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 | B | A | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 24 | 23 | 47 | 29 | 44 | 0 | 17 | 25 |
N.S. |
1 | 1.00 | 0.96 | 0.92 | 1.88 | 1.16 | 1.76 | 0.00 | 0.68 | 1.00 |
time (sec) |
N/A | 0.231 | 0.006 | 0.176 | 0.039 | 0.111 | 0.512 | 0.000 | 0.160 | 22.593 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 43 | 48 | 55 | 82 | 48 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.63 | 0.71 | 0.81 | 1.21 | 0.71 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.289 | 0.074 | 0.178 | 0.047 | 0.087 | 0.000 | 0.000 | 0.141 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 56 | 49 | 75 | 79 | 66 | 0 | 0 | 75 | 0 |
N.S. |
1 | 0.62 | 0.54 | 0.83 | 0.88 | 0.73 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.308 | 0.005 | 0.180 | 0.041 | 0.103 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 72 | 70 | 91 | 98 | 83 | 0 | 0 | 91 | 0 |
N.S. |
1 | 0.61 | 0.59 | 0.77 | 0.83 | 0.70 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.348 | 0.006 | 0.182 | 0.039 | 0.110 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 54 | 38 | 40 | 39 | 58 | 180 | 0 | 40 | 44 |
N.S. |
1 | 0.83 | 0.58 | 0.62 | 0.60 | 0.89 | 2.77 | 0.00 | 0.62 | 0.68 |
time (sec) |
N/A | 0.332 | 0.065 | 0.057 | 0.038 | 0.111 | 5.426 | 0.000 | 0.143 | 23.415 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 52 | 38 | 40 | 39 | 50 | 180 | 0 | 38 | 42 |
N.S. |
1 | 0.85 | 0.62 | 0.66 | 0.64 | 0.82 | 2.95 | 0.00 | 0.62 | 0.69 |
time (sec) |
N/A | 0.308 | 0.054 | 0.040 | 0.040 | 0.105 | 2.212 | 0.000 | 0.154 | 23.582 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 51 | 38 | 40 | 39 | 44 | 173 | 0 | 37 | 39 |
N.S. |
1 | 0.96 | 0.72 | 0.75 | 0.74 | 0.83 | 3.26 | 0.00 | 0.70 | 0.74 |
time (sec) |
N/A | 0.312 | 0.049 | 0.039 | 0.039 | 0.099 | 1.455 | 0.000 | 0.150 | 23.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 43 | 33 | 32 | 32 | 36 | 162 | 0 | 29 | 30 |
N.S. |
1 | 0.84 | 0.65 | 0.63 | 0.63 | 0.71 | 3.18 | 0.00 | 0.57 | 0.59 |
time (sec) |
N/A | 0.292 | 0.047 | 0.041 | 0.048 | 0.106 | 1.240 | 0.000 | 0.148 | 22.939 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 58 | 38 | 40 | 39 | 53 | 248 | 0 | 40 | 48 |
N.S. |
1 | 0.89 | 0.58 | 0.62 | 0.60 | 0.82 | 3.82 | 0.00 | 0.62 | 0.74 |
time (sec) |
N/A | 0.324 | 0.329 | 0.043 | 0.040 | 0.134 | 1.607 | 0.000 | 0.150 | 22.527 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 58 | 38 | 40 | 39 | 53 | 245 | 0 | 40 | 47 |
N.S. |
1 | 0.87 | 0.57 | 0.60 | 0.58 | 0.79 | 3.66 | 0.00 | 0.60 | 0.70 |
time (sec) |
N/A | 0.328 | 0.248 | 0.048 | 0.039 | 0.135 | 2.124 | 0.000 | 0.152 | 22.566 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 77 | 48 | 95 | 64 | 123 | 495 | 0 | 95 | 127 |
N.S. |
1 | 0.75 | 0.47 | 0.92 | 0.62 | 1.19 | 4.81 | 0.00 | 0.92 | 1.23 |
time (sec) |
N/A | 0.355 | 0.095 | 0.207 | 0.046 | 0.100 | 7.294 | 0.000 | 0.143 | 22.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 75 | 48 | 95 | 64 | 105 | 493 | 0 | 93 | 121 |
N.S. |
1 | 0.77 | 0.49 | 0.98 | 0.66 | 1.08 | 5.08 | 0.00 | 0.96 | 1.25 |
time (sec) |
N/A | 0.350 | 0.084 | 0.145 | 0.042 | 0.127 | 3.405 | 0.000 | 0.151 | 23.556 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 74 | 72 | 95 | 64 | 94 | 483 | 0 | 92 | 116 |
N.S. |
1 | 0.79 | 0.77 | 1.01 | 0.68 | 1.00 | 5.14 | 0.00 | 0.98 | 1.23 |
time (sec) |
N/A | 0.351 | 0.075 | 0.147 | 0.049 | 0.123 | 2.213 | 0.000 | 0.155 | 23.720 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 66 | 62 | 79 | 57 | 85 | 520 | 0 | 76 | 62 |
N.S. |
1 | 0.81 | 0.77 | 0.98 | 0.70 | 1.05 | 6.42 | 0.00 | 0.94 | 0.77 |
time (sec) |
N/A | 0.328 | 0.072 | 0.149 | 0.044 | 0.120 | 2.407 | 0.000 | 0.141 | 23.551 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 76 | 62 | 83 | 59 | 92 | 532 | 0 | 83 | 66 |
N.S. |
1 | 0.82 | 0.67 | 0.89 | 0.63 | 0.99 | 5.72 | 0.00 | 0.89 | 0.71 |
time (sec) |
N/A | 0.349 | 0.103 | 0.171 | 0.047 | 0.116 | 2.029 | 0.000 | 0.161 | 23.813 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 83 | 72 | 95 | 64 | 106 | 719 | 0 | 95 | 82 |
N.S. |
1 | 0.79 | 0.69 | 0.90 | 0.61 | 1.01 | 6.85 | 0.00 | 0.90 | 0.78 |
time (sec) |
N/A | 0.355 | 0.083 | 0.210 | 0.045 | 0.116 | 2.827 | 0.000 | 0.167 | 23.838 |
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 | 131 | 96 | 97 | 136 | 116 | 153 | 0 | 300 | 144 | 214 |
N.S. |
1 | 0.73 | 0.74 | 1.04 | 0.89 | 1.17 | 0.00 | 2.29 | 1.10 | 1.63 |
time (sec) |
N/A | 0.377 | 0.119 | 0.175 | 0.039 | 0.133 | 0.000 | 0.120 | 0.142 | 23.620 |
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 | 96 | 73 | 68 | 83 | 80 | 106 | 0 | 200 | 89 | 142 |
N.S. |
1 | 0.76 | 0.71 | 0.86 | 0.83 | 1.10 | 0.00 | 2.08 | 0.93 | 1.48 |
time (sec) |
N/A | 0.338 | 0.089 | 0.172 | 0.037 | 0.111 | 0.000 | 0.113 | 0.151 | 23.712 |
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 | 63 | 52 | 44 | 46 | 51 | 63 | 0 | 119 | 49 | 85 |
N.S. |
1 | 0.83 | 0.70 | 0.73 | 0.81 | 1.00 | 0.00 | 1.89 | 0.78 | 1.35 |
time (sec) |
N/A | 0.307 | 0.060 | 0.171 | 0.038 | 0.102 | 0.000 | 0.115 | 0.153 | 22.833 |
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 | 30 | 30 | 29 | 29 | 28 | 30 | 0 | 42 | 23 | 31 |
N.S. |
1 | 1.00 | 0.97 | 0.97 | 0.93 | 1.00 | 0.00 | 1.40 | 0.77 | 1.03 |
time (sec) |
N/A | 0.244 | 0.009 | 0.223 | 0.035 | 0.105 | 0.000 | 0.140 | 0.139 | 23.484 |
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 | 47 | 47 | 46 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.265 | 0.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
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 | 47 | 47 | 47 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.267 | 0.046 | 0.000 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 50 | 0 | 0 | 0 | 0 | 0 | 94 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.88 | 0.00 |
time (sec) |
N/A | 0.269 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 118 | 132 | 199 | 157 | 233 | 0 | 426 | 213 | 307 |
N.S. |
1 | 0.70 | 0.78 | 1.18 | 0.93 | 1.38 | 0.00 | 2.52 | 1.26 | 1.82 |
time (sec) |
N/A | 0.412 | 0.119 | 0.178 | 0.037 | 0.113 | 0.000 | 0.143 | 0.155 | 22.991 |
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 | 135 | 97 | 98 | 136 | 116 | 164 | 0 | 300 | 145 | 219 |
N.S. |
1 | 0.72 | 0.73 | 1.01 | 0.86 | 1.21 | 0.00 | 2.22 | 1.07 | 1.62 |
time (sec) |
N/A | 0.376 | 0.068 | 0.177 | 0.039 | 0.140 | 0.000 | 0.122 | 0.154 | 22.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 74 | 70 | 83 | 80 | 113 | 0 | 0 | 90 | 146 |
N.S. |
1 | 0.75 | 0.71 | 0.84 | 0.81 | 1.14 | 0.00 | 0.00 | 0.91 | 1.47 |
time (sec) |
N/A | 0.331 | 0.024 | 0.175 | 0.036 | 0.105 | 0.000 | 0.000 | 0.140 | 22.091 |
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 | 65 | 53 | 46 | 46 | 51 | 68 | 0 | 119 | 50 | 88 |
N.S. |
1 | 0.82 | 0.71 | 0.71 | 0.78 | 1.05 | 0.00 | 1.83 | 0.77 | 1.35 |
time (sec) |
N/A | 0.303 | 0.002 | 0.174 | 0.036 | 0.110 | 0.000 | 0.117 | 0.153 | 22.257 |
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 | 31 | 31 | 30 | 29 | 28 | 33 | 0 | 42 | 24 | 45 |
N.S. |
1 | 1.00 | 0.97 | 0.94 | 0.90 | 1.06 | 0.00 | 1.35 | 0.77 | 1.45 |
time (sec) |
N/A | 0.244 | 0.008 | 0.222 | 0.034 | 0.106 | 0.000 | 0.115 | 0.154 | 23.187 |
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 | 48 | 48 | 47 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.261 | 0.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |
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 | 48 | 48 | 47 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.264 | 0.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
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 | 51 | 51 | 50 | 0 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.86 | 0.00 |
time (sec) |
N/A | 0.263 | 0.017 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 143 | 172 | 280 | 203 | 352 | 0 | 571 | 297 | 424 |
N.S. |
1 | 0.66 | 0.79 | 1.29 | 0.94 | 1.62 | 0.00 | 2.63 | 1.37 | 1.95 |
time (sec) |
N/A | 0.436 | 0.151 | 0.198 | 0.040 | 0.100 | 0.000 | 0.116 | 0.150 | 24.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 120 | 133 | 199 | 157 | 265 | 0 | 0 | 215 | 319 |
N.S. |
1 | 0.67 | 0.74 | 1.11 | 0.88 | 1.48 | 0.00 | 0.00 | 1.20 | 1.78 |
time (sec) |
N/A | 0.403 | 0.043 | 0.270 | 0.036 | 0.103 | 0.000 | 0.000 | 0.159 | 23.791 |
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 | 143 | 99 | 99 | 136 | 116 | 186 | 0 | 300 | 147 | 229 |
N.S. |
1 | 0.69 | 0.69 | 0.95 | 0.81 | 1.30 | 0.00 | 2.10 | 1.03 | 1.60 |
time (sec) |
N/A | 0.366 | 0.040 | 0.259 | 0.037 | 0.119 | 0.000 | 0.121 | 0.151 | 23.400 |
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 | 105 | 76 | 70 | 83 | 80 | 127 | 0 | 200 | 92 | 154 |
N.S. |
1 | 0.72 | 0.67 | 0.79 | 0.76 | 1.21 | 0.00 | 1.90 | 0.88 | 1.47 |
time (sec) |
N/A | 0.335 | 0.055 | 0.222 | 0.036 | 0.106 | 0.000 | 0.120 | 0.143 | 22.350 |
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 | 69 | 55 | 46 | 46 | 51 | 76 | 0 | 119 | 52 | 94 |
N.S. |
1 | 0.80 | 0.67 | 0.67 | 0.74 | 1.10 | 0.00 | 1.72 | 0.75 | 1.36 |
time (sec) |
N/A | 0.298 | 0.003 | 0.256 | 0.037 | 0.104 | 0.000 | 0.120 | 0.163 | 22.529 |
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 | 33 | 33 | 30 | 29 | 28 | 37 | 0 | 42 | 26 | 49 |
N.S. |
1 | 1.00 | 0.91 | 0.88 | 0.85 | 1.12 | 0.00 | 1.27 | 0.79 | 1.48 |
time (sec) |
N/A | 0.237 | 0.008 | 0.389 | 0.034 | 0.098 | 0.000 | 0.133 | 0.152 | 22.856 |
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 | 50 | 50 | 47 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.265 | 0.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.144 | 0.000 |
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 | 50 | 50 | 47 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.266 | 0.016 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 94 | 96 | 134 | 104 | 158 | 0 | 0 | 147 | 186 |
N.S. |
1 | 0.76 | 0.78 | 1.09 | 0.85 | 1.28 | 0.00 | 0.00 | 1.20 | 1.51 |
time (sec) |
N/A | 0.354 | 0.045 | 0.177 | 0.035 | 0.104 | 0.000 | 0.000 | 0.152 | 22.774 |
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 | 90 | 71 | 67 | 81 | 83 | 110 | 0 | 0 | 92 | 121 |
N.S. |
1 | 0.79 | 0.74 | 0.90 | 0.92 | 1.22 | 0.00 | 0.00 | 1.02 | 1.34 |
time (sec) |
N/A | 0.317 | 0.038 | 0.176 | 0.036 | 0.086 | 0.000 | 0.000 | 0.141 | 22.142 |
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 | 59 | 50 | 43 | 44 | 45 | 66 | 0 | 0 | 52 | 71 |
N.S. |
1 | 0.85 | 0.73 | 0.75 | 0.76 | 1.12 | 0.00 | 0.00 | 0.88 | 1.20 |
time (sec) |
N/A | 0.290 | 0.026 | 0.172 | 0.035 | 0.086 | 0.000 | 0.000 | 0.153 | 22.440 |
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 | 28 | 28 | 28 | 27 | 31 | 33 | 0 | 0 | 26 | 36 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.11 | 1.18 | 0.00 | 0.00 | 0.93 | 1.29 |
time (sec) |
N/A | 0.226 | 0.002 | 0.169 | 0.036 | 0.115 | 0.000 | 0.000 | 0.164 | 21.856 |
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 | 45 | 45 | 45 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.256 | 0.002 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.141 | 0.000 |
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 | 45 | 45 | 48 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.247 | 0.016 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 51 | 0 | 0 | 0 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.02 | 0.00 |
time (sec) |
N/A | 0.250 | 0.017 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 97 | 98 | 136 | 104 | 168 | 0 | 0 | 147 | 201 |
N.S. |
1 | 0.72 | 0.73 | 1.01 | 0.77 | 1.24 | 0.00 | 0.00 | 1.09 | 1.49 |
time (sec) |
N/A | 0.364 | 0.056 | 0.212 | 0.040 | 0.111 | 0.000 | 0.000 | 0.140 | 23.823 |
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 | 99 | 74 | 69 | 83 | 83 | 118 | 0 | 0 | 92 | 133 |
N.S. |
1 | 0.75 | 0.70 | 0.84 | 0.84 | 1.19 | 0.00 | 0.00 | 0.93 | 1.34 |
time (sec) |
N/A | 0.323 | 0.046 | 0.240 | 0.039 | 0.121 | 0.000 | 0.000 | 0.157 | 23.517 |
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 | 65 | 53 | 45 | 46 | 45 | 72 | 0 | 0 | 52 | 80 |
N.S. |
1 | 0.82 | 0.69 | 0.71 | 0.69 | 1.11 | 0.00 | 0.00 | 0.80 | 1.23 |
time (sec) |
N/A | 0.297 | 0.032 | 0.172 | 0.035 | 0.102 | 0.000 | 0.000 | 0.151 | 22.456 |
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 | 31 | 31 | 30 | 29 | 31 | 37 | 0 | 0 | 26 | 42 |
N.S. |
1 | 1.00 | 0.97 | 0.94 | 1.00 | 1.19 | 0.00 | 0.00 | 0.84 | 1.35 |
time (sec) |
N/A | 0.241 | 0.009 | 0.170 | 0.039 | 0.130 | 0.000 | 0.000 | 0.149 | 21.930 |
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 | 48 | 48 | 47 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.256 | 0.015 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 47 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.259 | 0.010 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 50 | 0 | 0 | 0 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.90 | 0.00 |
time (sec) |
N/A | 0.258 | 0.002 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.144 | 0.000 |
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 | 50 | 50 | 50 | 0 | 0 | 0 | 0 | 0 | 166 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.32 | 0.00 |
time (sec) |
N/A | 0.264 | 0.047 | 0.000 | 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 | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 97 | 99 | 136 | 104 | 168 | 0 | 0 | 147 | 201 |
N.S. |
1 | 0.72 | 0.73 | 1.01 | 0.77 | 1.24 | 0.00 | 0.00 | 1.09 | 1.49 |
time (sec) |
N/A | 0.365 | 0.042 | 0.175 | 0.049 | 0.135 | 0.000 | 0.000 | 0.153 | 22.590 |
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 | 99 | 74 | 70 | 83 | 83 | 118 | 0 | 0 | 92 | 133 |
N.S. |
1 | 0.75 | 0.71 | 0.84 | 0.84 | 1.19 | 0.00 | 0.00 | 0.93 | 1.34 |
time (sec) |
N/A | 0.322 | 0.039 | 0.231 | 0.036 | 0.129 | 0.000 | 0.000 | 0.157 | 22.551 |
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 | 65 | 53 | 46 | 46 | 45 | 72 | 0 | 0 | 52 | 80 |
N.S. |
1 | 0.82 | 0.71 | 0.71 | 0.69 | 1.11 | 0.00 | 0.00 | 0.80 | 1.23 |
time (sec) |
N/A | 0.285 | 0.029 | 0.236 | 0.043 | 0.144 | 0.000 | 0.000 | 0.169 | 22.919 |
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 | 31 | 31 | 30 | 29 | 31 | 37 | 0 | 0 | 26 | 42 |
N.S. |
1 | 1.00 | 0.97 | 0.94 | 1.00 | 1.19 | 0.00 | 0.00 | 0.84 | 1.35 |
time (sec) |
N/A | 0.234 | 0.007 | 0.168 | 0.034 | 0.105 | 0.000 | 0.000 | 0.161 | 22.995 |
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 | 48 | 48 | 47 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.252 | 0.012 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 47 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.256 | 0.015 | 0.000 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 50 | 0 | 0 | 0 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.90 | 0.00 |
time (sec) |
N/A | 0.259 | 0.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.146 | 0.000 |
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 | 50 | 50 | 49 | 0 | 0 | 0 | 0 | 0 | 166 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.32 | 0.00 |
time (sec) |
N/A | 0.274 | 0.002 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 67 | 57 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.310 | 0.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
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 | 62 | 65 | 57 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.293 | 0.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
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 | 61 | 64 | 57 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.291 | 0.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
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 | 57 | 53 | 53 | 0 | 0 | 0 | 0 | 0 | 107 | 0 |
N.S. |
1 | 0.93 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.88 | 0.00 |
time (sec) |
N/A | 0.272 | 0.041 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 68 | 57 | 0 | 0 | 0 | 0 | 0 | 208 | 0 |
N.S. |
1 | 1.05 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.20 | 0.00 |
time (sec) |
N/A | 0.289 | 0.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.142 | 0.000 |
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 | 67 | 68 | 57 | 0 | 0 | 0 | 0 | 0 | 208 | 0 |
N.S. |
1 | 1.01 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.10 | 0.00 |
time (sec) |
N/A | 0.298 | 0.051 | 0.000 | 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 | A | A | A | F(-2) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 21 | 12 | 12 | 0 | 12 | 16 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.43 | 0.43 | 0.00 | 0.43 | 0.57 | 0.71 |
time (sec) |
N/A | 0.226 | 0.011 | 0.171 | 0.030 | 0.112 | 0.000 | 0.129 | 0.150 | 21.980 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 41 | 32 | 32 | 0 | 40 | 0 | 74 | 121 | 33 |
N.S. |
1 | 1.24 | 0.97 | 0.97 | 0.00 | 1.21 | 0.00 | 2.24 | 3.67 | 1.00 |
time (sec) |
N/A | 0.265 | 0.068 | 0.493 | 0.000 | 0.112 | 0.000 | 0.128 | 0.165 | 22.836 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 33 | 0 | 40 | 0 | 0 | 101 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.03 | 0.00 | 1.25 | 0.00 | 0.00 | 3.16 | 1.06 |
time (sec) |
N/A | 0.253 | 0.078 | 0.338 | 0.000 | 0.121 | 0.000 | 0.000 | 0.156 | 22.874 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 41 | 32 | 32 | 0 | 38 | 0 | 72 | 79 | 33 |
N.S. |
1 | 1.24 | 0.97 | 0.97 | 0.00 | 1.15 | 0.00 | 2.18 | 2.39 | 1.00 |
time (sec) |
N/A | 0.261 | 0.063 | 0.329 | 0.000 | 0.101 | 0.000 | 0.142 | 0.146 | 23.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 28 | 31 | 0 | 36 | 0 | 0 | 58 | 32 |
N.S. |
1 | 1.00 | 0.93 | 1.03 | 0.00 | 1.20 | 0.00 | 0.00 | 1.93 | 1.07 |
time (sec) |
N/A | 0.251 | 0.064 | 0.304 | 0.000 | 0.143 | 0.000 | 0.000 | 0.139 | 24.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 25 | 27 | 31 | 0 | 0 | 41 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.04 | 1.19 | 0.00 | 0.00 | 1.58 | 1.00 |
time (sec) |
N/A | 0.246 | 0.051 | 0.250 | 0.036 | 0.109 | 0.000 | 0.000 | 0.160 | 23.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 32 | 38 | 0 | 37 | 0 | 0 | 26 | 32 |
N.S. |
1 | 1.00 | 0.97 | 1.15 | 0.00 | 1.12 | 0.00 | 0.00 | 0.79 | 0.97 |
time (sec) |
N/A | 0.255 | 0.046 | 0.349 | 0.000 | 0.122 | 0.000 | 0.000 | 0.147 | 23.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 45 | 32 | 32 | 0 | 37 | 109 | 0 | 53 | 50 |
N.S. |
1 | 1.29 | 0.91 | 0.91 | 0.00 | 1.06 | 3.11 | 0.00 | 1.51 | 1.43 |
time (sec) |
N/A | 0.267 | 0.054 | 0.332 | 0.000 | 0.110 | 1.353 | 0.000 | 0.143 | 23.437 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 32 | 33 | 0 | 37 | 0 | 0 | 83 | 51 |
N.S. |
1 | 1.00 | 0.97 | 1.00 | 0.00 | 1.12 | 0.00 | 0.00 | 2.52 | 1.55 |
time (sec) |
N/A | 0.261 | 0.057 | 0.346 | 0.000 | 0.139 | 0.000 | 0.000 | 0.170 | 23.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 39 | 0 | 49 | 0 | 0 | 66 | 50 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 0.00 | 1.29 | 0.00 | 0.00 | 1.74 | 1.32 |
time (sec) |
N/A | 0.264 | 0.085 | 0.779 | 0.000 | 0.147 | 0.000 | 0.000 | 0.155 | 23.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 39 | 40 | 0 | 57 | 0 | 0 | 69 | 39 |
N.S. |
1 | 1.00 | 0.91 | 0.93 | 0.00 | 1.33 | 0.00 | 0.00 | 1.60 | 0.91 |
time (sec) |
N/A | 0.267 | 0.025 | 0.784 | 0.000 | 0.122 | 0.000 | 0.000 | 0.147 | 23.066 |
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 | 63 | 63 | 63 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.290 | 0.051 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 64 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.299 | 0.013 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 53 | 71 | 54 | 67 | 147 | 75 | 0 | 42 | 51 |
N.S. |
1 | 0.66 | 0.89 | 0.68 | 0.84 | 1.84 | 0.94 | 0.00 | 0.52 | 0.64 |
time (sec) |
N/A | 0.306 | 0.110 | 0.442 | 0.113 | 0.120 | 1.621 | 0.000 | 0.146 | 22.397 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 42 | 60 | 38 | 49 | 126 | 54 | 0 | 31 | 37 |
N.S. |
1 | 0.70 | 1.00 | 0.63 | 0.82 | 2.10 | 0.90 | 0.00 | 0.52 | 0.62 |
time (sec) |
N/A | 0.261 | 0.077 | 0.205 | 0.115 | 0.104 | 1.439 | 0.000 | 0.157 | 22.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 34 | 42 | 24 | 23 | 94 | 32 | 0 | 28 | 23 |
N.S. |
1 | 0.81 | 1.00 | 0.57 | 0.55 | 2.24 | 0.76 | 0.00 | 0.67 | 0.55 |
time (sec) |
N/A | 0.240 | 0.036 | 0.257 | 0.118 | 0.126 | 1.069 | 0.000 | 0.150 | 22.678 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 45 | 63 | 36 | 35 | 132 | 49 | 0 | 33 | 38 |
N.S. |
1 | 0.78 | 1.09 | 0.62 | 0.60 | 2.28 | 0.84 | 0.00 | 0.57 | 0.66 |
time (sec) |
N/A | 0.256 | 0.106 | 0.221 | 0.113 | 0.106 | 1.504 | 0.000 | 0.142 | 23.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 62 | 70 | 56 | 52 | 157 | 70 | 0 | 48 | 53 |
N.S. |
1 | 0.84 | 0.95 | 0.76 | 0.70 | 2.12 | 0.95 | 0.00 | 0.65 | 0.72 |
time (sec) |
N/A | 0.281 | 0.121 | 0.220 | 0.107 | 0.124 | 1.196 | 0.000 | 0.157 | 23.757 |
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 | 63 | 70 | 60 | 0 | 0 | 0 | 0 | 0 | 568 | 0 |
N.S. |
1 | 1.11 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 9.02 | 0.00 |
time (sec) |
N/A | 0.343 | 0.074 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 161 | 179 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.599 | 0.949 | 0.000 | 0.000 | 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 | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 34 | 42 | 27 | 0 | 42 | 0 | 27 | 24 | 0 |
N.S. |
1 | 0.77 | 0.95 | 0.61 | 0.00 | 0.95 | 0.00 | 0.61 | 0.55 | 0.00 |
time (sec) |
N/A | 0.249 | 0.050 | 0.174 | 0.000 | 0.118 | 0.000 | 0.134 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 77 | 43 | 22 | 0 | 31 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.93 | 0.52 | 0.27 | 0.00 | 0.37 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.306 | 10.016 | 0.209 | 0.000 | 0.116 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 19 | 18 | 17 | 19 | 9 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.86 | 0.82 | 0.77 | 0.86 | 0.41 | 0.86 |
time (sec) |
N/A | 0.232 | 0.007 | 0.155 | 0.114 | 0.124 | 0.146 | 0.139 | 0.151 | 22.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 163 | 27 | 20 | 0 | 12 | 36 | 0 | 21 | 0 |
N.S. |
1 | 1.24 | 0.21 | 0.15 | 0.00 | 0.09 | 0.27 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.422 | 10.028 | 0.219 | 0.000 | 0.106 | 0.570 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 27 | 22 | 0 | 9 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.50 | 0.41 | 0.00 | 0.17 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.260 | 10.030 | 0.218 | 0.000 | 0.113 | 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 | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 0 | 76 | 0 | 30 | 26 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.00 | 3.45 | 0.00 | 1.36 | 1.18 | 0.00 |
time (sec) |
N/A | 0.252 | 0.060 | 0.166 | 0.000 | 0.142 | 0.000 | 0.141 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 139 | 27 | 22 | 0 | 30 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.87 | 0.17 | 0.14 | 0.00 | 0.19 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.411 | 10.014 | 0.290 | 0.000 | 0.099 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 18 | 23 | 30 | 0 | 22 | 15 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 1.10 | 1.43 | 0.00 | 1.05 | 0.71 | 0.86 |
time (sec) |
N/A | 0.210 | 0.036 | 0.160 | 0.107 | 0.108 | 0.000 | 0.139 | 0.139 | 23.264 |
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 | 25 | 25 | 25 | 20 | 28 | 19 | 0 | 12 | 10 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.12 | 0.76 | 0.00 | 0.48 | 0.40 | 0.80 |
time (sec) |
N/A | 0.228 | 0.018 | 0.194 | 0.125 | 0.114 | 0.000 | 0.118 | 0.153 | 22.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 292 | 29 | 22 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.10 | 0.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.678 | 10.011 | 1.327 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 252 | 29 | 22 | 0 | 19 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.97 | 0.11 | 0.08 | 0.00 | 0.07 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.522 | 10.026 | 0.361 | 0.000 | 0.115 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 32 | 15 | 0 | 85 | 14 | 35 | 32 | 0 |
N.S. |
1 | 1.00 | 1.39 | 0.65 | 0.00 | 3.70 | 0.61 | 1.52 | 1.39 | 0.00 |
time (sec) |
N/A | 0.271 | 0.265 | 0.973 | 0.000 | 0.188 | 0.587 | 0.146 | 0.151 | 0.000 |