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 | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 90 | 77 | 59 | 84 | 141 | 112 | 132 | 0 |
N.S. |
1 | 1.05 | 0.90 | 0.69 | 0.98 | 1.64 | 1.30 | 1.53 | 0.00 |
time (sec) |
N/A | 0.185 | 0.150 | 1.894 | 0.220 | 0.277 | 2.152 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 84 | 68 | 57 | 104 | 140 | 105 | 168 | 0 |
N.S. |
1 | 1.02 | 0.83 | 0.70 | 1.27 | 1.71 | 1.28 | 2.05 | 0.00 |
time (sec) |
N/A | 0.194 | 0.103 | 1.908 | 0.207 | 0.273 | 2.373 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 18 | 17 | 46 | 95 | 113 | 71 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.81 | 2.19 | 4.52 | 5.38 | 3.38 |
time (sec) |
N/A | 0.143 | 0.072 | 1.889 | 0.205 | 0.257 | 0.644 | 0.317 | 5.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 31 | 28 | 36 | 60 | 121 | 220 | 91 |
N.S. |
1 | 1.00 | 0.70 | 0.64 | 0.82 | 1.36 | 2.75 | 5.00 | 2.07 |
time (sec) |
N/A | 0.158 | 0.086 | 1.938 | 0.202 | 0.262 | 0.813 | 0.301 | 5.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 74 | 42 | 39 | 56 | 71 | 481 | 246 | 111 |
N.S. |
1 | 1.09 | 0.62 | 0.57 | 0.82 | 1.04 | 7.07 | 3.62 | 1.63 |
time (sec) |
N/A | 0.177 | 0.096 | 1.991 | 0.197 | 0.265 | 1.110 | 0.295 | 5.677 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 104 | 53 | 50 | 76 | 82 | 721 | 274 | 131 |
N.S. |
1 | 1.13 | 0.58 | 0.54 | 0.83 | 0.89 | 7.84 | 2.98 | 1.42 |
time (sec) |
N/A | 0.199 | 0.107 | 2.070 | 0.222 | 0.291 | 1.415 | 0.331 | 6.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 134 | 64 | 61 | 96 | 93 | 1012 | 300 | 151 |
N.S. |
1 | 1.16 | 0.55 | 0.53 | 0.83 | 0.80 | 8.72 | 2.59 | 1.30 |
time (sec) |
N/A | 0.222 | 0.116 | 2.206 | 0.204 | 0.310 | 1.762 | 0.326 | 6.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 164 | 75 | 72 | 116 | 104 | 1346 | 328 | 171 |
N.S. |
1 | 1.17 | 0.54 | 0.51 | 0.83 | 0.74 | 9.61 | 2.34 | 1.22 |
time (sec) |
N/A | 0.242 | 0.127 | 2.414 | 0.226 | 0.371 | 2.275 | 0.329 | 7.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 166 | 94 | 91 | 153 | 145 | 301 | 113 | 141 |
N.S. |
1 | 1.03 | 0.58 | 0.57 | 0.95 | 0.90 | 1.87 | 0.70 | 0.88 |
time (sec) |
N/A | 0.267 | 0.058 | 2.127 | 0.213 | 0.276 | 2.827 | 0.308 | 4.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 145 | 83 | 80 | 133 | 134 | 277 | 99 | 130 |
N.S. |
1 | 1.04 | 0.59 | 0.57 | 0.95 | 0.96 | 1.98 | 0.71 | 0.93 |
time (sec) |
N/A | 0.252 | 0.050 | 1.999 | 0.201 | 0.288 | 2.455 | 0.292 | 4.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 126 | 72 | 69 | 113 | 123 | 253 | 85 | 119 |
N.S. |
1 | 1.03 | 0.59 | 0.57 | 0.93 | 1.01 | 2.07 | 0.70 | 0.98 |
time (sec) |
N/A | 0.238 | 0.039 | 1.947 | 0.204 | 0.266 | 2.021 | 0.300 | 4.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 105 | 61 | 58 | 93 | 112 | 230 | 71 | 108 |
N.S. |
1 | 1.04 | 0.60 | 0.57 | 0.92 | 1.11 | 2.28 | 0.70 | 1.07 |
time (sec) |
N/A | 0.218 | 0.035 | 1.889 | 0.199 | 0.260 | 1.650 | 0.309 | 4.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 84 | 50 | 47 | 73 | 101 | 204 | 57 | 97 |
N.S. |
1 | 1.05 | 0.62 | 0.59 | 0.91 | 1.26 | 2.55 | 0.71 | 1.21 |
time (sec) |
N/A | 0.203 | 0.036 | 1.855 | 0.203 | 0.267 | 1.362 | 0.292 | 4.604 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 63 | 39 | 36 | 53 | 90 | 180 | 43 | 86 |
N.S. |
1 | 1.07 | 0.66 | 0.61 | 0.90 | 1.53 | 3.05 | 0.73 | 1.46 |
time (sec) |
N/A | 0.190 | 0.031 | 1.849 | 0.210 | 0.269 | 1.138 | 0.300 | 4.729 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 42 | 28 | 25 | 33 | 78 | 156 | 29 | 29 |
N.S. |
1 | 1.11 | 0.74 | 0.66 | 0.87 | 2.05 | 4.11 | 0.76 | 0.76 |
time (sec) |
N/A | 0.176 | 0.033 | 1.857 | 0.186 | 0.260 | 0.908 | 0.298 | 4.624 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 65 | 133 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 3.61 | 7.39 | 0.78 | 0.78 |
time (sec) |
N/A | 0.138 | 0.004 | 1.836 | 0.185 | 0.257 | 0.675 | 0.276 | 4.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 115 | 84 | 75 | 82 | 170 | 160 | 90 | 87 |
N.S. |
1 | 1.06 | 0.78 | 0.69 | 0.76 | 1.57 | 1.48 | 0.83 | 0.81 |
time (sec) |
N/A | 0.207 | 0.051 | 1.888 | 0.204 | 0.271 | 10.493 | 0.291 | 4.632 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 119 | 90 | 90 | 106 | 188 | 167 | 116 | 95 |
N.S. |
1 | 1.01 | 0.76 | 0.76 | 0.90 | 1.59 | 1.42 | 0.98 | 0.81 |
time (sec) |
N/A | 0.207 | 0.083 | 1.931 | 0.290 | 0.265 | 10.107 | 0.296 | 4.899 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 125 | 92 | 92 | 136 | 192 | 175 | 124 | 132 |
N.S. |
1 | 0.99 | 0.73 | 0.73 | 1.08 | 1.52 | 1.39 | 0.98 | 1.05 |
time (sec) |
N/A | 0.211 | 0.116 | 1.939 | 0.280 | 0.277 | 9.624 | 0.299 | 5.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 131 | 92 | 92 | 156 | 190 | 175 | 124 | 149 |
N.S. |
1 | 1.04 | 0.73 | 0.73 | 1.24 | 1.51 | 1.39 | 0.98 | 1.18 |
time (sec) |
N/A | 0.209 | 0.117 | 1.945 | 0.205 | 0.278 | 9.210 | 0.290 | 5.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 137 | 92 | 93 | 178 | 189 | 173 | 122 | 105 |
N.S. |
1 | 1.07 | 0.72 | 0.73 | 1.39 | 1.48 | 1.35 | 0.95 | 0.82 |
time (sec) |
N/A | 0.214 | 0.128 | 1.957 | 0.207 | 0.275 | 9.417 | 0.302 | 5.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 143 | 92 | 90 | 201 | 202 | 153 | 121 | 106 |
N.S. |
1 | 1.09 | 0.70 | 0.69 | 1.53 | 1.54 | 1.17 | 0.92 | 0.81 |
time (sec) |
N/A | 0.215 | 0.162 | 1.978 | 0.205 | 0.273 | 10.168 | 0.299 | 6.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 169 | 106 | 100 | 221 | 223 | 204 | 143 | 123 |
N.S. |
1 | 1.09 | 0.68 | 0.65 | 1.43 | 1.44 | 1.32 | 0.92 | 0.79 |
time (sec) |
N/A | 0.223 | 0.169 | 2.075 | 0.209 | 0.284 | 46.067 | 0.284 | 6.859 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 199 | 117 | 111 | 241 | 245 | 0 | 160 | 140 |
N.S. |
1 | 1.11 | 0.65 | 0.62 | 1.35 | 1.37 | 0.00 | 0.89 | 0.78 |
time (sec) |
N/A | 0.235 | 0.200 | 2.162 | 0.208 | 0.324 | 0.000 | 0.298 | 7.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 229 | 137 | 117 | 161 | 255 | 0 | 133 | 0 |
N.S. |
1 | 1.13 | 0.68 | 0.58 | 0.80 | 1.26 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.290 | 0.749 | 2.052 | 0.207 | 0.363 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 199 | 126 | 106 | 141 | 234 | 0 | 119 | 0 |
N.S. |
1 | 1.12 | 0.71 | 0.60 | 0.79 | 1.31 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.277 | 0.624 | 1.969 | 0.201 | 0.317 | 0.000 | 0.430 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 169 | 115 | 95 | 121 | 211 | 204 | 105 | 0 |
N.S. |
1 | 1.10 | 0.75 | 0.62 | 0.79 | 1.37 | 1.32 | 0.68 | 0.00 |
time (sec) |
N/A | 0.251 | 0.520 | 1.925 | 0.212 | 0.311 | 46.980 | 0.401 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 134 | 93 | 81 | 88 | 190 | 151 | 91 | 37 |
N.S. |
1 | 1.10 | 0.76 | 0.66 | 0.72 | 1.56 | 1.24 | 0.75 | 0.30 |
time (sec) |
N/A | 0.206 | 0.116 | 1.876 | 0.198 | 0.299 | 10.227 | 0.428 | 4.565 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 132 | 95 | 83 | 91 | 184 | 173 | 115 | 40 |
N.S. |
1 | 1.07 | 0.77 | 0.67 | 0.74 | 1.50 | 1.41 | 0.93 | 0.33 |
time (sec) |
N/A | 0.204 | 0.117 | 1.954 | 0.217 | 0.300 | 9.720 | 0.296 | 6.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 132 | 95 | 83 | 120 | 189 | 175 | 160 | 0 |
N.S. |
1 | 1.03 | 0.74 | 0.65 | 0.94 | 1.48 | 1.37 | 1.25 | 0.00 |
time (sec) |
N/A | 0.209 | 0.133 | 1.927 | 0.212 | 0.323 | 9.538 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 136 | 95 | 83 | 140 | 191 | 175 | 200 | 0 |
N.S. |
1 | 1.05 | 0.74 | 0.64 | 1.09 | 1.48 | 1.36 | 1.55 | 0.00 |
time (sec) |
N/A | 0.210 | 0.152 | 1.938 | 0.212 | 0.287 | 9.783 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 138 | 99 | 81 | 160 | 0 | 167 | 240 | 0 |
N.S. |
1 | 1.10 | 0.79 | 0.64 | 1.27 | 0.00 | 1.33 | 1.90 | 0.00 |
time (sec) |
N/A | 0.221 | 0.190 | 1.968 | 0.211 | 0.000 | 10.320 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 126 | 90 | 79 | 180 | 184 | 160 | 276 | 0 |
N.S. |
1 | 1.02 | 0.73 | 0.64 | 1.45 | 1.48 | 1.29 | 2.23 | 0.00 |
time (sec) |
N/A | 0.218 | 0.157 | 2.007 | 0.209 | 0.270 | 11.160 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 18 | 17 | 68 | 150 | 167 | 111 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.81 | 3.24 | 7.14 | 7.95 | 5.29 |
time (sec) |
N/A | 0.139 | 0.102 | 2.079 | 0.219 | 0.271 | 1.237 | 0.319 | 6.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 31 | 28 | 36 | 82 | 175 | 328 | 131 |
N.S. |
1 | 1.00 | 0.70 | 0.64 | 0.82 | 1.86 | 3.98 | 7.45 | 2.98 |
time (sec) |
N/A | 0.152 | 0.125 | 2.163 | 0.205 | 0.287 | 1.526 | 0.322 | 6.902 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 74 | 42 | 39 | 56 | 93 | 604 | 354 | 151 |
N.S. |
1 | 1.09 | 0.62 | 0.57 | 0.82 | 1.37 | 8.88 | 5.21 | 2.22 |
time (sec) |
N/A | 0.170 | 0.133 | 2.243 | 0.206 | 0.309 | 1.958 | 0.303 | 7.604 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 104 | 53 | 50 | 76 | 104 | 867 | 382 | 171 |
N.S. |
1 | 1.13 | 0.58 | 0.54 | 0.83 | 1.13 | 9.42 | 4.15 | 1.86 |
time (sec) |
N/A | 0.189 | 0.150 | 2.423 | 0.201 | 0.334 | 2.438 | 0.307 | 8.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 134 | 64 | 61 | 96 | 115 | 1182 | 408 | 191 |
N.S. |
1 | 1.16 | 0.55 | 0.53 | 0.83 | 0.99 | 10.19 | 3.52 | 1.65 |
time (sec) |
N/A | 0.214 | 0.166 | 5.111 | 0.213 | 0.386 | 2.990 | 0.310 | 9.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 164 | 75 | 72 | 116 | 126 | 1540 | 436 | 211 |
N.S. |
1 | 1.17 | 0.54 | 0.51 | 0.83 | 0.90 | 11.00 | 3.11 | 1.51 |
time (sec) |
N/A | 0.231 | 0.178 | 12.454 | 0.207 | 0.474 | 3.672 | 0.314 | 10.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 164 | 194 | 86 | 83 | 136 | 137 | 1950 | 462 | 231 |
N.S. |
1 | 1.18 | 0.52 | 0.51 | 0.83 | 0.84 | 11.89 | 2.82 | 1.41 |
time (sec) |
N/A | 0.261 | 0.194 | 31.504 | 0.216 | 0.575 | 4.461 | 0.327 | 10.906 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 50 | 27 | 24 | 40 | 28 | 61 | 34 | 25 |
N.S. |
1 | 1.09 | 0.59 | 0.52 | 0.87 | 0.61 | 1.33 | 0.74 | 0.54 |
time (sec) |
N/A | 0.167 | 0.016 | 1.886 | 0.270 | 0.251 | 0.311 | 0.300 | 4.555 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 73 | 49 | 32 | 45 | 42 | 75 | 43 | 30 |
N.S. |
1 | 1.16 | 0.78 | 0.51 | 0.71 | 0.67 | 1.19 | 0.68 | 0.48 |
time (sec) |
N/A | 0.171 | 0.035 | 1.942 | 0.273 | 0.250 | 4.599 | 0.287 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 35 | 22 | 19 | 26 | 23 | 44 | 23 | 20 |
N.S. |
1 | 1.13 | 0.71 | 0.61 | 0.84 | 0.74 | 1.42 | 0.74 | 0.65 |
time (sec) |
N/A | 0.161 | 0.013 | 1.866 | 0.280 | 0.237 | 0.158 | 0.284 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 50 | 44 | 27 | 31 | 37 | 54 | 36 | 23 |
N.S. |
1 | 1.11 | 0.98 | 0.60 | 0.69 | 0.82 | 1.20 | 0.80 | 0.51 |
time (sec) |
N/A | 0.157 | 0.024 | 1.914 | 0.319 | 0.236 | 1.862 | 0.294 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 11 | 11 | 27 | 11 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 0.73 | 1.80 | 0.73 | 1.07 |
time (sec) |
N/A | 0.129 | 0.001 | 1.858 | 0.210 | 0.242 | 0.085 | 0.275 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 37 | 20 | 19 | 29 | 22 | 29 | 16 |
N.S. |
1 | 1.00 | 1.37 | 0.74 | 0.70 | 1.07 | 0.81 | 1.07 | 0.59 |
time (sec) |
N/A | 0.136 | 0.020 | 1.894 | 0.269 | 0.256 | 0.086 | 0.284 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 36 | 30 | 25 | 19 | 44 | 39 | 38 | 22 |
N.S. |
1 | 1.20 | 1.00 | 0.83 | 0.63 | 1.47 | 1.30 | 1.27 | 0.73 |
time (sec) |
N/A | 0.152 | 0.017 | 1.916 | 0.292 | 0.234 | 0.766 | 0.274 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 35 | 22 | 21 | 35 | 19 | 40 | 19 |
N.S. |
1 | 1.00 | 1.40 | 0.88 | 0.84 | 1.40 | 0.76 | 1.60 | 0.76 |
time (sec) |
N/A | 0.140 | 0.025 | 1.900 | 0.269 | 0.238 | 0.102 | 0.303 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 41 | 39 | 30 | 35 | 57 | 24 | 43 | 25 |
N.S. |
1 | 1.05 | 1.00 | 0.77 | 0.90 | 1.46 | 0.62 | 1.10 | 0.64 |
time (sec) |
N/A | 0.153 | 0.027 | 1.917 | 0.274 | 0.240 | 0.958 | 0.282 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 20 | 34 | 42 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 1.11 | 1.89 | 2.33 | 1.50 |
time (sec) |
N/A | 0.131 | 0.028 | 1.879 | 0.272 | 0.243 | 0.526 | 0.276 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 61 | 46 | 41 | 49 | 64 | 63 | 55 | 45 |
N.S. |
1 | 1.07 | 0.81 | 0.72 | 0.86 | 1.12 | 1.11 | 0.96 | 0.79 |
time (sec) |
N/A | 0.159 | 0.041 | 1.928 | 0.280 | 0.242 | 2.049 | 0.264 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 50 | 32 | 24 | 40 | 28 | 61 | 52 | 28 |
N.S. |
1 | 1.09 | 0.70 | 0.52 | 0.87 | 0.61 | 1.33 | 1.13 | 0.61 |
time (sec) |
N/A | 0.164 | 0.016 | 1.883 | 0.288 | 0.249 | 0.315 | 0.268 | 4.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 73 | 52 | 39 | 45 | 45 | 165 | 33 | 32 |
N.S. |
1 | 1.16 | 0.83 | 0.62 | 0.71 | 0.71 | 2.62 | 0.52 | 0.51 |
time (sec) |
N/A | 0.167 | 0.101 | 2.034 | 0.269 | 0.241 | 4.810 | 0.291 | 4.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 35 | 22 | 19 | 26 | 23 | 44 | 32 | 23 |
N.S. |
1 | 1.13 | 0.71 | 0.61 | 0.84 | 0.74 | 1.42 | 1.03 | 0.74 |
time (sec) |
N/A | 0.157 | 0.014 | 1.954 | 0.272 | 0.247 | 0.170 | 0.280 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 50 | 47 | 32 | 31 | 40 | 122 | 26 | 27 |
N.S. |
1 | 1.11 | 1.04 | 0.71 | 0.69 | 0.89 | 2.71 | 0.58 | 0.60 |
time (sec) |
N/A | 0.154 | 0.065 | 1.921 | 0.276 | 0.245 | 1.825 | 0.290 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 11 | 18 | 27 | 11 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 1.20 | 1.80 | 0.73 | 1.20 |
time (sec) |
N/A | 0.128 | 0.002 | 1.893 | 0.202 | 0.247 | 0.083 | 0.289 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 41 | 20 | 19 | 32 | 22 | 19 | 18 |
N.S. |
1 | 1.00 | 1.52 | 0.74 | 0.70 | 1.19 | 0.81 | 0.70 | 0.67 |
time (sec) |
N/A | 0.138 | 0.038 | 1.912 | 0.296 | 0.251 | 0.090 | 0.296 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 36 | 30 | 25 | 35 | 28 | 75 | 40 | 32 |
N.S. |
1 | 1.20 | 1.00 | 0.83 | 1.17 | 0.93 | 2.50 | 1.33 | 1.07 |
time (sec) |
N/A | 0.151 | 0.017 | 1.913 | 0.300 | 0.248 | 0.801 | 0.297 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 39 | 28 | 21 | 36 | 20 | 39 | 21 |
N.S. |
1 | 1.00 | 1.56 | 1.12 | 0.84 | 1.44 | 0.80 | 1.56 | 0.84 |
time (sec) |
N/A | 0.140 | 0.032 | 1.926 | 0.288 | 0.240 | 0.116 | 0.289 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 41 | 39 | 34 | 51 | 38 | 97 | 45 | 35 |
N.S. |
1 | 1.05 | 1.00 | 0.87 | 1.31 | 0.97 | 2.49 | 1.15 | 0.90 |
time (sec) |
N/A | 0.149 | 0.030 | 1.929 | 0.276 | 0.244 | 1.031 | 0.270 | 4.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 21 | 76 | 73 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 1.17 | 4.22 | 4.06 | 1.72 |
time (sec) |
N/A | 0.133 | 0.023 | 1.882 | 0.267 | 0.256 | 0.550 | 0.278 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 61 | 46 | 41 | 65 | 45 | 139 | 57 | 49 |
N.S. |
1 | 1.07 | 0.81 | 0.72 | 1.14 | 0.79 | 2.44 | 1.00 | 0.86 |
time (sec) |
N/A | 0.159 | 0.035 | 1.918 | 0.271 | 0.258 | 2.126 | 0.280 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 50 | 27 | 24 | 40 | 28 | 61 | 34 | 28 |
N.S. |
1 | 1.09 | 0.59 | 0.52 | 0.87 | 0.61 | 1.33 | 0.74 | 0.61 |
time (sec) |
N/A | 0.161 | 0.016 | 1.894 | 0.290 | 0.249 | 0.292 | 0.312 | 4.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 82 | 49 | 42 | 57 | 42 | 165 | 44 | 0 |
N.S. |
1 | 1.14 | 0.68 | 0.58 | 0.79 | 0.58 | 2.29 | 0.61 | 0.00 |
time (sec) |
N/A | 0.185 | 0.032 | 1.947 | 0.279 | 0.266 | 4.655 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 35 | 22 | 19 | 26 | 23 | 44 | 23 | 23 |
N.S. |
1 | 1.13 | 0.71 | 0.61 | 0.84 | 0.74 | 1.42 | 0.74 | 0.74 |
time (sec) |
N/A | 0.159 | 0.014 | 1.895 | 0.278 | 0.240 | 0.151 | 0.268 | 4.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 59 | 44 | 37 | 43 | 37 | 122 | 37 | 0 |
N.S. |
1 | 1.09 | 0.81 | 0.69 | 0.80 | 0.69 | 2.26 | 0.69 | 0.00 |
time (sec) |
N/A | 0.165 | 0.025 | 1.937 | 0.278 | 0.252 | 1.806 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 11 | 11 | 27 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 0.73 | 1.80 | 0.73 | 0.73 |
time (sec) |
N/A | 0.126 | 0.001 | 1.887 | 0.191 | 0.247 | 0.079 | 0.270 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 37 | 30 | 31 | 29 | 31 | 30 | 29 |
N.S. |
1 | 1.00 | 1.03 | 0.83 | 0.86 | 0.81 | 0.86 | 0.83 | 0.81 |
time (sec) |
N/A | 0.144 | 0.021 | 1.932 | 0.285 | 0.258 | 0.083 | 0.280 | 4.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 36 | 30 | 25 | 19 | 28 | 80 | 24 | 24 |
N.S. |
1 | 1.20 | 1.00 | 0.83 | 0.63 | 0.93 | 2.67 | 0.80 | 0.80 |
time (sec) |
N/A | 0.151 | 0.017 | 1.980 | 0.275 | 0.257 | 0.852 | 0.286 | 4.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 35 | 32 | 33 | 35 | 27 | 44 | 39 |
N.S. |
1 | 1.00 | 1.03 | 0.94 | 0.97 | 1.03 | 0.79 | 1.29 | 1.15 |
time (sec) |
N/A | 0.149 | 0.025 | 1.940 | 0.270 | 0.252 | 0.106 | 0.276 | 4.998 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 41 | 39 | 30 | 35 | 38 | 97 | 29 | 29 |
N.S. |
1 | 1.05 | 1.00 | 0.77 | 0.90 | 0.97 | 2.49 | 0.74 | 0.74 |
time (sec) |
N/A | 0.152 | 0.026 | 1.947 | 0.282 | 0.254 | 1.007 | 0.276 | 4.697 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 20 | 76 | 42 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 1.11 | 4.22 | 2.33 | 1.72 |
time (sec) |
N/A | 0.132 | 0.024 | 1.901 | 0.277 | 0.243 | 0.546 | 0.277 | 4.879 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 61 | 46 | 42 | 49 | 45 | 139 | 41 | 43 |
N.S. |
1 | 1.07 | 0.81 | 0.74 | 0.86 | 0.79 | 2.44 | 0.72 | 0.75 |
time (sec) |
N/A | 0.163 | 0.037 | 1.948 | 0.279 | 0.252 | 2.046 | 0.274 | 5.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 50 | 27 | 24 | 40 | 28 | 68 | 34 | 27 |
N.S. |
1 | 1.09 | 0.59 | 0.52 | 0.87 | 0.61 | 1.48 | 0.74 | 0.59 |
time (sec) |
N/A | 0.163 | 0.017 | 1.900 | 0.276 | 0.243 | 0.337 | 0.280 | 5.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 82 | 48 | 44 | 45 | 72 | 83 | 0 | 0 |
N.S. |
1 | 1.14 | 0.67 | 0.61 | 0.62 | 1.00 | 1.15 | 0.00 | 0.00 |
time (sec) |
N/A | 0.179 | 0.088 | 2.024 | 0.267 | 0.242 | 4.702 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 35 | 22 | 19 | 26 | 23 | 49 | 23 | 22 |
N.S. |
1 | 1.13 | 0.71 | 0.61 | 0.84 | 0.74 | 1.58 | 0.74 | 0.71 |
time (sec) |
N/A | 0.156 | 0.014 | 1.945 | 0.271 | 0.236 | 0.164 | 0.279 | 5.981 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 59 | 43 | 39 | 31 | 67 | 61 | 0 | 0 |
N.S. |
1 | 1.09 | 0.80 | 0.72 | 0.57 | 1.24 | 1.13 | 0.00 | 0.00 |
time (sec) |
N/A | 0.162 | 0.071 | 1.915 | 0.276 | 0.261 | 1.836 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 11 | 18 | 31 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 1.20 | 2.07 | 0.73 | 0.73 |
time (sec) |
N/A | 0.123 | 0.002 | 1.885 | 0.198 | 0.248 | 0.096 | 0.284 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 29 | 19 | 59 | 34 | 0 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.53 | 1.64 | 0.94 | 0.00 | 0.78 |
time (sec) |
N/A | 0.141 | 0.057 | 9.025 | 0.284 | 0.248 | 0.184 | 0.000 | 5.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | C | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 36 | 30 | 25 | 35 | 52 | 44 | 24 | 24 |
N.S. |
1 | 1.20 | 1.00 | 0.83 | 1.17 | 1.73 | 1.47 | 0.80 | 0.80 |
time (sec) |
N/A | 0.146 | 0.015 | 1.948 | 0.276 | 0.253 | 0.773 | 0.295 | 5.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 35 | 34 | 21 | 64 | 32 | 0 | 41 |
N.S. |
1 | 1.00 | 1.03 | 1.00 | 0.62 | 1.88 | 0.94 | 0.00 | 1.21 |
time (sec) |
N/A | 0.149 | 0.051 | 1.912 | 0.277 | 0.246 | 0.198 | 0.000 | 5.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | C | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 41 | 39 | 35 | 51 | 65 | 27 | 29 | 29 |
N.S. |
1 | 1.05 | 1.00 | 0.90 | 1.31 | 1.67 | 0.69 | 0.74 | 0.74 |
time (sec) |
N/A | 0.145 | 0.025 | 1.935 | 0.275 | 0.256 | 0.973 | 0.269 | 5.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 14 | 37 | 0 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 0.78 | 2.06 | 0.00 | 1.72 |
time (sec) |
N/A | 0.130 | 0.037 | 1.876 | 0.267 | 0.236 | 0.542 | 0.000 | 5.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | C | C | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 61 | 46 | 42 | 65 | 72 | 68 | 43 | 43 |
N.S. |
1 | 1.07 | 0.81 | 0.74 | 1.14 | 1.26 | 1.19 | 0.75 | 0.75 |
time (sec) |
N/A | 0.158 | 0.031 | 1.931 | 0.272 | 0.263 | 2.038 | 0.269 | 5.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 39 | 36 | 53 | 35 | 68 | 46 | 36 |
N.S. |
1 | 1.09 | 0.70 | 0.64 | 0.95 | 0.62 | 1.21 | 0.82 | 0.64 |
time (sec) |
N/A | 0.175 | 0.022 | 1.891 | 0.189 | 0.246 | 0.206 | 0.278 | 5.415 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 79 | 71 | 51 | 51 | 124 | 95 | 54 | 0 |
N.S. |
1 | 1.08 | 0.97 | 0.70 | 0.70 | 1.70 | 1.30 | 0.74 | 0.00 |
time (sec) |
N/A | 0.173 | 0.150 | 1.908 | 0.194 | 0.278 | 2.446 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 40 | 27 | 24 | 33 | 23 | 44 | 30 | 24 |
N.S. |
1 | 1.11 | 0.75 | 0.67 | 0.92 | 0.64 | 1.22 | 0.83 | 0.67 |
time (sec) |
N/A | 0.162 | 0.021 | 1.881 | 0.187 | 0.258 | 0.163 | 0.282 | 5.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 57 | 39 | 31 | 93 | 42 | 40 | 56 |
N.S. |
1 | 1.00 | 1.16 | 0.80 | 0.63 | 1.90 | 0.86 | 0.82 | 1.14 |
time (sec) |
N/A | 0.156 | 0.106 | 6.762 | 0.191 | 0.254 | 1.169 | 0.279 | 5.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 13 | 20 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 1.33 | 0.87 | 0.87 |
time (sec) |
N/A | 0.129 | 0.002 | 1.863 | 0.188 | 0.252 | 0.069 | 0.287 | 4.922 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 21 | 13 | 59 | 17 | 37 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.52 | 2.36 | 0.68 | 1.48 | 0.80 |
time (sec) |
N/A | 0.139 | 0.005 | 6.686 | 0.195 | 0.257 | 0.516 | 0.288 | 0.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 20 | 17 | 60 | 19 | 22 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.68 | 2.40 | 0.76 | 0.88 | 0.76 |
time (sec) |
N/A | 0.152 | 0.019 | 1.889 | 0.189 | 0.270 | 0.547 | 0.283 | 5.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 18 | 17 | 17 | 19 | 30 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.89 | 0.89 | 1.00 | 1.58 | 0.89 |
time (sec) |
N/A | 0.136 | 0.028 | 6.751 | 0.182 | 0.262 | 0.378 | 0.293 | 4.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 49 | 50 | 43 | 36 | 105 | 42 | 51 | 38 |
N.S. |
1 | 0.98 | 1.00 | 0.86 | 0.72 | 2.10 | 0.84 | 1.02 | 0.76 |
time (sec) |
N/A | 0.163 | 0.044 | 1.904 | 0.187 | 0.254 | 1.249 | 0.267 | 5.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 31 | 26 | 36 | 27 | 46 | 55 | 25 |
N.S. |
1 | 1.00 | 0.70 | 0.59 | 0.82 | 0.61 | 1.05 | 1.25 | 0.57 |
time (sec) |
N/A | 0.158 | 0.040 | 1.886 | 0.191 | 0.250 | 0.483 | 0.281 | 5.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 79 | 62 | 60 | 56 | 135 | 97 | 75 | 57 |
N.S. |
1 | 1.07 | 0.84 | 0.81 | 0.76 | 1.82 | 1.31 | 1.01 | 0.77 |
time (sec) |
N/A | 0.181 | 0.078 | 1.921 | 0.206 | 0.274 | 2.507 | 0.270 | 5.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 59 | 38 | 35 | 53 | 46 | 68 | 52 | 41 |
N.S. |
1 | 1.07 | 0.69 | 0.64 | 0.96 | 0.84 | 1.24 | 0.95 | 0.75 |
time (sec) |
N/A | 0.181 | 0.027 | 1.909 | 0.192 | 0.250 | 0.214 | 0.260 | 5.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 74 | 66 | 54 | 49 | 159 | 71 | 51 | 0 |
N.S. |
1 | 1.09 | 0.97 | 0.79 | 0.72 | 2.34 | 1.04 | 0.75 | 0.00 |
time (sec) |
N/A | 0.177 | 0.165 | 1.950 | 0.198 | 0.258 | 1.777 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 38 | 24 | 23 | 32 | 34 | 41 | 32 | 22 |
N.S. |
1 | 1.19 | 0.75 | 0.72 | 1.00 | 1.06 | 1.28 | 1.00 | 0.69 |
time (sec) |
N/A | 0.165 | 0.022 | 1.878 | 0.188 | 0.244 | 0.180 | 0.279 | 5.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 54 | 37 | 29 | 130 | 37 | 39 | 36 |
N.S. |
1 | 1.00 | 1.26 | 0.86 | 0.67 | 3.02 | 0.86 | 0.91 | 0.84 |
time (sec) |
N/A | 0.156 | 0.082 | 1.924 | 0.197 | 0.271 | 0.900 | 0.293 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 15 | 14 | 24 | 24 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 1.50 | 1.50 | 0.88 | 0.88 |
time (sec) |
N/A | 0.132 | 0.002 | 1.887 | 0.195 | 0.273 | 0.100 | 0.273 | 5.144 |