.00 | 0.78 | 0.67 | 0.00 | 1.76 | 8.02 | 0.82 | 0.97 | 0.58 |
time (sec) |
N/A | 0.638 | 0.071 | 3.660 | 0.000 | 0.118 | 159.420 | 0.130 | 0.143 | 25.835 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 252 | 161 | 167 | 0 | 429 | 0 | 207 | 239 | 149 |
N.S. |
1 | 1.00 | 0.64 | 0.66 | 0.00 | 1.70 | 0.00 | 0.82 | 0.95 | 0.59 |
time (sec) |
N/A | 0.726 | 0.036 | 4.610 | 0.000 | 0.112 | 0.000 | 0.132 | 0.169 | 25.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 181 | 143 | 410 | 0 | 0 | 0 | 0 | 261 | 0 |
N.S. |
1 | 0.96 | 0.76 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 0.775 | 0.116 | 4.696 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 107 | 91 | 358 | 0 | 0 | 0 | 0 | 173 | 0 |
N.S. |
1 | 0.96 | 0.81 | 3.20 | 0.00 | 0.00 | 0.00 | 0.00 | 1.54 | 0.00 |
time (sec) |
N/A | 0.612 | 0.048 | 2.876 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 68 | 64 | 301 | 138 | 0 | 0 | 0 | 113 | 0 |
N.S. |
1 | 0.97 | 0.91 | 4.30 | 1.97 | 0.00 | 0.00 | 0.00 | 1.61 | 0.00 |
time (sec) |
N/A | 0.554 | 0.011 | 3.599 | 0.034 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 113 | 92 | 420 | 140 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.95 | 0.77 | 3.53 | 1.18 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.647 | 0.044 | 2.387 | 0.157 | 0.000 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 168 | 168 | 471 | 178 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.95 | 0.95 | 2.68 | 1.01 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.755 | 0.066 | 4.079 | 0.163 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 667 | 667 | 697 | 616 | 0 | 0 | 0 | 0 | 148 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.632 | 0.676 | 2.835 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 585 | 585 | 619 | 525 | 0 | 0 | 0 | 0 | 75 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.384 | 0.413 | 2.193 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 533 | 506 | 564 | 449 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.95 | 1.06 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.207 | 0.110 | 1.569 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 581 | 581 | 613 | 526 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.390 | 0.417 | 3.103 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 651 | 651 | 670 | 602 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.508 | 0.572 | 4.935 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 191 | 166 | 442 | 0 | 0 | 0 | 0 | 1132 | 0 |
N.S. |
1 | 0.96 | 0.83 | 2.22 | 0.00 | 0.00 | 0.00 | 0.00 | 5.69 | 0.00 |
time (sec) |
N/A | 0.815 | 0.236 | 4.123 | 0.000 | 0.000 | 0.000 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 145 | 131 | 381 | 0 | 0 | 0 | 0 | 897 | 0 |
N.S. |
1 | 0.94 | 0.85 | 2.46 | 0.00 | 0.00 | 0.00 | 0.00 | 5.79 | 0.00 |
time (sec) |
N/A | 0.682 | 0.088 | 4.010 | 0.000 | 0.000 | 0.000 | 0.000 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 77 | 73 | 75 | 74 | 91 | 0 | 126 | 140 | 80 |
N.S. |
1 | 0.93 | 0.88 | 0.90 | 0.89 | 1.10 | 0.00 | 1.52 | 1.69 | 0.96 |
time (sec) |
N/A | 0.417 | 0.054 | 2.986 | 0.028 | 0.118 | 0.000 | 0.127 | 0.161 | 17.977 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 187 | 170 | 492 | 197 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.93 | 0.85 | 2.45 | 0.98 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.812 | 0.106 | 2.876 | 0.162 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 248 | 224 | 535 | 295 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.99 | 0.89 | 2.13 | 1.18 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.922 | 0.171 | 9.009 | 0.088 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 802 | 802 | 915 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.656 | 2.070 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 746 | 746 | 850 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.439 | 1.330 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 751 | 751 | 877 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.807 | 0.718 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 803 | 803 | 939 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.662 | 1.780 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 168 | 128 | 264 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.03 | 0.79 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.923 | 0.057 | 2.510 | 0.000 | 0.000 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 222 | 159 | 194 | 208 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.93 | 0.67 | 0.81 | 0.87 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.920 | 0.136 | 1.866 | 0.113 | 0.000 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 245 | 335 | 282 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.13 | 1.54 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.897 | 0.148 | 1.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 127 | 118 | 267 | 0 | 148 | 0 | 0 | 153 | 0 |
N.S. |
1 | 0.88 | 0.82 | 1.85 | 0.00 | 1.03 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.621 | 0.208 | 6.833 | 0.000 | 0.115 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 110 | 100 | 249 | 0 | 133 | 0 | 0 | 136 | 0 |
N.S. |
1 | 0.89 | 0.81 | 2.01 | 0.00 | 1.07 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.581 | 0.143 | 6.438 | 0.000 | 0.122 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 75 | 68 | 223 | 0 | 100 | 0 | 0 | 110 | 0 |
N.S. |
1 | 0.90 | 0.82 | 2.69 | 0.00 | 1.20 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.519 | 0.064 | 5.127 | 0.000 | 0.092 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 91 | 90 | 242 | 0 | 114 | 0 | 0 | 189 | 0 |
N.S. |
1 | 0.94 | 0.93 | 2.49 | 0.00 | 1.18 | 0.00 | 0.00 | 1.95 | 0.00 |
time (sec) |
N/A | 0.580 | 0.098 | 6.838 | 0.000 | 0.099 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 117 | 104 | 267 | 0 | 150 | 0 | 0 | 197 | 0 |
N.S. |
1 | 0.93 | 0.83 | 2.12 | 0.00 | 1.19 | 0.00 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 0.637 | 0.210 | 6.708 | 0.000 | 0.084 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 327 | 286 | 209 | 436 | 0 | 291 | 0 | 0 | 319 | 0 |
N.S. |
1 | 0.87 | 0.64 | 1.33 | 0.00 | 0.89 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.955 | 0.318 | 11.540 | 0.000 | 0.097 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 222 | 171 | 375 | 0 | 242 | 0 | 0 | 263 | 0 |
N.S. |
1 | 0.87 | 0.67 | 1.48 | 0.00 | 0.95 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.782 | 0.271 | 11.435 | 0.000 | 0.110 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 156 | 124 | 314 | 0 | 192 | 0 | 0 | 203 | 0 |
N.S. |
1 | 0.89 | 0.70 | 1.78 | 0.00 | 1.09 | 0.00 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.661 | 0.180 | 6.934 | 0.000 | 0.087 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 180 | 160 | 334 | 0 | 210 | 0 | 0 | 275 | 0 |
N.S. |
1 | 0.93 | 0.83 | 1.73 | 0.00 | 1.09 | 0.00 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.782 | 0.325 | 13.674 | 0.000 | 0.116 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 235 | 188 | 396 | 0 | 265 | 0 | 0 | 341 | 0 |
N.S. |
1 | 0.91 | 0.73 | 1.54 | 0.00 | 1.03 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.897 | 0.573 | 12.272 | 0.000 | 0.095 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 252 | 0 | 478 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.95 | 0.00 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.078 | 0.000 | 6.312 | 0.000 | 0.000 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 113 | 92 | 323 | 154 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.93 | 0.76 | 2.67 | 1.27 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.688 | 0.094 | 3.611 | 0.118 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 68 | 64 | 243 | 112 | 0 | 0 | 0 | 146 | 0 |
N.S. |
1 | 0.97 | 0.91 | 3.47 | 1.60 | 0.00 | 0.00 | 0.00 | 2.09 | 0.00 |
time (sec) |
N/A | 0.667 | 0.029 | 6.094 | 0.125 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 213 | 0 | 398 | 0 | 0 | 0 | 0 | 140 | 0 |
N.S. |
1 | 0.96 | 0.00 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 1.050 | 0.000 | 18.708 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 419 | 393 | 0 | 635 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 0.94 | 0.00 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.342 | 0.000 | 22.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 187 | 171 | 414 | 233 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 0.92 | 0.84 | 2.03 | 1.14 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.836 | 0.176 | 6.136 | 0.120 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 145 | 433 | 356 | 209 | 0 | 0 | 0 | 1267 | 0 |
N.S. |
1 | 0.93 | 2.78 | 2.28 | 1.34 | 0.00 | 0.00 | 0.00 | 8.12 | 0.00 |
time (sec) |
N/A | 0.781 | 1.462 | 16.210 | 0.118 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 377 | 357 | 0 | 561 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.00 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.379 | 0.000 | 118.098 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 26 | 26 | 23 | 106 | 25 | 0 | 0 | 233 | 0 |
N.S. |
1 | 1.04 | 1.04 | 0.92 | 4.24 | 1.00 | 0.00 | 0.00 | 9.32 | 0.00 |
time (sec) |
N/A | 0.543 | 0.084 | 4.539 | 0.119 | 0.112 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 26 | 26 | 23 | 109 | 25 | 0 | 0 | 233 | 21 |
N.S. |
1 | 1.04 | 1.04 | 0.92 | 4.36 | 1.00 | 0.00 | 0.00 | 9.32 | 0.84 |
time (sec) |
N/A | 0.497 | 0.004 | 6.309 | 0.040 | 0.100 | 0.000 | 0.000 | 0.165 | 14.889 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 27 | 34 | 24 | 0 | 30 | 0 | 0 | 252 | 0 |
N.S. |
1 | 1.04 | 1.31 | 0.92 | 0.00 | 1.15 | 0.00 | 0.00 | 9.69 | 0.00 |
time (sec) |
N/A | 0.537 | 0.087 | 8.892 | 0.000 | 0.075 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 0 | 42 | 0 | 31 | 496 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.00 | 1.45 | 0.00 | 1.07 | 17.10 | 1.07 |
time (sec) |
N/A | 0.408 | 0.404 | 0.319 | 0.000 | 0.079 | 0.000 | 3.833 | 0.181 | 14.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 27 | 0 | 40 | 0 | 29 | 492 | 29 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.00 | 1.48 | 0.00 | 1.07 | 18.22 | 1.07 |
time (sec) |
N/A | 0.395 | 0.281 | 0.319 | 0.000 | 0.096 | 0.000 | 2.675 | 0.178 | 14.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 0 | 47 | 0 | 31 | 514 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.00 | 1.62 | 0.00 | 1.07 | 17.72 | 1.07 |
time (sec) |
N/A | 0.456 | 0.464 | 0.631 | 0.000 | 0.106 | 0.000 | 2.493 | 0.189 | 14.766 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 31 | 0 | 49 | 0 | 33 | 532 | 33 |
N.S. |
1 | 1.00 | 1.07 | 1.07 | 0.00 | 1.69 | 0.00 | 1.14 | 18.34 | 1.14 |
time (sec) |
N/A | 0.459 | 0.415 | 0.547 | 0.000 | 0.098 | 0.000 | 2.464 | 0.226 | 14.747 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 0 | 31 | 0 | 31 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.00 | 1.07 | 0.00 | 1.07 | 1.07 | 1.07 |
time (sec) |
N/A | 0.406 | 1.487 | 0.872 | 0.000 | 0.087 | 0.000 | 2.537 | 0.264 | 15.843 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 27 | 0 | 29 | 22 | 29 | 29 | 29 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.00 | 1.07 | 0.81 | 1.07 | 1.07 | 1.07 |
time (sec) |
N/A | 0.397 | 1.254 | 1.012 | 0.000 | 0.120 | 8.911 | 2.511 | 0.183 | 15.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 0 | 32 | 0 | 31 | 285 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.00 | 1.10 | 0.00 | 1.07 | 9.83 | 1.07 |
time (sec) |
N/A | 0.528 | 1.598 | 1.463 | 0.000 | 0.103 | 0.000 | 2.515 | 0.187 | 15.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 31 | 0 | 36 | 0 | 33 | 279 | 33 |
N.S. |
1 | 1.00 | 1.07 | 1.07 | 0.00 | 1.24 | 0.00 | 1.14 | 9.62 | 1.14 |
time (sec) |
N/A | 0.793 | 0.334 | 1.429 | 0.000 | 0.076 | 0.000 | 2.537 | 0.200 | 15.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 88 | 75 | 66 | 0 | 76 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.28 | 1.09 | 0.96 | 0.00 | 1.10 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.735 | 0.069 | 2.611 | 0.000 | 0.076 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 12 | 34 | 9 | 59 | 11 | 0 | 68 | 14 | 8 |
N.S. |
1 | 1.50 | 4.25 | 1.12 | 7.38 | 1.38 | 0.00 | 8.50 | 1.75 | 1.00 |
time (sec) |
N/A | 0.281 | 0.006 | 1.117 | 0.030 | 0.089 | 0.000 | 0.146 | 0.166 | 15.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 76 | 69 | 15 | 0 | 0 | 16 | 10 |
N.S. |
1 | 1.00 | 1.00 | 6.33 | 5.75 | 1.25 | 0.00 | 0.00 | 1.33 | 0.83 |
time (sec) |
N/A | 0.305 | 0.006 | 0.549 | 0.028 | 0.064 | 0.000 | 0.000 | 0.154 | 15.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 0 | 61 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 0.00 | 4.36 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.311 | 0.008 | 5.154 | 0.000 | 0.089 | 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 | F | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 36 | 34 | 67 | 0 | 0 | 204 | 16 | 37 |
N.S. |
1 | 1.00 | 1.03 | 0.97 | 1.91 | 0.00 | 0.00 | 5.83 | 0.46 | 1.06 |
time (sec) |
N/A | 0.450 | 0.007 | 2.138 | 0.029 | 0.000 | 0.000 | 0.219 | 0.165 | 15.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 40 | 108 | 77 | 0 | 0 | 0 | 18 | 33 |
N.S. |
1 | 1.00 | 1.03 | 2.77 | 1.97 | 0.00 | 0.00 | 0.00 | 0.46 | 0.85 |
time (sec) |
N/A | 0.428 | 0.007 | 0.474 | 0.032 | 0.000 | 0.000 | 0.000 | 0.154 | 15.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 43 | 44 | 44 | 0 | 67 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.91 | 0.94 | 0.94 | 0.00 | 1.43 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.441 | 0.021 | 6.906 | 0.000 | 0.076 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 111 | 115 | 114 | 124 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.06 | 1.10 | 1.09 | 1.18 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.733 | 0.057 | 10.180 | 0.033 | 0.000 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 240 | 228 | 230 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.136 | 0.125 | 4.626 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 24 | 24 | 14 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.64 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.327 | 0.562 | 1.090 | 0.099 | 0.072 | 24.900 | 0.136 | 0.158 | 15.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 82 | 0 | 0 | 0 | 0 | 0 | 166 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.80 | 0.00 |
time (sec) |
N/A | 0.412 | 0.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 156 | 157 | 0 | 128 | 148 | 155 | 348 | 150 | 137 |
N.S. |
1 | 0.94 | 0.95 | 0.00 | 0.77 | 0.89 | 0.93 | 2.10 | 0.90 | 0.83 |
time (sec) |
N/A | 0.572 | 0.141 | 0.000 | 0.034 | 0.138 | 6.947 | 0.124 | 0.158 | 15.233 |