Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 50 | 50 | 36 | 47 | 72 | 0 | 47 | 27 | 77 |
N.S. |
1 | 0.91 | 0.91 | 0.65 | 0.85 | 1.31 | 0.00 | 0.85 | 0.49 | 1.40 |
time (sec) |
N/A | 0.259 | 0.091 | 0.457 | 0.054 | 0.079 | 0.000 | 0.158 | 0.184 | 0.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 34 | 23 | 27 | 33 | 0 | 27 | 27 | 25 |
N.S. |
1 | 1.00 | 1.26 | 0.85 | 1.00 | 1.22 | 0.00 | 1.00 | 1.00 | 0.93 |
time (sec) |
N/A | 0.228 | 0.049 | 1.298 | 0.050 | 0.095 | 0.000 | 0.160 | 0.157 | 0.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 24 | 23 | 23 | 20 | 26 | 0 | 17 | 27 | 19 |
N.S. |
1 | 1.04 | 1.00 | 1.00 | 0.87 | 1.13 | 0.00 | 0.74 | 1.17 | 0.83 |
time (sec) |
N/A | 0.223 | 0.024 | 0.672 | 0.056 | 0.116 | 0.000 | 0.147 | 0.152 | 0.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 35 | 26 | 0 | 32 | 60 | 53 | 18 | 29 |
N.S. |
1 | 1.00 | 1.06 | 0.79 | 0.00 | 0.97 | 1.82 | 1.61 | 0.55 | 0.88 |
time (sec) |
N/A | 0.193 | 0.074 | 0.232 | 0.000 | 0.115 | 0.097 | 0.141 | 0.164 | 0.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 93 | 87 | 61 | 0 | 54 | 151 | 83 | 27 | 60 |
N.S. |
1 | 1.06 | 0.99 | 0.69 | 0.00 | 0.61 | 1.72 | 0.94 | 0.31 | 0.68 |
time (sec) |
N/A | 0.295 | 0.173 | 0.984 | 0.000 | 0.082 | 0.173 | 0.154 | 0.152 | 0.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 137 | 131 | 96 | 0 | 76 | 219 | 103 | 27 | 123 |
N.S. |
1 | 0.91 | 0.87 | 0.64 | 0.00 | 0.51 | 1.46 | 0.69 | 0.18 | 0.82 |
time (sec) |
N/A | 0.320 | 0.194 | 1.678 | 0.000 | 0.079 | 0.232 | 0.156 | 0.186 | 0.819 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 85 | 60 | 122 | 288 | 266 | 0 | 138 | 27 | 193 |
N.S. |
1 | 1.01 | 0.71 | 1.45 | 3.43 | 3.17 | 0.00 | 1.64 | 0.32 | 2.30 |
time (sec) |
N/A | 0.459 | 0.724 | 0.749 | 0.044 | 0.118 | 0.000 | 0.225 | 0.151 | 4.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 59 | 50 | 100 | 186 | 174 | 0 | 99 | 27 | 116 |
N.S. |
1 | 0.98 | 0.83 | 1.67 | 3.10 | 2.90 | 0.00 | 1.65 | 0.45 | 1.93 |
time (sec) |
N/A | 0.362 | 0.494 | 0.690 | 0.041 | 0.083 | 0.000 | 0.206 | 0.158 | 2.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 34 | 70 | 83 | 80 | 0 | 58 | 27 | 43 |
N.S. |
1 | 1.00 | 1.10 | 2.26 | 2.68 | 2.58 | 0.00 | 1.87 | 0.87 | 1.39 |
time (sec) |
N/A | 0.277 | 0.420 | 1.117 | 0.046 | 0.082 | 0.000 | 0.199 | 0.158 | 0.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 25 | 19 | 29 | 17 | 34 | 21 | 25 | 25 |
N.S. |
1 | 1.00 | 0.89 | 0.68 | 1.04 | 0.61 | 1.21 | 0.75 | 0.89 | 0.89 |
time (sec) |
N/A | 0.208 | 0.186 | 0.680 | 0.041 | 0.071 | 0.382 | 0.166 | 0.187 | 0.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 50 | 49 | 0 | 41 | 126 | 67 | 25 | 78 |
N.S. |
1 | 1.00 | 1.06 | 1.04 | 0.00 | 0.87 | 2.68 | 1.43 | 0.53 | 1.66 |
time (sec) |
N/A | 0.274 | 0.271 | 0.806 | 0.000 | 0.090 | 0.190 | 0.183 | 0.167 | 0.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 64 | 72 | 84 | 0 | 63 | 196 | 119 | 27 | 134 |
N.S. |
1 | 0.96 | 1.07 | 1.25 | 0.00 | 0.94 | 2.93 | 1.78 | 0.40 | 2.00 |
time (sec) |
N/A | 0.314 | 0.402 | 1.289 | 0.000 | 0.099 | 0.261 | 0.179 | 0.163 | 1.912 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 76 | 94 | 119 | 0 | 85 | 264 | 171 | 27 | 188 |
N.S. |
1 | 0.89 | 1.11 | 1.40 | 0.00 | 1.00 | 3.11 | 2.01 | 0.32 | 2.21 |
time (sec) |
N/A | 0.320 | 0.549 | 1.099 | 0.000 | 0.086 | 0.344 | 0.192 | 0.188 | 4.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 72 | 44 | 47 | 77 | 138 | 0 | 77 | 37 | 93 |
N.S. |
1 | 0.88 | 0.54 | 0.57 | 0.94 | 1.68 | 0.00 | 0.94 | 0.45 | 1.13 |
time (sec) |
N/A | 0.273 | 0.201 | 0.470 | 0.041 | 0.104 | 0.000 | 0.178 | 0.167 | 0.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 50 | 50 | 36 | 47 | 97 | 0 | 47 | 37 | 77 |
N.S. |
1 | 0.91 | 0.91 | 0.65 | 0.85 | 1.76 | 0.00 | 0.85 | 0.67 | 1.40 |
time (sec) |
N/A | 0.253 | 0.123 | 0.460 | 0.036 | 0.091 | 0.000 | 0.186 | 0.170 | 0.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 50 | 20 | 35 | 54 | 0 | 35 | 37 | 33 |
N.S. |
1 | 1.00 | 1.85 | 0.74 | 1.30 | 2.00 | 0.00 | 1.30 | 1.37 | 1.22 |
time (sec) |
N/A | 0.225 | 0.044 | 0.447 | 0.039 | 0.082 | 0.000 | 0.173 | 0.162 | 0.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 39 | 38 | 30 | 32 | 70 | 0 | 32 | 37 | 28 |
N.S. |
1 | 1.03 | 1.00 | 0.79 | 0.84 | 1.84 | 0.00 | 0.84 | 0.97 | 0.74 |
time (sec) |
N/A | 0.247 | 0.041 | 0.780 | 0.030 | 0.085 | 0.000 | 0.169 | 0.153 | 0.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 25 | 19 | 19 | 21 | 17 | 65 | 17 | 37 | 22 |
N.S. |
1 | 0.96 | 0.73 | 0.73 | 0.81 | 0.65 | 2.50 | 0.65 | 1.42 | 0.85 |
time (sec) |
N/A | 0.223 | 0.108 | 1.408 | 0.042 | 0.082 | 0.547 | 0.147 | 0.190 | 0.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 65 | 52 | 44 | 0 | 43 | 117 | 61 | 28 | 39 |
N.S. |
1 | 1.07 | 0.85 | 0.72 | 0.00 | 0.70 | 1.92 | 1.00 | 0.46 | 0.64 |
time (sec) |
N/A | 0.271 | 0.121 | 0.272 | 0.000 | 0.074 | 0.152 | 0.145 | 0.196 | 0.451 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 115 | 97 | 79 | 0 | 65 | 189 | 93 | 37 | 71 |
N.S. |
1 | 1.01 | 0.85 | 0.69 | 0.00 | 0.57 | 1.66 | 0.82 | 0.32 | 0.62 |
time (sec) |
N/A | 0.296 | 0.257 | 1.854 | 0.000 | 0.086 | 0.230 | 0.187 | 0.199 | 0.563 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 159 | 142 | 114 | 0 | 87 | 258 | 113 | 37 | 149 |
N.S. |
1 | 0.96 | 0.86 | 0.69 | 0.00 | 0.53 | 1.56 | 0.68 | 0.22 | 0.90 |
time (sec) |
N/A | 0.332 | 0.278 | 1.069 | 0.000 | 0.105 | 0.280 | 0.161 | 0.204 | 1.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 130 | 294 | 133 | 421 | 326 | 0 | 203 | 37 | 191 |
N.S. |
1 | 1.05 | 2.37 | 1.07 | 3.40 | 2.63 | 0.00 | 1.64 | 0.30 | 1.54 |
time (sec) |
N/A | 0.606 | 2.230 | 0.829 | 0.050 | 0.112 | 0.000 | 0.246 | 0.199 | 3.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 104 | 215 | 111 | 295 | 230 | 0 | 151 | 37 | 136 |
N.S. |
1 | 1.04 | 2.15 | 1.11 | 2.95 | 2.30 | 0.00 | 1.51 | 0.37 | 1.36 |
time (sec) |
N/A | 0.484 | 1.291 | 0.793 | 0.061 | 0.104 | 0.000 | 0.236 | 0.193 | 3.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 146 | 89 | 167 | 134 | 0 | 95 | 37 | 104 |
N.S. |
1 | 1.00 | 1.97 | 1.20 | 2.26 | 1.81 | 0.00 | 1.28 | 0.50 | 1.41 |
time (sec) |
N/A | 0.382 | 0.675 | 0.798 | 0.039 | 0.087 | 0.000 | 0.220 | 0.189 | 1.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 184 | 54 | 117 | 64 | 0 | 57 | 37 | 44 |
N.S. |
1 | 1.00 | 3.83 | 1.12 | 2.44 | 1.33 | 0.00 | 1.19 | 0.77 | 0.92 |
time (sec) |
N/A | 0.291 | 0.395 | 0.820 | 0.154 | 0.082 | 0.000 | 0.211 | 0.152 | 0.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 64 | 38 | 38 | 45 | 30 | 112 | 47 | 35 | 79 |
N.S. |
1 | 0.98 | 0.58 | 0.58 | 0.69 | 0.46 | 1.72 | 0.72 | 0.54 | 1.22 |
time (sec) |
N/A | 0.305 | 0.220 | 1.128 | 0.065 | 0.095 | 0.571 | 0.189 | 0.157 | 0.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 68 | 68 | 67 | 0 | 52 | 163 | 93 | 35 | 90 |
N.S. |
1 | 0.96 | 0.96 | 0.94 | 0.00 | 0.73 | 2.30 | 1.31 | 0.49 | 1.27 |
time (sec) |
N/A | 0.310 | 0.454 | 1.191 | 0.000 | 0.071 | 0.231 | 0.220 | 0.166 | 0.876 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 80 | 95 | 102 | 0 | 74 | 231 | 145 | 37 | 161 |
N.S. |
1 | 0.90 | 1.07 | 1.15 | 0.00 | 0.83 | 2.60 | 1.63 | 0.42 | 1.81 |
time (sec) |
N/A | 0.323 | 0.490 | 0.984 | 0.000 | 0.099 | 0.337 | 0.221 | 0.186 | 3.924 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 88 | 117 | 137 | 0 | 96 | 299 | 197 | 37 | 216 |
N.S. |
1 | 0.82 | 1.09 | 1.28 | 0.00 | 0.90 | 2.79 | 1.84 | 0.35 | 2.02 |
time (sec) |
N/A | 0.323 | 0.712 | 1.298 | 0.000 | 0.075 | 0.413 | 0.240 | 0.201 | 2.862 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 94 | 56 | 58 | 87 | 194 | 0 | 87 | 197 | 119 |
N.S. |
1 | 0.86 | 0.51 | 0.53 | 0.80 | 1.78 | 0.00 | 0.80 | 1.81 | 1.09 |
time (sec) |
N/A | 0.283 | 0.247 | 0.536 | 0.048 | 0.102 | 0.000 | 0.240 | 0.194 | 0.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 72 | 46 | 47 | 87 | 153 | 0 | 87 | 160 | 103 |
N.S. |
1 | 0.88 | 0.56 | 0.57 | 1.06 | 1.87 | 0.00 | 1.06 | 1.95 | 1.26 |
time (sec) |
N/A | 0.273 | 0.189 | 0.510 | 0.037 | 0.082 | 0.000 | 0.243 | 0.216 | 0.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 50 | 34 | 36 | 67 | 112 | 0 | 67 | 123 | 114 |
N.S. |
1 | 0.91 | 0.62 | 0.65 | 1.22 | 2.04 | 0.00 | 1.22 | 2.24 | 2.07 |
time (sec) |
N/A | 0.254 | 0.106 | 0.510 | 0.041 | 0.078 | 0.000 | 0.236 | 0.212 | 0.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 50 | 21 | 47 | 69 | 0 | 47 | 85 | 77 |
N.S. |
1 | 1.00 | 1.85 | 0.78 | 1.74 | 2.56 | 0.00 | 1.74 | 3.15 | 2.85 |
time (sec) |
N/A | 0.220 | 0.089 | 0.491 | 0.045 | 0.070 | 0.000 | 0.219 | 0.202 | 0.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 48 | 68 | 45 | 113 | 0 | 53 | 299 | 41 |
N.S. |
1 | 1.00 | 0.83 | 1.17 | 0.78 | 1.95 | 0.00 | 0.91 | 5.16 | 0.71 |
time (sec) |
N/A | 0.246 | 0.085 | 0.567 | 0.035 | 0.081 | 0.000 | 0.208 | 0.195 | 0.435 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 45 | 44 | 56 | 66 | 55 | 0 | 36 | 0 | 42 |
N.S. |
1 | 0.94 | 0.92 | 1.17 | 1.38 | 1.15 | 0.00 | 0.75 | 0.00 | 0.88 |
time (sec) |
N/A | 0.245 | 0.077 | 0.561 | 0.031 | 0.096 | 0.000 | 0.203 | 0.290 | 0.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 24 | 24 | 21 | 30 | 153 | 18 | 386 | 20 |
N.S. |
1 | 1.00 | 0.89 | 0.89 | 0.78 | 1.11 | 5.67 | 0.67 | 14.30 | 0.74 |
time (sec) |
N/A | 0.225 | 0.113 | 0.480 | 0.034 | 0.070 | 0.880 | 0.183 | 0.191 | 0.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 97 | 65 | 62 | 0 | 54 | 155 | 73 | 40 | 50 |
N.S. |
1 | 1.10 | 0.74 | 0.70 | 0.00 | 0.61 | 1.76 | 0.83 | 0.45 | 0.57 |
time (sec) |
N/A | 0.356 | 0.147 | 0.333 | 0.000 | 0.069 | 0.198 | 0.165 | 0.169 | 0.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 137 | 137 | 97 | 0 | 76 | 224 | 103 | 49 | 124 |
N.S. |
1 | 0.94 | 0.94 | 0.67 | 0.00 | 0.52 | 1.54 | 0.71 | 0.34 | 0.86 |
time (sec) |
N/A | 0.301 | 0.218 | 0.961 | 0.000 | 0.088 | 0.274 | 0.221 | 0.192 | 0.826 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 181 | 159 | 129 | 0 | 98 | 292 | 123 | 49 | 173 |
N.S. |
1 | 0.87 | 0.76 | 0.62 | 0.00 | 0.47 | 1.40 | 0.59 | 0.23 | 0.83 |
time (sec) |
N/A | 0.349 | 0.333 | 1.133 | 0.000 | 0.076 | 0.312 | 0.222 | 0.201 | 2.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 128 | 113 | 122 | 341 | 278 | 0 | 164 | 278 | 150 |
N.S. |
1 | 1.08 | 0.95 | 1.03 | 2.87 | 2.34 | 0.00 | 1.38 | 2.34 | 1.26 |
time (sec) |
N/A | 0.659 | 0.915 | 0.836 | 0.051 | 0.089 | 0.000 | 0.359 | 0.172 | 3.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 98 | 63 | 100 | 215 | 182 | 0 | 112 | 179 | 135 |
N.S. |
1 | 1.05 | 0.68 | 1.08 | 2.31 | 1.96 | 0.00 | 1.20 | 1.92 | 1.45 |
time (sec) |
N/A | 0.507 | 0.710 | 0.884 | 0.046 | 0.089 | 0.000 | 0.325 | 0.176 | 2.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 70 | 108 | 86 | 319 | 112 | 0 | 110 | 0 | 105 |
N.S. |
1 | 1.08 | 1.66 | 1.32 | 4.91 | 1.72 | 0.00 | 1.69 | 0.00 | 1.62 |
time (sec) |
N/A | 0.415 | 0.620 | 0.874 | 0.144 | 0.084 | 0.000 | 0.341 | 0.485 | 0.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 19 | 29 | 17 | 80 | 36 | 759 | 68 |
N.S. |
1 | 1.00 | 1.00 | 0.59 | 0.91 | 0.53 | 2.50 | 1.12 | 23.72 | 2.12 |
time (sec) |
N/A | 0.219 | 0.316 | 1.519 | 0.039 | 0.093 | 0.873 | 0.309 | 0.214 | 0.527 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 102 | 54 | 56 | 69 | 41 | 219 | 73 | 821 | 133 |
N.S. |
1 | 1.04 | 0.55 | 0.57 | 0.70 | 0.42 | 2.23 | 0.74 | 8.38 | 1.36 |
time (sec) |
N/A | 0.427 | 0.320 | 0.775 | 0.058 | 0.100 | 0.865 | 0.271 | 0.212 | 0.730 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 106 | 76 | 85 | 0 | 63 | 197 | 119 | 47 | 134 |
N.S. |
1 | 1.05 | 0.75 | 0.84 | 0.00 | 0.62 | 1.95 | 1.18 | 0.47 | 1.33 |
time (sec) |
N/A | 0.436 | 0.363 | 0.832 | 0.000 | 0.090 | 0.285 | 0.329 | 0.185 | 3.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 120 | 98 | 120 | 0 | 85 | 265 | 171 | 49 | 188 |
N.S. |
1 | 0.99 | 0.81 | 0.99 | 0.00 | 0.70 | 2.19 | 1.41 | 0.40 | 1.55 |
time (sec) |
N/A | 0.458 | 0.506 | 1.098 | 0.000 | 0.089 | 0.381 | 0.320 | 0.196 | 3.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 128 | 120 | 155 | 0 | 107 | 333 | 223 | 49 | 136 |
N.S. |
1 | 0.92 | 0.86 | 1.12 | 0.00 | 0.77 | 2.40 | 1.60 | 0.35 | 0.98 |
time (sec) |
N/A | 0.469 | 0.930 | 1.367 | 0.000 | 0.107 | 0.464 | 0.344 | 0.201 | 2.677 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 72 | 44 | 47 | 97 | 168 | 0 | 97 | 184 | 120 |
N.S. |
1 | 0.88 | 0.54 | 0.57 | 1.18 | 2.05 | 0.00 | 1.18 | 2.24 | 1.46 |
time (sec) |
N/A | 0.278 | 0.215 | 0.654 | 0.045 | 0.090 | 0.000 | 0.249 | 0.199 | 0.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 50 | 34 | 36 | 67 | 127 | 0 | 67 | 147 | 113 |
N.S. |
1 | 0.91 | 0.62 | 0.65 | 1.22 | 2.31 | 0.00 | 1.22 | 2.67 | 2.05 |
time (sec) |
N/A | 0.250 | 0.149 | 0.629 | 0.040 | 0.098 | 0.000 | 0.240 | 0.179 | 0.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 58 | 20 | 55 | 84 | 0 | 55 | 110 | 93 |
N.S. |
1 | 1.00 | 2.15 | 0.74 | 2.04 | 3.11 | 0.00 | 2.04 | 4.07 | 3.44 |
time (sec) |
N/A | 0.226 | 0.116 | 0.608 | 0.038 | 0.091 | 0.000 | 0.226 | 0.173 | 0.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 79 | 56 | 84 | 53 | 156 | 0 | 72 | 413 | 60 |
N.S. |
1 | 0.88 | 0.62 | 0.93 | 0.59 | 1.73 | 0.00 | 0.80 | 4.59 | 0.67 |
time (sec) |
N/A | 0.262 | 0.101 | 0.624 | 0.061 | 0.111 | 0.000 | 0.225 | 0.184 | 0.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 59 | 52 | 41 | 95 | 102 | 0 | 49 | 0 | 55 |
N.S. |
1 | 0.94 | 0.83 | 0.65 | 1.51 | 1.62 | 0.00 | 0.78 | 0.00 | 0.87 |
time (sec) |
N/A | 0.258 | 0.232 | 0.965 | 0.051 | 0.090 | 0.000 | 0.207 | 0.656 | 0.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 28 | 36 | 19 | 66 | 17 | 95 | 24 | 542 | 25 |
N.S. |
1 | 0.97 | 1.24 | 0.66 | 2.28 | 0.59 | 3.28 | 0.83 | 18.69 | 0.86 |
time (sec) |
N/A | 0.219 | 0.046 | 1.256 | 0.052 | 0.075 | 1.342 | 0.208 | 0.205 | 0.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 22 | 24 | 21 | 41 | 272 | 18 | 542 | 19 |
N.S. |
1 | 1.00 | 0.81 | 0.89 | 0.78 | 1.52 | 10.07 | 0.67 | 20.07 | 0.70 |
time (sec) |
N/A | 0.223 | 0.158 | 0.534 | 0.042 | 0.091 | 1.331 | 0.194 | 0.204 | 0.451 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 129 | 113 | 80 | 0 | 65 | 189 | 83 | 48 | 60 |
N.S. |
1 | 1.11 | 0.97 | 0.69 | 0.00 | 0.56 | 1.63 | 0.72 | 0.41 | 0.52 |
time (sec) |
N/A | 0.465 | 0.182 | 0.379 | 0.000 | 0.076 | 0.240 | 0.189 | 0.172 | 0.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 159 | 142 | 115 | 0 | 87 | 258 | 113 | 57 | 90 |
N.S. |
1 | 0.94 | 0.84 | 0.68 | 0.00 | 0.51 | 1.53 | 0.67 | 0.34 | 0.53 |
time (sec) |
N/A | 0.319 | 0.256 | 0.995 | 0.000 | 0.077 | 0.320 | 0.226 | 0.261 | 1.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 203 | 164 | 143 | 0 | 109 | 326 | 133 | 57 | 197 |
N.S. |
1 | 0.89 | 0.72 | 0.63 | 0.00 | 0.48 | 1.43 | 0.58 | 0.25 | 0.86 |
time (sec) |
N/A | 0.367 | 0.449 | 1.178 | 0.000 | 0.084 | 0.400 | 0.226 | 0.210 | 2.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 143 | 237 | 111 | 295 | 230 | 0 | 151 | 216 | 197 |
N.S. |
1 | 1.08 | 1.78 | 0.83 | 2.22 | 1.73 | 0.00 | 1.14 | 1.62 | 1.48 |
time (sec) |
N/A | 0.668 | 1.381 | 0.997 | 0.049 | 0.092 | 0.000 | 0.392 | 0.217 | 4.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | F | A | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 113 | 988 | 107 | 457 | 160 | 0 | 113 | 0 | 162 |
N.S. |
1 | 1.06 | 9.23 | 1.00 | 4.27 | 1.50 | 0.00 | 1.06 | 0.00 | 1.51 |
time (sec) |
N/A | 0.549 | 6.504 | 1.013 | 0.160 | 0.089 | 0.000 | 0.374 | 1.016 | 2.679 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 89 | 247 | 71 | 141 | 76 | 0 | 71 | 0 | 88 |
N.S. |
1 | 1.09 | 3.01 | 0.87 | 1.72 | 0.93 | 0.00 | 0.87 | 0.00 | 1.07 |
time (sec) |
N/A | 0.436 | 0.561 | 1.002 | 0.140 | 0.108 | 0.000 | 0.333 | 0.362 | 0.799 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 40 | 38 | 53 | 30 | 182 | 73 | 669 | 133 |
N.S. |
1 | 1.00 | 0.59 | 0.56 | 0.78 | 0.44 | 2.68 | 1.07 | 9.84 | 1.96 |
time (sec) |
N/A | 0.336 | 0.319 | 0.962 | 0.049 | 0.082 | 1.325 | 0.302 | 0.256 | 0.754 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 140 | 73 | 74 | 91 | 52 | 354 | 99 | 746 | 64 |
N.S. |
1 | 1.06 | 0.55 | 0.56 | 0.69 | 0.39 | 2.68 | 0.75 | 5.65 | 0.48 |
time (sec) |
N/A | 0.549 | 0.336 | 0.866 | 0.047 | 0.077 | 1.408 | 0.282 | 0.270 | 0.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 144 | 95 | 103 | 0 | 74 | 231 | 145 | 55 | 161 |
N.S. |
1 | 1.07 | 0.71 | 0.77 | 0.00 | 0.55 | 1.72 | 1.08 | 0.41 | 1.20 |
time (sec) |
N/A | 0.582 | 0.391 | 0.961 | 0.000 | 0.108 | 0.353 | 0.374 | 0.198 | 4.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 160 | 117 | 138 | 0 | 96 | 299 | 197 | 57 | 216 |
N.S. |
1 | 1.03 | 0.75 | 0.88 | 0.00 | 0.62 | 1.92 | 1.26 | 0.37 | 1.38 |
time (sec) |
N/A | 0.625 | 0.688 | 1.069 | 0.000 | 0.076 | 0.481 | 0.374 | 0.210 | 2.829 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 168 | 139 | 173 | 0 | 118 | 367 | 249 | 57 | 262 |
N.S. |
1 | 0.97 | 0.80 | 0.99 | 0.00 | 0.68 | 2.11 | 1.43 | 0.33 | 1.51 |
time (sec) |
N/A | 0.638 | 1.040 | 1.357 | 0.000 | 0.082 | 0.551 | 0.380 | 0.228 | 4.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 121 | 98 | 124 | 229 | 273 | 0 | 122 | 0 | 105 |
N.S. |
1 | 0.90 | 0.73 | 0.93 | 1.71 | 2.04 | 0.00 | 0.91 | 0.00 | 0.78 |
time (sec) |
N/A | 0.294 | 0.789 | 0.790 | 0.044 | 0.121 | 0.000 | 0.450 | 9.298 | 0.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 113 | 88 | 120 | 212 | 199 | 0 | 100 | 0 | 114 |
N.S. |
1 | 0.90 | 0.70 | 0.95 | 1.68 | 1.58 | 0.00 | 0.79 | 0.00 | 0.90 |
time (sec) |
N/A | 0.285 | 0.770 | 0.780 | 0.063 | 0.156 | 0.000 | 0.459 | 4.578 | 0.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 101 | 79 | 68 | 191 | 124 | 0 | 69 | 0 | 104 |
N.S. |
1 | 0.87 | 0.68 | 0.59 | 1.65 | 1.07 | 0.00 | 0.59 | 0.00 | 0.90 |
time (sec) |
N/A | 0.282 | 0.707 | 1.184 | 0.051 | 0.096 | 0.000 | 0.418 | 2.593 | 0.593 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 42 | 36 | 19 | 158 | 17 | 160 | 35 | 0 | 73 |
N.S. |
1 | 0.98 | 0.84 | 0.44 | 3.67 | 0.40 | 3.72 | 0.81 | 0.00 | 1.70 |
time (sec) |
N/A | 0.232 | 0.041 | 1.570 | 0.054 | 0.107 | 10.208 | 0.396 | 0.586 | 0.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 69 | 44 | 49 | 141 | 41 | 466 | 38 | 0 | 85 |
N.S. |
1 | 0.85 | 0.54 | 0.60 | 1.74 | 0.51 | 5.75 | 0.47 | 0.00 | 1.05 |
time (sec) |
N/A | 0.265 | 0.146 | 0.675 | 0.044 | 0.074 | 10.179 | 0.368 | 0.618 | 0.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 50 | 34 | 36 | 121 | 63 | 774 | 28 | 0 | 85 |
N.S. |
1 | 0.91 | 0.62 | 0.65 | 2.20 | 1.15 | 14.07 | 0.51 | 0.00 | 1.55 |
time (sec) |
N/A | 0.246 | 0.112 | 0.663 | 0.059 | 0.081 | 10.448 | 0.331 | 0.634 | 0.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 22 | 24 | 21 | 85 | 1081 | 18 | 0 | 19 |
N.S. |
1 | 1.00 | 0.81 | 0.89 | 0.78 | 3.15 | 40.04 | 0.67 | 0.00 | 0.70 |
time (sec) |
N/A | 0.214 | 0.180 | 0.585 | 0.036 | 0.099 | 10.036 | 0.304 | 0.584 | 0.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 257 | 152 | 152 | 0 | 109 | 325 | 123 | 90 | 198 |
N.S. |
1 | 1.12 | 0.66 | 0.66 | 0.00 | 0.48 | 1.42 | 0.54 | 0.39 | 0.86 |
time (sec) |
N/A | 1.000 | 0.444 | 0.702 | 0.000 | 0.074 | 0.406 | 0.266 | 0.179 | 2.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 247 | 189 | 169 | 0 | 131 | 394 | 153 | 99 | 235 |
N.S. |
1 | 0.89 | 0.68 | 0.61 | 0.00 | 0.47 | 1.42 | 0.55 | 0.36 | 0.85 |
time (sec) |
N/A | 0.395 | 0.742 | 1.141 | 0.000 | 0.085 | 0.471 | 0.370 | 0.331 | 3.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 333 | 291 | 208 | 197 | 0 | 153 | 462 | 173 | 99 | 294 |
N.S. |
1 | 0.87 | 0.62 | 0.59 | 0.00 | 0.46 | 1.39 | 0.52 | 0.30 | 0.88 |
time (sec) |
N/A | 0.439 | 0.956 | 1.337 | 0.000 | 0.084 | 0.554 | 0.379 | 0.341 | 2.857 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | F | A | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 225 | 1704 | 147 | 786 | 267 | 0 | 195 | 0 | 344 |
N.S. |
1 | 1.10 | 8.31 | 0.72 | 3.83 | 1.30 | 0.00 | 0.95 | 0.00 | 1.68 |
time (sec) |
N/A | 1.163 | 7.185 | 1.232 | 0.227 | 0.150 | 0.000 | 0.930 | 5.820 | 4.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | F | A | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 199 | 1244 | 143 | 531 | 182 | 0 | 165 | 0 | 284 |
N.S. |
1 | 1.09 | 6.80 | 0.78 | 2.90 | 0.99 | 0.00 | 0.90 | 0.00 | 1.55 |
time (sec) |
N/A | 0.943 | 6.846 | 1.145 | 0.249 | 0.140 | 0.000 | 0.915 | 3.442 | 4.673 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 171 | 304 | 115 | 185 | 98 | 0 | 123 | 0 | 207 |
N.S. |
1 | 1.10 | 1.95 | 0.74 | 1.19 | 0.63 | 0.00 | 0.79 | 0.00 | 1.33 |
time (sec) |
N/A | 0.772 | 1.355 | 1.088 | 0.170 | 0.102 | 0.000 | 0.834 | 1.478 | 4.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 40 | 38 | 53 | 30 | 311 | 125 | 0 | 37 |
N.S. |
1 | 1.00 | 0.59 | 0.56 | 0.78 | 0.44 | 4.57 | 1.84 | 0.00 | 0.54 |
time (sec) |
N/A | 0.340 | 0.408 | 1.051 | 0.061 | 0.080 | 10.092 | 0.791 | 0.737 | 0.876 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 148 | 73 | 74 | 97 | 52 | 620 | 151 | 0 | 64 |
N.S. |
1 | 1.07 | 0.53 | 0.54 | 0.70 | 0.38 | 4.49 | 1.09 | 0.00 | 0.46 |
time (sec) |
N/A | 0.624 | 0.681 | 1.048 | 0.056 | 0.079 | 9.835 | 0.706 | 0.747 | 1.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 228 | 95 | 110 | 141 | 74 | 928 | 177 | 0 | 159 |
N.S. |
1 | 1.07 | 0.45 | 0.52 | 0.66 | 0.35 | 4.36 | 0.83 | 0.00 | 0.75 |
time (sec) |
N/A | 1.006 | 0.581 | 1.035 | 0.078 | 0.079 | 10.416 | 0.660 | 0.855 | 1.373 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 292 | 117 | 146 | 179 | 96 | 1221 | 203 | 0 | 224 |
N.S. |
1 | 1.09 | 0.43 | 0.54 | 0.67 | 0.36 | 4.54 | 0.75 | 0.00 | 0.83 |
time (sec) |
N/A | 1.248 | 0.696 | 0.925 | 0.075 | 0.082 | 10.256 | 0.550 | 0.874 | 2.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 296 | 139 | 175 | 0 | 118 | 367 | 249 | 97 | 262 |
N.S. |
1 | 1.09 | 0.51 | 0.65 | 0.00 | 0.44 | 1.35 | 0.92 | 0.36 | 0.97 |
time (sec) |
N/A | 1.340 | 1.126 | 1.059 | 0.000 | 0.076 | 0.580 | 0.775 | 0.336 | 3.931 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 320 | 161 | 210 | 0 | 140 | 435 | 301 | 99 | 308 |
N.S. |
1 | 1.06 | 0.53 | 0.70 | 0.00 | 0.47 | 1.45 | 1.00 | 0.33 | 1.02 |
time (sec) |
N/A | 1.397 | 1.490 | 1.240 | 0.000 | 0.076 | 0.664 | 0.818 | 0.330 | 6.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 125 | 156 | 229 | 0 | 208 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.02 | 1.27 | 1.86 | 0.00 | 1.69 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.577 | 1.965 | 33.579 | 0.000 | 0.078 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 95 | 57 | 102 | 0 | 154 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.01 | 0.61 | 1.09 | 0.00 | 1.64 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.456 | 0.751 | 32.657 | 0.000 | 0.101 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 91 | 102 | 196 | 0 | 116 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.01 | 1.13 | 2.18 | 0.00 | 1.29 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.450 | 0.918 | 7.308 | 0.000 | 0.078 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 44 | 82 | 0 | 59 | 0 | 0 | 29 | 40 |
N.S. |
1 | 1.00 | 0.73 | 1.37 | 0.00 | 0.98 | 0.00 | 0.00 | 0.48 | 0.67 |
time (sec) |
N/A | 0.330 | 0.527 | 5.345 | 0.000 | 0.075 | 0.000 | 0.000 | 0.205 | 0.548 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 73 | 194 | 0 | 27 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.22 | 3.23 | 0.00 | 0.45 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.335 | 0.655 | 4.981 | 0.000 | 0.079 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 97 | 62 | 102 | 0 | 76 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.01 | 0.65 | 1.06 | 0.00 | 0.79 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.456 | 0.686 | 6.140 | 0.000 | 0.089 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 97 | 99 | 210 | 0 | 109 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.01 | 1.03 | 2.19 | 0.00 | 1.14 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.437 | 1.054 | 10.004 | 0.000 | 0.091 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 133 | 121 | 116 | 0 | 118 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.06 | 0.97 | 0.93 | 0.00 | 0.94 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.579 | 1.079 | 10.941 | 0.000 | 0.097 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 135 | 267 | 220 | 0 | 166 | 0 | 0 | 74 | 0 |
N.S. |
1 | 0.98 | 1.93 | 1.59 | 0.00 | 1.20 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.656 | 2.986 | 13.818 | 0.000 | 0.088 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 104 | 67 | 92 | 0 | 108 | 0 | 0 | 52 | 0 |
N.S. |
1 | 0.98 | 0.63 | 0.87 | 0.00 | 1.02 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.497 | 1.463 | 10.220 | 0.000 | 0.098 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 111 | 132 | 379 | 0 | 69 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.04 | 1.23 | 3.54 | 0.00 | 0.64 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.500 | 2.070 | 9.870 | 0.000 | 0.091 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 114 | 102 | 0 | 82 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.00 | 1.34 | 1.20 | 0.00 | 0.96 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.392 | 1.484 | 10.615 | 0.000 | 0.085 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 114 | 226 | 0 | 94 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.00 | 1.34 | 2.66 | 0.00 | 1.11 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.389 | 1.893 | 13.750 | 0.000 | 0.080 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 121 | 133 | 116 | 0 | 96 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.04 | 1.15 | 1.00 | 0.00 | 0.83 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.510 | 1.778 | 15.165 | 0.000 | 0.081 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 121 | 133 | 236 | 0 | 131 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.04 | 1.15 | 2.03 | 0.00 | 1.13 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.524 | 2.445 | 24.535 | 0.000 | 0.111 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 157 | 155 | 128 | 0 | 142 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.07 | 1.05 | 0.87 | 0.00 | 0.97 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.640 | 2.102 | 28.623 | 0.000 | 0.086 | 0.000 | 0.000 | 0.225 | 0.000 |