Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 148 | 78 | 66 | 98 | 80 | 221 | 122 | 140 | 82 |
N.S. |
1 | 1.29 | 0.68 | 0.57 | 0.85 | 0.70 | 1.92 | 1.06 | 1.22 | 0.71 |
time (sec) |
N/A | 0.232 | 0.115 | 0.218 | 0.113 | 0.090 | 49.104 | 0.127 | 0.146 | 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 | 102 | 123 | 68 | 61 | 89 | 75 | 209 | 106 | 129 | 73 |
N.S. |
1 | 1.21 | 0.67 | 0.60 | 0.87 | 0.74 | 2.05 | 1.04 | 1.26 | 0.72 |
time (sec) |
N/A | 0.211 | 0.107 | 0.214 | 0.107 | 0.086 | 42.268 | 0.126 | 0.157 | 1.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 104 | 63 | 56 | 80 | 70 | 197 | 90 | 118 | 64 |
N.S. |
1 | 1.17 | 0.71 | 0.63 | 0.90 | 0.79 | 2.21 | 1.01 | 1.33 | 0.72 |
time (sec) |
N/A | 0.186 | 0.109 | 0.210 | 0.110 | 0.073 | 36.550 | 0.137 | 0.147 | 1.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 86 | 58 | 51 | 71 | 65 | 185 | 74 | 107 | 55 |
N.S. |
1 | 1.13 | 0.76 | 0.67 | 0.93 | 0.86 | 2.43 | 0.97 | 1.41 | 0.72 |
time (sec) |
N/A | 0.179 | 0.093 | 0.190 | 0.112 | 0.078 | 35.307 | 0.132 | 0.153 | 0.046 |
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 | 63 | 68 | 53 | 45 | 62 | 60 | 238 | 65 | 96 | 44 |
N.S. |
1 | 1.08 | 0.84 | 0.71 | 0.98 | 0.95 | 3.78 | 1.03 | 1.52 | 0.70 |
time (sec) |
N/A | 0.167 | 0.088 | 0.198 | 0.112 | 0.080 | 1.251 | 0.128 | 0.157 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 80 | 75 | 54 | 89 | 91 | 204 | 95 | 157 | 53 |
N.S. |
1 | 1.04 | 0.97 | 0.70 | 1.16 | 1.18 | 2.65 | 1.23 | 2.04 | 0.69 |
time (sec) |
N/A | 0.180 | 0.161 | 0.245 | 0.114 | 0.070 | 16.498 | 0.131 | 0.158 | 1.086 |
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 | 102 | 108 | 83 | 68 | 110 | 110 | 318 | 116 | 251 | 72 |
N.S. |
1 | 1.06 | 0.81 | 0.67 | 1.08 | 1.08 | 3.12 | 1.14 | 2.46 | 0.71 |
time (sec) |
N/A | 0.213 | 0.187 | 0.256 | 0.108 | 0.092 | 35.185 | 0.131 | 0.154 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 132 | 90 | 76 | 128 | 131 | 486 | 123 | 347 | 90 |
N.S. |
1 | 1.04 | 0.71 | 0.60 | 1.01 | 1.03 | 3.83 | 0.97 | 2.73 | 0.71 |
time (sec) |
N/A | 0.230 | 0.245 | 0.253 | 0.110 | 0.093 | 58.347 | 0.128 | 0.148 | 1.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 168 | 95 | 81 | 146 | 150 | 697 | 139 | 443 | 108 |
N.S. |
1 | 1.09 | 0.62 | 0.53 | 0.95 | 0.97 | 4.53 | 0.90 | 2.88 | 0.70 |
time (sec) |
N/A | 0.260 | 0.305 | 0.282 | 0.115 | 0.108 | 96.335 | 0.129 | 0.150 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 160 | 73 | 66 | 110 | 89 | 0 | 118 | 185 | 92 |
N.S. |
1 | 1.33 | 0.61 | 0.55 | 0.92 | 0.74 | 0.00 | 0.98 | 1.54 | 0.77 |
time (sec) |
N/A | 0.247 | 0.154 | 0.232 | 0.117 | 0.109 | 0.000 | 0.127 | 0.150 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 135 | 68 | 61 | 101 | 84 | 366 | 102 | 174 | 83 |
N.S. |
1 | 1.26 | 0.64 | 0.57 | 0.94 | 0.79 | 3.42 | 0.95 | 1.63 | 0.78 |
time (sec) |
N/A | 0.233 | 0.157 | 0.224 | 0.112 | 0.104 | 160.966 | 0.133 | 0.157 | 1.069 |
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 | 94 | 111 | 63 | 56 | 92 | 79 | 354 | 86 | 163 | 74 |
N.S. |
1 | 1.18 | 0.67 | 0.60 | 0.98 | 0.84 | 3.77 | 0.91 | 1.73 | 0.79 |
time (sec) |
N/A | 0.202 | 0.150 | 0.228 | 0.106 | 0.080 | 124.836 | 0.126 | 0.148 | 1.095 |
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 | 81 | 93 | 58 | 51 | 83 | 75 | 342 | 77 | 152 | 63 |
N.S. |
1 | 1.15 | 0.72 | 0.63 | 1.02 | 0.93 | 4.22 | 0.95 | 1.88 | 0.78 |
time (sec) |
N/A | 0.179 | 0.139 | 0.213 | 0.114 | 0.080 | 92.301 | 0.126 | 0.148 | 1.090 |
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 | 68 | 73 | 53 | 46 | 74 | 69 | 235 | 68 | 141 | 53 |
N.S. |
1 | 1.07 | 0.78 | 0.68 | 1.09 | 1.01 | 3.46 | 1.00 | 2.07 | 0.78 |
time (sec) |
N/A | 0.162 | 0.132 | 0.213 | 0.109 | 0.099 | 1.437 | 0.118 | 0.153 | 0.037 |
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 | 93 | 99 | 78 | 64 | 110 | 110 | 371 | 107 | 251 | 71 |
N.S. |
1 | 1.06 | 0.84 | 0.69 | 1.18 | 1.18 | 3.99 | 1.15 | 2.70 | 0.76 |
time (sec) |
N/A | 0.202 | 0.206 | 0.249 | 0.106 | 0.096 | 44.598 | 0.140 | 0.161 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 126 | 88 | 76 | 127 | 130 | 486 | 123 | 347 | 89 |
N.S. |
1 | 1.07 | 0.75 | 0.64 | 1.08 | 1.10 | 4.12 | 1.04 | 2.94 | 0.75 |
time (sec) |
N/A | 0.227 | 0.243 | 0.349 | 0.108 | 0.089 | 69.937 | 0.132 | 0.157 | 1.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 151 | 95 | 79 | 146 | 150 | 654 | 148 | 443 | 107 |
N.S. |
1 | 1.03 | 0.65 | 0.54 | 0.99 | 1.02 | 4.45 | 1.01 | 3.01 | 0.73 |
time (sec) |
N/A | 0.244 | 0.297 | 0.280 | 0.120 | 0.089 | 85.872 | 0.142 | 0.155 | 1.106 |
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 | 92 | 92 | 43 | 40 | 64 | 54 | 82 | 113 | 53 | 64 |
N.S. |
1 | 1.00 | 0.47 | 0.43 | 0.70 | 0.59 | 0.89 | 1.23 | 0.58 | 0.70 |
time (sec) |
N/A | 0.197 | 0.025 | 0.225 | 0.036 | 0.080 | 0.932 | 0.120 | 0.157 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 38 | 35 | 55 | 49 | 70 | 97 | 48 | 55 |
N.S. |
1 | 1.00 | 0.48 | 0.44 | 0.70 | 0.62 | 0.89 | 1.23 | 0.61 | 0.70 |
time (sec) |
N/A | 0.192 | 0.023 | 0.195 | 0.028 | 0.072 | 0.859 | 0.124 | 0.150 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 33 | 30 | 46 | 44 | 58 | 81 | 43 | 46 |
N.S. |
1 | 1.00 | 0.50 | 0.45 | 0.70 | 0.67 | 0.88 | 1.23 | 0.65 | 0.70 |
time (sec) |
N/A | 0.181 | 0.022 | 0.191 | 0.032 | 0.097 | 0.796 | 0.130 | 0.151 | 0.024 |
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 | 53 | 53 | 28 | 25 | 37 | 39 | 100 | 65 | 38 | 37 |
N.S. |
1 | 1.00 | 0.53 | 0.47 | 0.70 | 0.74 | 1.89 | 1.23 | 0.72 | 0.70 |
time (sec) |
N/A | 0.173 | 0.020 | 0.197 | 0.029 | 0.086 | 0.257 | 0.118 | 0.154 | 0.022 |
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 | 40 | 23 | 20 | 28 | 34 | 85 | 49 | 33 | 23 |
N.S. |
1 | 1.00 | 0.58 | 0.50 | 0.70 | 0.85 | 2.12 | 1.22 | 0.82 | 0.58 |
time (sec) |
N/A | 0.160 | 0.018 | 0.172 | 0.026 | 0.108 | 0.201 | 0.134 | 0.154 | 0.022 |
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 | 27 | 27 | 18 | 15 | 19 | 29 | 70 | 33 | 28 | 14 |
N.S. |
1 | 1.00 | 0.67 | 0.56 | 0.70 | 1.07 | 2.59 | 1.22 | 1.04 | 0.52 |
time (sec) |
N/A | 0.155 | 0.015 | 0.169 | 0.028 | 0.068 | 0.170 | 0.121 | 0.153 | 0.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 97 | 58 | 44 | 73 | 56 | 90 | 90 | 74 | 57 |
N.S. |
1 | 1.18 | 0.71 | 0.54 | 0.89 | 0.68 | 1.10 | 1.10 | 0.90 | 0.70 |
time (sec) |
N/A | 0.186 | 0.060 | 0.190 | 0.144 | 0.070 | 1.522 | 0.131 | 0.157 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 104 | 63 | 56 | 80 | 69 | 197 | 90 | 118 | 64 |
N.S. |
1 | 1.17 | 0.71 | 0.63 | 0.90 | 0.78 | 2.21 | 1.01 | 1.33 | 0.72 |
time (sec) |
N/A | 0.186 | 0.107 | 0.207 | 0.112 | 0.092 | 33.951 | 0.131 | 0.156 | 1.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 111 | 63 | 56 | 92 | 79 | 355 | 86 | 163 | 74 |
N.S. |
1 | 1.16 | 0.66 | 0.58 | 0.96 | 0.82 | 3.70 | 0.90 | 1.70 | 0.77 |
time (sec) |
N/A | 0.194 | 0.147 | 0.211 | 0.146 | 0.084 | 86.741 | 0.138 | 0.150 | 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 | 101 | 113 | 63 | 56 | 101 | 89 | 554 | 93 | 208 | 80 |
N.S. |
1 | 1.12 | 0.62 | 0.55 | 1.00 | 0.88 | 5.49 | 0.92 | 2.06 | 0.79 |
time (sec) |
N/A | 0.185 | 0.173 | 0.227 | 0.111 | 0.084 | 165.578 | 0.130 | 0.154 | 1.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 123 | 65 | 56 | 110 | 100 | 0 | 100 | 253 | 90 |
N.S. |
1 | 1.14 | 0.60 | 0.52 | 1.02 | 0.93 | 0.00 | 0.93 | 2.34 | 0.83 |
time (sec) |
N/A | 0.190 | 0.219 | 0.266 | 0.110 | 0.073 | 0.000 | 0.123 | 0.156 | 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 | 92 | 92 | 43 | 40 | 64 | 54 | 82 | 113 | 53 | 64 |
N.S. |
1 | 1.00 | 0.47 | 0.43 | 0.70 | 0.59 | 0.89 | 1.23 | 0.58 | 0.70 |
time (sec) |
N/A | 0.193 | 0.026 | 0.229 | 0.038 | 0.070 | 0.924 | 0.117 | 0.154 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 38 | 35 | 55 | 49 | 70 | 97 | 48 | 55 |
N.S. |
1 | 1.00 | 0.48 | 0.44 | 0.70 | 0.62 | 0.89 | 1.23 | 0.61 | 0.70 |
time (sec) |
N/A | 0.187 | 0.023 | 0.201 | 0.025 | 0.065 | 0.870 | 0.118 | 0.157 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 33 | 30 | 46 | 44 | 58 | 81 | 43 | 46 |
N.S. |
1 | 1.00 | 0.50 | 0.45 | 0.70 | 0.67 | 0.88 | 1.23 | 0.65 | 0.70 |
time (sec) |
N/A | 0.180 | 0.022 | 0.200 | 0.040 | 0.072 | 0.805 | 0.123 | 0.153 | 0.015 |
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 | 53 | 53 | 28 | 25 | 37 | 39 | 100 | 65 | 38 | 37 |
N.S. |
1 | 1.00 | 0.53 | 0.47 | 0.70 | 0.74 | 1.89 | 1.23 | 0.72 | 0.70 |
time (sec) |
N/A | 0.172 | 0.020 | 0.206 | 0.032 | 0.072 | 0.233 | 0.131 | 0.155 | 0.022 |
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 | 40 | 23 | 20 | 28 | 34 | 85 | 49 | 33 | 23 |
N.S. |
1 | 1.00 | 0.58 | 0.50 | 0.70 | 0.85 | 2.12 | 1.22 | 0.82 | 0.58 |
time (sec) |
N/A | 0.176 | 0.018 | 0.191 | 0.032 | 0.090 | 0.196 | 0.128 | 0.152 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 61 | 49 | 82 | 61 | 100 | 106 | 85 | 66 |
N.S. |
1 | 1.00 | 0.64 | 0.52 | 0.86 | 0.64 | 1.05 | 1.12 | 0.89 | 0.69 |
time (sec) |
N/A | 0.207 | 0.061 | 0.203 | 0.107 | 0.081 | 1.872 | 0.129 | 0.152 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 118 | 70 | 61 | 89 | 74 | 211 | 106 | 129 | 73 |
N.S. |
1 | 1.16 | 0.69 | 0.60 | 0.87 | 0.73 | 2.07 | 1.04 | 1.26 | 0.72 |
time (sec) |
N/A | 0.210 | 0.109 | 0.213 | 0.107 | 0.083 | 36.033 | 0.127 | 0.152 | 1.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 129 | 68 | 61 | 101 | 84 | 366 | 102 | 174 | 82 |
N.S. |
1 | 1.18 | 0.62 | 0.56 | 0.93 | 0.77 | 3.36 | 0.94 | 1.60 | 0.75 |
time (sec) |
N/A | 0.207 | 0.153 | 0.229 | 0.114 | 0.085 | 118.336 | 0.131 | 0.152 | 1.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 136 | 68 | 61 | 110 | 95 | 0 | 102 | 219 | 92 |
N.S. |
1 | 1.19 | 0.60 | 0.54 | 0.96 | 0.83 | 0.00 | 0.89 | 1.92 | 0.81 |
time (sec) |
N/A | 0.205 | 0.192 | 0.256 | 0.110 | 0.089 | 0.000 | 0.128 | 0.156 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 138 | 70 | 61 | 119 | 104 | 0 | 109 | 264 | 98 |
N.S. |
1 | 1.14 | 0.58 | 0.50 | 0.98 | 0.86 | 0.00 | 0.90 | 2.18 | 0.81 |
time (sec) |
N/A | 0.206 | 0.224 | 0.234 | 0.143 | 0.077 | 0.000 | 0.133 | 0.157 | 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 | 105 | 105 | 48 | 45 | 73 | 59 | 94 | 129 | 58 | 73 |
N.S. |
1 | 1.00 | 0.46 | 0.43 | 0.70 | 0.56 | 0.90 | 1.23 | 0.55 | 0.70 |
time (sec) |
N/A | 0.205 | 0.028 | 0.235 | 0.036 | 0.069 | 0.956 | 0.125 | 0.163 | 0.020 |
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 | 92 | 92 | 43 | 40 | 64 | 54 | 82 | 113 | 53 | 64 |
N.S. |
1 | 1.00 | 0.47 | 0.43 | 0.70 | 0.59 | 0.89 | 1.23 | 0.58 | 0.70 |
time (sec) |
N/A | 0.192 | 0.026 | 0.218 | 0.028 | 0.066 | 0.868 | 0.125 | 0.165 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 38 | 35 | 55 | 49 | 70 | 97 | 48 | 55 |
N.S. |
1 | 1.00 | 0.48 | 0.44 | 0.70 | 0.62 | 0.89 | 1.23 | 0.61 | 0.70 |
time (sec) |
N/A | 0.187 | 0.023 | 0.207 | 0.040 | 0.078 | 0.835 | 0.124 | 0.161 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 33 | 30 | 46 | 44 | 58 | 81 | 43 | 46 |
N.S. |
1 | 1.00 | 0.50 | 0.45 | 0.70 | 0.67 | 0.88 | 1.23 | 0.65 | 0.70 |
time (sec) |
N/A | 0.180 | 0.021 | 0.185 | 0.035 | 0.094 | 0.798 | 0.128 | 0.167 | 0.014 |
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 | 53 | 53 | 28 | 25 | 37 | 39 | 100 | 65 | 38 | 37 |
N.S. |
1 | 1.00 | 0.53 | 0.47 | 0.70 | 0.74 | 1.89 | 1.23 | 0.72 | 0.70 |
time (sec) |
N/A | 0.170 | 0.019 | 0.187 | 0.025 | 0.073 | 0.237 | 0.120 | 0.162 | 0.020 |
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 | 108 | 108 | 68 | 54 | 91 | 66 | 112 | 122 | 96 | 75 |
N.S. |
1 | 1.00 | 0.63 | 0.50 | 0.84 | 0.61 | 1.04 | 1.13 | 0.89 | 0.69 |
time (sec) |
N/A | 0.214 | 0.065 | 0.218 | 0.112 | 0.081 | 2.141 | 0.127 | 0.153 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 136 | 73 | 66 | 98 | 79 | 221 | 122 | 140 | 82 |
N.S. |
1 | 1.18 | 0.63 | 0.57 | 0.85 | 0.69 | 1.92 | 1.06 | 1.22 | 0.71 |
time (sec) |
N/A | 0.228 | 0.111 | 0.224 | 0.110 | 0.081 | 37.963 | 0.126 | 0.158 | 1.088 |
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 | 122 | 150 | 75 | 66 | 110 | 89 | 379 | 118 | 185 | 92 |
N.S. |
1 | 1.23 | 0.61 | 0.54 | 0.90 | 0.73 | 3.11 | 0.97 | 1.52 | 0.75 |
time (sec) |
N/A | 0.237 | 0.157 | 0.227 | 0.111 | 0.097 | 144.884 | 0.128 | 0.161 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 155 | 73 | 66 | 119 | 99 | 0 | 118 | 230 | 100 |
N.S. |
1 | 1.22 | 0.57 | 0.52 | 0.94 | 0.78 | 0.00 | 0.93 | 1.81 | 0.79 |
time (sec) |
N/A | 0.255 | 0.196 | 0.233 | 0.112 | 0.081 | 0.000 | 0.133 | 0.155 | 1.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 174 | 75 | 66 | 128 | 110 | 0 | 118 | 275 | 110 |
N.S. |
1 | 1.30 | 0.56 | 0.49 | 0.96 | 0.82 | 0.00 | 0.88 | 2.05 | 0.82 |
time (sec) |
N/A | 0.251 | 0.231 | 0.253 | 0.113 | 0.081 | 0.000 | 0.126 | 0.158 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 71 | 59 | 100 | 71 | 124 | 138 | 107 | 84 |
N.S. |
1 | 1.00 | 0.59 | 0.49 | 0.83 | 0.59 | 1.02 | 1.14 | 0.88 | 0.69 |
time (sec) |
N/A | 0.227 | 0.075 | 0.223 | 0.115 | 0.070 | 2.435 | 0.127 | 0.155 | 0.041 |
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 | 108 | 108 | 66 | 54 | 91 | 66 | 112 | 122 | 96 | 75 |
N.S. |
1 | 1.00 | 0.61 | 0.50 | 0.84 | 0.61 | 1.04 | 1.13 | 0.89 | 0.69 |
time (sec) |
N/A | 0.219 | 0.061 | 0.232 | 0.112 | 0.070 | 2.043 | 0.125 | 0.155 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 61 | 49 | 82 | 61 | 99 | 106 | 85 | 66 |
N.S. |
1 | 1.00 | 0.64 | 0.52 | 0.86 | 0.64 | 1.04 | 1.12 | 0.89 | 0.69 |
time (sec) |
N/A | 0.211 | 0.060 | 0.207 | 0.113 | 0.072 | 1.786 | 0.128 | 0.162 | 1.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 97 | 56 | 44 | 73 | 56 | 88 | 90 | 74 | 57 |
N.S. |
1 | 1.18 | 0.68 | 0.54 | 0.89 | 0.68 | 1.07 | 1.10 | 0.90 | 0.70 |
time (sec) |
N/A | 0.190 | 0.056 | 0.194 | 0.120 | 0.087 | 1.446 | 0.129 | 0.166 | 0.035 |
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 | 69 | 79 | 51 | 39 | 64 | 51 | 202 | 74 | 63 | 48 |
N.S. |
1 | 1.14 | 0.74 | 0.57 | 0.93 | 0.74 | 2.93 | 1.07 | 0.91 | 0.70 |
time (sec) |
N/A | 0.177 | 0.050 | 0.194 | 0.110 | 0.100 | 2.028 | 0.123 | 0.163 | 1.057 |
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 | 85 | 91 | 71 | 52 | 91 | 77 | 107 | 97 | 86 | 59 |
N.S. |
1 | 1.07 | 0.84 | 0.61 | 1.07 | 0.91 | 1.26 | 1.14 | 1.01 | 0.69 |
time (sec) |
N/A | 0.197 | 0.097 | 0.236 | 0.121 | 0.090 | 1.310 | 0.133 | 0.158 | 0.061 |
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 | 92 | 93 | 78 | 63 | 98 | 95 | 216 | 104 | 166 | 66 |
N.S. |
1 | 1.01 | 0.85 | 0.68 | 1.07 | 1.03 | 2.35 | 1.13 | 1.80 | 0.72 |
time (sec) |
N/A | 0.202 | 0.157 | 0.270 | 0.120 | 0.084 | 15.049 | 0.129 | 0.157 | 0.063 |
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 | 95 | 98 | 80 | 64 | 110 | 111 | 372 | 107 | 251 | 71 |
N.S. |
1 | 1.03 | 0.84 | 0.67 | 1.16 | 1.17 | 3.92 | 1.13 | 2.64 | 0.75 |
time (sec) |
N/A | 0.200 | 0.201 | 0.268 | 0.109 | 0.092 | 39.412 | 0.140 | 0.158 | 1.134 |
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 | 113 | 124 | 83 | 69 | 128 | 130 | 583 | 123 | 347 | 89 |
N.S. |
1 | 1.10 | 0.73 | 0.61 | 1.13 | 1.15 | 5.16 | 1.09 | 3.07 | 0.79 |
time (sec) |
N/A | 0.225 | 0.343 | 0.285 | 0.115 | 0.101 | 76.294 | 0.131 | 0.160 | 1.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 151 | 88 | 74 | 146 | 150 | 838 | 139 | 443 | 107 |
N.S. |
1 | 1.14 | 0.66 | 0.56 | 1.10 | 1.13 | 6.30 | 1.05 | 3.33 | 0.80 |
time (sec) |
N/A | 0.246 | 0.426 | 0.327 | 0.124 | 0.082 | 130.078 | 0.138 | 0.162 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 176 | 93 | 79 | 164 | 170 | 0 | 155 | 539 | 125 |
N.S. |
1 | 1.15 | 0.61 | 0.52 | 1.07 | 1.11 | 0.00 | 1.01 | 3.52 | 0.82 |
time (sec) |
N/A | 0.267 | 0.521 | 0.372 | 0.106 | 0.092 | 0.000 | 0.142 | 0.159 | 1.140 |
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 | 128 | 166 | 78 | 71 | 107 | 84 | 233 | 138 | 151 | 91 |
N.S. |
1 | 1.30 | 0.61 | 0.55 | 0.84 | 0.66 | 1.82 | 1.08 | 1.18 | 0.71 |
time (sec) |
N/A | 0.241 | 0.121 | 0.233 | 0.112 | 0.079 | 45.675 | 0.137 | 0.158 | 1.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 141 | 73 | 66 | 98 | 79 | 221 | 122 | 140 | 82 |
N.S. |
1 | 1.23 | 0.63 | 0.57 | 0.85 | 0.69 | 1.92 | 1.06 | 1.22 | 0.71 |
time (sec) |
N/A | 0.225 | 0.113 | 0.231 | 0.117 | 0.082 | 37.580 | 0.130 | 0.162 | 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 | 102 | 120 | 68 | 61 | 89 | 74 | 209 | 106 | 129 | 73 |
N.S. |
1 | 1.18 | 0.67 | 0.60 | 0.87 | 0.73 | 2.05 | 1.04 | 1.26 | 0.72 |
time (sec) |
N/A | 0.202 | 0.112 | 0.228 | 0.113 | 0.089 | 34.323 | 0.127 | 0.157 | 0.041 |
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 | 89 | 104 | 63 | 56 | 80 | 69 | 197 | 90 | 118 | 64 |
N.S. |
1 | 1.17 | 0.71 | 0.63 | 0.90 | 0.78 | 2.21 | 1.01 | 1.33 | 0.72 |
time (sec) |
N/A | 0.191 | 0.106 | 0.208 | 0.113 | 0.078 | 31.295 | 0.138 | 0.163 | 0.038 |
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 | 76 | 81 | 58 | 51 | 71 | 64 | 196 | 74 | 107 | 55 |
N.S. |
1 | 1.07 | 0.76 | 0.67 | 0.93 | 0.84 | 2.58 | 0.97 | 1.41 | 0.72 |
time (sec) |
N/A | 0.174 | 0.099 | 0.210 | 0.110 | 0.098 | 1.968 | 0.122 | 0.157 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 98 | 83 | 63 | 98 | 95 | 216 | 104 | 166 | 66 |
N.S. |
1 | 1.07 | 0.90 | 0.68 | 1.07 | 1.03 | 2.35 | 1.13 | 1.80 | 0.72 |
time (sec) |
N/A | 0.197 | 0.184 | 0.292 | 0.116 | 0.090 | 15.007 | 0.129 | 0.156 | 1.131 |
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 | 106 | 112 | 83 | 69 | 110 | 111 | 325 | 116 | 251 | 72 |
N.S. |
1 | 1.06 | 0.78 | 0.65 | 1.04 | 1.05 | 3.07 | 1.09 | 2.37 | 0.68 |
time (sec) |
N/A | 0.209 | 0.209 | 0.271 | 0.110 | 0.093 | 29.177 | 0.135 | 0.164 | 1.120 |
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 | 131 | 140 | 94 | 76 | 128 | 131 | 488 | 123 | 347 | 90 |
N.S. |
1 | 1.07 | 0.72 | 0.58 | 0.98 | 1.00 | 3.73 | 0.94 | 2.65 | 0.69 |
time (sec) |
N/A | 0.233 | 0.253 | 0.289 | 0.120 | 0.087 | 54.767 | 0.133 | 0.159 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 166 | 95 | 81 | 146 | 150 | 700 | 139 | 443 | 108 |
N.S. |
1 | 1.08 | 0.62 | 0.53 | 0.95 | 0.97 | 4.55 | 0.90 | 2.88 | 0.70 |
time (sec) |
N/A | 0.256 | 0.314 | 0.322 | 0.125 | 0.106 | 91.379 | 0.136 | 0.165 | 1.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 200 | 100 | 86 | 164 | 170 | 955 | 155 | 539 | 126 |
N.S. |
1 | 1.10 | 0.55 | 0.48 | 0.91 | 0.94 | 5.28 | 0.86 | 2.98 | 0.70 |
time (sec) |
N/A | 0.282 | 0.328 | 0.355 | 0.118 | 0.103 | 142.698 | 0.134 | 0.168 | 1.094 |
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 | 122 | 155 | 73 | 66 | 110 | 89 | 377 | 118 | 185 | 92 |
N.S. |
1 | 1.27 | 0.60 | 0.54 | 0.90 | 0.73 | 3.09 | 0.97 | 1.52 | 0.75 |
time (sec) |
N/A | 0.239 | 0.157 | 0.232 | 0.115 | 0.087 | 150.128 | 0.129 | 0.164 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 129 | 68 | 61 | 101 | 84 | 366 | 102 | 174 | 83 |
N.S. |
1 | 1.18 | 0.62 | 0.56 | 0.93 | 0.77 | 3.36 | 0.94 | 1.60 | 0.76 |
time (sec) |
N/A | 0.208 | 0.150 | 0.233 | 0.117 | 0.081 | 114.657 | 0.129 | 0.164 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 106 | 63 | 56 | 92 | 79 | 354 | 86 | 163 | 74 |
N.S. |
1 | 1.10 | 0.66 | 0.58 | 0.96 | 0.82 | 3.69 | 0.90 | 1.70 | 0.77 |
time (sec) |
N/A | 0.194 | 0.146 | 0.210 | 0.114 | 0.072 | 85.830 | 0.127 | 0.172 | 0.044 |
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 | 83 | 93 | 58 | 51 | 83 | 74 | 298 | 77 | 152 | 62 |
N.S. |
1 | 1.12 | 0.70 | 0.61 | 1.00 | 0.89 | 3.59 | 0.93 | 1.83 | 0.75 |
time (sec) |
N/A | 0.182 | 0.139 | 0.200 | 0.113 | 0.078 | 2.185 | 0.130 | 0.154 | 0.037 |
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 | 97 | 105 | 81 | 64 | 110 | 111 | 372 | 107 | 251 | 71 |
N.S. |
1 | 1.08 | 0.84 | 0.66 | 1.13 | 1.14 | 3.84 | 1.10 | 2.59 | 0.73 |
time (sec) |
N/A | 0.200 | 0.215 | 0.275 | 0.111 | 0.096 | 39.781 | 0.131 | 0.152 | 1.083 |
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 | 124 | 133 | 93 | 76 | 128 | 130 | 488 | 123 | 347 | 89 |
N.S. |
1 | 1.07 | 0.75 | 0.61 | 1.03 | 1.05 | 3.94 | 0.99 | 2.80 | 0.72 |
time (sec) |
N/A | 0.220 | 0.262 | 0.295 | 0.119 | 0.096 | 55.232 | 0.133 | 0.150 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 161 | 93 | 79 | 146 | 150 | 651 | 148 | 443 | 107 |
N.S. |
1 | 1.11 | 0.64 | 0.54 | 1.01 | 1.03 | 4.49 | 1.02 | 3.06 | 0.74 |
time (sec) |
N/A | 0.240 | 0.290 | 0.306 | 0.112 | 0.085 | 88.929 | 0.131 | 0.155 | 1.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 38 | 34 | 55 | 34 | 70 | 83 | 33 | 55 |
N.S. |
1 | 1.00 | 0.48 | 0.43 | 0.70 | 0.43 | 0.89 | 1.05 | 0.42 | 0.70 |
time (sec) |
N/A | 0.189 | 0.018 | 0.220 | 0.026 | 0.079 | 0.681 | 0.115 | 0.152 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 33 | 29 | 46 | 29 | 58 | 67 | 28 | 46 |
N.S. |
1 | 1.00 | 0.50 | 0.44 | 0.70 | 0.44 | 0.88 | 1.02 | 0.42 | 0.70 |
time (sec) |
N/A | 0.179 | 0.016 | 0.191 | 0.029 | 0.070 | 0.640 | 0.114 | 0.151 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 28 | 24 | 37 | 24 | 46 | 51 | 23 | 37 |
N.S. |
1 | 1.00 | 0.53 | 0.45 | 0.70 | 0.45 | 0.87 | 0.96 | 0.43 | 0.70 |
time (sec) |
N/A | 0.168 | 0.015 | 0.174 | 0.026 | 0.070 | 0.609 | 0.117 | 0.150 | 0.021 |
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 | 40 | 23 | 19 | 28 | 19 | 34 | 35 | 18 | 23 |
N.S. |
1 | 1.00 | 0.58 | 0.48 | 0.70 | 0.48 | 0.85 | 0.88 | 0.45 | 0.58 |
time (sec) |
N/A | 0.159 | 0.013 | 0.158 | 0.037 | 0.079 | 0.564 | 0.123 | 0.153 | 1.046 |
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 | 27 | 27 | 18 | 14 | 19 | 14 | 87 | 19 | 13 | 14 |
N.S. |
1 | 1.00 | 0.67 | 0.52 | 0.70 | 0.52 | 3.22 | 0.70 | 0.48 | 0.52 |
time (sec) |
N/A | 0.154 | 0.011 | 0.151 | 0.032 | 0.068 | 0.526 | 0.120 | 0.154 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 29 | 46 | 41 | 53 | 49 | 43 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.71 | 1.12 | 1.00 | 1.29 | 1.20 | 1.05 | 0.68 |
time (sec) |
N/A | 0.152 | 0.049 | 0.193 | 0.131 | 0.075 | 1.443 | 0.120 | 0.152 | 1.074 |
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 | 48 | 48 | 45 | 36 | 53 | 54 | 162 | 56 | 87 | 35 |
N.S. |
1 | 1.00 | 0.94 | 0.75 | 1.10 | 1.12 | 3.38 | 1.17 | 1.81 | 0.73 |
time (sec) |
N/A | 0.153 | 0.093 | 0.194 | 0.121 | 0.078 | 30.985 | 0.122 | 0.154 | 1.091 |
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 | 68 | 73 | 53 | 46 | 74 | 69 | 289 | 68 | 141 | 54 |
N.S. |
1 | 1.07 | 0.78 | 0.68 | 1.09 | 1.01 | 4.25 | 1.00 | 2.07 | 0.79 |
time (sec) |
N/A | 0.169 | 0.134 | 0.198 | 0.115 | 0.080 | 74.138 | 0.130 | 0.152 | 0.040 |
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 | 88 | 98 | 60 | 51 | 92 | 84 | 379 | 84 | 197 | 72 |
N.S. |
1 | 1.11 | 0.68 | 0.58 | 1.05 | 0.95 | 4.31 | 0.95 | 2.24 | 0.82 |
time (sec) |
N/A | 0.186 | 0.153 | 0.209 | 0.113 | 0.090 | 114.294 | 0.130 | 0.152 | 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 | 92 | 92 | 43 | 39 | 64 | 39 | 82 | 99 | 38 | 64 |
N.S. |
1 | 1.00 | 0.47 | 0.42 | 0.70 | 0.42 | 0.89 | 1.08 | 0.41 | 0.70 |
time (sec) |
N/A | 0.188 | 0.020 | 0.221 | 0.039 | 0.083 | 0.670 | 0.126 | 0.150 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 38 | 34 | 55 | 34 | 70 | 83 | 33 | 55 |
N.S. |
1 | 1.00 | 0.48 | 0.43 | 0.70 | 0.43 | 0.89 | 1.05 | 0.42 | 0.70 |
time (sec) |
N/A | 0.180 | 0.019 | 0.194 | 0.035 | 0.073 | 0.672 | 0.122 | 0.150 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 33 | 29 | 46 | 29 | 58 | 67 | 28 | 46 |
N.S. |
1 | 1.00 | 0.50 | 0.44 | 0.70 | 0.44 | 0.88 | 1.02 | 0.42 | 0.70 |
time (sec) |
N/A | 0.178 | 0.017 | 0.202 | 0.028 | 0.083 | 0.617 | 0.120 | 0.149 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 28 | 24 | 37 | 24 | 46 | 51 | 23 | 37 |
N.S. |
1 | 1.00 | 0.53 | 0.45 | 0.70 | 0.45 | 0.87 | 0.96 | 0.43 | 0.70 |
time (sec) |
N/A | 0.168 | 0.015 | 0.185 | 0.043 | 0.084 | 0.621 | 0.114 | 0.153 | 0.021 |
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 | 40 | 40 | 23 | 19 | 28 | 19 | 133 | 35 | 18 | 23 |
N.S. |
1 | 1.00 | 0.58 | 0.48 | 0.70 | 0.48 | 3.32 | 0.88 | 0.45 | 0.58 |
time (sec) |
N/A | 0.155 | 0.013 | 0.171 | 0.029 | 0.068 | 0.723 | 0.125 | 0.154 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 46 | 34 | 55 | 45 | 63 | 58 | 52 | 37 |
N.S. |
1 | 1.00 | 0.85 | 0.63 | 1.02 | 0.83 | 1.17 | 1.07 | 0.96 | 0.69 |
time (sec) |
N/A | 0.174 | 0.053 | 0.208 | 0.111 | 0.074 | 1.486 | 0.131 | 0.148 | 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 | 61 | 64 | 51 | 45 | 62 | 60 | 175 | 65 | 96 | 44 |
N.S. |
1 | 1.05 | 0.84 | 0.74 | 1.02 | 0.98 | 2.87 | 1.07 | 1.57 | 0.72 |
time (sec) |
N/A | 0.167 | 0.108 | 0.218 | 0.109 | 0.088 | 36.185 | 0.128 | 0.151 | 1.109 |
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 | 68 | 75 | 53 | 46 | 74 | 69 | 330 | 68 | 141 | 53 |
N.S. |
1 | 1.10 | 0.78 | 0.68 | 1.09 | 1.01 | 4.85 | 1.00 | 2.07 | 0.78 |
time (sec) |
N/A | 0.167 | 0.135 | 0.223 | 0.112 | 0.071 | 105.006 | 0.123 | 0.149 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 98 | 60 | 51 | 92 | 84 | 0 | 84 | 197 | 72 |
N.S. |
1 | 1.11 | 0.68 | 0.58 | 1.05 | 0.95 | 0.00 | 0.95 | 2.24 | 0.82 |
time (sec) |
N/A | 0.180 | 0.165 | 0.247 | 0.114 | 0.075 | 0.000 | 0.125 | 0.154 | 1.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 123 | 65 | 56 | 110 | 99 | 0 | 100 | 253 | 90 |
N.S. |
1 | 1.14 | 0.60 | 0.52 | 1.02 | 0.92 | 0.00 | 0.93 | 2.34 | 0.83 |
time (sec) |
N/A | 0.203 | 0.195 | 0.237 | 0.109 | 0.074 | 0.000 | 0.130 | 0.151 | 1.121 |
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 | 92 | 92 | 43 | 39 | 64 | 39 | 82 | 99 | 38 | 64 |
N.S. |
1 | 1.00 | 0.47 | 0.42 | 0.70 | 0.42 | 0.89 | 1.08 | 0.41 | 0.70 |
time (sec) |
N/A | 0.189 | 0.019 | 0.202 | 0.025 | 0.080 | 0.659 | 0.122 | 0.150 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 38 | 34 | 55 | 34 | 70 | 83 | 33 | 55 |
N.S. |
1 | 1.00 | 0.48 | 0.43 | 0.70 | 0.43 | 0.89 | 1.05 | 0.42 | 0.70 |
time (sec) |
N/A | 0.180 | 0.019 | 0.206 | 0.027 | 0.075 | 0.662 | 0.125 | 0.156 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 33 | 29 | 46 | 29 | 58 | 67 | 28 | 46 |
N.S. |
1 | 1.00 | 0.50 | 0.44 | 0.70 | 0.44 | 0.88 | 1.02 | 0.42 | 0.70 |
time (sec) |
N/A | 0.174 | 0.016 | 0.177 | 0.027 | 0.081 | 0.607 | 0.128 | 0.158 | 0.014 |
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 | 53 | 53 | 28 | 24 | 37 | 24 | 189 | 51 | 23 | 37 |
N.S. |
1 | 1.00 | 0.53 | 0.45 | 0.70 | 0.45 | 3.57 | 0.96 | 0.43 | 0.70 |
time (sec) |
N/A | 0.168 | 0.015 | 0.174 | 0.026 | 0.074 | 1.059 | 0.122 | 0.150 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 51 | 39 | 64 | 51 | 75 | 74 | 63 | 48 |
N.S. |
1 | 1.00 | 0.76 | 0.58 | 0.96 | 0.76 | 1.12 | 1.10 | 0.94 | 0.72 |
time (sec) |
N/A | 0.187 | 0.058 | 0.207 | 0.112 | 0.076 | 1.887 | 0.127 | 0.151 | 1.089 |