Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 84 | 46 | 43 | 46 | 42 | 0 | 64 | 34 | 42 |
N.S. |
1 | 1.08 | 0.59 | 0.55 | 0.59 | 0.54 | 0.00 | 0.82 | 0.44 | 0.54 |
time (sec) |
N/A | 0.375 | 0.029 | 0.790 | 0.037 | 0.071 | 0.000 | 0.112 | 0.171 | 16.986 |
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 | 50 | 50 | 34 | 32 | 34 | 30 | 0 | 48 | 22 | 33 |
N.S. |
1 | 1.00 | 0.68 | 0.64 | 0.68 | 0.60 | 0.00 | 0.96 | 0.44 | 0.66 |
time (sec) |
N/A | 0.326 | 0.022 | 0.649 | 0.037 | 0.078 | 0.000 | 0.114 | 0.172 | 17.629 |
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 | 22 | 21 | 13 | 20 | 0 | 28 | 12 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.59 | 0.91 | 0.00 | 1.27 | 0.55 | 0.91 |
time (sec) |
N/A | 0.262 | 0.004 | 0.546 | 0.035 | 0.069 | 0.000 | 0.153 | 0.170 | 18.640 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 52 | 50 | 0 | 75 | 0 | 46 | 53 | 0 |
N.S. |
1 | 1.00 | 1.73 | 1.67 | 0.00 | 2.50 | 0.00 | 1.53 | 1.77 | 0.00 |
time (sec) |
N/A | 0.252 | 0.022 | 0.480 | 0.000 | 0.078 | 0.000 | 0.154 | 0.172 | 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 | 59 | 59 | 76 | 73 | 0 | 128 | 0 | 52 | 79 | 76 |
N.S. |
1 | 1.00 | 1.29 | 1.24 | 0.00 | 2.17 | 0.00 | 0.88 | 1.34 | 1.29 |
time (sec) |
N/A | 0.305 | 0.060 | 0.561 | 0.000 | 0.090 | 0.000 | 0.137 | 0.181 | 18.351 |
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 | 87 | 93 | 91 | 94 | 0 | 158 | 0 | 79 | 101 | 0 |
N.S. |
1 | 1.07 | 1.05 | 1.08 | 0.00 | 1.82 | 0.00 | 0.91 | 1.16 | 0.00 |
time (sec) |
N/A | 0.362 | 0.080 | 0.670 | 0.000 | 0.085 | 0.000 | 0.175 | 0.177 | 0.000 |
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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 115 | 99 | 87 | 103 | 209 | 0 | 96 | 137 | 0 |
N.S. |
1 | 1.03 | 0.88 | 0.78 | 0.92 | 1.87 | 0.00 | 0.86 | 1.22 | 0.00 |
time (sec) |
N/A | 0.518 | 0.222 | 0.196 | 0.037 | 0.085 | 0.000 | 0.158 | 0.176 | 0.000 |
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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 85 | 85 | 73 | 77 | 180 | 0 | 74 | 114 | 0 |
N.S. |
1 | 1.05 | 1.05 | 0.90 | 0.95 | 2.22 | 0.00 | 0.91 | 1.41 | 0.00 |
time (sec) |
N/A | 0.404 | 0.172 | 0.182 | 0.044 | 0.081 | 0.000 | 0.119 | 0.179 | 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 | 55 | 60 | 73 | 63 | 54 | 150 | 0 | 57 | 88 | 55 |
N.S. |
1 | 1.09 | 1.33 | 1.15 | 0.98 | 2.73 | 0.00 | 1.04 | 1.60 | 1.00 |
time (sec) |
N/A | 0.329 | 0.086 | 0.160 | 0.045 | 0.079 | 0.000 | 0.127 | 0.176 | 18.339 |
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 | 22 | 21 | 20 | 26 | 0 | 18 | 39 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 1.18 | 0.00 | 0.82 | 1.77 | 1.18 |
time (sec) |
N/A | 0.251 | 0.032 | 0.128 | 0.037 | 0.067 | 0.000 | 0.138 | 0.185 | 17.546 |
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 | 28 | 28 | 29 | 27 | 41 | 41 | 0 | 58 | 56 | 26 |
N.S. |
1 | 1.00 | 1.04 | 0.96 | 1.46 | 1.46 | 0.00 | 2.07 | 2.00 | 0.93 |
time (sec) |
N/A | 0.272 | 0.045 | 0.156 | 0.038 | 0.070 | 0.000 | 0.121 | 0.172 | 16.913 |
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 | 57 | 57 | 46 | 41 | 65 | 54 | 0 | 114 | 81 | 51 |
N.S. |
1 | 1.00 | 0.81 | 0.72 | 1.14 | 0.95 | 0.00 | 2.00 | 1.42 | 0.89 |
time (sec) |
N/A | 0.331 | 0.063 | 0.173 | 0.038 | 0.074 | 0.000 | 0.145 | 0.179 | 17.293 |
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 | 85 | 91 | 57 | 52 | 89 | 63 | 0 | 169 | 102 | 60 |
N.S. |
1 | 1.07 | 0.67 | 0.61 | 1.05 | 0.74 | 0.00 | 1.99 | 1.20 | 0.71 |
time (sec) |
N/A | 0.397 | 0.078 | 0.182 | 0.041 | 0.078 | 0.000 | 0.128 | 0.180 | 17.397 |
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 | 113 | 125 | 68 | 65 | 113 | 76 | 0 | 222 | 121 | 114 |
N.S. |
1 | 1.11 | 0.60 | 0.58 | 1.00 | 0.67 | 0.00 | 1.96 | 1.07 | 1.01 |
time (sec) |
N/A | 0.469 | 0.086 | 0.211 | 0.039 | 0.084 | 0.000 | 0.137 | 0.180 | 18.547 |
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 | 106 | 113 | 54 | 60 | 45 | 62 | 0 | 86 | 53 | 61 |
N.S. |
1 | 1.07 | 0.51 | 0.57 | 0.42 | 0.58 | 0.00 | 0.81 | 0.50 | 0.58 |
time (sec) |
N/A | 0.429 | 0.033 | 1.196 | 0.043 | 0.071 | 0.000 | 0.104 | 0.178 | 18.612 |
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 | 78 | 79 | 43 | 50 | 34 | 51 | 0 | 76 | 42 | 51 |
N.S. |
1 | 1.01 | 0.55 | 0.64 | 0.44 | 0.65 | 0.00 | 0.97 | 0.54 | 0.65 |
time (sec) |
N/A | 0.362 | 0.030 | 0.970 | 0.039 | 0.076 | 0.000 | 0.110 | 0.171 | 18.168 |
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 | 45 | 45 | 29 | 37 | 22 | 39 | 0 | 51 | 30 | 38 |
N.S. |
1 | 1.00 | 0.64 | 0.82 | 0.49 | 0.87 | 0.00 | 1.13 | 0.67 | 0.84 |
time (sec) |
N/A | 0.295 | 0.025 | 0.789 | 0.039 | 0.083 | 0.000 | 0.122 | 0.173 | 18.441 |
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 | 29 | 14 | 29 | 0 | 28 | 22 | 30 |
N.S. |
1 | 1.00 | 1.00 | 1.38 | 0.67 | 1.38 | 0.00 | 1.33 | 1.05 | 1.43 |
time (sec) |
N/A | 0.245 | 0.004 | 0.648 | 0.040 | 0.078 | 0.000 | 0.129 | 0.184 | 18.154 |
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 | 51 | 51 | 59 | 65 | 0 | 157 | 0 | 79 | 136 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.27 | 0.00 | 3.08 | 0.00 | 1.55 | 2.67 | 0.00 |
time (sec) |
N/A | 0.302 | 0.040 | 0.560 | 0.000 | 0.082 | 0.000 | 0.118 | 0.179 | 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 | 81 | 87 | 78 | 77 | 0 | 194 | 0 | 80 | 172 | 42 |
N.S. |
1 | 1.07 | 0.96 | 0.95 | 0.00 | 2.40 | 0.00 | 0.99 | 2.12 | 0.52 |
time (sec) |
N/A | 0.375 | 0.074 | 0.522 | 0.000 | 0.083 | 0.000 | 0.153 | 0.179 | 17.838 |
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 | 109 | 121 | 92 | 94 | 0 | 224 | 0 | 99 | 195 | 44 |
N.S. |
1 | 1.11 | 0.84 | 0.86 | 0.00 | 2.06 | 0.00 | 0.91 | 1.79 | 0.40 |
time (sec) |
N/A | 0.439 | 0.096 | 0.602 | 0.000 | 0.095 | 0.000 | 0.131 | 0.182 | 17.498 |
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 | 36 | 40 | 58 | 27 | 26 | 43 | 0 | 30 | 22 | 42 |
N.S. |
1 | 1.11 | 1.61 | 0.75 | 0.72 | 1.19 | 0.00 | 0.83 | 0.61 | 1.17 |
time (sec) |
N/A | 0.301 | 0.037 | 0.351 | 0.117 | 0.070 | 0.000 | 0.133 | 0.168 | 17.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 40 | 59 | 27 | 26 | 59 | 0 | 43 | 23 | 41 |
N.S. |
1 | 1.11 | 1.64 | 0.75 | 0.72 | 1.64 | 0.00 | 1.19 | 0.64 | 1.14 |
time (sec) |
N/A | 0.297 | 0.034 | 0.333 | 0.108 | 0.065 | 0.000 | 0.117 | 0.178 | 17.487 |
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 | 45 | 49 | 58 | 37 | 41 | 45 | 0 | 43 | 32 | 40 |
N.S. |
1 | 1.09 | 1.29 | 0.82 | 0.91 | 1.00 | 0.00 | 0.96 | 0.71 | 0.89 |
time (sec) |
N/A | 0.306 | 0.006 | 0.246 | 0.115 | 0.070 | 0.000 | 0.114 | 0.175 | 18.456 |
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 | 45 | 49 | 58 | 42 | 41 | 45 | 0 | 44 | 32 | 40 |
N.S. |
1 | 1.09 | 1.29 | 0.93 | 0.91 | 1.00 | 0.00 | 0.98 | 0.71 | 0.89 |
time (sec) |
N/A | 0.323 | 0.006 | 0.263 | 0.109 | 0.070 | 0.000 | 0.125 | 0.181 | 18.501 |
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 | 58 | 57 | 83 | 63 | 52 | 114 | 0 | 59 | 41 | 53 |
N.S. |
1 | 0.98 | 1.43 | 1.09 | 0.90 | 1.97 | 0.00 | 1.02 | 0.71 | 0.91 |
time (sec) |
N/A | 0.340 | 0.127 | 0.216 | 0.036 | 0.085 | 0.000 | 0.116 | 0.170 | 18.460 |
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 | 60 | 59 | 88 | 56 | 42 | 120 | 0 | 73 | 32 | 60 |
N.S. |
1 | 0.98 | 1.47 | 0.93 | 0.70 | 2.00 | 0.00 | 1.22 | 0.53 | 1.00 |
time (sec) |
N/A | 0.337 | 0.117 | 0.612 | 0.115 | 0.092 | 0.000 | 0.176 | 0.172 | 17.930 |
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 | 323 | 344 | 102 | 237 | 0 | 73 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.07 | 0.32 | 0.73 | 0.00 | 0.23 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.799 | 10.047 | 0.666 | 0.000 | 0.088 | 0.000 | 0.000 | 0.203 | 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 | 176 | 187 | 102 | 157 | 0 | 68 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.06 | 0.58 | 0.89 | 0.00 | 0.39 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.554 | 10.038 | 0.358 | 0.000 | 0.090 | 0.000 | 0.000 | 0.206 | 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 | 293 | 308 | 86 | 226 | 0 | 61 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.05 | 0.29 | 0.77 | 0.00 | 0.21 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.685 | 10.032 | 0.352 | 0.000 | 0.094 | 0.000 | 0.000 | 0.201 | 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 | 146 | 151 | 86 | 145 | 0 | 58 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.03 | 0.59 | 0.99 | 0.00 | 0.40 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.467 | 9.824 | 0.287 | 0.000 | 0.104 | 0.000 | 0.000 | 0.199 | 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 | 263 | 272 | 57 | 213 | 0 | 48 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.03 | 0.22 | 0.81 | 0.00 | 0.18 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.629 | 7.925 | 0.279 | 0.000 | 0.089 | 0.000 | 0.000 | 0.201 | 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 | 118 | 118 | 55 | 130 | 0 | 43 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 0.47 | 1.10 | 0.00 | 0.36 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.398 | 6.835 | 0.276 | 0.000 | 0.091 | 0.000 | 0.000 | 0.192 | 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 | 254 | 268 | 55 | 202 | 0 | 48 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.06 | 0.22 | 0.80 | 0.00 | 0.19 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.612 | 10.013 | 0.356 | 0.000 | 0.090 | 0.000 | 0.000 | 0.207 | 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 | 118 | 118 | 57 | 125 | 0 | 41 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.00 | 0.48 | 1.06 | 0.00 | 0.35 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.394 | 10.013 | 0.373 | 0.000 | 0.093 | 0.000 | 0.000 | 0.219 | 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 | 293 | 304 | 57 | 224 | 0 | 59 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.04 | 0.19 | 0.76 | 0.00 | 0.20 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.696 | 10.013 | 0.460 | 0.000 | 0.086 | 0.000 | 0.000 | 0.226 | 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 | 146 | 151 | 57 | 142 | 0 | 53 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.03 | 0.39 | 0.97 | 0.00 | 0.36 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.467 | 10.014 | 0.494 | 0.000 | 0.092 | 0.000 | 0.000 | 0.254 | 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 | 323 | 340 | 57 | 239 | 0 | 72 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.05 | 0.18 | 0.74 | 0.00 | 0.22 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.751 | 10.014 | 0.600 | 0.000 | 0.093 | 0.000 | 0.000 | 0.282 | 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 | 176 | 187 | 57 | 156 | 0 | 64 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.06 | 0.32 | 0.89 | 0.00 | 0.36 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.596 | 10.012 | 0.625 | 0.000 | 0.089 | 0.000 | 0.000 | 0.304 | 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 | 350 | 374 | 101 | 248 | 0 | 84 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.07 | 0.29 | 0.71 | 0.00 | 0.24 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.838 | 10.066 | 1.457 | 0.000 | 0.098 | 0.000 | 0.000 | 0.207 | 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 | 203 | 217 | 101 | 168 | 0 | 79 | 0 | 0 | 106 | 0 |
N.S. |
1 | 1.07 | 0.50 | 0.83 | 0.00 | 0.39 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.609 | 10.042 | 1.138 | 0.000 | 0.098 | 0.000 | 0.000 | 0.212 | 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 | 320 | 338 | 90 | 237 | 0 | 72 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.06 | 0.28 | 0.74 | 0.00 | 0.22 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.755 | 10.032 | 0.950 | 0.000 | 0.095 | 0.000 | 0.000 | 0.210 | 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 | 173 | 181 | 90 | 157 | 0 | 69 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.05 | 0.52 | 0.91 | 0.00 | 0.40 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.518 | 10.035 | 0.740 | 0.000 | 0.091 | 0.000 | 0.000 | 0.198 | 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 | 290 | 302 | 58 | 226 | 0 | 62 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.04 | 0.20 | 0.78 | 0.00 | 0.21 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.698 | 10.013 | 0.636 | 0.000 | 0.085 | 0.000 | 0.000 | 0.194 | 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 | 143 | 148 | 56 | 145 | 0 | 56 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.03 | 0.39 | 1.01 | 0.00 | 0.39 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.474 | 9.242 | 0.586 | 0.000 | 0.089 | 0.000 | 0.000 | 0.201 | 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 | 286 | 298 | 56 | 216 | 0 | 59 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.04 | 0.20 | 0.76 | 0.00 | 0.21 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.680 | 10.014 | 0.678 | 0.000 | 0.078 | 0.000 | 0.000 | 0.211 | 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 | 143 | 146 | 58 | 130 | 0 | 50 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.02 | 0.41 | 0.91 | 0.00 | 0.35 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.452 | 10.014 | 0.798 | 0.000 | 0.093 | 0.000 | 0.000 | 0.223 | 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 | 287 | 298 | 58 | 220 | 0 | 56 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.04 | 0.20 | 0.77 | 0.00 | 0.20 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.680 | 10.014 | 1.036 | 0.000 | 0.086 | 0.000 | 0.000 | 0.230 | 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 | 143 | 148 | 58 | 140 | 0 | 49 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.03 | 0.41 | 0.98 | 0.00 | 0.34 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.451 | 10.016 | 1.241 | 0.000 | 0.070 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 320 | 334 | 58 | 239 | 0 | 72 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.04 | 0.18 | 0.75 | 0.00 | 0.22 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.748 | 10.014 | 1.527 | 0.000 | 0.070 | 0.000 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 181 | 58 | 156 | 0 | 64 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.05 | 0.34 | 0.90 | 0.00 | 0.37 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.544 | 10.018 | 1.806 | 0.000 | 0.070 | 0.000 | 0.000 | 0.317 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 350 | 370 | 58 | 250 | 0 | 83 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.06 | 0.17 | 0.71 | 0.00 | 0.24 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.853 | 10.016 | 2.265 | 0.000 | 0.077 | 0.000 | 0.000 | 0.389 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 217 | 58 | 167 | 0 | 75 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.07 | 0.29 | 0.82 | 0.00 | 0.37 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.603 | 10.031 | 2.651 | 0.000 | 0.079 | 0.000 | 0.000 | 0.430 | 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 | 179 | 193 | 97 | 148 | 0 | 69 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.08 | 0.54 | 0.83 | 0.00 | 0.39 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.570 | 10.042 | 1.073 | 0.000 | 0.082 | 0.000 | 0.000 | 0.215 | 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 | 296 | 314 | 86 | 217 | 0 | 62 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.06 | 0.29 | 0.73 | 0.00 | 0.21 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.714 | 10.039 | 0.947 | 0.000 | 0.077 | 0.000 | 0.000 | 0.207 | 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 | 149 | 157 | 86 | 137 | 0 | 57 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.05 | 0.58 | 0.92 | 0.00 | 0.38 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.485 | 10.023 | 0.713 | 0.000 | 0.082 | 0.000 | 0.000 | 0.200 | 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 | 266 | 278 | 70 | 206 | 0 | 47 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.05 | 0.26 | 0.77 | 0.00 | 0.18 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.631 | 10.022 | 0.626 | 0.000 | 0.080 | 0.000 | 0.000 | 0.209 | 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 | 121 | 121 | 70 | 123 | 0 | 43 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 0.58 | 1.02 | 0.00 | 0.36 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.428 | 10.029 | 0.290 | 0.000 | 0.086 | 0.000 | 0.000 | 0.195 | 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 | 231 | 244 | 57 | 131 | 0 | 22 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 0.25 | 0.57 | 0.00 | 0.10 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.567 | 10.017 | 0.237 | 0.000 | 0.075 | 0.000 | 0.000 | 0.179 | 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 | 90 | 90 | 55 | 106 | 0 | 14 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.61 | 1.18 | 0.00 | 0.16 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.358 | 10.014 | 0.629 | 0.000 | 0.074 | 0.000 | 0.000 | 0.177 | 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 | 259 | 274 | 55 | 195 | 0 | 50 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.06 | 0.21 | 0.75 | 0.00 | 0.19 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.624 | 10.013 | 0.856 | 0.000 | 0.080 | 0.000 | 0.000 | 0.181 | 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 | 121 | 121 | 57 | 119 | 0 | 42 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.47 | 0.98 | 0.00 | 0.35 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.428 | 10.016 | 1.137 | 0.000 | 0.071 | 0.000 | 0.000 | 0.195 | 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 | 296 | 310 | 57 | 215 | 0 | 61 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.05 | 0.19 | 0.73 | 0.00 | 0.21 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.712 | 10.013 | 1.396 | 0.000 | 0.078 | 0.000 | 0.000 | 0.185 | 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 | 149 | 157 | 57 | 134 | 0 | 53 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.05 | 0.38 | 0.90 | 0.00 | 0.36 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.475 | 10.013 | 1.802 | 0.000 | 0.087 | 0.000 | 0.000 | 0.193 | 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 | 326 | 346 | 57 | 230 | 0 | 72 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.06 | 0.17 | 0.71 | 0.00 | 0.22 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.782 | 10.025 | 2.252 | 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 | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 193 | 57 | 147 | 0 | 64 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.08 | 0.32 | 0.82 | 0.00 | 0.36 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.554 | 10.028 | 2.726 | 0.000 | 0.077 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 190 | 86 | 144 | 0 | 88 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.09 | 0.49 | 0.83 | 0.00 | 0.51 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.575 | 10.035 | 1.879 | 0.000 | 0.085 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 311 | 72 | 213 | 0 | 80 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.07 | 0.25 | 0.73 | 0.00 | 0.27 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.712 | 10.025 | 1.879 | 0.000 | 0.088 | 0.000 | 0.000 | 0.229 | 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 | 146 | 154 | 73 | 131 | 0 | 76 | 0 | 0 | 128 | 0 |
N.S. |
1 | 1.05 | 0.50 | 0.90 | 0.00 | 0.52 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.496 | 10.021 | 1.575 | 0.000 | 0.089 | 0.000 | 0.000 | 0.236 | 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 | 259 | 273 | 61 | 200 | 0 | 65 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.05 | 0.24 | 0.77 | 0.00 | 0.25 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.622 | 10.023 | 0.976 | 0.000 | 0.080 | 0.000 | 0.000 | 0.226 | 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 | 119 | 119 | 60 | 120 | 0 | 59 | 0 | 0 | 106 | 0 |
N.S. |
1 | 1.00 | 0.50 | 1.01 | 0.00 | 0.50 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.394 | 10.016 | 0.348 | 0.000 | 0.078 | 0.000 | 0.000 | 0.224 | 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 | 260 | 272 | 60 | 203 | 0 | 64 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.05 | 0.23 | 0.78 | 0.00 | 0.25 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.625 | 10.014 | 0.351 | 0.000 | 0.074 | 0.000 | 0.000 | 0.180 | 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 | 118 | 118 | 60 | 123 | 0 | 59 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.51 | 1.04 | 0.00 | 0.50 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.400 | 9.874 | 1.161 | 0.000 | 0.072 | 0.000 | 0.000 | 0.186 | 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 | 286 | 306 | 58 | 203 | 0 | 81 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.07 | 0.20 | 0.71 | 0.00 | 0.28 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.698 | 10.015 | 2.036 | 0.000 | 0.073 | 0.000 | 0.000 | 0.190 | 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 | 145 | 153 | 60 | 127 | 0 | 73 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.06 | 0.41 | 0.88 | 0.00 | 0.50 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.459 | 10.014 | 2.310 | 0.000 | 0.075 | 0.000 | 0.000 | 0.199 | 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 | 320 | 342 | 60 | 222 | 0 | 95 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.07 | 0.19 | 0.69 | 0.00 | 0.30 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.761 | 10.016 | 2.296 | 0.000 | 0.089 | 0.000 | 0.000 | 0.211 | 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 | 173 | 189 | 60 | 141 | 0 | 87 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.09 | 0.35 | 0.82 | 0.00 | 0.50 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.562 | 10.024 | 1.752 | 0.000 | 0.087 | 0.000 | 0.000 | 0.222 | 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 | 350 | 378 | 60 | 237 | 0 | 108 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.08 | 0.17 | 0.68 | 0.00 | 0.31 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.850 | 10.024 | 2.002 | 0.000 | 0.084 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 85 | 59 | 181 | 77 | 161 | 731 | 264 | 181 | 171 |
N.S. |
1 | 1.05 | 0.73 | 2.23 | 0.95 | 1.99 | 9.02 | 3.26 | 2.23 | 2.11 |
time (sec) |
N/A | 0.397 | 0.063 | 0.198 | 0.039 | 0.085 | 0.673 | 0.119 | 0.183 | 17.803 |
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 | 58 | 62 | 43 | 96 | 55 | 89 | 337 | 141 | 96 | 97 |
N.S. |
1 | 1.07 | 0.74 | 1.66 | 0.95 | 1.53 | 5.81 | 2.43 | 1.66 | 1.67 |
time (sec) |
N/A | 0.364 | 0.050 | 0.086 | 0.037 | 0.233 | 0.424 | 0.111 | 0.180 | 17.925 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 39 | 27 | 36 | 33 | 39 | 112 | 56 | 39 | 38 |
N.S. |
1 | 1.11 | 0.77 | 1.03 | 0.94 | 1.11 | 3.20 | 1.60 | 1.11 | 1.09 |
time (sec) |
N/A | 0.318 | 0.027 | 0.070 | 0.035 | 0.086 | 0.255 | 0.111 | 0.191 | 18.061 |
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 | 42 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.292 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 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 | 44 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.288 | 0.030 | 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 | 47 | 47 | 44 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.288 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 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 | 30 | 34 | 30 | 25 | 24 | 24 | 24 | 24 | 26 | 24 |
N.S. |
1 | 1.13 | 1.00 | 0.83 | 0.80 | 0.80 | 0.80 | 0.80 | 0.87 | 0.80 |
time (sec) |
N/A | 0.315 | 0.002 | 0.109 | 0.031 | 0.070 | 0.017 | 0.109 | 0.167 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 34 | 30 | 25 | 24 | 24 | 24 | 24 | 26 | 24 |
N.S. |
1 | 1.13 | 1.00 | 0.83 | 0.80 | 0.80 | 0.80 | 0.80 | 0.87 | 0.80 |
time (sec) |
N/A | 0.314 | 0.001 | 0.107 | 0.031 | 0.068 | 0.017 | 0.127 | 0.160 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 25 | 24 | 24 | 24 | 24 | 25 | 24 |
N.S. |
1 | 1.00 | 1.00 | 1.56 | 1.50 | 1.50 | 1.50 | 1.50 | 1.56 | 1.50 |
time (sec) |
N/A | 0.253 | 0.002 | 0.040 | 0.033 | 0.068 | 0.018 | 0.133 | 0.168 | 0.034 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 30 | 23 | 22 | 24 | 21 | 20 | 24 | 21 | 21 |
N.S. |
1 | 1.30 | 1.00 | 0.96 | 1.04 | 0.91 | 0.87 | 1.04 | 0.91 | 0.91 |
time (sec) |
N/A | 0.296 | 0.001 | 0.063 | 0.031 | 0.073 | 0.034 | 0.123 | 0.163 | 0.031 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 28 | 27 | 24 | 24 | 27 | 24 | 32 | 27 | 23 |
N.S. |
1 | 1.04 | 1.00 | 0.89 | 0.89 | 1.00 | 0.89 | 1.19 | 1.00 | 0.85 |
time (sec) |
N/A | 0.306 | 0.001 | 0.050 | 0.031 | 0.073 | 0.050 | 0.132 | 0.166 | 17.717 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 30 | 24 | 23 | 26 | 28 | 24 | 34 | 28 | 24 |
N.S. |
1 | 1.25 | 1.00 | 0.96 | 1.08 | 1.17 | 1.00 | 1.42 | 1.17 | 1.00 |
time (sec) |
N/A | 0.312 | 0.001 | 0.049 | 0.031 | 0.070 | 0.076 | 0.144 | 0.168 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 30 | 25 | 24 | 24 | 26 | 24 | 26 | 26 |
N.S. |
1 | 1.00 | 1.58 | 1.32 | 1.26 | 1.26 | 1.37 | 1.26 | 1.37 | 1.37 |
time (sec) |
N/A | 0.258 | 0.001 | 0.050 | 0.025 | 0.071 | 0.084 | 0.174 | 0.169 | 0.038 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 34 | 30 | 25 | 26 | 26 | 27 | 26 | 26 | 26 |
N.S. |
1 | 1.13 | 1.00 | 0.83 | 0.87 | 0.87 | 0.90 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.308 | 0.001 | 0.053 | 0.026 | 0.072 | 0.094 | 0.172 | 0.172 | 0.039 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 34 | 30 | 25 | 26 | 26 | 27 | 26 | 26 | 26 |
N.S. |
1 | 1.13 | 1.00 | 0.83 | 0.87 | 0.87 | 0.90 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.305 | 0.001 | 0.056 | 0.026 | 0.131 | 0.102 | 0.103 | 0.166 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 25 | 24 | 24 | 26 | 24 | 26 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.87 | 0.80 | 0.87 | 0.80 |
time (sec) |
N/A | 0.287 | 0.001 | 0.109 | 0.025 | 0.157 | 0.017 | 0.133 | 0.169 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 25 | 24 | 24 | 26 | 24 | 26 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.87 | 0.80 | 0.87 | 0.80 |
time (sec) |
N/A | 0.286 | 0.001 | 0.042 | 0.029 | 0.105 | 0.017 | 0.105 | 0.169 | 0.034 |
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 | 25 | 25 | 25 | 22 | 21 | 21 | 22 | 21 | 24 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.84 | 0.84 | 0.88 | 0.84 | 0.96 | 0.84 |
time (sec) |
N/A | 0.250 | 0.000 | 0.036 | 0.025 | 0.188 | 0.017 | 0.138 | 0.159 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 23 | 22 | 25 | 19 | 22 | 25 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.92 | 1.04 | 0.79 | 0.92 | 1.04 | 0.92 |
time (sec) |
N/A | 0.302 | 0.001 | 0.046 | 0.029 | 0.157 | 0.034 | 0.133 | 0.169 | 0.036 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 22 | 22 | 26 | 22 | 22 | 26 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.96 | 1.13 | 0.96 | 0.96 | 1.13 | 1.04 |
time (sec) |
N/A | 0.302 | 0.001 | 0.044 | 0.026 | 0.105 | 0.058 | 0.152 | 0.174 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 25 | 26 | 26 | 27 | 26 | 26 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.93 | 0.93 | 0.96 | 0.93 | 0.93 | 0.89 |
time (sec) |
N/A | 0.294 | 0.001 | 0.049 | 0.025 | 0.061 | 0.078 | 0.109 | 0.162 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 25 | 26 | 26 | 27 | 26 | 26 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.87 | 0.87 | 0.90 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.288 | 0.001 | 0.049 | 0.026 | 0.135 | 0.087 | 0.100 | 0.169 | 0.038 |