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 | 33 | 34 | 33 | 28 | 27 | 27 | 29 | 29 | 25 | 28 |
N.S. |
1 | 1.03 | 1.00 | 0.85 | 0.82 | 0.82 | 0.88 | 0.88 | 0.76 | 0.85 |
time (sec) |
N/A | 0.291 | 0.010 | 0.398 | 0.036 | 0.072 | 0.018 | 0.118 | 0.204 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 32 | 29 | 27 | 28 | 25 | 27 | 28 | 22 | 26 |
N.S. |
1 | 1.10 | 1.00 | 0.93 | 0.97 | 0.86 | 0.93 | 0.97 | 0.76 | 0.90 |
time (sec) |
N/A | 0.286 | 0.012 | 0.334 | 0.027 | 0.075 | 0.054 | 0.117 | 0.245 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 30 | 29 | 26 | 28 | 30 | 26 | 40 | 27 | 25 |
N.S. |
1 | 1.03 | 1.00 | 0.90 | 0.97 | 1.03 | 0.90 | 1.38 | 0.93 | 0.86 |
time (sec) |
N/A | 0.294 | 0.013 | 0.096 | 0.032 | 0.088 | 0.112 | 0.122 | 0.202 | 0.756 |
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 | 29 | 33 | 31 | 26 | 30 | 31 | 29 | 37 | 28 | 29 |
N.S. |
1 | 1.14 | 1.07 | 0.90 | 1.03 | 1.07 | 1.00 | 1.28 | 0.97 | 1.00 |
time (sec) |
N/A | 0.300 | 0.020 | 0.072 | 0.033 | 0.087 | 0.285 | 0.116 | 0.230 | 0.722 |
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 | 33 | 33 | 28 | 27 | 27 | 29 | 29 | 26 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.82 | 0.82 | 0.88 | 0.88 | 0.79 | 0.85 |
time (sec) |
N/A | 0.290 | 0.007 | 0.424 | 0.026 | 0.093 | 0.021 | 0.120 | 0.248 | 0.771 |
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 | 28 | 28 | 28 | 25 | 24 | 24 | 26 | 26 | 24 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.86 | 0.86 | 0.93 | 0.93 | 0.86 | 0.89 |
time (sec) |
N/A | 0.286 | 0.006 | 0.418 | 0.031 | 0.071 | 0.019 | 0.123 | 0.231 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 30 | 27 | 29 | 26 | 29 | 25 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.87 | 0.94 | 0.84 | 0.94 | 0.81 | 0.90 |
time (sec) |
N/A | 0.293 | 0.012 | 0.093 | 0.032 | 0.106 | 0.052 | 0.121 | 0.211 | 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 | 28 | 28 | 28 | 24 | 24 | 28 | 24 | 23 | 25 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.86 | 1.00 | 0.86 | 0.82 | 0.89 | 0.86 |
time (sec) |
N/A | 0.290 | 0.011 | 0.095 | 0.031 | 0.066 | 0.057 | 0.121 | 0.238 | 0.806 |
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 | 31 | 31 | 32 | 28 | 29 | 29 | 31 | 31 | 26 | 29 |
N.S. |
1 | 1.00 | 1.03 | 0.90 | 0.94 | 0.94 | 1.00 | 1.00 | 0.84 | 0.94 |
time (sec) |
N/A | 0.293 | 0.012 | 0.096 | 0.039 | 0.092 | 0.147 | 0.122 | 0.231 | 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 | 28 | 28 | 30 | 25 | 27 | 29 | 29 | 29 | 26 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.89 | 0.96 | 1.04 | 1.04 | 1.04 | 0.93 | 1.00 |
time (sec) |
N/A | 0.286 | 0.014 | 0.096 | 0.027 | 0.074 | 0.151 | 0.121 | 0.230 | 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 | 42 | 46 | 51 | 52 | 51 | 51 | 54 | 53 | 36 | 51 |
N.S. |
1 | 1.10 | 1.21 | 1.24 | 1.21 | 1.21 | 1.29 | 1.26 | 0.86 | 1.21 |
time (sec) |
N/A | 0.345 | 0.018 | 0.753 | 0.031 | 0.090 | 0.024 | 0.122 | 0.224 | 0.062 |
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 | 46 | 50 | 51 | 50 | 52 | 49 | 53 | 52 | 32 | 49 |
N.S. |
1 | 1.09 | 1.11 | 1.09 | 1.13 | 1.07 | 1.15 | 1.13 | 0.70 | 1.07 |
time (sec) |
N/A | 0.308 | 0.018 | 0.556 | 0.027 | 0.094 | 0.069 | 0.120 | 0.213 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 52 | 49 | 49 | 52 | 54 | 51 | 69 | 38 | 49 |
N.S. |
1 | 1.02 | 0.96 | 0.96 | 1.02 | 1.06 | 1.00 | 1.35 | 0.75 | 0.96 |
time (sec) |
N/A | 0.327 | 0.028 | 0.763 | 0.031 | 0.065 | 0.144 | 0.118 | 0.252 | 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 | 51 | 52 | 51 | 46 | 54 | 55 | 51 | 70 | 39 | 52 |
N.S. |
1 | 1.02 | 1.00 | 0.90 | 1.06 | 1.08 | 1.00 | 1.37 | 0.76 | 1.02 |
time (sec) |
N/A | 0.334 | 0.023 | 0.558 | 0.026 | 0.078 | 0.418 | 0.116 | 0.212 | 0.065 |
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 | 55 | 55 | 55 | 52 | 51 | 51 | 54 | 53 | 37 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.93 | 0.93 | 0.98 | 0.96 | 0.67 | 0.93 |
time (sec) |
N/A | 0.325 | 0.009 | 0.685 | 0.035 | 0.090 | 0.026 | 0.124 | 0.234 | 0.051 |
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 | 50 | 50 | 50 | 49 | 48 | 48 | 51 | 50 | 35 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.96 | 0.96 | 1.02 | 1.00 | 0.70 | 0.96 |
time (sec) |
N/A | 0.322 | 0.008 | 0.687 | 0.029 | 0.081 | 0.025 | 0.129 | 0.223 | 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 | 53 | 53 | 53 | 52 | 51 | 53 | 49 | 52 | 37 | 50 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.96 | 1.00 | 0.92 | 0.98 | 0.70 | 0.94 |
time (sec) |
N/A | 0.325 | 0.021 | 0.558 | 0.030 | 0.076 | 0.066 | 0.125 | 0.247 | 0.053 |
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 | 50 | 50 | 50 | 49 | 48 | 53 | 49 | 48 | 37 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.96 | 1.06 | 0.98 | 0.96 | 0.74 | 0.96 |
time (sec) |
N/A | 0.316 | 0.019 | 0.555 | 0.028 | 0.096 | 0.078 | 0.126 | 0.237 | 0.051 |
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 | 53 | 51 | 50 | 53 | 53 | 53 | 54 | 37 | 52 |
N.S. |
1 | 1.00 | 0.96 | 0.94 | 1.00 | 1.00 | 1.00 | 1.02 | 0.70 | 0.98 |
time (sec) |
N/A | 0.333 | 0.020 | 0.557 | 0.037 | 0.072 | 0.170 | 0.123 | 0.218 | 0.055 |
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 | 50 | 50 | 50 | 46 | 51 | 53 | 53 | 51 | 37 | 50 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.02 | 1.06 | 1.06 | 1.02 | 0.74 | 1.00 |
time (sec) |
N/A | 0.322 | 0.022 | 0.556 | 0.033 | 0.083 | 0.194 | 0.123 | 0.212 | 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 | 53 | 53 | 54 | 48 | 54 | 53 | 58 | 56 | 37 | 53 |
N.S. |
1 | 1.00 | 1.02 | 0.91 | 1.02 | 1.00 | 1.09 | 1.06 | 0.70 | 1.00 |
time (sec) |
N/A | 0.329 | 0.019 | 0.559 | 0.036 | 0.093 | 0.487 | 0.119 | 0.223 | 0.055 |
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 | 50 | 50 | 50 | 45 | 51 | 53 | 54 | 53 | 37 | 50 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 1.02 | 1.06 | 1.08 | 1.06 | 0.74 | 1.00 |
time (sec) |
N/A | 0.323 | 0.026 | 0.554 | 0.035 | 0.088 | 0.526 | 0.113 | 0.273 | 0.782 |
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 | 95 | 99 | 107 | 121 | 119 | 119 | 136 | 125 | 70 | 107 |
N.S. |
1 | 1.04 | 1.13 | 1.27 | 1.25 | 1.25 | 1.43 | 1.32 | 0.74 | 1.13 |
time (sec) |
N/A | 0.471 | 0.033 | 0.700 | 0.034 | 0.093 | 0.032 | 0.118 | 0.234 | 0.697 |
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 | 67 | 71 | 107 | 121 | 119 | 119 | 138 | 125 | 70 | 107 |
N.S. |
1 | 1.06 | 1.60 | 1.81 | 1.78 | 1.78 | 2.06 | 1.87 | 1.04 | 1.60 |
time (sec) |
N/A | 0.396 | 0.028 | 0.675 | 0.032 | 0.077 | 0.033 | 0.123 | 0.239 | 0.043 |
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 | 42 | 46 | 107 | 121 | 119 | 119 | 136 | 125 | 69 | 107 |
N.S. |
1 | 1.10 | 2.55 | 2.88 | 2.83 | 2.83 | 3.24 | 2.98 | 1.64 | 2.55 |
time (sec) |
N/A | 0.336 | 0.039 | 0.677 | 0.027 | 0.097 | 0.032 | 0.119 | 0.219 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 87 | 113 | 119 | 120 | 117 | 134 | 124 | 66 | 105 |
N.S. |
1 | 0.99 | 1.28 | 1.35 | 1.36 | 1.33 | 1.52 | 1.41 | 0.75 | 1.19 |
time (sec) |
N/A | 0.368 | 0.036 | 0.555 | 0.029 | 0.081 | 0.111 | 0.128 | 0.201 | 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 | 113 | 113 | 115 | 121 | 120 | 123 | 133 | 143 | 72 | 105 |
N.S. |
1 | 1.00 | 1.02 | 1.07 | 1.06 | 1.09 | 1.18 | 1.27 | 0.64 | 0.93 |
time (sec) |
N/A | 0.466 | 0.051 | 0.563 | 0.032 | 0.093 | 0.193 | 0.126 | 0.207 | 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 | 114 | 116 | 106 | 117 | 122 | 123 | 131 | 148 | 71 | 113 |
N.S. |
1 | 1.02 | 0.93 | 1.03 | 1.07 | 1.08 | 1.15 | 1.30 | 0.62 | 0.99 |
time (sec) |
N/A | 0.468 | 0.055 | 0.566 | 0.036 | 0.086 | 0.546 | 0.122 | 0.263 | 0.053 |
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 | 114 | 116 | 106 | 111 | 123 | 123 | 129 | 150 | 71 | 118 |
N.S. |
1 | 1.02 | 0.93 | 0.97 | 1.08 | 1.08 | 1.13 | 1.32 | 0.62 | 1.04 |
time (sec) |
N/A | 0.461 | 0.064 | 0.562 | 0.033 | 0.088 | 1.281 | 0.121 | 0.253 | 0.908 |
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 | 114 | 115 | 118 | 106 | 123 | 123 | 129 | 149 | 72 | 122 |
N.S. |
1 | 1.01 | 1.04 | 0.93 | 1.08 | 1.08 | 1.13 | 1.31 | 0.63 | 1.07 |
time (sec) |
N/A | 0.463 | 0.046 | 0.770 | 0.034 | 0.084 | 3.673 | 0.119 | 0.234 | 0.072 |
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 | 113 | 112 | 116 | 102 | 123 | 123 | 129 | 145 | 72 | 121 |
N.S. |
1 | 0.99 | 1.03 | 0.90 | 1.09 | 1.09 | 1.14 | 1.28 | 0.64 | 1.07 |
time (sec) |
N/A | 0.491 | 0.161 | 0.566 | 0.028 | 0.078 | 19.233 | 0.123 | 0.212 | 0.739 |
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 | 90 | 121 | 102 | 123 | 123 | 133 | 136 | 72 | 121 |
N.S. |
1 | 0.99 | 1.33 | 1.12 | 1.35 | 1.35 | 1.46 | 1.49 | 0.79 | 1.33 |
time (sec) |
N/A | 0.388 | 0.060 | 0.546 | 0.033 | 0.095 | 84.217 | 0.116 | 0.252 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 52 | 118 | 104 | 121 | 121 | 0 | 127 | 70 | 122 |
N.S. |
1 | 1.08 | 2.46 | 2.17 | 2.52 | 2.52 | 0.00 | 2.65 | 1.46 | 2.54 |
time (sec) |
N/A | 0.295 | 0.034 | 0.550 | 0.028 | 0.077 | 0.000 | 0.127 | 0.227 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 80 | 121 | 104 | 121 | 121 | 0 | 127 | 70 | 122 |
N.S. |
1 | 1.05 | 1.59 | 1.37 | 1.59 | 1.59 | 0.00 | 1.67 | 0.92 | 1.61 |
time (sec) |
N/A | 0.332 | 0.033 | 0.555 | 0.044 | 0.073 | 0.000 | 0.123 | 0.223 | 0.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 119 | 121 | 104 | 121 | 121 | 0 | 127 | 70 | 122 |
N.S. |
1 | 1.02 | 1.03 | 0.89 | 1.03 | 1.03 | 0.00 | 1.09 | 0.60 | 1.04 |
time (sec) |
N/A | 0.447 | 0.034 | 0.572 | 0.033 | 0.077 | 0.000 | 0.122 | 0.236 | 0.072 |
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 | 117 | 117 | 117 | 121 | 119 | 119 | 136 | 125 | 70 | 107 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.02 | 1.02 | 1.16 | 1.07 | 0.60 | 0.91 |
time (sec) |
N/A | 0.474 | 0.023 | 0.720 | 0.031 | 0.095 | 0.042 | 0.124 | 0.245 | 0.045 |
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 | 117 | 117 | 117 | 121 | 119 | 119 | 134 | 125 | 70 | 107 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.02 | 1.02 | 1.15 | 1.07 | 0.60 | 0.91 |
time (sec) |
N/A | 0.451 | 0.021 | 0.688 | 0.028 | 0.074 | 0.031 | 0.131 | 0.221 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 117 | 121 | 119 | 119 | 136 | 125 | 70 | 107 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.02 | 1.02 | 1.16 | 1.07 | 0.60 | 0.91 |
time (sec) |
N/A | 0.433 | 0.021 | 0.710 | 0.034 | 0.065 | 0.036 | 0.120 | 0.194 | 0.045 |
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 | 117 | 117 | 117 | 121 | 119 | 119 | 136 | 125 | 70 | 107 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.02 | 1.02 | 1.16 | 1.07 | 0.60 | 0.91 |
time (sec) |
N/A | 0.447 | 0.018 | 0.719 | 0.033 | 0.084 | 0.035 | 0.126 | 0.219 | 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 | 117 | 117 | 117 | 120 | 119 | 119 | 133 | 124 | 70 | 107 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.02 | 1.02 | 1.14 | 1.06 | 0.60 | 0.91 |
time (sec) |
N/A | 0.440 | 0.019 | 0.722 | 0.026 | 0.105 | 0.031 | 0.120 | 0.218 | 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 | 117 | 117 | 117 | 120 | 119 | 119 | 134 | 124 | 70 | 106 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.02 | 1.02 | 1.15 | 1.06 | 0.60 | 0.91 |
time (sec) |
N/A | 0.443 | 0.020 | 0.710 | 0.037 | 0.082 | 0.036 | 0.120 | 0.233 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 109 | 116 | 115 | 115 | 128 | 120 | 68 | 103 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.06 | 1.06 | 1.17 | 1.10 | 0.62 | 0.94 |
time (sec) |
N/A | 0.434 | 0.017 | 0.711 | 0.026 | 0.095 | 0.043 | 0.125 | 0.218 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 112 | 121 | 118 | 121 | 129 | 124 | 70 | 106 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.05 | 1.08 | 1.15 | 1.11 | 0.62 | 0.95 |
time (sec) |
N/A | 0.423 | 0.040 | 0.580 | 0.026 | 0.087 | 0.116 | 0.121 | 0.283 | 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 | 112 | 112 | 112 | 120 | 116 | 121 | 128 | 119 | 70 | 104 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.04 | 1.08 | 1.14 | 1.06 | 0.62 | 0.93 |
time (sec) |
N/A | 0.427 | 0.036 | 0.585 | 0.028 | 0.116 | 0.118 | 0.123 | 0.217 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 115 | 122 | 121 | 121 | 133 | 127 | 70 | 109 |
N.S. |
1 | 1.00 | 1.02 | 1.08 | 1.07 | 1.07 | 1.18 | 1.12 | 0.62 | 0.96 |
time (sec) |
N/A | 0.432 | 0.041 | 0.569 | 0.026 | 0.091 | 0.220 | 0.122 | 0.215 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 113 | 119 | 120 | 121 | 133 | 124 | 70 | 108 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.06 | 1.07 | 1.18 | 1.10 | 0.62 | 0.96 |
time (sec) |
N/A | 0.427 | 0.039 | 0.571 | 0.035 | 0.074 | 0.243 | 0.117 | 0.200 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 110 | 117 | 121 | 121 | 129 | 127 | 70 | 113 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.10 | 1.10 | 1.17 | 1.15 | 0.64 | 1.03 |
time (sec) |
N/A | 0.434 | 0.043 | 0.569 | 0.033 | 0.082 | 0.622 | 0.112 | 0.223 | 0.051 |
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 | 113 | 113 | 113 | 114 | 120 | 121 | 133 | 124 | 70 | 111 |
N.S. |
1 | 1.00 | 1.00 | 1.01 | 1.06 | 1.07 | 1.18 | 1.10 | 0.62 | 0.98 |
time (sec) |
N/A | 0.420 | 0.039 | 0.568 | 0.026 | 0.075 | 0.638 | 0.123 | 0.217 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 118 | 111 | 122 | 121 | 131 | 127 | 70 | 118 |
N.S. |
1 | 1.00 | 1.03 | 0.97 | 1.06 | 1.05 | 1.14 | 1.10 | 0.61 | 1.03 |
time (sec) |
N/A | 0.439 | 0.026 | 0.572 | 0.028 | 0.070 | 1.820 | 0.123 | 0.218 | 0.077 |
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 | 109 | 109 | 108 | 120 | 121 | 131 | 124 | 70 | 116 |
N.S. |
1 | 1.00 | 1.00 | 0.99 | 1.10 | 1.11 | 1.20 | 1.14 | 0.64 | 1.06 |
time (sec) |
N/A | 0.439 | 0.044 | 0.570 | 0.027 | 0.079 | 2.155 | 0.121 | 0.230 | 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 | 115 | 115 | 117 | 107 | 122 | 121 | 134 | 128 | 70 | 123 |
N.S. |
1 | 1.00 | 1.02 | 0.93 | 1.06 | 1.05 | 1.17 | 1.11 | 0.61 | 1.07 |
time (sec) |
N/A | 0.438 | 0.038 | 0.571 | 0.028 | 0.099 | 7.069 | 0.114 | 0.235 | 0.764 |
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 | 110 | 110 | 110 | 102 | 119 | 121 | 129 | 123 | 70 | 120 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.08 | 1.10 | 1.17 | 1.12 | 0.64 | 1.09 |
time (sec) |
N/A | 0.450 | 0.044 | 0.569 | 0.039 | 0.079 | 15.061 | 0.124 | 0.196 | 0.080 |
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 | 115 | 115 | 118 | 104 | 122 | 121 | 134 | 128 | 70 | 121 |
N.S. |
1 | 1.00 | 1.03 | 0.90 | 1.06 | 1.05 | 1.17 | 1.11 | 0.61 | 1.05 |
time (sec) |
N/A | 0.437 | 0.034 | 0.570 | 0.043 | 0.091 | 32.742 | 0.118 | 0.201 | 0.084 |
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 | 110 | 110 | 110 | 101 | 119 | 121 | 131 | 125 | 70 | 119 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.08 | 1.10 | 1.19 | 1.14 | 0.64 | 1.08 |
time (sec) |
N/A | 0.420 | 0.048 | 0.554 | 0.029 | 0.098 | 102.683 | 0.118 | 0.247 | 0.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 119 | 104 | 121 | 121 | 0 | 127 | 70 | 119 |
N.S. |
1 | 1.00 | 1.05 | 0.92 | 1.07 | 1.07 | 0.00 | 1.12 | 0.62 | 1.05 |
time (sec) |
N/A | 0.438 | 0.034 | 0.599 | 0.036 | 0.094 | 0.000 | 0.122 | 0.200 | 0.717 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 121 | 104 | 121 | 121 | 0 | 127 | 70 | 121 |
N.S. |
1 | 1.00 | 1.03 | 0.89 | 1.03 | 1.03 | 0.00 | 1.09 | 0.60 | 1.03 |
time (sec) |
N/A | 0.433 | 0.036 | 0.553 | 0.035 | 0.088 | 0.000 | 0.121 | 0.189 | 0.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 117 | 104 | 121 | 121 | 0 | 127 | 70 | 121 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.03 | 1.03 | 0.00 | 1.09 | 0.60 | 1.03 |
time (sec) |
N/A | 0.427 | 0.051 | 0.539 | 0.035 | 0.117 | 0.000 | 0.114 | 0.204 | 0.070 |
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 | 75 | 74 | 71 | 68 | 74 | 75 | 70 | 77 | 5 | 76 |
N.S. |
1 | 0.99 | 0.95 | 0.91 | 0.99 | 1.00 | 0.93 | 1.03 | 0.07 | 1.01 |
time (sec) |
N/A | 0.410 | 0.036 | 0.728 | 0.027 | 0.109 | 0.335 | 0.119 | 0.237 | 0.072 |
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 | 53 | 47 | 49 | 50 | 51 | 46 | 52 | 5 | 52 |
N.S. |
1 | 0.98 | 0.87 | 0.91 | 0.93 | 0.94 | 0.85 | 0.96 | 0.09 | 0.96 |
time (sec) |
N/A | 0.348 | 0.023 | 0.931 | 0.036 | 0.101 | 0.254 | 0.126 | 0.207 | 0.728 |
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 | 35 | 33 | 31 | 32 | 31 | 30 | 27 | 32 | 5 | 31 |
N.S. |
1 | 0.94 | 0.89 | 0.91 | 0.89 | 0.86 | 0.77 | 0.91 | 0.14 | 0.89 |
time (sec) |
N/A | 0.318 | 0.015 | 0.721 | 0.027 | 0.125 | 0.264 | 0.124 | 0.254 | 0.710 |
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 | 34 | 33 | 35 | 32 | 26 | 34 | 2 | 36 |
N.S. |
1 | 1.12 | 1.00 | 0.97 | 1.03 | 0.94 | 0.76 | 1.00 | 0.06 | 1.06 |
time (sec) |
N/A | 0.335 | 0.016 | 0.710 | 0.027 | 0.109 | 0.606 | 0.128 | 0.206 | 0.830 |
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 | 50 | 51 | 49 | 46 | 48 | 47 | 41 | 69 | 5 | 46 |
N.S. |
1 | 1.02 | 0.98 | 0.92 | 0.96 | 0.94 | 0.82 | 1.38 | 0.10 | 0.92 |
time (sec) |
N/A | 0.365 | 0.025 | 0.720 | 0.032 | 0.111 | 0.614 | 0.131 | 0.249 | 0.771 |
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 | 69 | 70 | 70 | 64 | 70 | 73 | 61 | 99 | 5 | 70 |
N.S. |
1 | 1.01 | 1.01 | 0.93 | 1.01 | 1.06 | 0.88 | 1.43 | 0.07 | 1.01 |
time (sec) |
N/A | 0.384 | 0.032 | 0.724 | 0.033 | 0.108 | 0.709 | 0.124 | 0.213 | 0.763 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 156 | 171 | 84 | 182 | 167 | 114 | 217 | 5 | 164 |
N.S. |
1 | 0.85 | 0.93 | 0.46 | 0.99 | 0.91 | 0.62 | 1.19 | 0.03 | 0.90 |
time (sec) |
N/A | 0.521 | 0.113 | 0.815 | 0.114 | 0.111 | 0.327 | 0.117 | 0.210 | 0.292 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 157 | 154 | 65 | 157 | 162 | 114 | 207 | 5 | 144 |
N.S. |
1 | 0.94 | 0.92 | 0.39 | 0.94 | 0.97 | 0.68 | 1.24 | 0.03 | 0.86 |
time (sec) |
N/A | 0.564 | 0.116 | 0.812 | 0.109 | 0.109 | 0.258 | 0.125 | 0.217 | 1.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 147 | 152 | 60 | 154 | 145 | 87 | 186 | 5 | 162 |
N.S. |
1 | 0.91 | 0.94 | 0.37 | 0.95 | 0.90 | 0.54 | 1.15 | 0.03 | 1.00 |
time (sec) |
N/A | 0.532 | 0.095 | 0.816 | 0.109 | 0.108 | 0.277 | 0.131 | 0.241 | 1.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 140 | 152 | 45 | 131 | 382 | 92 | 161 | 5 | 126 |
N.S. |
1 | 0.93 | 1.01 | 0.30 | 0.87 | 2.55 | 0.61 | 1.07 | 0.03 | 0.84 |
time (sec) |
N/A | 0.490 | 0.052 | 0.805 | 0.107 | 0.103 | 0.230 | 0.134 | 0.250 | 0.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 130 | 129 | 42 | 128 | 369 | 71 | 133 | 1 | 123 |
N.S. |
1 | 0.90 | 0.89 | 0.29 | 0.88 | 2.54 | 0.49 | 0.92 | 0.01 | 0.85 |
time (sec) |
N/A | 0.469 | 0.067 | 0.933 | 0.109 | 0.112 | 0.259 | 0.127 | 0.213 | 0.288 |
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 | 147 | 139 | 134 | 114 | 140 | 372 | 90 | 155 | 5 | 126 |
N.S. |
1 | 0.95 | 0.91 | 0.78 | 0.95 | 2.53 | 0.61 | 1.05 | 0.03 | 0.86 |
time (sec) |
N/A | 0.509 | 0.094 | 0.806 | 0.111 | 0.162 | 0.245 | 0.128 | 0.248 | 0.910 |
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 | 149 | 136 | 135 | 113 | 140 | 411 | 73 | 161 | 5 | 126 |
N.S. |
1 | 0.91 | 0.91 | 0.76 | 0.94 | 2.76 | 0.49 | 1.08 | 0.03 | 0.85 |
time (sec) |
N/A | 0.496 | 0.104 | 0.815 | 0.110 | 0.118 | 0.313 | 0.129 | 0.216 | 0.274 |
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 | 165 | 156 | 154 | 130 | 147 | 158 | 112 | 197 | 5 | 178 |
N.S. |
1 | 0.95 | 0.93 | 0.79 | 0.89 | 0.96 | 0.68 | 1.19 | 0.03 | 1.08 |
time (sec) |
N/A | 0.559 | 0.120 | 0.813 | 0.113 | 0.091 | 0.328 | 0.131 | 0.202 | 0.996 |
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 | 168 | 153 | 154 | 130 | 148 | 176 | 99 | 176 | 5 | 145 |
N.S. |
1 | 0.91 | 0.92 | 0.77 | 0.88 | 1.05 | 0.59 | 1.05 | 0.03 | 0.86 |
time (sec) |
N/A | 0.542 | 0.130 | 0.799 | 0.114 | 0.093 | 0.355 | 0.123 | 0.196 | 0.941 |
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 | 184 | 173 | 173 | 150 | 178 | 180 | 139 | 216 | 5 | 161 |
N.S. |
1 | 0.94 | 0.94 | 0.82 | 0.97 | 0.98 | 0.76 | 1.17 | 0.03 | 0.88 |
time (sec) |
N/A | 0.585 | 0.141 | 0.815 | 0.107 | 0.100 | 0.357 | 0.135 | 0.258 | 0.922 |
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 | 79 | 72 | 76 | 82 | 121 | 82 | 106 | 61 | 86 |
N.S. |
1 | 0.96 | 0.88 | 0.93 | 1.00 | 1.48 | 1.00 | 1.29 | 0.74 | 1.05 |
time (sec) |
N/A | 0.403 | 0.077 | 0.848 | 0.031 | 0.096 | 0.630 | 0.129 | 0.249 | 0.882 |
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 | 60 | 55 | 50 | 57 | 60 | 81 | 56 | 91 | 48 | 62 |
N.S. |
1 | 0.92 | 0.83 | 0.95 | 1.00 | 1.35 | 0.93 | 1.52 | 0.80 | 1.03 |
time (sec) |
N/A | 0.351 | 0.043 | 0.729 | 0.026 | 0.099 | 0.515 | 0.126 | 0.219 | 0.085 |
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 | 41 | 40 | 41 | 38 | 40 | 44 | 36 | 65 | 37 | 37 |
N.S. |
1 | 0.98 | 1.00 | 0.93 | 0.98 | 1.07 | 0.88 | 1.59 | 0.90 | 0.90 |
time (sec) |
N/A | 0.322 | 0.017 | 0.707 | 0.033 | 0.109 | 0.323 | 0.122 | 0.206 | 0.060 |
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 | 52 | 46 | 48 | 51 | 70 | 46 | 61 | 45 | 47 |
N.S. |
1 | 1.02 | 0.90 | 0.94 | 1.00 | 1.37 | 0.90 | 1.20 | 0.88 | 0.92 |
time (sec) |
N/A | 0.346 | 0.034 | 0.715 | 0.036 | 0.089 | 0.317 | 0.129 | 0.239 | 0.152 |
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 | 76 | 75 | 64 | 76 | 76 | 118 | 70 | 80 | 61 | 78 |
N.S. |
1 | 0.99 | 0.84 | 1.00 | 1.00 | 1.55 | 0.92 | 1.05 | 0.80 | 1.03 |
time (sec) |
N/A | 0.404 | 0.052 | 0.731 | 0.032 | 0.090 | 0.811 | 0.127 | 0.225 | 0.777 |
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 | 97 | 95 | 85 | 96 | 106 | 154 | 100 | 149 | 78 | 100 |
N.S. |
1 | 0.98 | 0.88 | 0.99 | 1.09 | 1.59 | 1.03 | 1.54 | 0.80 | 1.03 |
time (sec) |
N/A | 0.447 | 0.103 | 0.732 | 0.027 | 0.088 | 0.975 | 0.128 | 0.237 | 0.824 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 193 | 203 | 114 | 218 | 271 | 156 | 244 | 99 | 209 |
N.S. |
1 | 0.89 | 0.94 | 0.53 | 1.00 | 1.25 | 0.72 | 1.12 | 0.46 | 0.96 |
time (sec) |
N/A | 0.556 | 0.149 | 0.804 | 0.109 | 0.105 | 0.589 | 0.128 | 0.232 | 1.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 186 | 185 | 94 | 192 | 257 | 151 | 236 | 98 | 179 |
N.S. |
1 | 0.93 | 0.92 | 0.47 | 0.96 | 1.28 | 0.75 | 1.17 | 0.49 | 0.89 |
time (sec) |
N/A | 0.548 | 0.138 | 0.809 | 0.107 | 0.145 | 0.670 | 0.124 | 0.254 | 0.962 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 182 | 181 | 87 | 187 | 240 | 126 | 211 | 88 | 193 |
N.S. |
1 | 0.94 | 0.93 | 0.45 | 0.96 | 1.24 | 0.65 | 1.09 | 0.45 | 0.99 |
time (sec) |
N/A | 0.533 | 0.130 | 0.824 | 0.119 | 0.117 | 0.543 | 0.127 | 0.211 | 1.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 183 | 165 | 71 | 162 | 578 | 126 | 189 | 81 | 158 |
N.S. |
1 | 1.01 | 0.91 | 0.39 | 0.89 | 3.18 | 0.69 | 1.04 | 0.45 | 0.87 |
time (sec) |
N/A | 0.602 | 0.124 | 0.835 | 0.106 | 0.154 | 0.587 | 0.125 | 0.203 | 0.304 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 172 | 160 | 65 | 157 | 573 | 102 | 166 | 78 | 150 |
N.S. |
1 | 1.00 | 0.93 | 0.38 | 0.91 | 3.33 | 0.59 | 0.97 | 0.45 | 0.87 |
time (sec) |
N/A | 0.590 | 0.135 | 0.822 | 0.111 | 0.106 | 0.472 | 0.124 | 0.223 | 0.933 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 165 | 146 | 67 | 160 | 548 | 117 | 186 | 65 | 145 |
N.S. |
1 | 0.96 | 0.85 | 0.39 | 0.94 | 3.20 | 0.68 | 1.09 | 0.38 | 0.85 |
time (sec) |
N/A | 0.548 | 0.096 | 0.799 | 0.108 | 0.153 | 0.405 | 0.131 | 0.212 | 0.934 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 158 | 145 | 65 | 158 | 537 | 97 | 160 | 67 | 143 |
N.S. |
1 | 0.93 | 0.86 | 0.38 | 0.93 | 3.18 | 0.57 | 0.95 | 0.40 | 0.85 |
time (sec) |
N/A | 0.578 | 0.095 | 0.803 | 0.112 | 0.159 | 0.388 | 0.128 | 0.222 | 0.295 |
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 | 180 | 181 | 164 | 139 | 166 | 570 | 122 | 180 | 84 | 156 |
N.S. |
1 | 1.01 | 0.91 | 0.77 | 0.92 | 3.17 | 0.68 | 1.00 | 0.47 | 0.87 |
time (sec) |
N/A | 0.602 | 0.136 | 0.830 | 0.110 | 0.161 | 0.415 | 0.133 | 0.207 | 1.004 |
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 | 180 | 178 | 163 | 138 | 172 | 618 | 109 | 188 | 96 | 159 |
N.S. |
1 | 0.99 | 0.91 | 0.77 | 0.96 | 3.43 | 0.61 | 1.04 | 0.53 | 0.88 |
time (sec) |
N/A | 0.595 | 0.244 | 0.822 | 0.111 | 0.115 | 0.435 | 0.132 | 0.274 | 0.285 |
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 | 199 | 198 | 185 | 155 | 186 | 259 | 153 | 231 | 107 | 209 |
N.S. |
1 | 0.99 | 0.93 | 0.78 | 0.93 | 1.30 | 0.77 | 1.16 | 0.54 | 1.05 |
time (sec) |
N/A | 0.646 | 0.153 | 0.814 | 0.112 | 0.102 | 0.477 | 0.125 | 0.222 | 1.004 |
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 | 200 | 195 | 183 | 154 | 186 | 277 | 138 | 206 | 114 | 176 |
N.S. |
1 | 0.98 | 0.92 | 0.77 | 0.93 | 1.38 | 0.69 | 1.03 | 0.57 | 0.88 |
time (sec) |
N/A | 0.649 | 0.158 | 0.832 | 0.115 | 0.093 | 0.485 | 0.130 | 0.214 | 1.060 |
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 | 106 | 94 | 100 | 115 | 179 | 112 | 131 | 130 | 117 |
N.S. |
1 | 0.99 | 0.88 | 0.93 | 1.07 | 1.67 | 1.05 | 1.22 | 1.21 | 1.09 |
time (sec) |
N/A | 0.491 | 0.073 | 0.855 | 0.029 | 0.111 | 1.381 | 0.134 | 0.217 | 0.134 |
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 | 83 | 92 | 76 | 94 | 142 | 94 | 93 | 115 | 94 |
N.S. |
1 | 0.94 | 1.05 | 0.86 | 1.07 | 1.61 | 1.07 | 1.06 | 1.31 | 1.07 |
time (sec) |
N/A | 0.421 | 0.043 | 0.749 | 0.033 | 0.113 | 1.450 | 0.138 | 0.249 | 0.118 |
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 | 65 | 64 | 57 | 72 | 89 | 70 | 61 | 97 | 70 |
N.S. |
1 | 0.98 | 0.97 | 0.86 | 1.09 | 1.35 | 1.06 | 0.92 | 1.47 | 1.06 |
time (sec) |
N/A | 0.371 | 0.029 | 0.721 | 0.026 | 0.131 | 1.222 | 0.136 | 0.204 | 0.741 |
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 | 32 | 32 | 30 | 29 | 42 | 42 | 42 | 28 | 17 | 44 |
N.S. |
1 | 1.00 | 0.94 | 0.91 | 1.31 | 1.31 | 1.31 | 0.88 | 0.53 | 1.38 |
time (sec) |
N/A | 0.271 | 0.017 | 0.714 | 0.030 | 0.088 | 0.633 | 0.129 | 0.207 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 69 | 59 | 61 | 77 | 119 | 75 | 74 | 114 | 71 |
N.S. |
1 | 1.01 | 0.87 | 0.90 | 1.13 | 1.75 | 1.10 | 1.09 | 1.68 | 1.04 |
time (sec) |
N/A | 0.374 | 0.051 | 0.721 | 0.033 | 0.114 | 0.450 | 0.133 | 0.250 | 0.176 |
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 | 101 | 100 | 87 | 98 | 109 | 197 | 107 | 136 | 142 | 107 |
N.S. |
1 | 0.99 | 0.86 | 0.97 | 1.08 | 1.95 | 1.06 | 1.35 | 1.41 | 1.06 |
time (sec) |
N/A | 0.459 | 0.063 | 0.733 | 0.034 | 0.109 | 0.885 | 0.135 | 0.226 | 0.806 |
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 | 122 | 122 | 108 | 123 | 136 | 229 | 133 | 131 | 157 | 130 |
N.S. |
1 | 1.00 | 0.89 | 1.01 | 1.11 | 1.88 | 1.09 | 1.07 | 1.29 | 1.07 |
time (sec) |
N/A | 0.520 | 0.089 | 0.744 | 0.029 | 0.090 | 0.985 | 0.136 | 0.232 | 0.825 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 213 | 216 | 116 | 228 | 364 | 192 | 259 | 197 | 213 |
N.S. |
1 | 0.92 | 0.93 | 0.50 | 0.98 | 1.57 | 0.83 | 1.12 | 0.85 | 0.92 |
time (sec) |
N/A | 0.593 | 0.203 | 0.971 | 0.111 | 0.098 | 1.716 | 0.135 | 0.234 | 0.959 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 209 | 210 | 109 | 223 | 347 | 163 | 234 | 187 | 227 |
N.S. |
1 | 0.94 | 0.94 | 0.49 | 1.00 | 1.56 | 0.73 | 1.05 | 0.84 | 1.02 |
time (sec) |
N/A | 0.591 | 0.167 | 0.829 | 0.117 | 0.114 | 1.169 | 0.125 | 0.248 | 0.348 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 209 | 194 | 90 | 196 | 792 | 162 | 210 | 180 | 187 |
N.S. |
1 | 1.00 | 0.93 | 0.43 | 0.94 | 3.81 | 0.78 | 1.01 | 0.87 | 0.90 |
time (sec) |
N/A | 0.676 | 0.175 | 0.864 | 0.112 | 0.128 | 1.488 | 0.135 | 0.224 | 0.976 |