Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 169 | 111 | 176 | 112 | 334 | 0 | 106 | 216 | 0 |
N.S. |
1 | 0.68 | 0.45 | 0.71 | 0.45 | 1.35 | 0.00 | 0.43 | 0.87 | 0.00 |
time (sec) |
N/A | 0.447 | 1.056 | 4.197 | 0.120 | 0.087 | 0.000 | 0.162 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 156 | 106 | 146 | 103 | 320 | 0 | 87 | 211 | 0 |
N.S. |
1 | 0.74 | 0.50 | 0.70 | 0.49 | 1.52 | 0.00 | 0.41 | 1.00 | 0.00 |
time (sec) |
N/A | 0.434 | 1.033 | 3.040 | 0.117 | 0.093 | 0.000 | 0.110 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 154 | 105 | 149 | 109 | 324 | 0 | 93 | 211 | 0 |
N.S. |
1 | 0.73 | 0.50 | 0.71 | 0.52 | 1.54 | 0.00 | 0.44 | 1.00 | 0.00 |
time (sec) |
N/A | 0.425 | 1.036 | 2.137 | 0.118 | 0.085 | 0.000 | 0.145 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 152 | 105 | 147 | 111 | 324 | 0 | 93 | 211 | 0 |
N.S. |
1 | 0.72 | 0.50 | 0.69 | 0.52 | 1.53 | 0.00 | 0.44 | 1.00 | 0.00 |
time (sec) |
N/A | 0.421 | 1.036 | 1.497 | 0.112 | 0.087 | 0.000 | 0.140 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 150 | 105 | 149 | 109 | 324 | 0 | 93 | 211 | 0 |
N.S. |
1 | 0.70 | 0.49 | 0.70 | 0.51 | 1.52 | 0.00 | 0.44 | 0.99 | 0.00 |
time (sec) |
N/A | 0.411 | 1.030 | 1.014 | 0.122 | 0.086 | 0.000 | 0.145 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 174 | 105 | 146 | 102 | 320 | 0 | 87 | 211 | 0 |
N.S. |
1 | 0.85 | 0.51 | 0.72 | 0.50 | 1.57 | 0.00 | 0.43 | 1.03 | 0.00 |
time (sec) |
N/A | 0.436 | 1.028 | 0.681 | 0.109 | 0.077 | 0.000 | 0.137 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 172 | 115 | 162 | 115 | 334 | 0 | 109 | 219 | 0 |
N.S. |
1 | 0.70 | 0.47 | 0.66 | 0.47 | 1.36 | 0.00 | 0.44 | 0.89 | 0.00 |
time (sec) |
N/A | 0.464 | 1.035 | 1.023 | 0.110 | 0.075 | 0.000 | 0.117 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 189 | 127 | 175 | 130 | 370 | 0 | 123 | 235 | 0 |
N.S. |
1 | 0.65 | 0.43 | 0.60 | 0.44 | 1.26 | 0.00 | 0.42 | 0.80 | 0.00 |
time (sec) |
N/A | 0.486 | 1.035 | 1.539 | 0.119 | 0.076 | 0.000 | 0.112 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 63 | 44 | 39 | 25 | 26 | 0 | 45 | 22 | 0 |
N.S. |
1 | 0.68 | 0.47 | 0.42 | 0.27 | 0.28 | 0.00 | 0.48 | 0.24 | 0.00 |
time (sec) |
N/A | 0.345 | 0.019 | 0.115 | 0.030 | 0.069 | 0.000 | 0.152 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 63 | 44 | 39 | 25 | 22 | 0 | 42 | 20 | 0 |
N.S. |
1 | 0.68 | 0.47 | 0.42 | 0.27 | 0.24 | 0.00 | 0.45 | 0.22 | 0.00 |
time (sec) |
N/A | 0.346 | 0.019 | 0.114 | 0.037 | 0.067 | 0.000 | 0.122 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 63 | 44 | 39 | 25 | 18 | 0 | 37 | 17 | 0 |
N.S. |
1 | 0.68 | 0.47 | 0.42 | 0.27 | 0.19 | 0.00 | 0.40 | 0.18 | 0.00 |
time (sec) |
N/A | 0.351 | 0.017 | 0.068 | 0.033 | 0.064 | 0.000 | 0.105 | 0.166 | 0.000 |
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 | 91 | 61 | 43 | 38 | 24 | 19 | 0 | 40 | 18 | 47 |
N.S. |
1 | 0.67 | 0.47 | 0.42 | 0.26 | 0.21 | 0.00 | 0.44 | 0.20 | 0.52 |
time (sec) |
N/A | 0.344 | 0.018 | 0.070 | 0.036 | 0.077 | 0.000 | 0.116 | 0.167 | 18.581 |
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 | 91 | 61 | 44 | 39 | 25 | 22 | 0 | 41 | 20 | 52 |
N.S. |
1 | 0.67 | 0.48 | 0.43 | 0.27 | 0.24 | 0.00 | 0.45 | 0.22 | 0.57 |
time (sec) |
N/A | 0.337 | 0.021 | 0.078 | 0.027 | 0.068 | 0.000 | 0.131 | 0.163 | 18.884 |
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 | 91 | 61 | 42 | 37 | 24 | 23 | 0 | 47 | 24 | 53 |
N.S. |
1 | 0.67 | 0.46 | 0.41 | 0.26 | 0.25 | 0.00 | 0.52 | 0.26 | 0.58 |
time (sec) |
N/A | 0.342 | 0.018 | 0.082 | 0.027 | 0.070 | 0.000 | 0.107 | 0.171 | 18.192 |
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 | 91 | 61 | 42 | 37 | 25 | 21 | 0 | 44 | 24 | 56 |
N.S. |
1 | 0.67 | 0.46 | 0.41 | 0.27 | 0.23 | 0.00 | 0.48 | 0.26 | 0.62 |
time (sec) |
N/A | 0.340 | 0.019 | 0.084 | 0.027 | 0.070 | 0.000 | 0.129 | 0.167 | 17.626 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 103 | 66 | 61 | 83 | 54 | 0 | 99 | 44 | 0 |
N.S. |
1 | 0.53 | 0.34 | 0.31 | 0.43 | 0.28 | 0.00 | 0.51 | 0.23 | 0.00 |
time (sec) |
N/A | 0.401 | 0.029 | 0.122 | 0.042 | 0.064 | 0.000 | 0.148 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 103 | 66 | 61 | 83 | 46 | 0 | 90 | 42 | 0 |
N.S. |
1 | 0.53 | 0.34 | 0.31 | 0.43 | 0.24 | 0.00 | 0.46 | 0.22 | 0.00 |
time (sec) |
N/A | 0.393 | 0.026 | 0.125 | 0.037 | 0.068 | 0.000 | 0.116 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 103 | 66 | 61 | 83 | 40 | 0 | 85 | 39 | 0 |
N.S. |
1 | 0.53 | 0.34 | 0.31 | 0.43 | 0.21 | 0.00 | 0.44 | 0.20 | 0.00 |
time (sec) |
N/A | 0.392 | 0.022 | 0.121 | 0.035 | 0.077 | 0.000 | 0.123 | 0.167 | 0.000 |
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 | 193 | 101 | 66 | 61 | 87 | 42 | 0 | 89 | 41 | 76 |
N.S. |
1 | 0.52 | 0.34 | 0.32 | 0.45 | 0.22 | 0.00 | 0.46 | 0.21 | 0.39 |
time (sec) |
N/A | 0.403 | 0.023 | 0.081 | 0.037 | 0.068 | 0.000 | 0.128 | 0.166 | 18.787 |
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 | 191 | 99 | 66 | 61 | 87 | 45 | 0 | 102 | 43 | 87 |
N.S. |
1 | 0.52 | 0.35 | 0.32 | 0.46 | 0.24 | 0.00 | 0.53 | 0.23 | 0.46 |
time (sec) |
N/A | 0.428 | 0.027 | 0.086 | 0.039 | 0.066 | 0.000 | 0.124 | 0.173 | 18.875 |
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 | 193 | 101 | 66 | 61 | 86 | 45 | 0 | 107 | 46 | 88 |
N.S. |
1 | 0.52 | 0.34 | 0.32 | 0.45 | 0.23 | 0.00 | 0.55 | 0.24 | 0.46 |
time (sec) |
N/A | 0.406 | 0.031 | 0.090 | 0.042 | 0.066 | 0.000 | 0.120 | 0.165 | 18.275 |
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 | 191 | 99 | 66 | 61 | 86 | 45 | 0 | 107 | 46 | 91 |
N.S. |
1 | 0.52 | 0.35 | 0.32 | 0.45 | 0.24 | 0.00 | 0.56 | 0.24 | 0.48 |
time (sec) |
N/A | 0.394 | 0.028 | 0.092 | 0.045 | 0.063 | 0.000 | 0.128 | 0.164 | 18.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 143 | 88 | 83 | 147 | 82 | 0 | 153 | 66 | 0 |
N.S. |
1 | 0.48 | 0.30 | 0.28 | 0.49 | 0.28 | 0.00 | 0.52 | 0.22 | 0.00 |
time (sec) |
N/A | 0.460 | 0.036 | 0.131 | 0.051 | 0.068 | 0.000 | 0.110 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 143 | 88 | 83 | 147 | 70 | 0 | 138 | 64 | 0 |
N.S. |
1 | 0.48 | 0.30 | 0.28 | 0.49 | 0.24 | 0.00 | 0.46 | 0.22 | 0.00 |
time (sec) |
N/A | 0.447 | 0.030 | 0.128 | 0.042 | 0.069 | 0.000 | 0.194 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 143 | 88 | 83 | 147 | 62 | 0 | 133 | 61 | 0 |
N.S. |
1 | 0.48 | 0.30 | 0.28 | 0.49 | 0.21 | 0.00 | 0.45 | 0.21 | 0.00 |
time (sec) |
N/A | 0.440 | 0.030 | 0.125 | 0.059 | 0.071 | 0.000 | 0.188 | 0.170 | 0.000 |
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 | 293 | 139 | 88 | 83 | 151 | 64 | 0 | 137 | 63 | 112 |
N.S. |
1 | 0.47 | 0.30 | 0.28 | 0.52 | 0.22 | 0.00 | 0.47 | 0.22 | 0.38 |
time (sec) |
N/A | 0.454 | 0.030 | 0.084 | 0.042 | 0.067 | 0.000 | 0.148 | 0.164 | 17.947 |
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 | 295 | 141 | 88 | 83 | 151 | 67 | 0 | 156 | 65 | 116 |
N.S. |
1 | 0.48 | 0.30 | 0.28 | 0.51 | 0.23 | 0.00 | 0.53 | 0.22 | 0.39 |
time (sec) |
N/A | 0.449 | 0.032 | 0.093 | 0.044 | 0.069 | 0.000 | 0.135 | 0.167 | 18.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 139 | 88 | 83 | 151 | 67 | 0 | 161 | 68 | 116 |
N.S. |
1 | 0.47 | 0.30 | 0.28 | 0.52 | 0.23 | 0.00 | 0.55 | 0.23 | 0.40 |
time (sec) |
N/A | 0.454 | 0.039 | 0.093 | 0.049 | 0.068 | 0.000 | 0.116 | 0.171 | 19.030 |
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 | 295 | 141 | 88 | 83 | 150 | 67 | 0 | 162 | 68 | 118 |
N.S. |
1 | 0.48 | 0.30 | 0.28 | 0.51 | 0.23 | 0.00 | 0.55 | 0.23 | 0.40 |
time (sec) |
N/A | 0.427 | 0.042 | 0.097 | 0.043 | 0.067 | 0.000 | 0.134 | 0.162 | 18.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 348 | 344 | 163 | 208 | 266 | 219 | 0 | 282 | 162 | 0 |
N.S. |
1 | 0.99 | 0.47 | 0.60 | 0.76 | 0.63 | 0.00 | 0.81 | 0.47 | 0.00 |
time (sec) |
N/A | 0.961 | 0.194 | 0.172 | 0.116 | 0.085 | 0.000 | 0.148 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 321 | 151 | 200 | 241 | 208 | 0 | 254 | 152 | 0 |
N.S. |
1 | 1.06 | 0.50 | 0.66 | 0.80 | 0.69 | 0.00 | 0.84 | 0.50 | 0.00 |
time (sec) |
N/A | 0.934 | 0.164 | 0.173 | 0.113 | 0.078 | 0.000 | 0.155 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 319 | 150 | 195 | 250 | 160 | 0 | 255 | 148 | 0 |
N.S. |
1 | 1.06 | 0.50 | 0.65 | 0.83 | 0.53 | 0.00 | 0.84 | 0.49 | 0.00 |
time (sec) |
N/A | 0.907 | 0.154 | 0.168 | 0.127 | 0.086 | 0.000 | 0.146 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 298 | 123 | 183 | 216 | 172 | 0 | 242 | 114 | 0 |
N.S. |
1 | 1.15 | 0.47 | 0.70 | 0.83 | 0.66 | 0.00 | 0.93 | 0.44 | 0.00 |
time (sec) |
N/A | 0.876 | 0.121 | 0.154 | 0.135 | 0.086 | 0.000 | 0.162 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 302 | 125 | 182 | 226 | 156 | 0 | 251 | 117 | 0 |
N.S. |
1 | 1.17 | 0.48 | 0.70 | 0.87 | 0.60 | 0.00 | 0.97 | 0.45 | 0.00 |
time (sec) |
N/A | 0.853 | 0.125 | 0.153 | 0.114 | 0.085 | 0.000 | 0.178 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 321 | 150 | 196 | 234 | 201 | 0 | 264 | 160 | 0 |
N.S. |
1 | 1.06 | 0.50 | 0.65 | 0.77 | 0.66 | 0.00 | 0.87 | 0.53 | 0.00 |
time (sec) |
N/A | 0.892 | 0.165 | 0.176 | 0.112 | 0.090 | 0.000 | 0.132 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 325 | 152 | 200 | 242 | 226 | 0 | 256 | 168 | 0 |
N.S. |
1 | 1.06 | 0.50 | 0.65 | 0.79 | 0.74 | 0.00 | 0.84 | 0.55 | 0.00 |
time (sec) |
N/A | 0.921 | 0.157 | 0.174 | 0.116 | 0.088 | 0.000 | 0.120 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 348 | 160 | 208 | 259 | 252 | 0 | 284 | 185 | 0 |
N.S. |
1 | 0.99 | 0.46 | 0.59 | 0.74 | 0.72 | 0.00 | 0.81 | 0.53 | 0.00 |
time (sec) |
N/A | 0.944 | 0.184 | 0.181 | 0.129 | 0.092 | 0.000 | 0.131 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 445 | 414 | 206 | 256 | 0 | 364 | 0 | 386 | 502 | 0 |
N.S. |
1 | 0.93 | 0.46 | 0.58 | 0.00 | 0.82 | 0.00 | 0.87 | 1.13 | 0.00 |
time (sec) |
N/A | 1.095 | 0.428 | 0.187 | 0.000 | 0.117 | 0.000 | 0.186 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 398 | 391 | 195 | 244 | 0 | 359 | 0 | 357 | 490 | 0 |
N.S. |
1 | 0.98 | 0.49 | 0.61 | 0.00 | 0.90 | 0.00 | 0.90 | 1.23 | 0.00 |
time (sec) |
N/A | 1.041 | 0.429 | 0.185 | 0.000 | 0.108 | 0.000 | 0.133 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 398 | 389 | 195 | 244 | 0 | 330 | 0 | 358 | 489 | 0 |
N.S. |
1 | 0.98 | 0.49 | 0.61 | 0.00 | 0.83 | 0.00 | 0.90 | 1.23 | 0.00 |
time (sec) |
N/A | 1.017 | 0.411 | 0.183 | 0.000 | 0.105 | 0.000 | 0.161 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 352 | 366 | 184 | 612 | 0 | 337 | 0 | 345 | 483 | 0 |
N.S. |
1 | 1.04 | 0.52 | 1.74 | 0.00 | 0.96 | 0.00 | 0.98 | 1.37 | 0.00 |
time (sec) |
N/A | 0.966 | 0.460 | 0.141 | 0.000 | 0.096 | 0.000 | 0.174 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 352 | 366 | 184 | 666 | 279 | 336 | 0 | 344 | 482 | 0 |
N.S. |
1 | 1.04 | 0.52 | 1.89 | 0.79 | 0.95 | 0.00 | 0.98 | 1.37 | 0.00 |
time (sec) |
N/A | 1.018 | 0.386 | 0.137 | 0.134 | 0.098 | 0.000 | 0.145 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 366 | 179 | 617 | 272 | 350 | 0 | 348 | 483 | 0 |
N.S. |
1 | 1.04 | 0.51 | 1.75 | 0.77 | 0.99 | 0.00 | 0.99 | 1.37 | 0.00 |
time (sec) |
N/A | 0.978 | 0.384 | 0.139 | 0.139 | 0.100 | 0.000 | 0.177 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 370 | 180 | 668 | 281 | 328 | 0 | 346 | 480 | 0 |
N.S. |
1 | 1.05 | 0.51 | 1.89 | 0.80 | 0.93 | 0.00 | 0.98 | 1.36 | 0.00 |
time (sec) |
N/A | 0.985 | 0.368 | 0.136 | 0.134 | 0.106 | 0.000 | 0.130 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 354 | 365 | 181 | 617 | 265 | 328 | 0 | 333 | 480 | 0 |
N.S. |
1 | 1.03 | 0.51 | 1.74 | 0.75 | 0.93 | 0.00 | 0.94 | 1.36 | 0.00 |
time (sec) |
N/A | 0.994 | 0.259 | 0.126 | 0.133 | 0.095 | 0.000 | 0.171 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 354 | 369 | 181 | 638 | 0 | 324 | 0 | 339 | 482 | 0 |
N.S. |
1 | 1.04 | 0.51 | 1.80 | 0.00 | 0.92 | 0.00 | 0.96 | 1.36 | 0.00 |
time (sec) |
N/A | 0.989 | 0.259 | 0.126 | 0.000 | 0.104 | 0.000 | 0.181 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 400 | 389 | 193 | 241 | 0 | 375 | 0 | 368 | 511 | 0 |
N.S. |
1 | 0.97 | 0.48 | 0.60 | 0.00 | 0.94 | 0.00 | 0.92 | 1.28 | 0.00 |
time (sec) |
N/A | 1.030 | 0.411 | 0.191 | 0.000 | 0.101 | 0.000 | 0.124 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 400 | 393 | 193 | 246 | 0 | 401 | 0 | 359 | 518 | 0 |
N.S. |
1 | 0.98 | 0.48 | 0.62 | 0.00 | 1.00 | 0.00 | 0.90 | 1.30 | 0.00 |
time (sec) |
N/A | 1.023 | 0.412 | 0.190 | 0.000 | 0.102 | 0.000 | 0.123 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 447 | 416 | 204 | 253 | 0 | 420 | 0 | 390 | 537 | 0 |
N.S. |
1 | 0.93 | 0.46 | 0.57 | 0.00 | 0.94 | 0.00 | 0.87 | 1.20 | 0.00 |
time (sec) |
N/A | 1.073 | 0.433 | 0.194 | 0.000 | 0.096 | 0.000 | 0.152 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 541 | 484 | 229 | 288 | 0 | 502 | 0 | 424 | 844 | 0 |
N.S. |
1 | 0.89 | 0.42 | 0.53 | 0.00 | 0.93 | 0.00 | 0.78 | 1.56 | 0.00 |
time (sec) |
N/A | 1.202 | 0.865 | 0.211 | 0.000 | 0.100 | 0.000 | 0.161 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 494 | 461 | 218 | 276 | 0 | 497 | 0 | 395 | 832 | 0 |
N.S. |
1 | 0.93 | 0.44 | 0.56 | 0.00 | 1.01 | 0.00 | 0.80 | 1.68 | 0.00 |
time (sec) |
N/A | 1.185 | 0.883 | 0.214 | 0.000 | 0.099 | 0.000 | 0.151 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 494 | 459 | 218 | 276 | 0 | 468 | 0 | 396 | 831 | 0 |
N.S. |
1 | 0.93 | 0.44 | 0.56 | 0.00 | 0.95 | 0.00 | 0.80 | 1.68 | 0.00 |
time (sec) |
N/A | 1.111 | 0.808 | 0.204 | 0.000 | 0.087 | 0.000 | 0.130 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 448 | 436 | 207 | 1046 | 0 | 475 | 0 | 383 | 825 | 0 |
N.S. |
1 | 0.97 | 0.46 | 2.33 | 0.00 | 1.06 | 0.00 | 0.85 | 1.84 | 0.00 |
time (sec) |
N/A | 1.073 | 0.795 | 0.151 | 0.000 | 0.106 | 0.000 | 0.127 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | C | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 448 | 436 | 201 | 1134 | 583 | 474 | 0 | 382 | 824 | 0 |
N.S. |
1 | 0.97 | 0.45 | 2.53 | 1.30 | 1.06 | 0.00 | 0.85 | 1.84 | 0.00 |
time (sec) |
N/A | 1.066 | 0.671 | 0.148 | 0.177 | 0.087 | 0.000 | 0.121 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | C | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 451 | 436 | 201 | 1051 | 577 | 498 | 0 | 386 | 825 | 0 |
N.S. |
1 | 0.97 | 0.45 | 2.33 | 1.28 | 1.10 | 0.00 | 0.86 | 1.83 | 0.00 |
time (sec) |
N/A | 1.132 | 0.661 | 0.148 | 0.166 | 0.088 | 0.000 | 0.173 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 451 | 440 | 202 | 1136 | 595 | 497 | 0 | 385 | 824 | 0 |
N.S. |
1 | 0.98 | 0.45 | 2.52 | 1.32 | 1.10 | 0.00 | 0.85 | 1.83 | 0.00 |
time (sec) |
N/A | 1.120 | 0.657 | 0.149 | 0.169 | 0.098 | 0.000 | 0.128 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 454 | 435 | 201 | 1051 | 584 | 508 | 0 | 386 | 825 | 0 |
N.S. |
1 | 0.96 | 0.44 | 2.31 | 1.29 | 1.12 | 0.00 | 0.85 | 1.82 | 0.00 |
time (sec) |
N/A | 1.113 | 0.582 | 0.145 | 0.161 | 0.087 | 0.000 | 0.128 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 454 | 439 | 201 | 1136 | 597 | 507 | 0 | 385 | 824 | 0 |
N.S. |
1 | 0.97 | 0.44 | 2.50 | 1.31 | 1.12 | 0.00 | 0.85 | 1.81 | 0.00 |
time (sec) |
N/A | 1.108 | 0.583 | 0.145 | 0.159 | 0.088 | 0.000 | 0.139 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 451 | 434 | 201 | 1051 | 582 | 498 | 0 | 386 | 825 | 0 |
N.S. |
1 | 0.96 | 0.45 | 2.33 | 1.29 | 1.10 | 0.00 | 0.86 | 1.83 | 0.00 |
time (sec) |
N/A | 1.084 | 0.566 | 0.145 | 0.171 | 0.089 | 0.000 | 0.133 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 451 | 438 | 201 | 1136 | 586 | 473 | 0 | 385 | 822 | 0 |
N.S. |
1 | 0.97 | 0.45 | 2.52 | 1.30 | 1.05 | 0.00 | 0.85 | 1.82 | 0.00 |
time (sec) |
N/A | 1.074 | 0.540 | 0.155 | 0.157 | 0.091 | 0.000 | 0.186 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 450 | 433 | 201 | 1051 | 569 | 460 | 0 | 371 | 822 | 0 |
N.S. |
1 | 0.96 | 0.45 | 2.34 | 1.26 | 1.02 | 0.00 | 0.82 | 1.83 | 0.00 |
time (sec) |
N/A | 1.131 | 0.365 | 0.143 | 0.166 | 0.093 | 0.000 | 0.126 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 450 | 437 | 201 | 1133 | 0 | 466 | 0 | 377 | 824 | 0 |
N.S. |
1 | 0.97 | 0.45 | 2.52 | 0.00 | 1.04 | 0.00 | 0.84 | 1.83 | 0.00 |
time (sec) |
N/A | 1.134 | 0.366 | 0.142 | 0.000 | 0.087 | 0.000 | 0.125 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 496 | 457 | 213 | 273 | 0 | 537 | 0 | 406 | 865 | 0 |
N.S. |
1 | 0.92 | 0.43 | 0.55 | 0.00 | 1.08 | 0.00 | 0.82 | 1.74 | 0.00 |
time (sec) |
N/A | 1.153 | 0.707 | 0.214 | 0.000 | 0.100 | 0.000 | 0.127 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 496 | 461 | 213 | 278 | 0 | 563 | 0 | 397 | 872 | 0 |
N.S. |
1 | 0.93 | 0.43 | 0.56 | 0.00 | 1.14 | 0.00 | 0.80 | 1.76 | 0.00 |
time (sec) |
N/A | 1.147 | 0.696 | 0.212 | 0.000 | 0.092 | 0.000 | 0.119 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 543 | 484 | 224 | 285 | 0 | 582 | 0 | 428 | 891 | 0 |
N.S. |
1 | 0.89 | 0.41 | 0.52 | 0.00 | 1.07 | 0.00 | 0.79 | 1.64 | 0.00 |
time (sec) |
N/A | 1.210 | 0.703 | 0.222 | 0.000 | 0.105 | 0.000 | 0.173 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 285 | 64 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.96 | 0.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.518 | 4.428 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 256 | 48 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.432 | 4.363 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 289 | 272 | 51 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.94 | 0.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.473 | 5.116 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 618 | 582 | 64 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.94 | 0.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.770 | 5.221 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 609 | 576 | 64 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.95 | 0.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.756 | 4.860 | 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 | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 649 | 598 | 61 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.92 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.814 | 5.551 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 105 | 602 | 144 | 507 | 3104 | 847 | 602 | 540 |
N.S. |
1 | 1.00 | 0.70 | 4.01 | 0.96 | 3.38 | 20.69 | 5.65 | 4.01 | 3.60 |
time (sec) |
N/A | 0.551 | 0.224 | 0.454 | 0.044 | 0.096 | 0.825 | 0.152 | 0.169 | 18.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 73 | 292 | 100 | 253 | 1278 | 415 | 292 | 263 |
N.S. |
1 | 1.00 | 0.70 | 2.81 | 0.96 | 2.43 | 12.29 | 3.99 | 2.81 | 2.53 |
time (sec) |
N/A | 0.449 | 0.077 | 0.184 | 0.048 | 0.089 | 0.493 | 0.113 | 0.160 | 18.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 41 | 57 | 56 | 87 | 330 | 135 | 94 | 95 |
N.S. |
1 | 1.00 | 0.71 | 0.98 | 0.97 | 1.50 | 5.69 | 2.33 | 1.62 | 1.64 |
time (sec) |
N/A | 0.349 | 0.050 | 0.089 | 0.042 | 0.098 | 0.281 | 0.135 | 0.170 | 18.889 |
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 | 42 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.298 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 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 | 42 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.297 | 0.040 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 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 | 42 | 0 | 0 | 0 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.68 | 0.00 |
time (sec) |
N/A | 0.295 | 0.032 | 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 | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 159 | 111 | 453 | 243 | 369 | 0 | 900 | 433 | 0 |
N.S. |
1 | 0.51 | 0.35 | 1.45 | 0.78 | 1.18 | 0.00 | 2.88 | 1.38 | 0.00 |
time (sec) |
N/A | 0.527 | 0.140 | 0.095 | 0.039 | 0.086 | 0.000 | 0.164 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 113 | 131 | 199 | 119 | 159 | 0 | 384 | 179 | 0 |
N.S. |
1 | 0.55 | 0.64 | 0.97 | 0.58 | 0.78 | 0.00 | 1.87 | 0.87 | 0.00 |
time (sec) |
N/A | 0.436 | 0.074 | 0.076 | 0.034 | 0.086 | 0.000 | 0.146 | 0.178 | 0.000 |
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 | 97 | 67 | 53 | 56 | 34 | 35 | 0 | 83 | 36 | 55 |
N.S. |
1 | 0.69 | 0.55 | 0.58 | 0.35 | 0.36 | 0.00 | 0.86 | 0.37 | 0.57 |
time (sec) |
N/A | 0.368 | 0.029 | 0.063 | 0.036 | 0.090 | 0.000 | 0.110 | 0.173 | 18.386 |
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 | 73 | 73 | 62 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.334 | 0.033 | 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 | 73 | 73 | 60 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.321 | 0.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 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 | 73 | 73 | 60 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.324 | 0.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 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 | 77 | 77 | 66 | 0 | 0 | 0 | 0 | 0 | 218 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.83 | 0.00 |
time (sec) |
N/A | 0.333 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 163 | 110 | 150 | 115 | 163 | 0 | 375 | 162 | 206 |
N.S. |
1 | 0.94 | 0.63 | 0.86 | 0.66 | 0.94 | 0.00 | 2.16 | 0.93 | 1.18 |
time (sec) |
N/A | 0.510 | 0.069 | 0.201 | 0.037 | 0.072 | 0.000 | 0.156 | 0.198 | 17.772 |
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 | 130 | 128 | 77 | 96 | 79 | 108 | 0 | 235 | 104 | 137 |
N.S. |
1 | 0.98 | 0.59 | 0.74 | 0.61 | 0.83 | 0.00 | 1.81 | 0.80 | 1.05 |
time (sec) |
N/A | 0.448 | 0.053 | 0.145 | 0.037 | 0.079 | 0.000 | 0.115 | 0.188 | 17.899 |
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 | 77 | 83 | 51 | 58 | 54 | 70 | 0 | 132 | 67 | 85 |
N.S. |
1 | 1.08 | 0.66 | 0.75 | 0.70 | 0.91 | 0.00 | 1.71 | 0.87 | 1.10 |
time (sec) |
N/A | 0.359 | 0.045 | 0.109 | 0.038 | 0.076 | 0.000 | 0.149 | 0.184 | 18.423 |
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 | 41 | 45 | 29 | 31 | 30 | 37 | 0 | 58 | 39 | 46 |
N.S. |
1 | 1.10 | 0.71 | 0.76 | 0.73 | 0.90 | 0.00 | 1.41 | 0.95 | 1.12 |
time (sec) |
N/A | 0.293 | 0.003 | 0.079 | 0.045 | 0.074 | 0.000 | 0.116 | 0.168 | 18.536 |
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 | 54 | 0 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.334 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 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 | 64 | 67 | 55 | 0 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.05 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.336 | 0.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 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 | 60 | 60 | 51 | 0 | 0 | 0 | 0 | 0 | 529 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.82 | 0.00 |
time (sec) |
N/A | 0.298 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 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 | 60 | 60 | 51 | 0 | 0 | 0 | 0 | 0 | 299 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.98 | 0.00 |
time (sec) |
N/A | 0.291 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 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 | 55 | 55 | 46 | 0 | 0 | 0 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.31 | 0.00 |
time (sec) |
N/A | 0.289 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 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 | 49 | 0 | 0 | 0 | 0 | 0 | 148 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.55 | 0.00 |
time (sec) |
N/A | 0.296 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 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 | 60 | 60 | 51 | 0 | 0 | 0 | 0 | 0 | 152 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.53 | 0.00 |
time (sec) |
N/A | 0.290 | 0.041 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 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 | 67 | 67 | 56 | 0 | 0 | 0 | 0 | 0 | 323 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.82 | 0.00 |
time (sec) |
N/A | 0.307 | 0.121 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 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 | 67 | 67 | 56 | 0 | 0 | 0 | 0 | 0 | 142 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.12 | 0.00 |
time (sec) |
N/A | 0.300 | 0.094 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 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 | 54 | 0 | 0 | 0 | 0 | 0 | 144 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.22 | 0.00 |
time (sec) |
N/A | 0.304 | 0.108 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 54 | 0 | 0 | 0 | 0 | 0 | 161 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.48 | 0.00 |
time (sec) |
N/A | 0.301 | 0.143 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 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 | 67 | 67 | 56 | 0 | 0 | 0 | 0 | 0 | 166 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.48 | 0.00 |
time (sec) |
N/A | 0.310 | 0.157 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |