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 | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 250 | 200 | 57 | 212 | 255 | 63 | 204 | 474 | 80 |
N.S. |
1 | 1.49 | 1.19 | 0.34 | 1.26 | 1.52 | 0.38 | 1.21 | 2.82 | 0.48 |
time (sec) |
N/A | 0.709 | 0.054 | 0.468 | 0.108 | 0.083 | 0.287 | 0.124 | 0.239 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 269 | 216 | 81 | 225 | 270 | 80 | 217 | 485 | 91 |
N.S. |
1 | 1.48 | 1.19 | 0.45 | 1.24 | 1.48 | 0.44 | 1.19 | 2.66 | 0.50 |
time (sec) |
N/A | 0.758 | 0.075 | 0.503 | 0.116 | 0.097 | 0.296 | 0.128 | 0.219 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 128 | 27 | 179 | 273 | 42 | 219 | 136 | 121 |
N.S. |
1 | 1.00 | 1.62 | 0.34 | 2.27 | 3.46 | 0.53 | 2.77 | 1.72 | 1.53 |
time (sec) |
N/A | 0.340 | 0.056 | 0.494 | 0.107 | 0.079 | 0.139 | 0.123 | 0.194 | 0.241 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 128 | 27 | 179 | 273 | 42 | 219 | 136 | 121 |
N.S. |
1 | 1.00 | 1.62 | 0.34 | 2.27 | 3.46 | 0.53 | 2.77 | 1.72 | 1.53 |
time (sec) |
N/A | 0.301 | 0.010 | 0.438 | 0.109 | 0.085 | 0.159 | 0.104 | 0.221 | 0.003 |
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 | 33 | 33 | 33 | 26 | 25 | 85 | 110 | 24 | 78 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.76 | 2.58 | 3.33 | 0.73 | 2.36 | 0.97 |
time (sec) |
N/A | 0.261 | 0.009 | 0.452 | 0.104 | 0.079 | 0.142 | 0.125 | 0.203 | 0.188 |
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 | 33 | 33 | 33 | 26 | 25 | 85 | 110 | 24 | 78 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.76 | 2.58 | 3.33 | 0.73 | 2.36 | 0.97 |
time (sec) |
N/A | 0.252 | 0.005 | 0.451 | 0.105 | 0.083 | 0.122 | 0.122 | 0.204 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 128 | 27 | 179 | 145 | 29 | 219 | 134 | 53 |
N.S. |
1 | 1.00 | 1.62 | 0.34 | 2.27 | 1.84 | 0.37 | 2.77 | 1.70 | 0.67 |
time (sec) |
N/A | 0.308 | 0.018 | 0.464 | 0.114 | 0.080 | 0.108 | 0.122 | 0.242 | 0.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 128 | 27 | 179 | 145 | 29 | 219 | 134 | 53 |
N.S. |
1 | 1.00 | 1.62 | 0.34 | 2.27 | 1.84 | 0.37 | 2.77 | 1.70 | 0.67 |
time (sec) |
N/A | 0.296 | 0.009 | 0.443 | 0.110 | 0.087 | 0.124 | 0.115 | 0.224 | 0.003 |
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 | 14 | 14 | 15 | 14 | 13 | 13 | 12 | 14 | 54 | 13 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.93 | 0.93 | 0.86 | 1.00 | 3.86 | 0.93 |
time (sec) |
N/A | 0.223 | 0.005 | 0.435 | 0.029 | 0.068 | 0.085 | 0.122 | 0.192 | 0.175 |
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 | 14 | 14 | 15 | 14 | 13 | 13 | 12 | 14 | 54 | 13 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.93 | 0.93 | 0.86 | 1.00 | 3.86 | 0.93 |
time (sec) |
N/A | 0.232 | 0.003 | 0.432 | 0.030 | 0.072 | 0.087 | 0.122 | 0.198 | 0.003 |
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 | 98 | 138 | 101 | 22 | 107 | 75 | 124 | 95 | 83 | 45 |
N.S. |
1 | 1.41 | 1.03 | 0.22 | 1.09 | 0.77 | 1.27 | 0.97 | 0.85 | 0.46 |
time (sec) |
N/A | 0.507 | 0.036 | 0.412 | 0.111 | 0.077 | 0.199 | 0.134 | 0.206 | 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 | 21 | 21 | 21 | 14 | 13 | 18 | 19 | 13 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.62 | 0.86 | 0.90 | 0.62 | 0.81 | 0.71 |
time (sec) |
N/A | 0.251 | 0.013 | 0.083 | 0.025 | 0.086 | 0.408 | 0.116 | 0.267 | 0.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 19 | 14 | 13 | 18 | 19 | 13 | 17 | 15 |
N.S. |
1 | 1.00 | 0.90 | 0.67 | 0.62 | 0.86 | 0.90 | 0.62 | 0.81 | 0.71 |
time (sec) |
N/A | 0.247 | 0.012 | 0.071 | 0.025 | 0.073 | 0.280 | 0.119 | 0.232 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 19 | 14 | 13 | 16 | 19 | 13 | 15 | 15 |
N.S. |
1 | 1.00 | 0.90 | 0.67 | 0.62 | 0.76 | 0.90 | 0.62 | 0.71 | 0.71 |
time (sec) |
N/A | 0.254 | 0.012 | 0.069 | 0.032 | 0.073 | 0.392 | 0.112 | 0.186 | 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 | 19 | 19 | 20 | 14 | 13 | 14 | 17 | 13 | 13 | 14 |
N.S. |
1 | 1.00 | 1.05 | 0.74 | 0.68 | 0.74 | 0.89 | 0.68 | 0.68 | 0.74 |
time (sec) |
N/A | 0.243 | 0.012 | 0.083 | 0.025 | 0.069 | 0.146 | 0.116 | 0.197 | 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 | 19 | 19 | 19 | 14 | 13 | 14 | 17 | 13 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.68 | 0.74 | 0.89 | 0.68 | 0.79 | 0.79 |
time (sec) |
N/A | 0.252 | 0.017 | 0.093 | 0.026 | 0.072 | 0.218 | 0.125 | 0.221 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 19 | 14 | 13 | 15 | 19 | 13 | 19 | 15 |
N.S. |
1 | 1.00 | 0.90 | 0.67 | 0.62 | 0.71 | 0.90 | 0.62 | 0.90 | 0.71 |
time (sec) |
N/A | 0.246 | 0.016 | 0.086 | 0.034 | 0.073 | 0.251 | 0.124 | 0.199 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 19 | 14 | 13 | 15 | 19 | 13 | 19 | 15 |
N.S. |
1 | 1.00 | 0.90 | 0.67 | 0.62 | 0.71 | 0.90 | 0.62 | 0.90 | 0.71 |
time (sec) |
N/A | 0.246 | 0.016 | 0.079 | 0.031 | 0.074 | 0.313 | 0.125 | 0.201 | 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 | 36 | 36 | 30 | 25 | 24 | 29 | 34 | 24 | 28 | 25 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.78 | 0.69 |
time (sec) |
N/A | 0.262 | 0.018 | 0.414 | 0.029 | 0.069 | 0.911 | 0.116 | 0.211 | 0.177 |
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 | 36 | 36 | 30 | 25 | 24 | 29 | 34 | 24 | 28 | 26 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.78 | 0.72 |
time (sec) |
N/A | 0.269 | 0.017 | 0.374 | 0.025 | 0.072 | 0.697 | 0.123 | 0.259 | 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 | 36 | 36 | 30 | 25 | 24 | 27 | 34 | 24 | 26 | 26 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.75 | 0.94 | 0.67 | 0.72 | 0.72 |
time (sec) |
N/A | 0.269 | 0.016 | 0.375 | 0.026 | 0.067 | 0.652 | 0.127 | 0.211 | 0.172 |
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 | 34 | 30 | 25 | 24 | 26 | 32 | 24 | 25 | 26 |
N.S. |
1 | 1.00 | 0.88 | 0.74 | 0.71 | 0.76 | 0.94 | 0.71 | 0.74 | 0.76 |
time (sec) |
N/A | 0.266 | 0.016 | 0.374 | 0.024 | 0.070 | 0.380 | 0.123 | 0.194 | 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 | 34 | 30 | 25 | 24 | 26 | 32 | 24 | 27 | 25 |
N.S. |
1 | 1.00 | 0.88 | 0.74 | 0.71 | 0.76 | 0.94 | 0.71 | 0.79 | 0.74 |
time (sec) |
N/A | 0.263 | 0.020 | 0.369 | 0.026 | 0.081 | 0.470 | 0.121 | 0.223 | 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 | 36 | 36 | 30 | 25 | 24 | 26 | 34 | 24 | 30 | 26 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.72 | 0.94 | 0.67 | 0.83 | 0.72 |
time (sec) |
N/A | 0.260 | 0.020 | 0.375 | 0.028 | 0.074 | 0.530 | 0.124 | 0.211 | 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 | 36 | 36 | 30 | 25 | 24 | 26 | 34 | 24 | 30 | 26 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.72 | 0.94 | 0.67 | 0.83 | 0.72 |
time (sec) |
N/A | 0.265 | 0.021 | 0.382 | 0.025 | 0.070 | 0.674 | 0.117 | 0.195 | 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 | 51 | 51 | 47 | 36 | 35 | 40 | 49 | 35 | 39 | 35 |
N.S. |
1 | 1.00 | 0.92 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.76 | 0.69 |
time (sec) |
N/A | 0.292 | 0.021 | 0.509 | 0.026 | 0.073 | 1.831 | 0.118 | 0.208 | 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 | 51 | 51 | 47 | 36 | 35 | 40 | 49 | 35 | 39 | 35 |
N.S. |
1 | 1.00 | 0.92 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.76 | 0.69 |
time (sec) |
N/A | 0.284 | 0.022 | 0.371 | 0.030 | 0.085 | 1.352 | 0.117 | 0.228 | 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 | 51 | 51 | 41 | 36 | 35 | 38 | 49 | 35 | 37 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 0.69 | 0.75 | 0.96 | 0.69 | 0.73 | 0.69 |
time (sec) |
N/A | 0.271 | 0.020 | 0.373 | 0.024 | 0.067 | 1.209 | 0.112 | 0.216 | 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 | 49 | 49 | 41 | 36 | 35 | 37 | 48 | 35 | 36 | 35 |
N.S. |
1 | 1.00 | 0.84 | 0.73 | 0.71 | 0.76 | 0.98 | 0.71 | 0.73 | 0.71 |
time (sec) |
N/A | 0.275 | 0.018 | 0.371 | 0.024 | 0.071 | 1.003 | 0.108 | 0.233 | 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 | 49 | 49 | 41 | 36 | 35 | 37 | 48 | 35 | 38 | 35 |
N.S. |
1 | 1.00 | 0.84 | 0.73 | 0.71 | 0.76 | 0.98 | 0.71 | 0.78 | 0.71 |
time (sec) |
N/A | 0.278 | 0.022 | 0.373 | 0.031 | 0.069 | 1.047 | 0.115 | 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 | 51 | 51 | 41 | 36 | 35 | 37 | 49 | 35 | 41 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 0.69 | 0.73 | 0.96 | 0.69 | 0.80 | 0.69 |
time (sec) |
N/A | 0.276 | 0.023 | 0.374 | 0.025 | 0.083 | 1.189 | 0.126 | 0.221 | 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 | 49 | 49 | 41 | 36 | 35 | 37 | 48 | 35 | 41 | 35 |
N.S. |
1 | 1.00 | 0.84 | 0.73 | 0.71 | 0.76 | 0.98 | 0.71 | 0.84 | 0.71 |
time (sec) |
N/A | 0.275 | 0.024 | 0.370 | 0.040 | 0.072 | 1.715 | 0.117 | 0.212 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 345 | 268 | 39 | 0 | 314 | 299 | 453 | 752 | 126 |
N.S. |
1 | 1.44 | 1.12 | 0.16 | 0.00 | 1.31 | 1.25 | 1.89 | 3.13 | 0.52 |
time (sec) |
N/A | 1.051 | 0.831 | 0.486 | 0.000 | 0.089 | 54.788 | 0.241 | 0.233 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 347 | 266 | 39 | 0 | 250 | 296 | 453 | 371 | 126 |
N.S. |
1 | 1.46 | 1.12 | 0.16 | 0.00 | 1.05 | 1.24 | 1.90 | 1.56 | 0.53 |
time (sec) |
N/A | 1.008 | 0.715 | 0.490 | 0.000 | 0.090 | 29.225 | 0.201 | 0.210 | 0.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 324 | 237 | 29 | 0 | 288 | 289 | 445 | 321 | 118 |
N.S. |
1 | 1.42 | 1.04 | 0.13 | 0.00 | 1.26 | 1.27 | 1.95 | 1.41 | 0.52 |
time (sec) |
N/A | 0.933 | 0.645 | 0.459 | 0.000 | 0.083 | 18.877 | 0.223 | 0.253 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 328 | 239 | 29 | 0 | 304 | 291 | 445 | 649 | 118 |
N.S. |
1 | 1.44 | 1.05 | 0.13 | 0.00 | 1.33 | 1.28 | 1.95 | 2.85 | 0.52 |
time (sec) |
N/A | 0.941 | 0.674 | 0.452 | 0.000 | 0.100 | 12.917 | 0.217 | 0.223 | 0.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 328 | 239 | 29 | 0 | 288 | 291 | 445 | 649 | 118 |
N.S. |
1 | 1.44 | 1.05 | 0.13 | 0.00 | 1.26 | 1.28 | 1.95 | 2.85 | 0.52 |
time (sec) |
N/A | 0.935 | 0.675 | 0.454 | 0.000 | 0.091 | 8.578 | 0.224 | 0.233 | 0.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 332 | 239 | 29 | 0 | 264 | 289 | 445 | 321 | 118 |
N.S. |
1 | 1.46 | 1.05 | 0.13 | 0.00 | 1.16 | 1.27 | 1.95 | 1.41 | 0.52 |
time (sec) |
N/A | 0.952 | 0.675 | 0.452 | 0.000 | 0.089 | 12.229 | 0.172 | 0.238 | 0.284 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 339 | 276 | 38 | 0 | 293 | 299 | 461 | 389 | 126 |
N.S. |
1 | 1.42 | 1.16 | 0.16 | 0.00 | 1.23 | 1.26 | 1.94 | 1.63 | 0.53 |
time (sec) |
N/A | 0.984 | 0.762 | 0.483 | 0.000 | 0.092 | 21.169 | 0.220 | 0.252 | 0.258 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 345 | 288 | 38 | 0 | 357 | 303 | 461 | 804 | 126 |
N.S. |
1 | 1.44 | 1.20 | 0.16 | 0.00 | 1.49 | 1.26 | 1.92 | 3.35 | 0.52 |
time (sec) |
N/A | 0.985 | 0.779 | 0.479 | 0.000 | 0.093 | 42.662 | 0.218 | 0.262 | 0.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 351 | 277 | 47 | 0 | 408 | 0 | 486 | 775 | 135 |
N.S. |
1 | 1.41 | 1.11 | 0.19 | 0.00 | 1.64 | 0.00 | 1.95 | 3.11 | 0.54 |
time (sec) |
N/A | 1.014 | 1.196 | 0.522 | 0.000 | 0.092 | 0.000 | 0.256 | 0.269 | 0.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 355 | 277 | 47 | 0 | 424 | 0 | 486 | 1555 | 135 |
N.S. |
1 | 1.43 | 1.11 | 0.19 | 0.00 | 1.70 | 0.00 | 1.95 | 6.24 | 0.54 |
time (sec) |
N/A | 0.998 | 1.245 | 0.513 | 0.000 | 0.087 | 0.000 | 0.258 | 0.303 | 0.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 355 | 277 | 47 | 0 | 424 | 0 | 486 | 1553 | 135 |
N.S. |
1 | 1.43 | 1.11 | 0.19 | 0.00 | 1.70 | 0.00 | 1.95 | 6.24 | 0.54 |
time (sec) |
N/A | 1.021 | 1.323 | 0.513 | 0.000 | 0.092 | 0.000 | 0.248 | 0.282 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 359 | 275 | 47 | 0 | 388 | 0 | 486 | 768 | 135 |
N.S. |
1 | 1.44 | 1.10 | 0.19 | 0.00 | 1.56 | 0.00 | 1.95 | 3.08 | 0.54 |
time (sec) |
N/A | 1.010 | 1.208 | 0.511 | 0.000 | 0.086 | 0.000 | 0.217 | 0.313 | 0.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 351 | 277 | 50 | 0 | 421 | 0 | 462 | 771 | 135 |
N.S. |
1 | 1.41 | 1.11 | 0.20 | 0.00 | 1.69 | 0.00 | 1.86 | 3.10 | 0.54 |
time (sec) |
N/A | 1.000 | 1.147 | 0.515 | 0.000 | 0.097 | 0.000 | 0.269 | 0.293 | 0.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 355 | 277 | 50 | 0 | 421 | 0 | 462 | 1555 | 135 |
N.S. |
1 | 1.43 | 1.11 | 0.20 | 0.00 | 1.69 | 0.00 | 1.86 | 6.24 | 0.54 |
time (sec) |
N/A | 1.018 | 1.160 | 0.454 | 0.000 | 0.104 | 0.000 | 0.266 | 0.279 | 0.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 355 | 277 | 50 | 0 | 405 | 0 | 462 | 1553 | 135 |
N.S. |
1 | 1.43 | 1.11 | 0.20 | 0.00 | 1.63 | 0.00 | 1.86 | 6.24 | 0.54 |
time (sec) |
N/A | 1.005 | 1.170 | 0.458 | 0.000 | 0.095 | 0.000 | 0.247 | 0.323 | 0.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 359 | 277 | 50 | 0 | 397 | 0 | 462 | 772 | 135 |
N.S. |
1 | 1.44 | 1.11 | 0.20 | 0.00 | 1.59 | 0.00 | 1.86 | 3.10 | 0.54 |
time (sec) |
N/A | 1.000 | 1.202 | 0.463 | 0.000 | 0.085 | 0.000 | 0.214 | 0.259 | 0.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 368 | 287 | 56 | 0 | 430 | 0 | 481 | 811 | 148 |
N.S. |
1 | 1.41 | 1.10 | 0.21 | 0.00 | 1.65 | 0.00 | 1.84 | 3.11 | 0.57 |
time (sec) |
N/A | 1.038 | 1.244 | 0.513 | 0.000 | 0.100 | 0.000 | 0.240 | 0.290 | 0.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 388 | 287 | 59 | 0 | 535 | 0 | 496 | 1182 | 158 |
N.S. |
1 | 1.44 | 1.06 | 0.22 | 0.00 | 1.98 | 0.00 | 1.84 | 4.38 | 0.59 |
time (sec) |
N/A | 1.078 | 1.528 | 0.838 | 0.000 | 0.098 | 0.000 | 0.235 | 0.323 | 0.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 380 | 275 | 61 | 0 | 563 | 0 | 499 | 1185 | 156 |
N.S. |
1 | 1.39 | 1.01 | 0.22 | 0.00 | 2.06 | 0.00 | 1.83 | 4.34 | 0.57 |
time (sec) |
N/A | 1.045 | 1.591 | 0.800 | 0.000 | 0.099 | 0.000 | 0.275 | 0.320 | 0.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 384 | 277 | 61 | 0 | 563 | 0 | 499 | 2367 | 156 |
N.S. |
1 | 1.41 | 1.01 | 0.22 | 0.00 | 2.06 | 0.00 | 1.83 | 8.67 | 0.57 |
time (sec) |
N/A | 1.074 | 1.528 | 0.786 | 0.000 | 0.102 | 0.000 | 0.288 | 0.344 | 0.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 384 | 277 | 61 | 0 | 561 | 0 | 499 | 2365 | 156 |
N.S. |
1 | 1.41 | 1.01 | 0.22 | 0.00 | 2.05 | 0.00 | 1.83 | 8.66 | 0.57 |
time (sec) |
N/A | 1.062 | 1.544 | 0.761 | 0.000 | 0.106 | 0.000 | 0.272 | 0.315 | 0.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 388 | 276 | 61 | 0 | 543 | 0 | 498 | 1182 | 156 |
N.S. |
1 | 1.42 | 1.01 | 0.22 | 0.00 | 1.99 | 0.00 | 1.82 | 4.33 | 0.57 |
time (sec) |
N/A | 1.084 | 1.554 | 0.766 | 0.000 | 0.101 | 0.000 | 0.248 | 0.292 | 0.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 380 | 287 | 62 | 0 | 551 | 0 | 472 | 1185 | 157 |
N.S. |
1 | 1.41 | 1.06 | 0.23 | 0.00 | 2.04 | 0.00 | 1.75 | 4.39 | 0.58 |
time (sec) |
N/A | 1.042 | 1.043 | 0.737 | 0.000 | 0.107 | 0.000 | 0.283 | 0.362 | 0.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 384 | 287 | 62 | 0 | 551 | 0 | 472 | 2367 | 157 |
N.S. |
1 | 1.42 | 1.06 | 0.23 | 0.00 | 2.04 | 0.00 | 1.75 | 8.77 | 0.58 |
time (sec) |
N/A | 1.054 | 1.015 | 0.484 | 0.000 | 0.095 | 0.000 | 0.268 | 0.312 | 0.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 384 | 287 | 62 | 0 | 533 | 0 | 472 | 2365 | 157 |
N.S. |
1 | 1.42 | 1.06 | 0.23 | 0.00 | 1.97 | 0.00 | 1.75 | 8.76 | 0.58 |
time (sec) |
N/A | 1.073 | 1.035 | 0.546 | 0.000 | 0.099 | 0.000 | 0.270 | 0.317 | 0.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 388 | 287 | 62 | 0 | 524 | 0 | 472 | 1182 | 157 |
N.S. |
1 | 1.44 | 1.06 | 0.23 | 0.00 | 1.94 | 0.00 | 1.75 | 4.38 | 0.58 |
time (sec) |
N/A | 1.067 | 1.023 | 0.550 | 0.000 | 0.099 | 0.000 | 0.229 | 0.302 | 0.290 |
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 | 81 | 57 | 179 | 78 | 159 | 722 | 256 | 179 | 169 |
N.S. |
1 | 1.00 | 0.70 | 2.21 | 0.96 | 1.96 | 8.91 | 3.16 | 2.21 | 2.09 |
time (sec) |
N/A | 0.372 | 0.071 | 0.579 | 0.039 | 0.081 | 0.749 | 0.132 | 0.194 | 0.355 |
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 | 58 | 41 | 94 | 56 | 87 | 333 | 135 | 94 | 95 |
N.S. |
1 | 1.00 | 0.71 | 1.62 | 0.97 | 1.50 | 5.74 | 2.33 | 1.62 | 1.64 |
time (sec) |
N/A | 0.332 | 0.053 | 0.418 | 0.034 | 0.079 | 0.569 | 0.123 | 0.208 | 0.267 |
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 | 35 | 25 | 34 | 34 | 35 | 105 | 51 | 36 | 35 |
N.S. |
1 | 1.00 | 0.71 | 0.97 | 0.97 | 1.00 | 3.00 | 1.46 | 1.03 | 1.00 |
time (sec) |
N/A | 0.288 | 0.027 | 0.058 | 0.037 | 0.083 | 0.287 | 0.135 | 0.243 | 0.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 42 | 0 | 0 | 0 | 95 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 2.16 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.268 | 0.029 | 0.000 | 0.000 | 0.000 | 1.624 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 42 | 0 | 0 | 0 | 551 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 12.52 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.256 | 0.035 | 0.000 | 0.000 | 0.000 | 19.626 | 0.000 | 0.183 | 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 | 62 | 66 | 51 | 37 | 50 | 47 | 87 | 68 | 46 | 46 |
N.S. |
1 | 1.06 | 0.82 | 0.60 | 0.81 | 0.76 | 1.40 | 1.10 | 0.74 | 0.74 |
time (sec) |
N/A | 0.308 | 0.031 | 0.617 | 0.031 | 0.073 | 0.434 | 0.127 | 0.215 | 0.397 |
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 | 40 | 44 | 40 | 26 | 32 | 36 | 61 | 42 | 35 | 35 |
N.S. |
1 | 1.10 | 1.00 | 0.65 | 0.80 | 0.90 | 1.52 | 1.05 | 0.88 | 0.88 |
time (sec) |
N/A | 0.290 | 0.031 | 0.600 | 0.025 | 0.073 | 0.298 | 0.121 | 0.196 | 0.332 |
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 | 19 | 19 | 19 | 16 | 15 | 24 | 39 | 15 | 23 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.79 | 1.26 | 2.05 | 0.79 | 1.21 | 0.79 |
time (sec) |
N/A | 0.231 | 0.014 | 0.580 | 0.025 | 0.071 | 0.122 | 0.118 | 0.202 | 0.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 45 | 34 | 52 | 96 | 146 | 38 | 35 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 1.16 | 2.13 | 3.24 | 0.84 | 0.78 | 0.73 |
time (sec) |
N/A | 0.288 | 0.031 | 0.573 | 0.106 | 0.085 | 1.008 | 0.121 | 0.202 | 0.394 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 48 | 49 | 42 | 56 | 120 | 126 | 47 | 44 | 37 |
N.S. |
1 | 0.98 | 1.00 | 0.86 | 1.14 | 2.45 | 2.57 | 0.96 | 0.90 | 0.76 |
time (sec) |
N/A | 0.272 | 0.068 | 0.628 | 0.115 | 0.085 | 1.264 | 0.112 | 0.217 | 0.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 77 | 63 | 57 | 108 | 145 | 206 | 75 | 77 | 57 |
N.S. |
1 | 1.04 | 0.85 | 0.77 | 1.46 | 1.96 | 2.78 | 1.01 | 1.04 | 0.77 |
time (sec) |
N/A | 0.309 | 0.096 | 0.622 | 0.106 | 0.085 | 2.368 | 0.128 | 0.201 | 0.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 84 | 73 | 54 | 105 | 134 | 206 | 64 | 59 | 0 |
N.S. |
1 | 1.09 | 0.95 | 0.70 | 1.36 | 1.74 | 2.68 | 0.83 | 0.77 | 0.00 |
time (sec) |
N/A | 0.324 | 0.168 | 1.353 | 0.116 | 0.090 | 2.314 | 0.127 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 56 | 58 | 41 | 59 | 107 | 126 | 47 | 35 | 0 |
N.S. |
1 | 1.08 | 1.12 | 0.79 | 1.13 | 2.06 | 2.42 | 0.90 | 0.67 | 0.00 |
time (sec) |
N/A | 0.271 | 0.145 | 0.803 | 0.114 | 0.088 | 1.045 | 0.123 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 57 | 40 | 39 | 102 | 146 | 70 | 35 | 0 |
N.S. |
1 | 1.00 | 1.12 | 0.78 | 0.76 | 2.00 | 2.86 | 1.37 | 0.69 | 0.00 |
time (sec) |
N/A | 0.279 | 0.149 | 0.711 | 0.107 | 0.088 | 0.971 | 0.139 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 27 | 94 | 75 | 26 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.23 | 4.27 | 3.41 | 1.18 | 0.82 |
time (sec) |
N/A | 0.237 | 0.125 | 0.805 | 0.026 | 0.081 | 0.668 | 0.131 | 0.220 | 0.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 42 | 29 | 37 | 38 | 260 | 152 | 37 | 38 |
N.S. |
1 | 1.00 | 0.91 | 0.63 | 0.80 | 0.83 | 5.65 | 3.30 | 0.80 | 0.83 |
time (sec) |
N/A | 0.272 | 0.153 | 0.952 | 0.031 | 0.085 | 0.813 | 0.130 | 0.216 | 0.565 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 77 | 54 | 40 | 55 | 50 | 733 | 188 | 49 | 77 |
N.S. |
1 | 1.08 | 0.76 | 0.56 | 0.77 | 0.70 | 10.32 | 2.65 | 0.69 | 1.08 |
time (sec) |
N/A | 0.317 | 0.167 | 1.249 | 0.028 | 0.081 | 3.797 | 0.142 | 0.197 | 0.757 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 102 | 64 | 98 | 0 | 57 | 41 | 0 | 61 | 0 |
N.S. |
1 | 1.05 | 0.66 | 1.01 | 0.00 | 0.59 | 0.42 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.369 | 5.322 | 0.619 | 0.000 | 0.081 | 0.549 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 88 | 80 | 0 | 42 | 39 | 0 | 38 | 38 |
N.S. |
1 | 1.00 | 1.19 | 1.08 | 0.00 | 0.57 | 0.53 | 0.00 | 0.51 | 0.51 |
time (sec) |
N/A | 0.299 | 0.075 | 0.579 | 0.000 | 0.073 | 0.542 | 0.000 | 0.217 | 0.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 52 | 82 | 0 | 43 | 36 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 0.68 | 1.08 | 0.00 | 0.57 | 0.47 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.308 | 10.011 | 0.648 | 0.000 | 0.084 | 0.697 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 104 | 52 | 100 | 0 | 59 | 48 | 0 | 49 | 0 |
N.S. |
1 | 1.05 | 0.53 | 1.01 | 0.00 | 0.60 | 0.48 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.356 | 10.012 | 0.889 | 0.000 | 0.076 | 0.702 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 133 | 52 | 104 | 0 | 90 | 41 | 0 | 43 | 0 |
N.S. |
1 | 1.01 | 0.39 | 0.79 | 0.00 | 0.68 | 0.31 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.524 | 4.258 | 0.605 | 0.000 | 0.081 | 0.574 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 129 | 50 | 104 | 0 | 0 | 36 | 0 | 44 | 40 |
N.S. |
1 | 1.02 | 0.40 | 0.83 | 0.00 | 0.00 | 0.29 | 0.00 | 0.35 | 0.32 |
time (sec) |
N/A | 0.500 | 8.467 | 0.609 | 0.000 | 0.000 | 0.587 | 0.000 | 0.216 | 0.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 160 | 52 | 115 | 0 | 86 | 37 | 0 | 49 | 0 |
N.S. |
1 | 1.03 | 0.34 | 0.74 | 0.00 | 0.55 | 0.24 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.573 | 10.010 | 0.784 | 0.000 | 0.091 | 0.748 | 0.000 | 0.205 | 0.000 |
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 | 62 | 66 | 40 | 37 | 50 | 58 | 109 | 79 | 57 | 55 |
N.S. |
1 | 1.06 | 0.65 | 0.60 | 0.81 | 0.94 | 1.76 | 1.27 | 0.92 | 0.89 |
time (sec) |
N/A | 0.318 | 0.042 | 0.577 | 0.036 | 0.069 | 0.648 | 0.121 | 0.220 | 0.377 |
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 | 40 | 44 | 29 | 26 | 32 | 46 | 83 | 53 | 46 | 44 |
N.S. |
1 | 1.10 | 0.72 | 0.65 | 0.80 | 1.15 | 2.08 | 1.32 | 1.15 | 1.10 |
time (sec) |
N/A | 0.293 | 0.036 | 0.567 | 0.029 | 0.069 | 0.436 | 0.120 | 0.210 | 0.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 16 | 15 | 33 | 60 | 26 | 35 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.79 | 1.74 | 3.16 | 1.37 | 1.84 | 0.79 |
time (sec) |
N/A | 0.231 | 0.015 | 0.578 | 0.026 | 0.071 | 0.189 | 0.120 | 0.228 | 0.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 64 | 55 | 44 | 65 | 115 | 196 | 53 | 53 | 46 |
N.S. |
1 | 1.03 | 0.89 | 0.71 | 1.05 | 1.85 | 3.16 | 0.85 | 0.85 | 0.74 |
time (sec) |
N/A | 0.304 | 0.044 | 0.582 | 0.113 | 0.082 | 1.439 | 0.117 | 0.219 | 0.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 68 | 59 | 51 | 70 | 130 | 206 | 65 | 64 | 51 |
N.S. |
1 | 1.01 | 0.88 | 0.76 | 1.04 | 1.94 | 3.07 | 0.97 | 0.96 | 0.76 |
time (sec) |
N/A | 0.307 | 0.082 | 0.639 | 0.115 | 0.085 | 1.686 | 0.123 | 0.210 | 0.604 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 73 | 61 | 59 | 106 | 150 | 189 | 73 | 64 | 55 |
N.S. |
1 | 1.01 | 0.85 | 0.82 | 1.47 | 2.08 | 2.62 | 1.01 | 0.89 | 0.76 |
time (sec) |
N/A | 0.296 | 0.095 | 0.651 | 0.109 | 0.110 | 2.140 | 0.128 | 0.215 | 0.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 109 | 84 | 67 | 147 | 157 | 262 | 147 | 82 | 0 |
N.S. |
1 | 1.10 | 0.85 | 0.68 | 1.48 | 1.59 | 2.65 | 1.48 | 0.83 | 0.00 |
time (sec) |
N/A | 0.358 | 0.193 | 0.783 | 0.113 | 0.097 | 3.682 | 0.137 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 81 | 70 | 53 | 103 | 135 | 189 | 116 | 57 | 0 |
N.S. |
1 | 1.09 | 0.95 | 0.72 | 1.39 | 1.82 | 2.55 | 1.57 | 0.77 | 0.00 |
time (sec) |
N/A | 0.300 | 0.174 | 0.697 | 0.109 | 0.099 | 1.737 | 0.139 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 77 | 68 | 50 | 76 | 124 | 206 | 89 | 52 | 0 |
N.S. |
1 | 1.05 | 0.93 | 0.68 | 1.04 | 1.70 | 2.82 | 1.22 | 0.71 | 0.00 |
time (sec) |
N/A | 0.313 | 0.178 | 0.741 | 0.113 | 0.092 | 1.578 | 0.149 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 74 | 67 | 48 | 55 | 125 | 201 | 146 | 52 | 0 |
N.S. |
1 | 1.03 | 0.93 | 0.67 | 0.76 | 1.74 | 2.79 | 2.03 | 0.72 | 0.00 |
time (sec) |
N/A | 0.323 | 0.214 | 0.842 | 0.107 | 0.086 | 1.596 | 0.144 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 36 | 143 | 116 | 38 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.64 | 6.50 | 5.27 | 1.73 | 0.82 |
time (sec) |
N/A | 0.233 | 0.171 | 0.970 | 0.036 | 0.075 | 0.875 | 0.155 | 0.194 | 0.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 32 | 29 | 37 | 49 | 335 | 226 | 49 | 75 |
N.S. |
1 | 1.00 | 0.70 | 0.63 | 0.80 | 1.07 | 7.28 | 4.91 | 1.07 | 1.63 |
time (sec) |
N/A | 0.271 | 0.213 | 1.215 | 0.028 | 0.082 | 1.203 | 0.144 | 0.218 | 1.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 77 | 43 | 40 | 55 | 61 | 857 | 262 | 60 | 96 |
N.S. |
1 | 1.08 | 0.61 | 0.56 | 0.77 | 0.86 | 12.07 | 3.69 | 0.85 | 1.35 |
time (sec) |
N/A | 0.319 | 0.216 | 1.588 | 0.027 | 0.102 | 10.017 | 0.152 | 0.213 | 1.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 127 | 70 | 109 | 0 | 71 | 41 | 0 | 81 | 0 |
N.S. |
1 | 1.07 | 0.59 | 0.92 | 0.00 | 0.60 | 0.34 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.392 | 8.885 | 0.632 | 0.000 | 0.083 | 0.580 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 97 | 48 | 92 | 0 | 52 | 39 | 0 | 56 | 38 |
N.S. |
1 | 1.05 | 0.52 | 1.00 | 0.00 | 0.57 | 0.42 | 0.00 | 0.61 | 0.41 |
time (sec) |
N/A | 0.327 | 0.003 | 0.562 | 0.000 | 0.077 | 0.587 | 0.000 | 0.256 | 0.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 97 | 53 | 90 | 0 | 0 | 39 | 0 | 67 | 0 |
N.S. |
1 | 1.02 | 0.56 | 0.95 | 0.00 | 0.00 | 0.41 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.335 | 10.011 | 0.622 | 0.000 | 0.000 | 0.585 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 101 | 53 | 92 | 0 | 55 | 37 | 0 | 66 | 0 |
N.S. |
1 | 1.04 | 0.55 | 0.95 | 0.00 | 0.57 | 0.38 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.348 | 10.011 | 0.927 | 0.000 | 0.084 | 0.671 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 158 | 53 | 114 | 0 | 105 | 41 | 0 | 61 | 0 |
N.S. |
1 | 1.04 | 0.35 | 0.75 | 0.00 | 0.69 | 0.27 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.553 | 6.938 | 0.593 | 0.000 | 0.082 | 0.561 | 0.000 | 0.225 | 0.000 |