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 | 56 | 60 | 56 | 47 | 46 | 46 | 49 | 46 | 48 | 46 |
N.S. |
1 | 1.07 | 1.00 | 0.84 | 0.82 | 0.82 | 0.88 | 0.82 | 0.86 | 0.82 |
time (sec) |
N/A | 0.360 | 0.002 | 0.125 | 0.030 | 0.131 | 0.020 | 0.105 | 0.169 | 0.027 |
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 | 56 | 57 | 56 | 47 | 46 | 46 | 51 | 46 | 48 | 46 |
N.S. |
1 | 1.02 | 1.00 | 0.84 | 0.82 | 0.82 | 0.91 | 0.82 | 0.86 | 0.82 |
time (sec) |
N/A | 0.357 | 0.002 | 0.125 | 0.026 | 0.067 | 0.019 | 0.120 | 0.170 | 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 | 53 | 57 | 56 | 47 | 46 | 46 | 49 | 46 | 48 | 46 |
N.S. |
1 | 1.08 | 1.06 | 0.89 | 0.87 | 0.87 | 0.92 | 0.87 | 0.91 | 0.87 |
time (sec) |
N/A | 0.346 | 0.002 | 0.115 | 0.026 | 0.066 | 0.021 | 0.122 | 0.181 | 0.025 |
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 | 34 | 38 | 56 | 47 | 46 | 46 | 53 | 46 | 48 | 46 |
N.S. |
1 | 1.12 | 1.65 | 1.38 | 1.35 | 1.35 | 1.56 | 1.35 | 1.41 | 1.35 |
time (sec) |
N/A | 0.312 | 0.002 | 0.113 | 0.031 | 0.144 | 0.021 | 0.109 | 0.165 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 45 | 44 | 44 | 44 | 44 | 47 | 44 |
N.S. |
1 | 1.00 | 1.00 | 2.81 | 2.75 | 2.75 | 2.75 | 2.75 | 2.94 | 2.75 |
time (sec) |
N/A | 0.247 | 0.002 | 0.099 | 0.025 | 0.134 | 0.021 | 0.116 | 0.169 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 54 | 50 | 45 | 47 | 44 | 49 | 47 | 44 | 44 |
N.S. |
1 | 1.08 | 1.00 | 0.90 | 0.94 | 0.88 | 0.98 | 0.94 | 0.88 | 0.88 |
time (sec) |
N/A | 0.333 | 0.003 | 0.102 | 0.031 | 0.142 | 0.047 | 0.102 | 0.168 | 0.028 |
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 | 48 | 53 | 48 | 45 | 46 | 49 | 46 | 56 | 49 | 44 |
N.S. |
1 | 1.10 | 1.00 | 0.94 | 0.96 | 1.02 | 0.96 | 1.17 | 1.02 | 0.92 |
time (sec) |
N/A | 0.344 | 0.004 | 0.060 | 0.026 | 0.084 | 0.064 | 0.135 | 0.167 | 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 | 49 | 55 | 49 | 46 | 48 | 49 | 49 | 59 | 49 | 48 |
N.S. |
1 | 1.12 | 1.00 | 0.94 | 0.98 | 1.00 | 1.00 | 1.20 | 1.00 | 0.98 |
time (sec) |
N/A | 0.348 | 0.004 | 0.076 | 0.030 | 0.077 | 0.096 | 0.171 | 0.168 | 0.040 |
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 | 49 | 52 | 49 | 46 | 48 | 50 | 49 | 57 | 50 | 47 |
N.S. |
1 | 1.06 | 1.00 | 0.94 | 0.98 | 1.02 | 1.00 | 1.16 | 1.02 | 0.96 |
time (sec) |
N/A | 0.340 | 0.004 | 0.058 | 0.031 | 0.088 | 0.124 | 0.139 | 0.167 | 0.046 |
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 | 50 | 54 | 50 | 45 | 50 | 50 | 49 | 58 | 50 | 47 |
N.S. |
1 | 1.08 | 1.00 | 0.90 | 1.00 | 1.00 | 0.98 | 1.16 | 1.00 | 0.94 |
time (sec) |
N/A | 0.346 | 0.004 | 0.056 | 0.028 | 0.165 | 0.155 | 0.138 | 0.170 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 52 | 47 | 46 | 46 | 49 | 46 | 48 | 46 |
N.S. |
1 | 1.00 | 2.74 | 2.47 | 2.42 | 2.42 | 2.58 | 2.42 | 2.53 | 2.42 |
time (sec) |
N/A | 0.261 | 0.004 | 0.056 | 0.031 | 0.113 | 0.168 | 0.124 | 0.174 | 17.652 |
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 | 40 | 44 | 56 | 47 | 48 | 48 | 51 | 48 | 48 | 48 |
N.S. |
1 | 1.10 | 1.40 | 1.18 | 1.20 | 1.20 | 1.28 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.288 | 0.003 | 0.060 | 0.033 | 0.158 | 0.186 | 0.125 | 0.166 | 18.646 |
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 | 56 | 58 | 56 | 47 | 48 | 48 | 51 | 48 | 48 | 48 |
N.S. |
1 | 1.04 | 1.00 | 0.84 | 0.86 | 0.86 | 0.91 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.344 | 0.004 | 0.062 | 0.026 | 0.100 | 0.197 | 0.134 | 0.167 | 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 | 56 | 58 | 56 | 47 | 48 | 48 | 51 | 48 | 48 | 48 |
N.S. |
1 | 1.04 | 1.00 | 0.84 | 0.86 | 0.86 | 0.91 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.341 | 0.004 | 0.066 | 0.031 | 0.078 | 0.213 | 0.108 | 0.177 | 0.040 |
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 | 56 | 60 | 56 | 47 | 48 | 48 | 51 | 48 | 48 | 48 |
N.S. |
1 | 1.07 | 1.00 | 0.84 | 0.86 | 0.86 | 0.91 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.342 | 0.004 | 0.065 | 0.027 | 0.141 | 0.224 | 0.144 | 0.165 | 18.800 |
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 | 56 | 56 | 56 | 47 | 46 | 46 | 53 | 46 | 48 | 46 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.82 | 0.82 | 0.95 | 0.82 | 0.86 | 0.82 |
time (sec) |
N/A | 0.333 | 0.003 | 0.121 | 0.025 | 0.136 | 0.019 | 0.103 | 0.168 | 0.025 |
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 | 56 | 56 | 56 | 47 | 46 | 46 | 53 | 46 | 48 | 46 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.82 | 0.82 | 0.95 | 0.82 | 0.86 | 0.82 |
time (sec) |
N/A | 0.338 | 0.002 | 0.113 | 0.029 | 0.064 | 0.020 | 0.124 | 0.167 | 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 | 56 | 56 | 56 | 47 | 46 | 46 | 53 | 46 | 48 | 46 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.82 | 0.82 | 0.95 | 0.82 | 0.86 | 0.82 |
time (sec) |
N/A | 0.333 | 0.002 | 0.111 | 0.031 | 0.153 | 0.019 | 0.101 | 0.165 | 0.025 |
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 | 51 | 60 | 51 | 44 | 55 | 43 | 49 | 43 | 46 | 43 |
N.S. |
1 | 1.18 | 1.00 | 0.86 | 1.08 | 0.84 | 0.96 | 0.84 | 0.90 | 0.84 |
time (sec) |
N/A | 0.347 | 0.001 | 0.040 | 0.032 | 0.147 | 0.019 | 0.142 | 0.172 | 0.023 |
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 | 48 | 48 | 48 | 45 | 44 | 48 | 44 | 44 | 48 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.92 | 1.00 | 0.92 | 0.92 | 1.00 | 0.92 |
time (sec) |
N/A | 0.338 | 0.006 | 0.088 | 0.026 | 0.089 | 0.041 | 0.126 | 0.164 | 0.026 |
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 | 50 | 50 | 50 | 45 | 45 | 48 | 49 | 45 | 48 | 47 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.90 | 0.96 | 0.98 | 0.90 | 0.96 | 0.94 |
time (sec) |
N/A | 0.328 | 0.005 | 0.057 | 0.031 | 0.119 | 0.065 | 0.120 | 0.161 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 50 | 45 | 47 | 48 | 49 | 47 | 48 | 47 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.94 | 0.96 | 0.98 | 0.94 | 0.96 | 0.94 |
time (sec) |
N/A | 0.323 | 0.006 | 0.056 | 0.026 | 0.141 | 0.094 | 0.171 | 0.171 | 0.044 |
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 | 47 | 47 | 47 | 44 | 46 | 48 | 48 | 46 | 48 | 46 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.98 | 1.02 | 1.02 | 0.98 | 1.02 | 0.98 |
time (sec) |
N/A | 0.320 | 0.005 | 0.056 | 0.027 | 0.090 | 0.128 | 0.111 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 47 | 48 | 48 | 51 | 48 | 48 | 47 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.89 | 0.89 | 0.94 | 0.89 | 0.89 | 0.87 |
time (sec) |
N/A | 0.330 | 0.008 | 0.056 | 0.028 | 0.099 | 0.155 | 0.106 | 0.175 | 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 | 56 | 56 | 56 | 47 | 48 | 48 | 51 | 48 | 48 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.86 | 0.86 | 0.91 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.327 | 0.006 | 0.056 | 0.031 | 0.081 | 0.170 | 0.108 | 0.161 | 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 | 56 | 56 | 56 | 47 | 48 | 48 | 51 | 48 | 48 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.86 | 0.86 | 0.91 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.339 | 0.008 | 0.060 | 0.035 | 0.163 | 0.180 | 0.103 | 0.163 | 18.651 |
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 | 82 | 86 | 82 | 69 | 68 | 68 | 80 | 68 | 70 | 68 |
N.S. |
1 | 1.05 | 1.00 | 0.84 | 0.83 | 0.83 | 0.98 | 0.83 | 0.85 | 0.83 |
time (sec) |
N/A | 0.405 | 0.003 | 0.139 | 0.026 | 0.091 | 0.022 | 0.129 | 0.167 | 0.032 |
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 | 91 | 95 | 82 | 69 | 68 | 68 | 78 | 68 | 70 | 68 |
N.S. |
1 | 1.04 | 0.90 | 0.76 | 0.75 | 0.75 | 0.86 | 0.75 | 0.77 | 0.75 |
time (sec) |
N/A | 0.414 | 0.002 | 0.131 | 0.031 | 0.127 | 0.024 | 0.130 | 0.159 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 76 | 82 | 69 | 68 | 68 | 78 | 68 | 70 | 68 |
N.S. |
1 | 1.06 | 1.14 | 0.96 | 0.94 | 0.94 | 1.08 | 0.94 | 0.97 | 0.94 |
time (sec) |
N/A | 0.386 | 0.002 | 0.127 | 0.025 | 0.163 | 0.024 | 0.130 | 0.161 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 57 | 82 | 69 | 68 | 68 | 80 | 68 | 70 | 68 |
N.S. |
1 | 1.08 | 1.55 | 1.30 | 1.28 | 1.28 | 1.51 | 1.28 | 1.32 | 1.28 |
time (sec) |
N/A | 0.351 | 0.002 | 0.124 | 0.035 | 0.133 | 0.024 | 0.166 | 0.179 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 38 | 77 | 68 | 67 | 67 | 75 | 67 | 70 | 67 |
N.S. |
1 | 1.12 | 2.26 | 2.00 | 1.97 | 1.97 | 2.21 | 1.97 | 2.06 | 1.97 |
time (sec) |
N/A | 0.317 | 0.002 | 0.118 | 0.030 | 0.082 | 0.025 | 0.105 | 0.163 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 69 | 68 | 68 | 78 | 68 | 69 | 68 |
N.S. |
1 | 1.00 | 1.00 | 4.31 | 4.25 | 4.25 | 4.88 | 4.25 | 4.31 | 4.25 |
time (sec) |
N/A | 0.254 | 0.002 | 0.109 | 0.027 | 0.085 | 0.024 | 0.127 | 0.158 | 0.032 |
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 | 76 | 82 | 76 | 67 | 69 | 66 | 76 | 69 | 66 | 66 |
N.S. |
1 | 1.08 | 1.00 | 0.88 | 0.91 | 0.87 | 1.00 | 0.91 | 0.87 | 0.87 |
time (sec) |
N/A | 0.366 | 0.004 | 0.128 | 0.030 | 0.125 | 0.049 | 0.103 | 0.167 | 0.035 |
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 | 77 | 77 | 77 | 68 | 69 | 72 | 76 | 79 | 72 | 67 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.90 | 0.94 | 0.99 | 1.03 | 0.94 | 0.87 |
time (sec) |
N/A | 0.383 | 0.006 | 0.063 | 0.027 | 0.097 | 0.067 | 0.128 | 0.166 | 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 | 72 | 79 | 72 | 67 | 69 | 71 | 73 | 80 | 71 | 69 |
N.S. |
1 | 1.10 | 1.00 | 0.93 | 0.96 | 0.99 | 1.01 | 1.11 | 0.99 | 0.96 |
time (sec) |
N/A | 0.380 | 0.004 | 0.064 | 0.034 | 0.083 | 0.098 | 0.141 | 0.174 | 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 | 79 | 77 | 79 | 68 | 70 | 71 | 76 | 81 | 71 | 70 |
N.S. |
1 | 0.97 | 1.00 | 0.86 | 0.89 | 0.90 | 0.96 | 1.03 | 0.90 | 0.89 |
time (sec) |
N/A | 0.381 | 0.004 | 0.065 | 0.027 | 0.081 | 0.134 | 0.137 | 0.166 | 18.698 |
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 | 73 | 79 | 73 | 68 | 70 | 72 | 73 | 81 | 72 | 69 |
N.S. |
1 | 1.08 | 1.00 | 0.93 | 0.96 | 0.99 | 1.00 | 1.11 | 0.99 | 0.95 |
time (sec) |
N/A | 0.380 | 0.006 | 0.083 | 0.028 | 0.109 | 0.175 | 0.152 | 0.162 | 17.659 |
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 | 77 | 76 | 77 | 68 | 72 | 72 | 75 | 81 | 72 | 70 |
N.S. |
1 | 0.99 | 1.00 | 0.88 | 0.94 | 0.94 | 0.97 | 1.05 | 0.94 | 0.91 |
time (sec) |
N/A | 0.372 | 0.004 | 0.063 | 0.029 | 0.124 | 0.220 | 0.113 | 0.168 | 0.052 |
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 | 76 | 82 | 76 | 67 | 72 | 72 | 73 | 80 | 72 | 69 |
N.S. |
1 | 1.08 | 1.00 | 0.88 | 0.95 | 0.95 | 0.96 | 1.05 | 0.95 | 0.91 |
time (sec) |
N/A | 0.383 | 0.004 | 0.062 | 0.040 | 0.149 | 0.260 | 0.124 | 0.164 | 17.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 82 | 69 | 68 | 68 | 73 | 68 | 70 | 70 |
N.S. |
1 | 1.00 | 4.32 | 3.63 | 3.58 | 3.58 | 3.84 | 3.58 | 3.68 | 3.68 |
time (sec) |
N/A | 0.259 | 0.006 | 0.064 | 0.028 | 0.088 | 0.283 | 0.133 | 0.163 | 0.053 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 44 | 78 | 69 | 70 | 70 | 75 | 70 | 70 | 69 |
N.S. |
1 | 1.10 | 1.95 | 1.72 | 1.75 | 1.75 | 1.88 | 1.75 | 1.75 | 1.72 |
time (sec) |
N/A | 0.296 | 0.004 | 0.069 | 0.026 | 0.110 | 0.300 | 0.108 | 0.175 | 17.909 |
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 | 62 | 72 | 82 | 69 | 70 | 70 | 75 | 70 | 70 | 70 |
N.S. |
1 | 1.16 | 1.32 | 1.11 | 1.13 | 1.13 | 1.21 | 1.13 | 1.13 | 1.13 |
time (sec) |
N/A | 0.309 | 0.004 | 0.071 | 0.030 | 0.085 | 0.309 | 0.105 | 0.169 | 0.050 |
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 | 84 | 100 | 82 | 69 | 70 | 70 | 75 | 70 | 70 | 70 |
N.S. |
1 | 1.19 | 0.98 | 0.82 | 0.83 | 0.83 | 0.89 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.339 | 0.006 | 0.075 | 0.025 | 0.093 | 0.327 | 0.103 | 0.165 | 18.890 |
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 | 82 | 84 | 82 | 69 | 70 | 70 | 75 | 70 | 70 | 70 |
N.S. |
1 | 1.02 | 1.00 | 0.84 | 0.85 | 0.85 | 0.91 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.375 | 0.004 | 0.079 | 0.026 | 0.083 | 0.344 | 0.127 | 0.160 | 0.054 |
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 | 82 | 86 | 82 | 69 | 70 | 70 | 75 | 70 | 70 | 70 |
N.S. |
1 | 1.05 | 1.00 | 0.84 | 0.85 | 0.85 | 0.91 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.389 | 0.004 | 0.081 | 0.028 | 0.115 | 0.376 | 0.125 | 0.165 | 19.286 |
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 | 82 | 82 | 82 | 69 | 68 | 68 | 80 | 68 | 70 | 68 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.83 | 0.83 | 0.98 | 0.83 | 0.85 | 0.83 |
time (sec) |
N/A | 0.381 | 0.002 | 0.131 | 0.029 | 0.132 | 0.022 | 0.113 | 0.168 | 0.032 |
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 | 79 | 79 | 79 | 68 | 67 | 67 | 76 | 67 | 70 | 67 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.85 | 0.85 | 0.96 | 0.85 | 0.89 | 0.85 |
time (sec) |
N/A | 0.384 | 0.002 | 0.128 | 0.026 | 0.078 | 0.021 | 0.141 | 0.161 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 82 | 69 | 68 | 68 | 80 | 68 | 70 | 68 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.83 | 0.83 | 0.98 | 0.83 | 0.85 | 0.83 |
time (sec) |
N/A | 0.367 | 0.002 | 0.122 | 0.030 | 0.142 | 0.021 | 0.120 | 0.158 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 82 | 69 | 68 | 68 | 80 | 68 | 70 | 68 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.83 | 0.83 | 0.98 | 0.83 | 0.85 | 0.83 |
time (sec) |
N/A | 0.384 | 0.002 | 0.116 | 0.027 | 0.104 | 0.021 | 0.108 | 0.167 | 0.032 |
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 | 73 | 82 | 73 | 66 | 100 | 65 | 73 | 65 | 68 | 65 |
N.S. |
1 | 1.12 | 1.00 | 0.90 | 1.37 | 0.89 | 1.00 | 0.89 | 0.93 | 0.89 |
time (sec) |
N/A | 0.390 | 0.001 | 0.048 | 0.033 | 0.150 | 0.021 | 0.112 | 0.167 | 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 | 72 | 72 | 72 | 67 | 66 | 70 | 70 | 66 | 70 | 66 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.92 | 0.97 | 0.97 | 0.92 | 0.97 | 0.92 |
time (sec) |
N/A | 0.375 | 0.007 | 0.200 | 0.026 | 0.123 | 0.049 | 0.105 | 0.160 | 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 | 74 | 74 | 74 | 67 | 67 | 70 | 75 | 67 | 70 | 69 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.91 | 0.95 | 1.01 | 0.91 | 0.95 | 0.93 |
time (sec) |
N/A | 0.371 | 0.007 | 0.069 | 0.024 | 0.156 | 0.073 | 0.108 | 0.167 | 0.032 |
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 | 72 | 72 | 72 | 67 | 67 | 70 | 73 | 67 | 70 | 69 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.93 | 0.97 | 1.01 | 0.93 | 0.97 | 0.96 |
time (sec) |
N/A | 0.376 | 0.005 | 0.065 | 0.025 | 0.082 | 0.103 | 0.124 | 0.168 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 72 | 67 | 69 | 70 | 73 | 69 | 70 | 69 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.96 | 0.97 | 1.01 | 0.96 | 0.97 | 0.96 |
time (sec) |
N/A | 0.371 | 0.008 | 0.066 | 0.027 | 0.083 | 0.138 | 0.105 | 0.167 | 0.054 |
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 | 74 | 74 | 74 | 67 | 69 | 70 | 73 | 69 | 70 | 70 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.93 | 0.95 | 0.99 | 0.93 | 0.95 | 0.95 |
time (sec) |
N/A | 0.370 | 0.007 | 0.067 | 0.030 | 0.081 | 0.179 | 0.125 | 0.164 | 0.054 |
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 | 71 | 71 | 71 | 66 | 68 | 70 | 71 | 68 | 70 | 68 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.96 | 0.99 | 1.00 | 0.96 | 0.99 | 0.96 |
time (sec) |
N/A | 0.367 | 0.005 | 0.062 | 0.036 | 0.135 | 0.219 | 0.106 | 0.164 | 0.048 |
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 | 76 | 76 | 76 | 69 | 70 | 70 | 75 | 70 | 70 | 69 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.92 | 0.92 | 0.99 | 0.92 | 0.92 | 0.91 |
time (sec) |
N/A | 0.376 | 0.007 | 0.066 | 0.026 | 0.075 | 0.249 | 0.149 | 0.167 | 18.443 |
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 | 82 | 82 | 82 | 69 | 70 | 70 | 75 | 70 | 70 | 70 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.85 | 0.85 | 0.91 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.372 | 0.008 | 0.067 | 0.027 | 0.172 | 0.267 | 0.107 | 0.170 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 82 | 72 | 74 | 77 | 93 | 80 | 92 | 93 | 79 |
N.S. |
1 | 0.99 | 0.87 | 0.89 | 0.93 | 1.12 | 0.96 | 1.11 | 1.12 | 0.95 |
time (sec) |
N/A | 0.420 | 0.015 | 0.084 | 0.034 | 0.154 | 0.131 | 0.103 | 0.166 | 19.390 |
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 | 70 | 68 | 60 | 63 | 65 | 81 | 66 | 80 | 81 | 68 |
N.S. |
1 | 0.97 | 0.86 | 0.90 | 0.93 | 1.16 | 0.94 | 1.14 | 1.16 | 0.97 |
time (sec) |
N/A | 0.396 | 0.017 | 0.076 | 0.028 | 0.186 | 0.124 | 0.110 | 0.173 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 56 | 49 | 53 | 54 | 70 | 53 | 67 | 70 | 57 |
N.S. |
1 | 0.98 | 0.86 | 0.93 | 0.95 | 1.23 | 0.93 | 1.18 | 1.23 | 1.00 |
time (sec) |
N/A | 0.364 | 0.012 | 0.096 | 0.027 | 0.120 | 0.118 | 0.108 | 0.166 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 43 | 38 | 41 | 43 | 56 | 39 | 49 | 57 | 45 |
N.S. |
1 | 0.98 | 0.86 | 0.93 | 0.98 | 1.27 | 0.89 | 1.11 | 1.30 | 1.02 |
time (sec) |
N/A | 0.333 | 0.012 | 0.062 | 0.034 | 0.119 | 0.103 | 0.126 | 0.166 | 19.210 |
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 | 33 | 31 | 27 | 30 | 32 | 35 | 29 | 30 | 44 | 29 |
N.S. |
1 | 0.94 | 0.82 | 0.91 | 0.97 | 1.06 | 0.88 | 0.91 | 1.33 | 0.88 |
time (sec) |
N/A | 0.317 | 0.009 | 0.056 | 0.030 | 0.104 | 0.083 | 0.154 | 0.167 | 0.050 |
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 | 16 | 16 | 16 | 15 | 15 | 15 | 15 | 14 | 17 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.94 | 0.94 | 0.94 | 0.88 | 1.06 | 0.88 |
time (sec) |
N/A | 0.258 | 0.002 | 0.050 | 0.026 | 0.085 | 0.064 | 0.164 | 0.164 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 39 | 33 | 35 | 37 | 47 | 34 | 47 | 59 | 34 |
N.S. |
1 | 1.03 | 0.87 | 0.92 | 0.97 | 1.24 | 0.89 | 1.24 | 1.55 | 0.89 |
time (sec) |
N/A | 0.332 | 0.010 | 0.076 | 0.028 | 0.103 | 0.136 | 0.110 | 0.171 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 52 | 41 | 51 | 52 | 73 | 51 | 51 | 81 | 51 |
N.S. |
1 | 1.06 | 0.84 | 1.04 | 1.06 | 1.49 | 1.04 | 1.04 | 1.65 | 1.04 |
time (sec) |
N/A | 0.359 | 0.024 | 0.089 | 0.030 | 0.153 | 0.169 | 0.156 | 0.161 | 0.075 |
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 | 66 | 68 | 57 | 65 | 70 | 90 | 68 | 86 | 94 | 67 |
N.S. |
1 | 1.03 | 0.86 | 0.98 | 1.06 | 1.36 | 1.03 | 1.30 | 1.42 | 1.02 |
time (sec) |
N/A | 0.376 | 0.039 | 0.097 | 0.034 | 0.117 | 0.203 | 0.129 | 0.160 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 95 | 82 | 76 | 82 | 212 | 134 | 84 | 107 | 77 |
N.S. |
1 | 1.08 | 0.93 | 0.86 | 0.93 | 2.41 | 1.52 | 0.95 | 1.22 | 0.88 |
time (sec) |
N/A | 0.399 | 0.039 | 0.099 | 0.106 | 0.097 | 0.146 | 0.152 | 0.174 | 19.469 |
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 | 78 | 82 | 71 | 65 | 71 | 190 | 124 | 73 | 96 | 66 |
N.S. |
1 | 1.05 | 0.91 | 0.83 | 0.91 | 2.44 | 1.59 | 0.94 | 1.23 | 0.85 |
time (sec) |
N/A | 0.379 | 0.034 | 0.086 | 0.111 | 0.273 | 0.137 | 0.113 | 0.167 | 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 | 65 | 69 | 60 | 54 | 59 | 164 | 107 | 61 | 83 | 56 |
N.S. |
1 | 1.06 | 0.92 | 0.83 | 0.91 | 2.52 | 1.65 | 0.94 | 1.28 | 0.86 |
time (sec) |
N/A | 0.361 | 0.032 | 0.078 | 0.109 | 0.100 | 0.128 | 0.135 | 0.167 | 0.059 |
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 | 51 | 58 | 51 | 42 | 45 | 136 | 83 | 42 | 69 | 43 |
N.S. |
1 | 1.14 | 1.00 | 0.82 | 0.88 | 2.67 | 1.63 | 0.82 | 1.35 | 0.84 |
time (sec) |
N/A | 0.315 | 0.024 | 0.072 | 0.117 | 0.159 | 0.114 | 0.152 | 0.167 | 18.857 |
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 | 45 | 45 | 45 | 36 | 36 | 120 | 78 | 35 | 62 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.80 | 2.67 | 1.73 | 0.78 | 1.38 | 0.73 |
time (sec) |
N/A | 0.287 | 0.015 | 0.075 | 0.110 | 0.104 | 0.089 | 0.106 | 0.163 | 0.043 |
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 | 45 | 52 | 45 | 36 | 35 | 120 | 78 | 35 | 61 | 33 |
N.S. |
1 | 1.16 | 1.00 | 0.80 | 0.78 | 2.67 | 1.73 | 0.78 | 1.36 | 0.73 |
time (sec) |
N/A | 0.282 | 0.016 | 0.064 | 0.103 | 0.207 | 0.095 | 0.118 | 0.172 | 18.397 |
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 | 54 | 61 | 54 | 45 | 49 | 136 | 92 | 47 | 72 | 44 |
N.S. |
1 | 1.13 | 1.00 | 0.83 | 0.91 | 2.52 | 1.70 | 0.87 | 1.33 | 0.81 |
time (sec) |
N/A | 0.302 | 0.027 | 0.099 | 0.107 | 0.203 | 0.135 | 0.163 | 0.166 | 0.075 |
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 | 67 | 78 | 67 | 55 | 64 | 172 | 114 | 59 | 88 | 58 |
N.S. |
1 | 1.16 | 1.00 | 0.82 | 0.96 | 2.57 | 1.70 | 0.88 | 1.31 | 0.87 |
time (sec) |
N/A | 0.326 | 0.028 | 0.125 | 0.106 | 0.083 | 0.161 | 0.119 | 0.165 | 18.401 |
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 | 80 | 95 | 80 | 67 | 75 | 198 | 126 | 70 | 101 | 70 |
N.S. |
1 | 1.19 | 1.00 | 0.84 | 0.94 | 2.48 | 1.58 | 0.88 | 1.26 | 0.88 |
time (sec) |
N/A | 0.350 | 0.032 | 0.119 | 0.105 | 0.092 | 0.186 | 0.168 | 0.173 | 18.227 |
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 | 91 | 95 | 78 | 76 | 99 | 137 | 100 | 91 | 147 | 98 |
N.S. |
1 | 1.04 | 0.86 | 0.84 | 1.09 | 1.51 | 1.10 | 1.00 | 1.62 | 1.08 |
time (sec) |
N/A | 0.424 | 0.023 | 0.142 | 0.031 | 0.079 | 0.284 | 0.103 | 0.167 | 17.762 |
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 | 77 | 79 | 59 | 65 | 88 | 124 | 90 | 73 | 134 | 88 |
N.S. |
1 | 1.03 | 0.77 | 0.84 | 1.14 | 1.61 | 1.17 | 0.95 | 1.74 | 1.14 |
time (sec) |
N/A | 0.406 | 0.040 | 0.099 | 0.027 | 0.080 | 0.250 | 0.106 | 0.168 | 17.657 |
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 | 71 | 70 | 50 | 54 | 77 | 102 | 76 | 53 | 122 | 75 |
N.S. |
1 | 0.99 | 0.70 | 0.76 | 1.08 | 1.44 | 1.07 | 0.75 | 1.72 | 1.06 |
time (sec) |
N/A | 0.379 | 0.014 | 0.091 | 0.027 | 0.067 | 0.209 | 0.123 | 0.169 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 35 | 37 | 58 | 58 | 60 | 33 | 39 | 60 |
N.S. |
1 | 1.00 | 1.84 | 1.95 | 3.05 | 3.05 | 3.16 | 1.74 | 2.05 | 3.16 |
time (sec) |
N/A | 0.259 | 0.011 | 0.087 | 0.031 | 0.071 | 0.176 | 0.155 | 0.165 | 0.040 |
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 | 34 | 38 | 24 | 26 | 47 | 47 | 48 | 22 | 46 | 48 |
N.S. |
1 | 1.12 | 0.71 | 0.76 | 1.38 | 1.38 | 1.41 | 0.65 | 1.35 | 1.41 |
time (sec) |
N/A | 0.318 | 0.007 | 0.088 | 0.033 | 0.062 | 0.155 | 0.143 | 0.171 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 15 | 37 | 37 | 39 | 14 | 36 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 2.31 | 2.31 | 2.44 | 0.88 | 2.25 | 2.44 |
time (sec) |
N/A | 0.259 | 0.002 | 0.082 | 0.027 | 0.063 | 0.141 | 0.135 | 0.164 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 71 | 54 | 63 | 82 | 134 | 80 | 70 | 161 | 78 |
N.S. |
1 | 1.01 | 0.77 | 0.90 | 1.17 | 1.91 | 1.14 | 1.00 | 2.30 | 1.11 |
time (sec) |
N/A | 0.382 | 0.028 | 0.113 | 0.027 | 0.069 | 0.242 | 0.119 | 0.164 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 70 | 76 | 99 | 163 | 102 | 93 | 187 | 97 |
N.S. |
1 | 1.00 | 0.83 | 0.90 | 1.18 | 1.94 | 1.21 | 1.11 | 2.23 | 1.15 |
time (sec) |
N/A | 0.412 | 0.044 | 0.130 | 0.028 | 0.067 | 0.288 | 0.131 | 0.171 | 17.482 |
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 | 101 | 107 | 85 | 89 | 114 | 178 | 116 | 108 | 202 | 111 |
N.S. |
1 | 1.06 | 0.84 | 0.88 | 1.13 | 1.76 | 1.15 | 1.07 | 2.00 | 1.10 |
time (sec) |
N/A | 0.452 | 0.044 | 0.139 | 0.035 | 0.069 | 0.313 | 0.161 | 0.168 | 17.425 |
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 | 118 | 136 | 99 | 85 | 116 | 322 | 172 | 96 | 194 | 109 |
N.S. |
1 | 1.15 | 0.84 | 0.72 | 0.98 | 2.73 | 1.46 | 0.81 | 1.64 | 0.92 |
time (sec) |
N/A | 0.456 | 0.037 | 0.125 | 0.112 | 0.072 | 0.291 | 0.127 | 0.161 | 0.059 |
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 | 105 | 123 | 89 | 74 | 104 | 296 | 156 | 84 | 181 | 99 |
N.S. |
1 | 1.17 | 0.85 | 0.70 | 0.99 | 2.82 | 1.49 | 0.80 | 1.72 | 0.94 |
time (sec) |
N/A | 0.427 | 0.032 | 0.109 | 0.110 | 0.071 | 0.279 | 0.136 | 0.163 | 0.076 |
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 | 91 | 112 | 77 | 62 | 90 | 268 | 131 | 65 | 167 | 86 |
N.S. |
1 | 1.23 | 0.85 | 0.68 | 0.99 | 2.95 | 1.44 | 0.71 | 1.84 | 0.95 |
time (sec) |
N/A | 0.387 | 0.032 | 0.101 | 0.107 | 0.073 | 0.252 | 0.115 | 0.162 | 17.423 |
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 | 83 | 99 | 66 | 58 | 81 | 254 | 134 | 56 | 162 | 78 |
N.S. |
1 | 1.19 | 0.80 | 0.70 | 0.98 | 3.06 | 1.61 | 0.67 | 1.95 | 0.94 |
time (sec) |
N/A | 0.361 | 0.027 | 0.108 | 0.106 | 0.071 | 0.209 | 0.116 | 0.160 | 17.205 |
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 | 84 | 97 | 69 | 58 | 87 | 258 | 143 | 62 | 162 | 75 |
N.S. |
1 | 1.15 | 0.82 | 0.69 | 1.04 | 3.07 | 1.70 | 0.74 | 1.93 | 0.89 |
time (sec) |
N/A | 0.351 | 0.033 | 0.109 | 0.105 | 0.104 | 0.188 | 0.132 | 0.159 | 17.191 |
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 | 85 | 95 | 69 | 58 | 87 | 258 | 139 | 62 | 162 | 74 |
N.S. |
1 | 1.12 | 0.81 | 0.68 | 1.02 | 3.04 | 1.64 | 0.73 | 1.91 | 0.87 |
time (sec) |
N/A | 0.335 | 0.028 | 0.111 | 0.104 | 0.083 | 0.184 | 0.168 | 0.160 | 17.070 |
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 | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 114 | 66 | 78 | 80 | 254 | 129 | 56 | 162 | 77 |
N.S. |
1 | 1.44 | 0.84 | 0.99 | 1.01 | 3.22 | 1.63 | 0.71 | 2.05 | 0.97 |
time (sec) |
N/A | 0.348 | 0.024 | 0.095 | 0.106 | 0.086 | 0.186 | 0.132 | 0.154 | 17.288 |
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 | 90 | 115 | 79 | 65 | 93 | 268 | 139 | 68 | 170 | 88 |
N.S. |
1 | 1.28 | 0.88 | 0.72 | 1.03 | 2.98 | 1.54 | 0.76 | 1.89 | 0.98 |
time (sec) |
N/A | 0.372 | 0.029 | 0.135 | 0.116 | 0.080 | 0.250 | 0.127 | 0.154 | 17.433 |
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 | 107 | 132 | 91 | 75 | 108 | 304 | 162 | 82 | 186 | 102 |
N.S. |
1 | 1.23 | 0.85 | 0.70 | 1.01 | 2.84 | 1.51 | 0.77 | 1.74 | 0.95 |
time (sec) |
N/A | 0.403 | 0.035 | 0.152 | 0.113 | 0.085 | 0.276 | 0.123 | 0.147 | 17.663 |
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 | 120 | 149 | 101 | 87 | 119 | 330 | 173 | 93 | 199 | 114 |
N.S. |
1 | 1.24 | 0.84 | 0.72 | 0.99 | 2.75 | 1.44 | 0.78 | 1.66 | 0.95 |
time (sec) |
N/A | 0.436 | 0.037 | 0.164 | 0.111 | 0.084 | 0.305 | 0.135 | 0.154 | 0.158 |
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 | 133 | 131 | 114 | 98 | 143 | 203 | 150 | 113 | 229 | 142 |
N.S. |
1 | 0.98 | 0.86 | 0.74 | 1.08 | 1.53 | 1.13 | 0.85 | 1.72 | 1.07 |
time (sec) |
N/A | 0.512 | 0.017 | 0.190 | 0.043 | 0.063 | 0.450 | 0.106 | 0.149 | 17.749 |
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 | 118 | 115 | 101 | 87 | 132 | 190 | 138 | 95 | 216 | 132 |
N.S. |
1 | 0.97 | 0.86 | 0.74 | 1.12 | 1.61 | 1.17 | 0.81 | 1.83 | 1.12 |
time (sec) |
N/A | 0.508 | 0.019 | 0.142 | 0.043 | 0.070 | 0.428 | 0.167 | 0.154 | 17.402 |
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 | 109 | 106 | 72 | 76 | 121 | 168 | 124 | 75 | 204 | 119 |
N.S. |
1 | 0.97 | 0.66 | 0.70 | 1.11 | 1.54 | 1.14 | 0.69 | 1.87 | 1.09 |
time (sec) |
N/A | 0.449 | 0.019 | 0.129 | 0.034 | 0.065 | 0.365 | 0.152 | 0.149 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 57 | 59 | 102 | 102 | 107 | 55 | 61 | 104 |
N.S. |
1 | 1.00 | 3.00 | 3.11 | 5.37 | 5.37 | 5.63 | 2.89 | 3.21 | 5.47 |
time (sec) |
N/A | 0.265 | 0.014 | 0.125 | 0.027 | 0.075 | 0.315 | 0.110 | 0.152 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 43 | 46 | 48 | 91 | 91 | 95 | 44 | 90 | 93 |
N.S. |
1 | 1.10 | 1.18 | 1.23 | 2.33 | 2.33 | 2.44 | 1.13 | 2.31 | 2.38 |
time (sec) |
N/A | 0.289 | 0.011 | 0.125 | 0.037 | 0.061 | 0.285 | 0.107 | 0.159 | 17.861 |