Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 8 | 7 | 7 | 8 | 7 | 9 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.64 | 0.64 | 0.73 | 0.64 | 0.82 | 0.64 |
time (sec) |
N/A | 0.192 | 0.001 | 0.026 | 0.031 | 0.072 | 0.017 | 0.127 | 0.208 | 22.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 24 | 22 | 7 | 26 | 0 | 7 | 9 | 22 |
N.S. |
1 | 1.00 | 2.18 | 2.00 | 0.64 | 2.36 | 0.00 | 0.64 | 0.82 | 2.00 |
time (sec) |
N/A | 0.199 | 0.076 | 0.046 | 0.027 | 0.071 | 0.000 | 0.113 | 0.192 | 22.632 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 8 | 7 | 7 | 8 | 7 | 10 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.64 | 0.64 | 0.73 | 0.64 | 0.91 | 0.64 |
time (sec) |
N/A | 0.208 | 0.002 | 0.032 | 0.031 | 0.066 | 0.018 | 0.125 | 0.202 | 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 | 11 | 11 | 11 | 8 | 7 | 7 | 8 | 7 | 10 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.64 | 0.64 | 0.73 | 0.64 | 0.91 | 0.64 |
time (sec) |
N/A | 0.223 | 0.001 | 0.030 | 0.024 | 0.066 | 0.484 | 0.132 | 0.191 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 48 | 67 | 41 | 52 | 100 | 39 | 31 | 172 |
N.S. |
1 | 1.00 | 1.37 | 1.91 | 1.17 | 1.49 | 2.86 | 1.11 | 0.89 | 4.91 |
time (sec) |
N/A | 0.238 | 0.131 | 0.042 | 0.103 | 0.080 | 1.035 | 0.123 | 0.190 | 24.967 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 49 | 81 | 0 | 96 | 0 | 39 | 31 | 0 |
N.S. |
1 | 1.00 | 1.40 | 2.31 | 0.00 | 2.74 | 0.00 | 1.11 | 0.89 | 0.00 |
time (sec) |
N/A | 0.250 | 2.719 | 0.062 | 0.000 | 0.091 | 0.000 | 0.141 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 59 | 32 | 53 | 63 | 0 | 44 | 49 | 37 |
N.S. |
1 | 1.00 | 1.69 | 0.91 | 1.51 | 1.80 | 0.00 | 1.26 | 1.40 | 1.06 |
time (sec) |
N/A | 0.283 | 0.211 | 0.155 | 0.103 | 0.082 | 0.000 | 0.129 | 0.203 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 43 | 69 | 67 | 53 | 74 | 0 | 163 | 150 | 0 |
N.S. |
1 | 1.23 | 1.97 | 1.91 | 1.51 | 2.11 | 0.00 | 4.66 | 4.29 | 0.00 |
time (sec) |
N/A | 0.262 | 0.312 | 0.059 | 0.103 | 0.089 | 0.000 | 0.168 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 69 | 99 | 65 | 82 | 0 | 87 | 65 | 82 |
N.S. |
1 | 1.00 | 1.53 | 2.20 | 1.44 | 1.82 | 0.00 | 1.93 | 1.44 | 1.82 |
time (sec) |
N/A | 0.346 | 0.338 | 0.112 | 0.104 | 0.091 | 0.000 | 0.136 | 0.177 | 0.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 51 | 82 | 128 | 65 | 93 | 0 | 196 | 163 | 0 |
N.S. |
1 | 1.13 | 1.82 | 2.84 | 1.44 | 2.07 | 0.00 | 4.36 | 3.62 | 0.00 |
time (sec) |
N/A | 0.311 | 0.488 | 0.093 | 0.109 | 0.087 | 0.000 | 0.222 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 20 | 3 | 2 | 18 | 2 | 17 | 2 | 2 |
N.S. |
1 | 1.00 | 10.00 | 1.50 | 1.00 | 9.00 | 1.00 | 8.50 | 1.00 | 1.00 |
time (sec) |
N/A | 0.206 | 0.003 | 0.192 | 0.109 | 0.077 | 0.081 | 0.106 | 0.182 | 0.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 32 | 29 | 0 | 28 | 0 | 0 | 2 | 0 |
N.S. |
1 | 1.00 | 16.00 | 14.50 | 0.00 | 14.00 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.226 | 0.013 | 0.058 | 0.000 | 0.070 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 16 | 3 | 2 | 14 | 2 | 25 | 9 | 2 |
N.S. |
1 | 1.00 | 8.00 | 1.50 | 1.00 | 7.00 | 1.00 | 12.50 | 4.50 | 1.00 |
time (sec) |
N/A | 0.199 | 0.020 | 0.065 | 0.101 | 0.075 | 0.061 | 0.130 | 0.201 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 42 | 29 | 0 | 81 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.00 | 21.00 | 14.50 | 0.00 | 40.50 | 0.00 | 0.00 | 4.50 | 0.00 |
time (sec) |
N/A | 0.223 | 0.011 | 0.053 | 0.000 | 0.072 | 0.000 | 0.000 | 0.184 | 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 | 23 | 23 | 37 | 18 | 17 | 31 | 15 | 17 | 16 | 17 |
N.S. |
1 | 1.00 | 1.61 | 0.78 | 0.74 | 1.35 | 0.65 | 0.74 | 0.70 | 0.74 |
time (sec) |
N/A | 0.223 | 0.005 | 0.082 | 0.104 | 0.081 | 0.093 | 0.118 | 0.211 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 50 | 42 | 0 | 61 | 0 | 17 | 24 | 0 |
N.S. |
1 | 1.00 | 2.17 | 1.83 | 0.00 | 2.65 | 0.00 | 0.74 | 1.04 | 0.00 |
time (sec) |
N/A | 0.245 | 0.956 | 0.046 | 0.000 | 0.088 | 0.000 | 0.117 | 0.189 | 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 | 21 | 21 | 33 | 16 | 15 | 25 | 15 | 25 | 21 | 15 |
N.S. |
1 | 1.00 | 1.57 | 0.76 | 0.71 | 1.19 | 0.71 | 1.19 | 1.00 | 0.71 |
time (sec) |
N/A | 0.220 | 0.004 | 0.086 | 0.106 | 0.068 | 0.089 | 0.140 | 0.210 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 70 | 40 | 0 | 120 | 0 | 25 | 21 | 0 |
N.S. |
1 | 1.00 | 3.33 | 1.90 | 0.00 | 5.71 | 0.00 | 1.19 | 1.00 | 0.00 |
time (sec) |
N/A | 0.244 | 0.050 | 0.056 | 0.000 | 0.074 | 0.000 | 0.129 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 57 | 53 | 0 | 0 | 0 | 0 | 0 | 198 | 54 |
N.S. |
1 | 1.16 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.04 | 1.10 |
time (sec) |
N/A | 0.306 | 0.041 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 23.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 33 | 21 | 0 | 30 | 65 | 30 | 27 | 20 |
N.S. |
1 | 1.00 | 1.18 | 0.75 | 0.00 | 1.07 | 2.32 | 1.07 | 0.96 | 0.71 |
time (sec) |
N/A | 0.257 | 0.044 | 0.046 | 0.000 | 0.073 | 0.184 | 0.134 | 0.175 | 22.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 39 | 197 | 0 | 84 | 17 | 140 | 20 | 105 |
N.S. |
1 | 1.00 | 1.05 | 5.32 | 0.00 | 2.27 | 0.46 | 3.78 | 0.54 | 2.84 |
time (sec) |
N/A | 0.367 | 0.078 | 0.141 | 0.000 | 0.071 | 0.072 | 0.158 | 0.171 | 22.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 68 | 33 | 0 | 90 | 27 | 88 | 99 | 57 |
N.S. |
1 | 1.00 | 1.70 | 0.82 | 0.00 | 2.25 | 0.68 | 2.20 | 2.48 | 1.42 |
time (sec) |
N/A | 0.388 | 0.187 | 0.121 | 0.000 | 0.077 | 0.089 | 0.135 | 0.182 | 22.578 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 79 | 35 | 94 | 67 | 0 | 117 | 101 | 86 |
N.S. |
1 | 1.00 | 1.46 | 0.65 | 1.74 | 1.24 | 0.00 | 2.17 | 1.87 | 1.59 |
time (sec) |
N/A | 0.524 | 0.192 | 0.187 | 0.108 | 0.075 | 0.000 | 0.148 | 0.198 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 60 | 78 | 45 | 0 | 67 | 0 | 117 | 71 | 86 |
N.S. |
1 | 1.11 | 1.44 | 0.83 | 0.00 | 1.24 | 0.00 | 2.17 | 1.31 | 1.59 |
time (sec) |
N/A | 0.722 | 0.147 | 0.063 | 0.000 | 0.080 | 0.000 | 0.141 | 0.182 | 22.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 45 | 35 | 0 | 66 | 0 | 50 | 47 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.69 | 0.00 | 1.29 | 0.00 | 0.98 | 0.92 | 0.00 |
time (sec) |
N/A | 0.474 | 0.220 | 0.056 | 0.000 | 0.072 | 0.000 | 0.148 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 45 | 35 | 54 | 66 | 0 | 50 | 51 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.69 | 1.06 | 1.29 | 0.00 | 0.98 | 1.00 | 0.00 |
time (sec) |
N/A | 0.461 | 0.188 | 0.102 | 0.124 | 0.082 | 0.000 | 0.133 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 51 | 45 | 51 | 54 | 64 | 0 | 109 | 51 | 56 |
N.S. |
1 | 0.94 | 0.83 | 0.94 | 1.00 | 1.19 | 0.00 | 2.02 | 0.94 | 1.04 |
time (sec) |
N/A | 0.447 | 0.007 | 0.079 | 0.147 | 0.073 | 0.000 | 0.186 | 0.185 | 23.804 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 58 | 69 | 51 | 0 | 64 | 0 | 109 | 47 | 56 |
N.S. |
1 | 1.16 | 1.38 | 1.02 | 0.00 | 1.28 | 0.00 | 2.18 | 0.94 | 1.12 |
time (sec) |
N/A | 0.473 | 0.209 | 0.020 | 0.000 | 0.073 | 0.000 | 0.172 | 0.195 | 22.678 |
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 | 27 | 25 | 23 | 20 | 0 | 20 | 0 | 0 | 15 | 20 |
N.S. |
1 | 0.93 | 0.85 | 0.74 | 0.00 | 0.74 | 0.00 | 0.00 | 0.56 | 0.74 |
time (sec) |
N/A | 0.264 | 0.024 | 0.052 | 0.000 | 0.067 | 0.000 | 0.000 | 0.171 | 22.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 12 | 13 | 0 | 16 | 0 | 0 | 17 | 138 |
N.S. |
1 | 1.00 | 0.86 | 0.93 | 0.00 | 1.14 | 0.00 | 0.00 | 1.21 | 9.86 |
time (sec) |
N/A | 0.334 | 0.265 | 0.139 | 0.000 | 0.075 | 0.000 | 0.000 | 0.196 | 22.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 11 | 0 | 16 | 0 | 0 | 17 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.00 | 1.33 | 0.00 | 0.00 | 1.42 | 0.83 |
time (sec) |
N/A | 0.322 | 0.003 | 0.086 | 0.000 | 0.081 | 0.000 | 0.000 | 0.188 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 29 | 31 | 0 | 30 | 0 | 0 | 17 | 48 |
N.S. |
1 | 1.00 | 0.81 | 0.86 | 0.00 | 0.83 | 0.00 | 0.00 | 0.47 | 1.33 |
time (sec) |
N/A | 0.486 | 0.016 | 0.188 | 0.000 | 0.074 | 0.000 | 0.000 | 0.199 | 22.369 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 29 | 31 | 0 | 30 | 0 | 0 | 17 | 43 |
N.S. |
1 | 1.00 | 0.88 | 0.94 | 0.00 | 0.91 | 0.00 | 0.00 | 0.52 | 1.30 |
time (sec) |
N/A | 0.598 | 0.003 | 0.037 | 0.000 | 0.074 | 0.000 | 0.000 | 0.191 | 23.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 70 | 103 | 0 | 208 | 0 | 92 | 39 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.47 | 0.00 | 2.97 | 0.00 | 1.31 | 0.56 | 0.00 |
time (sec) |
N/A | 0.345 | 0.605 | 0.106 | 0.000 | 0.090 | 0.000 | 0.166 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 62 | 56 | 59 | 0 | 38 | 0 | 46 | 59 | 0 |
N.S. |
1 | 0.75 | 0.67 | 0.71 | 0.00 | 0.46 | 0.00 | 0.55 | 0.71 | 0.00 |
time (sec) |
N/A | 0.493 | 0.054 | 0.782 | 0.000 | 0.077 | 0.000 | 0.118 | 0.194 | 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 | 148 | 115 | 76 | 62 | 0 | 117 | 0 | 86 | 116 | 0 |
N.S. |
1 | 0.78 | 0.51 | 0.42 | 0.00 | 0.79 | 0.00 | 0.58 | 0.78 | 0.00 |
time (sec) |
N/A | 0.484 | 0.385 | 0.180 | 0.000 | 0.074 | 0.000 | 0.137 | 0.195 | 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 | 80 | 76 | 56 | 49 | 0 | 83 | 0 | 67 | 67 | 0 |
N.S. |
1 | 0.95 | 0.70 | 0.61 | 0.00 | 1.04 | 0.00 | 0.84 | 0.84 | 0.00 |
time (sec) |
N/A | 0.433 | 0.226 | 0.075 | 0.000 | 0.079 | 0.000 | 0.124 | 0.207 | 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 | 61 | 43 | 53 | 42 | 0 | 75 | 0 | 49 | 16 | 0 |
N.S. |
1 | 0.70 | 0.87 | 0.69 | 0.00 | 1.23 | 0.00 | 0.80 | 0.26 | 0.00 |
time (sec) |
N/A | 0.372 | 0.014 | 0.066 | 0.000 | 0.071 | 0.000 | 0.133 | 0.182 | 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 | 109 | 71 | 82 | 79 | 0 | 142 | 0 | 88 | 51 | 0 |
N.S. |
1 | 0.65 | 0.75 | 0.72 | 0.00 | 1.30 | 0.00 | 0.81 | 0.47 | 0.00 |
time (sec) |
N/A | 0.436 | 0.194 | 0.151 | 0.000 | 0.088 | 0.000 | 0.202 | 0.192 | 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 | 164 | 103 | 108 | 109 | 0 | 205 | 0 | 170 | 198 | 0 |
N.S. |
1 | 0.63 | 0.66 | 0.66 | 0.00 | 1.25 | 0.00 | 1.04 | 1.21 | 0.00 |
time (sec) |
N/A | 0.497 | 0.460 | 0.153 | 0.000 | 0.097 | 0.000 | 0.203 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 25 | 24 | 0 | 31 | 0 | 30 | 29 | 23 |
N.S. |
1 | 1.00 | 0.89 | 0.86 | 0.00 | 1.11 | 0.00 | 1.07 | 1.04 | 0.82 |
time (sec) |
N/A | 0.466 | 0.146 | 0.039 | 0.000 | 0.071 | 0.000 | 0.136 | 0.177 | 22.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 233 | 230 | 218 | 0 | 436 | 0 | 459 | 299 | 0 |
N.S. |
1 | 1.05 | 1.04 | 0.99 | 0.00 | 1.97 | 0.00 | 2.08 | 1.35 | 0.00 |
time (sec) |
N/A | 2.210 | 5.882 | 0.148 | 0.000 | 0.123 | 0.000 | 0.250 | 0.290 | 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 | 14 | 14 | 16 | 12 | 14 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.719 | 0.158 | 0.008 | 0.074 | 0.071 | 0.289 | 0.151 | 0.176 | 22.889 |
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 | 14 | 14 | 16 | 12 | 14 | 24 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 1.00 | 1.71 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.660 | 0.345 | 0.011 | 0.068 | 0.068 | 0.287 | 0.155 | 0.188 | 22.514 |
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 | 17 | 17 | 19 | 13 | 15 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.12 | 0.76 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.558 | 0.007 | 0.010 | 0.065 | 0.066 | 1.427 | 0.132 | 0.170 | 23.320 |
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 | 17 | 17 | 19 | 13 | 15 | 25 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.12 | 0.76 | 0.88 | 1.47 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.481 | 0.008 | 0.010 | 0.082 | 0.071 | 0.591 | 0.112 | 0.188 | 22.667 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.349 | 0.011 | 0.004 | 0.039 | 0.056 | 0.179 | 0.122 | 0.185 | 23.079 |
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 | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.351 | 0.010 | 0.005 | 0.030 | 0.054 | 0.196 | 0.123 | 0.187 | 23.227 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.281 | 0.011 | 0.005 | 0.032 | 0.063 | 0.191 | 0.118 | 0.186 | 23.594 |
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 | 14 | 14 | 16 | 14 | 16 | 16 | 12 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 0.86 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.294 | 0.014 | 0.001 | 0.034 | 0.059 | 0.224 | 0.891 | 0.170 | 23.337 |
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 | 12 | 12 | 14 | 12 | 14 | 25 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 2.08 | 1.00 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.291 | 0.017 | 0.004 | 0.052 | 0.086 | 0.242 | 0.127 | 0.186 | 23.539 |
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 | 14 | 14 | 16 | 14 | 16 | 27 | 14 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.93 | 1.00 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.291 | 0.017 | 0.003 | 0.030 | 0.055 | 0.272 | 0.108 | 0.181 | 23.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 75 | 0 | 0 | 168 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.00 | 1.60 | 0.00 | 0.00 | 3.57 | 0.00 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.420 | 0.558 | 0.000 | 0.000 | 0.888 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 82 | 0 | 0 | 169 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 1.71 | 0.00 | 0.00 | 3.52 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.414 | 0.495 | 0.000 | 0.000 | 0.899 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 364 | 0 | 0 | 0 | 0 | 0 | 1008 | 0 |
N.S. |
1 | 1.00 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.96 | 0.00 |
time (sec) |
N/A | 0.705 | 1.405 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 309 | 1464 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 5.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.848 | 5.874 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 5.384 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 99 | 109 | 0 | 193 | 99 | 0 | 186 | 42 |
N.S. |
1 | 1.00 | 2.91 | 3.21 | 0.00 | 5.68 | 2.91 | 0.00 | 5.47 | 1.24 |
time (sec) |
N/A | 0.659 | 0.105 | 0.103 | 0.000 | 0.114 | 0.732 | 0.000 | 0.206 | 23.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 99 | 109 | 0 | 193 | 99 | 0 | 186 | 42 |
N.S. |
1 | 1.00 | 2.91 | 3.21 | 0.00 | 5.68 | 2.91 | 0.00 | 5.47 | 1.24 |
time (sec) |
N/A | 1.139 | 0.079 | 0.076 | 0.000 | 0.140 | 0.650 | 0.000 | 0.173 | 23.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | A | B | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 34 | 109 | 0 | 193 | 99 | 0 | 186 | 42 |
N.S. |
1 | 0.00 | 1.00 | 3.21 | 0.00 | 5.68 | 2.91 | 0.00 | 5.47 | 1.24 |
time (sec) |
N/A | 0.000 | 0.028 | 0.072 | 0.000 | 0.148 | 0.634 | 0.000 | 0.196 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 101 | 132 | 0 | 200 | 102 | 99 | 188 | 45 |
N.S. |
1 | 1.00 | 2.59 | 3.38 | 0.00 | 5.13 | 2.62 | 2.54 | 4.82 | 1.15 |
time (sec) |
N/A | 0.834 | 0.125 | 0.593 | 0.000 | 0.172 | 1.053 | 8.648 | 0.193 | 0.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 101 | 132 | 0 | 200 | 102 | 99 | 188 | 45 |
N.S. |
1 | 1.00 | 2.59 | 3.38 | 0.00 | 5.13 | 2.62 | 2.54 | 4.82 | 1.15 |
time (sec) |
N/A | 1.208 | 0.109 | 0.074 | 0.000 | 0.140 | 1.083 | 8.320 | 0.184 | 22.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 0 | 101 | 132 | 0 | 200 | 102 | 44 | 188 | 45 |
N.S. |
1 | 0.00 | 2.59 | 3.38 | 0.00 | 5.13 | 2.62 | 1.13 | 4.82 | 1.15 |
time (sec) |
N/A | 0.000 | 0.110 | 0.077 | 0.000 | 0.117 | 1.202 | 7.479 | 0.193 | 23.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 101 | 105 | 0 | 194 | 94 | 0 | 193 | 42 |
N.S. |
1 | 1.00 | 2.97 | 3.09 | 0.00 | 5.71 | 2.76 | 0.00 | 5.68 | 1.24 |
time (sec) |
N/A | 0.683 | 0.101 | 0.092 | 0.000 | 0.096 | 0.711 | 0.000 | 0.194 | 23.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 101 | 105 | 0 | 194 | 94 | 0 | 193 | 42 |
N.S. |
1 | 1.00 | 2.97 | 3.09 | 0.00 | 5.71 | 2.76 | 0.00 | 5.68 | 1.24 |
time (sec) |
N/A | 1.220 | 0.086 | 0.074 | 0.000 | 0.104 | 0.669 | 0.000 | 0.202 | 23.305 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | A | B | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 34 | 105 | 0 | 194 | 94 | 0 | 193 | 42 |
N.S. |
1 | 0.00 | 1.00 | 3.09 | 0.00 | 5.71 | 2.76 | 0.00 | 5.68 | 1.24 |
time (sec) |
N/A | 0.000 | 0.029 | 0.072 | 0.000 | 0.097 | 0.663 | 0.000 | 0.184 | 23.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 103 | 136 | 0 | 200 | 97 | 95 | 195 | 170 |
N.S. |
1 | 1.00 | 2.64 | 3.49 | 0.00 | 5.13 | 2.49 | 2.44 | 5.00 | 4.36 |
time (sec) |
N/A | 0.924 | 0.129 | 0.553 | 0.000 | 0.117 | 1.095 | 8.404 | 0.190 | 23.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 103 | 136 | 0 | 200 | 97 | 95 | 195 | 170 |
N.S. |
1 | 1.00 | 2.64 | 3.49 | 0.00 | 5.13 | 2.49 | 2.44 | 5.00 | 4.36 |
time (sec) |
N/A | 1.292 | 0.112 | 0.077 | 0.000 | 0.115 | 1.252 | 7.771 | 0.184 | 23.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 0 | 103 | 136 | 0 | 200 | 97 | 46 | 195 | 170 |
N.S. |
1 | 0.00 | 2.64 | 3.49 | 0.00 | 5.13 | 2.49 | 1.18 | 5.00 | 4.36 |
time (sec) |
N/A | 0.000 | 0.114 | 0.076 | 0.000 | 0.110 | 1.079 | 7.647 | 0.179 | 0.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 22291 | 130 | 0 | 454 | 0 | 0 | 113 | 0 |
N.S. |
1 | 1.00 | 619.19 | 3.61 | 0.00 | 12.61 | 0.00 | 0.00 | 3.14 | 0.00 |
time (sec) |
N/A | 0.813 | 16.791 | 0.355 | 0.000 | 0.765 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 22291 | 130 | 0 | 454 | 0 | 0 | 113 | 0 |
N.S. |
1 | 1.00 | 619.19 | 3.61 | 0.00 | 12.61 | 0.00 | 0.00 | 3.14 | 0.00 |
time (sec) |
N/A | 1.228 | 6.271 | 0.116 | 0.000 | 0.803 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 23155 | 131 | 0 | 451 | 0 | 0 | 118 | 0 |
N.S. |
1 | 1.00 | 643.19 | 3.64 | 0.00 | 12.53 | 0.00 | 0.00 | 3.28 | 0.00 |
time (sec) |
N/A | 0.845 | 17.213 | 0.289 | 0.000 | 0.764 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 23156 | 131 | 0 | 451 | 0 | 0 | 118 | 0 |
N.S. |
1 | 1.00 | 643.22 | 3.64 | 0.00 | 12.53 | 0.00 | 0.00 | 3.28 | 0.00 |
time (sec) |
N/A | 1.331 | 16.922 | 0.112 | 0.000 | 0.755 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 45669 | 163 | 0 | 463 | 0 | 0 | 116 | 0 |
N.S. |
1 | 1.00 | 1113.88 | 3.98 | 0.00 | 11.29 | 0.00 | 0.00 | 2.83 | 0.00 |
time (sec) |
N/A | 1.453 | 17.448 | 0.414 | 0.000 | 3.652 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 45669 | 163 | 0 | 463 | 0 | 0 | 116 | 0 |
N.S. |
1 | 1.00 | 1113.88 | 3.98 | 0.00 | 11.29 | 0.00 | 0.00 | 2.83 | 0.00 |
time (sec) |
N/A | 1.936 | 6.118 | 0.286 | 0.000 | 3.627 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 45669 | 165 | 0 | 459 | 0 | 0 | 121 | 0 |
N.S. |
1 | 1.00 | 1113.88 | 4.02 | 0.00 | 11.20 | 0.00 | 0.00 | 2.95 | 0.00 |
time (sec) |
N/A | 1.526 | 17.825 | 0.724 | 0.000 | 3.718 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 45670 | 165 | 0 | 459 | 0 | 0 | 121 | 0 |
N.S. |
1 | 1.00 | 1113.90 | 4.02 | 0.00 | 11.20 | 0.00 | 0.00 | 2.95 | 0.00 |
time (sec) |
N/A | 2.003 | 17.411 | 0.157 | 0.000 | 3.911 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 62 | 0 | 31 | 0 | 0 | 70 | 170 |
N.S. |
1 | 1.00 | 1.00 | 3.88 | 0.00 | 1.94 | 0.00 | 0.00 | 4.38 | 10.62 |
time (sec) |
N/A | 0.535 | 2.197 | 0.383 | 0.000 | 0.105 | 0.000 | 0.000 | 0.185 | 23.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | F | B | F | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 16 | 62 | 0 | 31 | 0 | 0 | 70 | 170 |
N.S. |
1 | 0.00 | 1.00 | 3.88 | 0.00 | 1.94 | 0.00 | 0.00 | 4.38 | 10.62 |
time (sec) |
N/A | 0.000 | 2.424 | 0.215 | 0.000 | 0.097 | 0.000 | 0.000 | 0.186 | 23.070 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 45 | 42 | 28 | 27 | 25 | 37 | 27 | 26 | 27 |
N.S. |
1 | 1.10 | 1.02 | 0.68 | 0.66 | 0.61 | 0.90 | 0.66 | 0.63 | 0.66 |
time (sec) |
N/A | 0.441 | 0.057 | 0.034 | 0.121 | 0.081 | 3.292 | 0.137 | 0.186 | 22.847 |
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 | 26 | 30 | 26 | 21 | 20 | 20 | 24 | 20 | 20 | 22 |
N.S. |
1 | 1.15 | 1.00 | 0.81 | 0.77 | 0.77 | 0.92 | 0.77 | 0.77 | 0.85 |
time (sec) |
N/A | 0.353 | 0.064 | 252.066 | 0.120 | 0.073 | 0.692 | 0.133 | 0.209 | 22.649 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 36 | 42 | 31 | 30 | 30 | 39 | 30 | 30 | 42 |
N.S. |
1 | 0.86 | 1.00 | 0.74 | 0.71 | 0.71 | 0.93 | 0.71 | 0.71 | 1.00 |
time (sec) |
N/A | 0.418 | 0.056 | 0.031 | 0.133 | 0.099 | 4.544 | 0.136 | 0.173 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 22 | 48 | 50 | 0 | 69 | 0 | 44 | 53 | 17 |
N.S. |
1 | 1.10 | 2.40 | 2.50 | 0.00 | 3.45 | 0.00 | 2.20 | 2.65 | 0.85 |
time (sec) |
N/A | 0.257 | 0.043 | 0.066 | 0.000 | 0.099 | 0.000 | 0.121 | 0.184 | 23.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 22 | 52 | 61 | 0 | 72 | 0 | 40 | 28 | 21 |
N.S. |
1 | 1.10 | 2.60 | 3.05 | 0.00 | 3.60 | 0.00 | 2.00 | 1.40 | 1.05 |
time (sec) |
N/A | 0.260 | 0.044 | 0.069 | 0.000 | 0.078 | 0.000 | 0.107 | 0.175 | 22.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 124 | 160 | 247 | 0 | 1508 | 0 | 0 | 148 | 0 |
N.S. |
1 | 1.02 | 1.32 | 2.04 | 0.00 | 12.46 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.604 | 0.415 | 0.104 | 0.000 | 0.540 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 184 | 186 | 395 | 0 | 2411 | 0 | 0 | 163 | 0 |
N.S. |
1 | 1.02 | 1.03 | 2.18 | 0.00 | 13.32 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.843 | 0.769 | 0.131 | 0.000 | 39.156 | 0.000 | 0.000 | 0.409 | 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 | 26 | 26 | 26 | 17 | 16 | 16 | 22 | 11 | 11 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.65 | 0.62 | 0.62 | 0.85 | 0.42 | 0.42 | 0.62 |
time (sec) |
N/A | 0.261 | 8.246 | 0.066 | 0.041 | 0.072 | 45.694 | 0.114 | 0.186 | 22.668 |
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 | 26 | 28 | 47 | 23 | 22 | 34 | 17 | 22 | 29 | 22 |
N.S. |
1 | 1.08 | 1.81 | 0.88 | 0.85 | 1.31 | 0.65 | 0.85 | 1.12 | 0.85 |
time (sec) |
N/A | 0.265 | 0.099 | 0.263 | 0.135 | 0.098 | 0.381 | 0.130 | 0.168 | 22.686 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 13 | 10 | 11 | 11 | 12 | 11 | 25 | 9 |
N.S. |
1 | 1.00 | 0.87 | 0.67 | 0.73 | 0.73 | 0.80 | 0.73 | 1.67 | 0.60 |
time (sec) |
N/A | 0.218 | 10.016 | 0.065 | 0.031 | 0.073 | 0.065 | 0.112 | 0.693 | 22.889 |
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 | 22 | 22 | 19 | 16 | 28 | 27 | 0 | 27 | 33 | 18 |
N.S. |
1 | 1.00 | 0.86 | 0.73 | 1.27 | 1.23 | 0.00 | 1.23 | 1.50 | 0.82 |
time (sec) |
N/A | 0.225 | 0.103 | 0.082 | 0.031 | 0.080 | 0.000 | 0.126 | 0.183 | 22.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 41 | 9 | 9 | 17 | 0 | 17 | 23 | 0 |
N.S. |
1 | 1.00 | 3.42 | 0.75 | 0.75 | 1.42 | 0.00 | 1.42 | 1.92 | 0.00 |
time (sec) |
N/A | 0.229 | 0.081 | 0.190 | 0.114 | 0.087 | 0.000 | 0.125 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 43 | 11 | 11 | 17 | 0 | 17 | 45 | 0 |
N.S. |
1 | 1.00 | 3.58 | 0.92 | 0.92 | 1.42 | 0.00 | 1.42 | 3.75 | 0.00 |
time (sec) |
N/A | 0.239 | 0.065 | 0.217 | 0.129 | 0.071 | 0.000 | 0.119 | 0.185 | 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 | 15 | 15 | 12 | 11 | 13 | 13 | 10 | 13 | 10 | 10 |
N.S. |
1 | 1.00 | 0.80 | 0.73 | 0.87 | 0.87 | 0.67 | 0.87 | 0.67 | 0.67 |
time (sec) |
N/A | 0.219 | 0.053 | 0.061 | 0.042 | 0.068 | 0.065 | 0.131 | 0.164 | 22.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 58 | 82 | 47 | 42 | 52 | 0 | 53 | 107 | 0 |
N.S. |
1 | 1.07 | 1.52 | 0.87 | 0.78 | 0.96 | 0.00 | 0.98 | 1.98 | 0.00 |
time (sec) |
N/A | 0.360 | 0.179 | 0.520 | 0.127 | 0.075 | 0.000 | 0.122 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 47 | 38 | 0 | 0 | 0 | 45 | 51 | 27 |
N.S. |
1 | 1.00 | 0.80 | 0.64 | 0.00 | 0.00 | 0.00 | 0.76 | 0.86 | 0.46 |
time (sec) |
N/A | 0.355 | 0.428 | 0.590 | 0.000 | 0.000 | 0.000 | 0.578 | 0.194 | 22.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 64 | 39 | 28 | 0 | 30 | 0 | 33 | 21 | 27 |
N.S. |
1 | 1.08 | 0.66 | 0.47 | 0.00 | 0.51 | 0.00 | 0.56 | 0.36 | 0.46 |
time (sec) |
N/A | 0.306 | 0.045 | 0.056 | 0.000 | 0.142 | 0.000 | 0.126 | 0.165 | 22.737 |
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 | 94 | 109 | 51 | 38 | 0 | 40 | 0 | 51 | 33 | 0 |
N.S. |
1 | 1.16 | 0.54 | 0.40 | 0.00 | 0.43 | 0.00 | 0.54 | 0.35 | 0.00 |
time (sec) |
N/A | 0.401 | 0.052 | 0.036 | 0.000 | 0.108 | 0.000 | 0.117 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 20 | 0 | 20 | 29 | 18 | 10 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 0.00 | 1.11 | 1.61 | 1.00 | 0.56 | 1.06 |
time (sec) |
N/A | 0.253 | 0.081 | 0.063 | 0.000 | 0.073 | 0.328 | 0.151 | 0.167 | 22.778 |
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 | 96 | 91 | 82 | 47 | 0 | 62 | 0 | 60 | 55 | 0 |
N.S. |
1 | 0.95 | 0.85 | 0.49 | 0.00 | 0.65 | 0.00 | 0.62 | 0.57 | 0.00 |
time (sec) |
N/A | 0.367 | 0.126 | 0.237 | 0.000 | 0.077 | 0.000 | 0.126 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 24 | 25 | 24 | 14 | 64 | 0 | 14 | 30 | 25 |
N.S. |
1 | 0.96 | 1.00 | 0.96 | 0.56 | 2.56 | 0.00 | 0.56 | 1.20 | 1.00 |
time (sec) |
N/A | 0.260 | 0.056 | 0.901 | 0.043 | 0.075 | 0.000 | 0.124 | 0.181 | 23.340 |
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 | 42 | 44 | 42 | 34 | 33 | 35 | 49 | 33 | 29 | 35 |
N.S. |
1 | 1.05 | 1.00 | 0.81 | 0.79 | 0.83 | 1.17 | 0.79 | 0.69 | 0.83 |
time (sec) |
N/A | 0.316 | 0.056 | 0.175 | 0.125 | 0.077 | 0.110 | 0.109 | 0.183 | 0.054 |