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 | 91 | 77 | 56 | 50 | 63 | 68 | 68 | 94 | 53 | 63 |
N.S. |
1 | 0.85 | 0.62 | 0.55 | 0.69 | 0.75 | 0.75 | 1.03 | 0.58 | 0.69 |
time (sec) |
N/A | 0.277 | 0.010 | 0.168 | 0.029 | 0.074 | 0.079 | 0.128 | 0.151 | 14.748 |
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 | 73 | 62 | 48 | 42 | 52 | 57 | 56 | 82 | 45 | 52 |
N.S. |
1 | 0.85 | 0.66 | 0.58 | 0.71 | 0.78 | 0.77 | 1.12 | 0.62 | 0.71 |
time (sec) |
N/A | 0.262 | 0.007 | 0.162 | 0.033 | 0.085 | 0.071 | 0.111 | 0.143 | 14.542 |
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 | 46 | 39 | 34 | 41 | 45 | 41 | 68 | 37 | 41 |
N.S. |
1 | 0.85 | 0.72 | 0.63 | 0.76 | 0.83 | 0.76 | 1.26 | 0.69 | 0.76 |
time (sec) |
N/A | 0.248 | 0.007 | 0.161 | 0.032 | 0.101 | 0.064 | 0.110 | 0.145 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 25 | 25 | 24 | 24 | 28 | 24 | 50 | 26 | 26 |
N.S. |
1 | 0.96 | 0.96 | 0.92 | 0.92 | 1.08 | 0.92 | 1.92 | 1.00 | 1.00 |
time (sec) |
N/A | 0.220 | 0.008 | 0.142 | 0.028 | 0.077 | 0.053 | 0.109 | 0.145 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 14 | 13 | 13 | 10 | 27 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.00 | 0.77 | 2.08 | 1.00 | 1.00 |
time (sec) |
N/A | 0.204 | 0.004 | 0.155 | 0.035 | 0.076 | 0.025 | 0.112 | 0.147 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 24 | 29 | 23 | 22 | 25 | 29 | 11 |
N.S. |
1 | 1.00 | 1.00 | 2.18 | 2.64 | 2.09 | 2.00 | 2.27 | 2.64 | 1.00 |
time (sec) |
N/A | 0.204 | 0.005 | 0.158 | 0.027 | 0.074 | 0.069 | 0.438 | 0.147 | 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 | 33 | 31 | 31 | 40 | 48 | 46 | 39 | 43 | 53 | 31 |
N.S. |
1 | 0.94 | 0.94 | 1.21 | 1.45 | 1.39 | 1.18 | 1.30 | 1.61 | 0.94 |
time (sec) |
N/A | 0.238 | 0.010 | 0.164 | 0.028 | 0.084 | 0.112 | 0.845 | 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 | 51 | 46 | 35 | 51 | 63 | 76 | 56 | 58 | 94 | 47 |
N.S. |
1 | 0.90 | 0.69 | 1.00 | 1.24 | 1.49 | 1.10 | 1.14 | 1.84 | 0.92 |
time (sec) |
N/A | 0.252 | 0.011 | 0.165 | 0.029 | 0.065 | 0.146 | 0.119 | 0.151 | 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 | 69 | 61 | 44 | 57 | 84 | 113 | 76 | 89 | 137 | 64 |
N.S. |
1 | 0.88 | 0.64 | 0.83 | 1.22 | 1.64 | 1.10 | 1.29 | 1.99 | 0.93 |
time (sec) |
N/A | 0.263 | 0.014 | 0.166 | 0.035 | 0.069 | 0.188 | 0.110 | 0.150 | 14.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 147 | 45 | 120 | 233 | 118 | 0 | 103 | 181 | 166 |
N.S. |
1 | 1.08 | 0.33 | 0.88 | 1.71 | 0.87 | 0.00 | 0.76 | 1.33 | 1.22 |
time (sec) |
N/A | 0.516 | 0.017 | 0.251 | 0.121 | 0.095 | 0.000 | 0.144 | 0.152 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 118 | 45 | 113 | 196 | 106 | 0 | 91 | 154 | 150 |
N.S. |
1 | 1.06 | 0.41 | 1.02 | 1.77 | 0.95 | 0.00 | 0.82 | 1.39 | 1.35 |
time (sec) |
N/A | 0.411 | 0.015 | 0.249 | 0.117 | 0.089 | 0.000 | 0.132 | 0.150 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 80 | 43 | 99 | 109 | 81 | 0 | 73 | 125 | 96 |
N.S. |
1 | 1.01 | 0.54 | 1.25 | 1.38 | 1.03 | 0.00 | 0.92 | 1.58 | 1.22 |
time (sec) |
N/A | 0.309 | 0.013 | 0.230 | 0.112 | 0.076 | 0.000 | 0.124 | 0.147 | 14.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 39 | 59 | 593 | 0 | 60 | 0 | 53 | 47 | 70 |
N.S. |
1 | 0.95 | 1.44 | 14.46 | 0.00 | 1.46 | 0.00 | 1.29 | 1.15 | 1.71 |
time (sec) |
N/A | 0.231 | 0.052 | 0.264 | 0.000 | 0.076 | 0.000 | 0.120 | 0.151 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 27 | 28 | 0 | 35 | 0 | 69 | 26 | 46 |
N.S. |
1 | 1.00 | 0.96 | 1.00 | 0.00 | 1.25 | 0.00 | 2.46 | 0.93 | 1.64 |
time (sec) |
N/A | 0.223 | 0.011 | 0.286 | 0.000 | 0.080 | 0.000 | 0.126 | 0.148 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 18 | 0 | 33 | 0 | 29 | 18 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.00 | 1.74 | 0.00 | 1.53 | 0.95 | 0.89 |
time (sec) |
N/A | 0.215 | 0.011 | 0.262 | 0.000 | 0.080 | 0.000 | 0.126 | 0.148 | 14.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 53 | 45 | 49 | 0 | 89 | 0 | 0 | 70 | 48 |
N.S. |
1 | 0.96 | 0.82 | 0.89 | 0.00 | 1.62 | 0.00 | 0.00 | 1.27 | 0.87 |
time (sec) |
N/A | 0.236 | 0.016 | 0.336 | 0.000 | 0.092 | 0.000 | 0.000 | 0.150 | 14.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 52 | 56 | 0 | 98 | 0 | 174 | 105 | 233 |
N.S. |
1 | 1.00 | 0.60 | 0.64 | 0.00 | 1.13 | 0.00 | 2.00 | 1.21 | 2.68 |
time (sec) |
N/A | 0.267 | 0.019 | 0.354 | 0.000 | 0.079 | 0.000 | 0.153 | 0.161 | 13.900 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 121 | 61 | 65 | 0 | 144 | 0 | 0 | 140 | 347 |
N.S. |
1 | 1.02 | 0.51 | 0.55 | 0.00 | 1.21 | 0.00 | 0.00 | 1.18 | 2.92 |
time (sec) |
N/A | 0.299 | 0.022 | 0.454 | 0.000 | 0.100 | 0.000 | 0.000 | 0.161 | 14.094 |
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 | 176 | 188 | 70 | 71 | 150 | 91 | 0 | 87 | 54 | 90 |
N.S. |
1 | 1.07 | 0.40 | 0.40 | 0.85 | 0.52 | 0.00 | 0.49 | 0.31 | 0.51 |
time (sec) |
N/A | 0.384 | 0.035 | 0.185 | 0.050 | 0.073 | 0.000 | 0.133 | 0.171 | 14.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 149 | 62 | 63 | 128 | 80 | 0 | 0 | 46 | 79 |
N.S. |
1 | 1.06 | 0.44 | 0.45 | 0.91 | 0.57 | 0.00 | 0.00 | 0.33 | 0.56 |
time (sec) |
N/A | 0.317 | 0.030 | 0.182 | 0.049 | 0.066 | 0.000 | 0.000 | 0.157 | 14.707 |
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 | 106 | 110 | 54 | 55 | 106 | 69 | 0 | 61 | 38 | 68 |
N.S. |
1 | 1.04 | 0.51 | 0.52 | 1.00 | 0.65 | 0.00 | 0.58 | 0.36 | 0.64 |
time (sec) |
N/A | 0.288 | 0.026 | 0.187 | 0.051 | 0.075 | 0.000 | 0.124 | 0.163 | 14.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 44 | 47 | 82 | 52 | 0 | 0 | 28 | 49 |
N.S. |
1 | 1.00 | 0.62 | 0.66 | 1.15 | 0.73 | 0.00 | 0.00 | 0.39 | 0.69 |
time (sec) |
N/A | 0.251 | 0.021 | 0.177 | 0.048 | 0.072 | 0.000 | 0.000 | 0.147 | 14.668 |
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 | 35 | 35 | 37 | 34 | 58 | 39 | 0 | 34 | 18 | 37 |
N.S. |
1 | 1.00 | 1.06 | 0.97 | 1.66 | 1.11 | 0.00 | 0.97 | 0.51 | 1.06 |
time (sec) |
N/A | 0.217 | 0.012 | 0.171 | 0.046 | 0.074 | 0.000 | 0.112 | 0.149 | 14.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 88 | 62 | 84 | 0 | 212 | 0 | 88 | 42 | 0 |
N.S. |
1 | 1.06 | 0.75 | 1.01 | 0.00 | 2.55 | 0.00 | 1.06 | 0.51 | 0.00 |
time (sec) |
N/A | 0.285 | 0.024 | 0.187 | 0.000 | 0.080 | 0.000 | 0.119 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 87 | 80 | 111 | 0 | 255 | 0 | 58 | 69 | 0 |
N.S. |
1 | 1.06 | 0.98 | 1.35 | 0.00 | 3.11 | 0.00 | 0.71 | 0.84 | 0.00 |
time (sec) |
N/A | 0.285 | 0.051 | 0.184 | 0.000 | 0.099 | 0.000 | 0.145 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 132 | 57 | 156 | 0 | 305 | 0 | 76 | 89 | 0 |
N.S. |
1 | 1.08 | 0.47 | 1.28 | 0.00 | 2.50 | 0.00 | 0.62 | 0.73 | 0.00 |
time (sec) |
N/A | 0.315 | 0.020 | 0.182 | 0.000 | 0.087 | 0.000 | 0.174 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 172 | 57 | 208 | 0 | 361 | 0 | 92 | 164 | 0 |
N.S. |
1 | 1.10 | 0.36 | 1.32 | 0.00 | 2.30 | 0.00 | 0.59 | 1.04 | 0.00 |
time (sec) |
N/A | 0.351 | 0.017 | 0.187 | 0.000 | 0.121 | 0.000 | 0.161 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 45 | 34 | 21 | 32 | 60 | 56 | 205 | 47 | 32 |
N.S. |
1 | 1.12 | 0.85 | 0.52 | 0.80 | 1.50 | 1.40 | 5.12 | 1.18 | 0.80 |
time (sec) |
N/A | 0.253 | 0.019 | 0.213 | 0.036 | 0.084 | 2.899 | 0.117 | 0.146 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 45 | 34 | 21 | 32 | 49 | 56 | 141 | 38 | 32 |
N.S. |
1 | 1.12 | 0.85 | 0.52 | 0.80 | 1.22 | 1.40 | 3.52 | 0.95 | 0.80 |
time (sec) |
N/A | 0.252 | 0.017 | 0.213 | 0.029 | 0.070 | 2.912 | 0.109 | 0.145 | 14.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 45 | 30 | 21 | 32 | 32 | 56 | 71 | 29 | 32 |
N.S. |
1 | 1.12 | 0.75 | 0.52 | 0.80 | 0.80 | 1.40 | 1.78 | 0.72 | 0.80 |
time (sec) |
N/A | 0.251 | 0.013 | 0.206 | 0.029 | 0.065 | 2.676 | 0.112 | 0.153 | 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 | 38 | 43 | 23 | 20 | 30 | 19 | 54 | 44 | 20 | 32 |
N.S. |
1 | 1.13 | 0.61 | 0.53 | 0.79 | 0.50 | 1.42 | 1.16 | 0.53 | 0.84 |
time (sec) |
N/A | 0.252 | 0.010 | 0.195 | 0.032 | 0.065 | 2.407 | 0.112 | 0.156 | 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 | 36 | 41 | 21 | 20 | 30 | 29 | 54 | 32 | 25 | 20 |
N.S. |
1 | 1.14 | 0.58 | 0.56 | 0.83 | 0.81 | 1.50 | 0.89 | 0.69 | 0.56 |
time (sec) |
N/A | 0.244 | 0.013 | 0.199 | 0.029 | 0.077 | 2.591 | 0.114 | 0.146 | 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 | 38 | 43 | 34 | 21 | 26 | 44 | 54 | 36 | 32 | 20 |
N.S. |
1 | 1.13 | 0.89 | 0.55 | 0.68 | 1.16 | 1.42 | 0.95 | 0.84 | 0.53 |
time (sec) |
N/A | 0.250 | 0.014 | 0.201 | 0.037 | 0.081 | 3.116 | 0.114 | 0.153 | 14.213 |
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 | 45 | 34 | 21 | 24 | 56 | 56 | 34 | 40 | 20 |
N.S. |
1 | 1.12 | 0.85 | 0.52 | 0.60 | 1.40 | 1.40 | 0.85 | 1.00 | 0.50 |
time (sec) |
N/A | 0.252 | 0.013 | 0.199 | 0.035 | 0.090 | 3.318 | 0.133 | 0.147 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 45 | 34 | 21 | 26 | 66 | 56 | 36 | 48 | 20 |
N.S. |
1 | 1.12 | 0.85 | 0.52 | 0.65 | 1.65 | 1.40 | 0.90 | 1.20 | 0.50 |
time (sec) |
N/A | 0.251 | 0.014 | 0.201 | 0.035 | 0.073 | 3.518 | 0.116 | 0.149 | 14.218 |
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 | 141 | 151 | 62 | 63 | 254 | 91 | 0 | 73 | 54 | 90 |
N.S. |
1 | 1.07 | 0.44 | 0.45 | 1.80 | 0.65 | 0.00 | 0.52 | 0.38 | 0.64 |
time (sec) |
N/A | 0.327 | 0.034 | 0.197 | 0.090 | 0.070 | 0.000 | 0.132 | 0.166 | 14.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 112 | 54 | 55 | 210 | 80 | 0 | 0 | 46 | 79 |
N.S. |
1 | 1.06 | 0.51 | 0.52 | 1.98 | 0.75 | 0.00 | 0.00 | 0.43 | 0.75 |
time (sec) |
N/A | 0.294 | 0.026 | 0.198 | 0.078 | 0.101 | 0.000 | 0.000 | 0.158 | 14.448 |
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 | 71 | 73 | 46 | 47 | 164 | 68 | 0 | 47 | 38 | 68 |
N.S. |
1 | 1.03 | 0.65 | 0.66 | 2.31 | 0.96 | 0.00 | 0.66 | 0.54 | 0.96 |
time (sec) |
N/A | 0.261 | 0.023 | 0.194 | 0.079 | 0.110 | 0.000 | 0.131 | 0.157 | 14.494 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 37 | 34 | 121 | 49 | 0 | 0 | 27 | 49 |
N.S. |
1 | 1.00 | 1.06 | 0.97 | 3.46 | 1.40 | 0.00 | 0.00 | 0.77 | 1.40 |
time (sec) |
N/A | 0.231 | 0.019 | 0.196 | 0.074 | 0.070 | 0.000 | 0.000 | 0.166 | 14.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 131 | 67 | 95 | 0 | 217 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.10 | 0.56 | 0.80 | 0.00 | 1.82 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.319 | 0.034 | 0.205 | 0.000 | 0.085 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 130 | 57 | 127 | 0 | 256 | 0 | 70 | 90 | 0 |
N.S. |
1 | 1.13 | 0.50 | 1.10 | 0.00 | 2.23 | 0.00 | 0.61 | 0.78 | 0.00 |
time (sec) |
N/A | 0.320 | 0.020 | 0.218 | 0.000 | 0.088 | 0.000 | 0.148 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 132 | 91 | 158 | 0 | 309 | 0 | 73 | 115 | 0 |
N.S. |
1 | 1.08 | 0.75 | 1.30 | 0.00 | 2.53 | 0.00 | 0.60 | 0.94 | 0.00 |
time (sec) |
N/A | 0.330 | 0.083 | 0.200 | 0.000 | 0.092 | 0.000 | 0.152 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 177 | 57 | 208 | 0 | 361 | 0 | 92 | 164 | 0 |
N.S. |
1 | 1.13 | 0.36 | 1.32 | 0.00 | 2.30 | 0.00 | 0.59 | 1.04 | 0.00 |
time (sec) |
N/A | 0.363 | 0.025 | 0.209 | 0.000 | 0.084 | 0.000 | 0.164 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 217 | 57 | 258 | 0 | 417 | 0 | 105 | 129 | 0 |
N.S. |
1 | 1.13 | 0.30 | 1.34 | 0.00 | 2.17 | 0.00 | 0.55 | 0.67 | 0.00 |
time (sec) |
N/A | 0.393 | 0.021 | 0.201 | 0.000 | 0.086 | 0.000 | 0.184 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 229 | 73 | 72 | 82 | 91 | 0 | 0 | 54 | 96 |
N.S. |
1 | 1.11 | 0.35 | 0.35 | 0.40 | 0.44 | 0.00 | 0.00 | 0.26 | 0.47 |
time (sec) |
N/A | 0.413 | 0.037 | 0.202 | 0.045 | 0.074 | 0.000 | 0.000 | 0.147 | 14.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 190 | 65 | 64 | 71 | 80 | 0 | 0 | 46 | 88 |
N.S. |
1 | 1.11 | 0.38 | 0.37 | 0.42 | 0.47 | 0.00 | 0.00 | 0.27 | 0.51 |
time (sec) |
N/A | 0.365 | 0.025 | 0.210 | 0.044 | 0.086 | 0.000 | 0.000 | 0.146 | 14.345 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 151 | 57 | 56 | 60 | 69 | 0 | 0 | 38 | 80 |
N.S. |
1 | 1.11 | 0.42 | 0.41 | 0.44 | 0.51 | 0.00 | 0.00 | 0.28 | 0.59 |
time (sec) |
N/A | 0.318 | 0.024 | 0.200 | 0.044 | 0.072 | 0.000 | 0.000 | 0.150 | 14.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 112 | 49 | 48 | 49 | 52 | 0 | 0 | 28 | 76 |
N.S. |
1 | 1.11 | 0.49 | 0.48 | 0.49 | 0.51 | 0.00 | 0.00 | 0.28 | 0.75 |
time (sec) |
N/A | 0.292 | 0.019 | 0.202 | 0.043 | 0.069 | 0.000 | 0.000 | 0.157 | 14.314 |
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 | 66 | 73 | 38 | 39 | 37 | 39 | 0 | 50 | 19 | 56 |
N.S. |
1 | 1.11 | 0.58 | 0.59 | 0.56 | 0.59 | 0.00 | 0.76 | 0.29 | 0.85 |
time (sec) |
N/A | 0.258 | 0.014 | 0.199 | 0.044 | 0.076 | 0.000 | 0.123 | 0.142 | 14.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 27 | 15 | 36 | 0 | 0 | 16 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.50 | 1.20 | 0.00 | 0.00 | 0.53 | 0.87 |
time (sec) |
N/A | 0.222 | 0.015 | 0.195 | 0.040 | 0.073 | 0.000 | 0.000 | 0.149 | 14.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 44 | 68 | 0 | 130 | 0 | 62 | 29 | 0 |
N.S. |
1 | 1.00 | 0.86 | 1.33 | 0.00 | 2.55 | 0.00 | 1.22 | 0.57 | 0.00 |
time (sec) |
N/A | 0.245 | 0.021 | 0.201 | 0.000 | 0.107 | 0.000 | 0.119 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 91 | 70 | 111 | 0 | 255 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.01 | 0.78 | 1.23 | 0.00 | 2.83 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.287 | 0.058 | 0.206 | 0.000 | 0.091 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 131 | 52 | 158 | 0 | 309 | 0 | 80 | 115 | 0 |
N.S. |
1 | 1.05 | 0.42 | 1.26 | 0.00 | 2.47 | 0.00 | 0.64 | 0.92 | 0.00 |
time (sec) |
N/A | 0.316 | 0.021 | 0.211 | 0.000 | 0.085 | 0.000 | 0.146 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 147 | 88 | 79 | 123 | 210 | 146 | 161 | 108 | 112 |
N.S. |
1 | 1.07 | 0.64 | 0.58 | 0.90 | 1.53 | 1.07 | 1.18 | 0.79 | 0.82 |
time (sec) |
N/A | 0.319 | 0.072 | 0.210 | 0.107 | 0.107 | 6.697 | 0.114 | 0.149 | 14.444 |
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 | 116 | 125 | 80 | 70 | 109 | 188 | 129 | 134 | 93 | 95 |
N.S. |
1 | 1.08 | 0.69 | 0.60 | 0.94 | 1.62 | 1.11 | 1.16 | 0.80 | 0.82 |
time (sec) |
N/A | 0.301 | 0.050 | 0.211 | 0.123 | 0.093 | 6.067 | 0.125 | 0.146 | 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 | 95 | 103 | 71 | 61 | 95 | 152 | 112 | 107 | 76 | 78 |
N.S. |
1 | 1.08 | 0.75 | 0.64 | 1.00 | 1.60 | 1.18 | 1.13 | 0.80 | 0.82 |
time (sec) |
N/A | 0.283 | 0.040 | 0.198 | 0.113 | 0.101 | 5.798 | 0.121 | 0.148 | 0.052 |
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 | 81 | 61 | 57 | 79 | 125 | 95 | 77 | 60 | 61 |
N.S. |
1 | 1.07 | 0.80 | 0.75 | 1.04 | 1.64 | 1.25 | 1.01 | 0.79 | 0.80 |
time (sec) |
N/A | 0.266 | 0.038 | 0.195 | 0.110 | 0.080 | 5.664 | 0.114 | 0.149 | 14.273 |
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 | 58 | 59 | 58 | 45 | 67 | 110 | 78 | 51 | 50 | 47 |
N.S. |
1 | 1.02 | 1.00 | 0.78 | 1.16 | 1.90 | 1.34 | 0.88 | 0.86 | 0.81 |
time (sec) |
N/A | 0.266 | 0.020 | 0.193 | 0.116 | 0.087 | 5.659 | 0.119 | 0.146 | 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 | 38 | 38 | 38 | 30 | 52 | 82 | 60 | 35 | 39 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 1.37 | 2.16 | 1.58 | 0.92 | 1.03 | 0.76 |
time (sec) |
N/A | 0.252 | 0.014 | 0.184 | 0.122 | 0.082 | 4.618 | 0.111 | 0.146 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 61 | 36 | 50 | 71 | 152 | 80 | 53 | 66 | 46 |
N.S. |
1 | 1.07 | 0.63 | 0.88 | 1.25 | 2.67 | 1.40 | 0.93 | 1.16 | 0.81 |
time (sec) |
N/A | 0.258 | 0.021 | 0.183 | 0.112 | 0.101 | 5.102 | 0.135 | 0.153 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 90 | 39 | 64 | 81 | 202 | 100 | 73 | 128 | 64 |
N.S. |
1 | 1.08 | 0.47 | 0.77 | 0.98 | 2.43 | 1.20 | 0.88 | 1.54 | 0.77 |
time (sec) |
N/A | 0.274 | 0.023 | 0.208 | 0.116 | 0.078 | 5.613 | 0.111 | 0.146 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 119 | 39 | 78 | 101 | 258 | 117 | 93 | 202 | 78 |
N.S. |
1 | 1.14 | 0.38 | 0.75 | 0.97 | 2.48 | 1.12 | 0.89 | 1.94 | 0.75 |
time (sec) |
N/A | 0.294 | 0.027 | 0.206 | 0.111 | 0.088 | 6.431 | 0.112 | 0.148 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 186 | 70 | 71 | 73 | 82 | 0 | 0 | 48 | 116 |
N.S. |
1 | 1.09 | 0.41 | 0.42 | 0.43 | 0.48 | 0.00 | 0.00 | 0.28 | 0.68 |
time (sec) |
N/A | 0.368 | 0.027 | 0.220 | 0.050 | 0.104 | 0.000 | 0.000 | 0.146 | 14.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 147 | 61 | 62 | 61 | 62 | 0 | 0 | 38 | 99 |
N.S. |
1 | 1.08 | 0.45 | 0.46 | 0.45 | 0.46 | 0.00 | 0.00 | 0.28 | 0.73 |
time (sec) |
N/A | 0.324 | 0.022 | 0.214 | 0.048 | 0.079 | 0.000 | 0.000 | 0.148 | 14.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 108 | 51 | 54 | 50 | 49 | 0 | 0 | 28 | 40 |
N.S. |
1 | 1.05 | 0.50 | 0.52 | 0.49 | 0.48 | 0.00 | 0.00 | 0.27 | 0.39 |
time (sec) |
N/A | 0.295 | 0.016 | 0.221 | 0.049 | 0.069 | 0.000 | 0.000 | 0.143 | 14.752 |
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 | 67 | 69 | 40 | 46 | 30 | 43 | 0 | 50 | 24 | 64 |
N.S. |
1 | 1.03 | 0.60 | 0.69 | 0.45 | 0.64 | 0.00 | 0.75 | 0.36 | 0.96 |
time (sec) |
N/A | 0.259 | 0.017 | 0.211 | 0.056 | 0.080 | 0.000 | 0.125 | 0.155 | 14.379 |
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 | 33 | 33 | 35 | 34 | 28 | 42 | 0 | 30 | 18 | 43 |
N.S. |
1 | 1.00 | 1.06 | 1.03 | 0.85 | 1.27 | 0.00 | 0.91 | 0.55 | 1.30 |
time (sec) |
N/A | 0.244 | 0.022 | 0.205 | 0.050 | 0.063 | 0.000 | 0.141 | 0.147 | 14.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 86 | 55 | 82 | 0 | 231 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.01 | 0.65 | 0.96 | 0.00 | 2.72 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.293 | 0.024 | 0.205 | 0.000 | 0.092 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 126 | 57 | 124 | 0 | 307 | 0 | 82 | 109 | 0 |
N.S. |
1 | 1.01 | 0.46 | 0.99 | 0.00 | 2.46 | 0.00 | 0.66 | 0.87 | 0.00 |
time (sec) |
N/A | 0.327 | 0.025 | 0.256 | 0.000 | 0.102 | 0.000 | 0.141 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 166 | 57 | 173 | 0 | 325 | 0 | 0 | 174 | 0 |
N.S. |
1 | 1.04 | 0.36 | 1.08 | 0.00 | 2.03 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.359 | 0.025 | 0.226 | 0.000 | 0.108 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 86 | 80 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.01 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.278 | 0.046 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 86 | 78 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.04 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.276 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 86 | 77 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.05 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.267 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 86 | 78 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.05 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.277 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 83 | 78 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.06 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.277 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 83 | 80 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.01 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.283 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 65 | 0 | 0 | 0 | 0 | 0 | 479 | 0 |
N.S. |
1 | 1.00 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 11.40 | 0.00 |
time (sec) |
N/A | 0.237 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 41 | 0 | 0 | 0 | 0 | 0 | 106 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.52 | 0.00 |
time (sec) |
N/A | 0.231 | 0.007 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 45 | 28 | 31 | 99 | 30 | 124 | 0 | 28 | 28 |
N.S. |
1 | 1.12 | 0.70 | 0.78 | 2.48 | 0.75 | 3.10 | 0.00 | 0.70 | 0.70 |
time (sec) |
N/A | 0.256 | 0.009 | 0.183 | 0.042 | 0.120 | 0.416 | 0.000 | 0.145 | 14.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 71 | 50 | 73 | 389 | 78 | 541 | 0 | 75 | 57 |
N.S. |
1 | 1.15 | 0.81 | 1.18 | 6.27 | 1.26 | 8.73 | 0.00 | 1.21 | 0.92 |
time (sec) |
N/A | 0.279 | 0.049 | 0.204 | 0.064 | 0.090 | 0.909 | 0.000 | 0.151 | 14.772 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 97 | 100 | 146 | 928 | 195 | 2426 | 0 | 197 | 81 |
N.S. |
1 | 1.10 | 1.14 | 1.66 | 10.55 | 2.22 | 27.57 | 0.00 | 2.24 | 0.92 |
time (sec) |
N/A | 0.308 | 0.035 | 0.217 | 0.091 | 0.090 | 1.856 | 0.000 | 0.155 | 14.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 59 | 0 | 0 | 0 | 0 | 0 | 252 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.88 | 0.00 |
time (sec) |
N/A | 0.241 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 56 | 0 | 0 | 0 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.23 | 0.00 |
time (sec) |
N/A | 0.239 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 56 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.234 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 51 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.238 | 0.016 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 55 | 0 | 0 | 0 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.259 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 100 | 96 | 145 | 161 | 194 | 2426 | 0 | 200 | 84 |
N.S. |
1 | 1.10 | 1.05 | 1.59 | 1.77 | 2.13 | 26.66 | 0.00 | 2.20 | 0.92 |
time (sec) |
N/A | 0.302 | 0.032 | 0.224 | 0.083 | 0.094 | 3.002 | 0.000 | 0.152 | 14.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 75 | 50 | 74 | 77 | 81 | 541 | 0 | 78 | 57 |
N.S. |
1 | 1.14 | 0.76 | 1.12 | 1.17 | 1.23 | 8.20 | 0.00 | 1.18 | 0.86 |
time (sec) |
N/A | 0.274 | 0.055 | 0.220 | 0.082 | 0.088 | 1.185 | 0.000 | 0.143 | 14.360 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 46 | 29 | 30 | 35 | 29 | 126 | 0 | 31 | 29 |
N.S. |
1 | 1.12 | 0.71 | 0.73 | 0.85 | 0.71 | 3.07 | 0.00 | 0.76 | 0.71 |
time (sec) |
N/A | 0.249 | 0.006 | 0.198 | 0.077 | 0.102 | 0.367 | 0.000 | 0.149 | 15.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 43 | 0 | 0 | 0 | 0 | 0 | 112 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.55 | 0.00 |
time (sec) |
N/A | 0.218 | 0.012 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 67 | 0 | 0 | 0 | 0 | 0 | 488 | 0 |
N.S. |
1 | 1.00 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 11.09 | 0.00 |
time (sec) |
N/A | 0.231 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 58 | 0 | 0 | 0 | 0 | 0 | 141 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.17 | 0.00 |
time (sec) |
N/A | 0.240 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 53 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.235 | 0.024 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 59 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.236 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 60 | 0 | 0 | 0 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.235 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 62 | 0 | 0 | 0 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.31 | 0.00 |
time (sec) |
N/A | 0.232 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 77 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.246 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 56 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.250 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 32 | 32 | 26 | 38 | 0 | 0 | 32 | 37 |
N.S. |
1 | 1.00 | 0.86 | 0.86 | 0.70 | 1.03 | 0.00 | 0.00 | 0.86 | 1.00 |
time (sec) |
N/A | 0.218 | 0.019 | 0.934 | 0.039 | 0.085 | 0.000 | 0.000 | 0.157 | 14.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 65 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.240 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |