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 | 25 | 23 | 27 | 24 | 26 | 26 | 26 | 28 | 23 | 53 |
N.S. |
1 | 0.92 | 1.08 | 0.96 | 1.04 | 1.04 | 1.04 | 1.12 | 0.92 | 2.12 |
time (sec) |
N/A | 0.587 | 0.427 | 0.947 | 0.148 | 0.086 | 0.225 | 0.124 | 0.219 | 0.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 43 | 49 | 28 | 37 | 32 | 32 | 33 | 30 | 32 |
N.S. |
1 | 2.15 | 2.45 | 1.40 | 1.85 | 1.60 | 1.60 | 1.65 | 1.50 | 1.60 |
time (sec) |
N/A | 0.185 | 0.011 | 0.177 | 0.028 | 0.058 | 0.044 | 0.113 | 0.226 | 0.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | B | F(-1) | F | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 44 | 77 | 81 | 76 | 0 | 650 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.38 | 2.41 | 2.53 | 2.38 | 0.00 | 20.31 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 4.364 | 0.185 | 0.085 | 0.814 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 36 | 0 | 33 | 29 | 54 | 36 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.24 | 0.00 | 1.14 | 1.00 | 1.86 | 1.24 | 0.00 |
time (sec) |
N/A | 0.000 | 5.036 | 21.902 | 0.000 | 0.072 | 46.093 | 0.140 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 37 | 32 | 0 | 36 | 32 | 84 | 0 | 95 |
N.S. |
1 | 0.00 | 1.12 | 0.97 | 0.00 | 1.09 | 0.97 | 2.55 | 0.00 | 2.88 |
time (sec) |
N/A | 0.000 | 0.155 | 3.945 | 0.000 | 0.075 | 1.496 | 0.932 | 16.111 | 0.652 |
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 | 15 | 17 | 24 | 14 | 26 | 26 | 22 | 13 | 35 | 31 |
N.S. |
1 | 1.13 | 1.60 | 0.93 | 1.73 | 1.73 | 1.47 | 0.87 | 2.33 | 2.07 |
time (sec) |
N/A | 0.270 | 0.127 | 0.089 | 0.040 | 0.060 | 0.055 | 0.110 | 0.233 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 30 | 30 | 27 | 29 | 0 | 29 | 30 | 28 |
N.S. |
1 | 0.00 | 1.03 | 1.03 | 0.93 | 1.00 | 0.00 | 1.00 | 1.03 | 0.97 |
time (sec) |
N/A | 0.000 | 0.082 | 54.516 | 0.109 | 0.073 | 0.000 | 0.188 | 0.274 | 0.826 |
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 | 25 | 44 | 39 | 35 | 32 | 32 | 36 | 32 | 37 | 34 |
N.S. |
1 | 1.76 | 1.56 | 1.40 | 1.28 | 1.28 | 1.44 | 1.28 | 1.48 | 1.36 |
time (sec) |
N/A | 0.214 | 0.027 | 0.297 | 0.039 | 0.065 | 0.062 | 0.107 | 0.284 | 0.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 70 | 42 | 49 | 79 | 51 | 54 | 69 | 76 | 59 |
N.S. |
1 | 2.06 | 1.24 | 1.44 | 2.32 | 1.50 | 1.59 | 2.03 | 2.24 | 1.74 |
time (sec) |
N/A | 0.471 | 2.183 | 0.722 | 0.070 | 0.067 | 0.081 | 0.111 | 0.227 | 0.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 42 | 33 | 57 | 34 | 31 | 34 | 42 | 80 |
N.S. |
1 | 0.00 | 1.31 | 1.03 | 1.78 | 1.06 | 0.97 | 1.06 | 1.31 | 2.50 |
time (sec) |
N/A | 0.000 | 0.182 | 0.035 | 0.144 | 0.076 | 0.339 | 0.215 | 0.230 | 0.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 451 | 59 | 27 | 127 | 45 | 27 | 45 | 43 | 28 |
N.S. |
1 | 15.55 | 2.03 | 0.93 | 4.38 | 1.55 | 0.93 | 1.55 | 1.48 | 0.97 |
time (sec) |
N/A | 2.966 | 0.393 | 0.977 | 0.166 | 0.062 | 0.078 | 0.124 | 0.263 | 0.511 |
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 | 14 | 13 | 11 | 10 | 9 | 9 | 10 | 9 | 9 | 10 |
N.S. |
1 | 0.93 | 0.79 | 0.71 | 0.64 | 0.64 | 0.71 | 0.64 | 0.64 | 0.71 |
time (sec) |
N/A | 0.138 | 0.001 | 0.056 | 0.032 | 0.060 | 0.026 | 0.108 | 0.246 | 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 | 24 | 27 | 24 | 19 | 23 | 20 | 17 | 22 | 18 | 18 |
N.S. |
1 | 1.12 | 1.00 | 0.79 | 0.96 | 0.83 | 0.71 | 0.92 | 0.75 | 0.75 |
time (sec) |
N/A | 0.213 | 0.005 | 0.132 | 0.030 | 0.070 | 0.069 | 0.110 | 0.229 | 0.462 |
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 | 29 | 21 | 19 | 17 | 24 | 22 | 14 | 16 | 21 | 14 |
N.S. |
1 | 0.72 | 0.66 | 0.59 | 0.83 | 0.76 | 0.48 | 0.55 | 0.72 | 0.48 |
time (sec) |
N/A | 0.253 | 0.030 | 0.152 | 0.034 | 0.063 | 0.046 | 0.111 | 0.240 | 0.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 43 | 45 | 59 | 56 | 41 | 0 | 63 | 52 |
N.S. |
1 | 0.00 | 1.23 | 1.29 | 1.69 | 1.60 | 1.17 | 0.00 | 1.80 | 1.49 |
time (sec) |
N/A | 0.000 | 0.136 | 14.395 | 0.099 | 0.081 | 0.142 | 0.000 | 0.279 | 0.738 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 32 | 37 | 31 | 36 | 34 | 31 | 208 | 36 |
N.S. |
1 | 0.00 | 1.28 | 1.48 | 1.24 | 1.44 | 1.36 | 1.24 | 8.32 | 1.44 |
time (sec) |
N/A | 0.000 | 0.146 | 53.555 | 0.109 | 0.076 | 0.790 | 0.252 | 200.019 | 0.704 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 40 | 34 | 38 | 52 | 49 | 0 | 46 | 43 |
N.S. |
1 | 0.00 | 1.14 | 0.97 | 1.09 | 1.49 | 1.40 | 0.00 | 1.31 | 1.23 |
time (sec) |
N/A | 0.000 | 1.394 | 23.184 | 0.299 | 0.067 | 0.312 | 0.000 | 0.261 | 0.615 |
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 | 16 | 18 | 15 | 14 | 13 | 13 | 8 | 13 | 15 | 13 |
N.S. |
1 | 1.12 | 0.94 | 0.88 | 0.81 | 0.81 | 0.50 | 0.81 | 0.94 | 0.81 |
time (sec) |
N/A | 0.234 | 0.025 | 0.508 | 0.034 | 0.070 | 0.069 | 0.112 | 0.203 | 0.475 |
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 | 14 | 11 | 9 | 9 | 9 | 9 | 8 | 9 | 8 | 8 |
N.S. |
1 | 0.79 | 0.64 | 0.64 | 0.64 | 0.64 | 0.57 | 0.64 | 0.57 | 0.57 |
time (sec) |
N/A | 0.139 | 0.000 | 0.047 | 0.041 | 0.058 | 0.018 | 0.112 | 0.225 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 31 | 116 | 33 | 29 | 33 | 34 | 58 |
N.S. |
1 | 0.00 | 1.00 | 1.29 | 4.83 | 1.38 | 1.21 | 1.38 | 1.42 | 2.42 |
time (sec) |
N/A | 0.000 | 0.034 | 9.936 | 14.018 | 0.065 | 0.108 | 0.188 | 0.203 | 0.545 |
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 | 23 | 43 | 43 | 41 | 43 | 38 | 39 | 41 | 43 | 25 |
N.S. |
1 | 1.87 | 1.87 | 1.78 | 1.87 | 1.65 | 1.70 | 1.78 | 1.87 | 1.09 |
time (sec) |
N/A | 0.293 | 0.010 | 0.768 | 0.033 | 0.062 | 0.083 | 0.120 | 0.205 | 0.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 63 | 85 | 186 | 186 | 129 | 274 | 291 | 0 |
N.S. |
1 | 0.00 | 2.10 | 2.83 | 6.20 | 6.20 | 4.30 | 9.13 | 9.70 | 0.00 |
time (sec) |
N/A | 0.000 | 17.628 | 1.154 | 0.240 | 0.082 | 0.391 | 0.199 | 0.267 | 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 | 18 | 36 | 16 | 14 | 13 | 13 | 14 | 19 | 35 | 12 |
N.S. |
1 | 2.00 | 0.89 | 0.78 | 0.72 | 0.72 | 0.78 | 1.06 | 1.94 | 0.67 |
time (sec) |
N/A | 0.175 | 0.025 | 0.250 | 0.028 | 0.064 | 0.085 | 0.110 | 0.234 | 0.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 33 | 15 | 0 | 21 | 22 | 0 | 33 | 18 |
N.S. |
1 | 0.00 | 1.74 | 0.79 | 0.00 | 1.11 | 1.16 | 0.00 | 1.74 | 0.95 |
time (sec) |
N/A | 0.000 | 0.319 | 10.322 | 0.000 | 0.081 | 0.315 | 0.000 | 0.214 | 0.539 |
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 | 24 | 20 | 23 | 21 | 23 | 23 | 20 | 23 | 20 | 22 |
N.S. |
1 | 0.83 | 0.96 | 0.88 | 0.96 | 0.96 | 0.83 | 0.96 | 0.83 | 0.92 |
time (sec) |
N/A | 0.160 | 0.000 | 0.085 | 0.038 | 0.057 | 0.018 | 0.122 | 0.212 | 0.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 167 | 102 | 144 | 175 | 146 | 153 | 170 | 134 | 110 |
N.S. |
1 | 6.68 | 4.08 | 5.76 | 7.00 | 5.84 | 6.12 | 6.80 | 5.36 | 4.40 |
time (sec) |
N/A | 1.013 | 0.434 | 105.558 | 0.130 | 0.072 | 0.239 | 0.118 | 0.220 | 0.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 18 | 18 | 113 | 17 | 16 | 17 | 17 | 18 | 0 |
N.S. |
1 | 0.78 | 0.78 | 4.91 | 0.74 | 0.70 | 0.74 | 0.74 | 0.78 | 0.00 |
time (sec) |
N/A | 4.633 | 0.332 | 0.043 | 0.120 | 0.072 | 103.852 | 0.112 | 0.230 | 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 | 29 | 27 | 28 | 20 | 18 | 18 | 19 | 18 | 19 | 19 |
N.S. |
1 | 0.93 | 0.97 | 0.69 | 0.62 | 0.62 | 0.66 | 0.62 | 0.66 | 0.66 |
time (sec) |
N/A | 0.361 | 0.033 | 0.240 | 0.029 | 0.070 | 0.164 | 0.113 | 0.223 | 0.798 |
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 | 13 | 15 | 10 | 11 | 10 | 10 | 10 | 10 | 9 | 11 |
N.S. |
1 | 1.15 | 0.77 | 0.85 | 0.77 | 0.77 | 0.77 | 0.77 | 0.69 | 0.85 |
time (sec) |
N/A | 0.143 | 0.000 | 0.064 | 0.032 | 0.058 | 0.018 | 0.111 | 0.232 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 20 | 14 | 14 | 0 | 18 | 0 | 18 | 19 | 13 |
N.S. |
1 | 1.43 | 1.00 | 1.00 | 0.00 | 1.29 | 0.00 | 1.29 | 1.36 | 0.93 |
time (sec) |
N/A | 0.430 | 0.164 | 16.127 | 0.000 | 0.067 | 0.000 | 0.117 | 0.224 | 0.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 99 | 50 | 50 | 0 | 54 | 65 | 78 | 58 | 69 |
N.S. |
1 | 3.41 | 1.72 | 1.72 | 0.00 | 1.86 | 2.24 | 2.69 | 2.00 | 2.38 |
time (sec) |
N/A | 0.701 | 0.804 | 0.604 | 0.000 | 0.071 | 0.233 | 0.113 | 0.209 | 0.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 29 | 29 | 31 | 68 | 72 | 66 | 0 | 88 | 65 |
N.S. |
1 | 1.04 | 1.04 | 1.11 | 2.43 | 2.57 | 2.36 | 0.00 | 3.14 | 2.32 |
time (sec) |
N/A | 1.304 | 0.159 | 1.260 | 0.477 | 0.074 | 0.136 | 0.000 | 0.212 | 0.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 29 | 29 | 77 | 74 | 70 | 70 | 0 | 63 | 54 |
N.S. |
1 | 0.97 | 0.97 | 2.57 | 2.47 | 2.33 | 2.33 | 0.00 | 2.10 | 1.80 |
time (sec) |
N/A | 12.319 | 0.020 | 7.407 | 0.226 | 0.071 | 0.228 | 0.000 | 0.253 | 0.713 |
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 | 17 | 27 | 25 | 20 | 19 | 17 | 20 | 21 | 19 | 21 |
N.S. |
1 | 1.59 | 1.47 | 1.18 | 1.12 | 1.00 | 1.18 | 1.24 | 1.12 | 1.24 |
time (sec) |
N/A | 0.315 | 0.003 | 0.122 | 0.029 | 0.062 | 0.059 | 0.109 | 0.226 | 0.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 32 | 28 | 28 | 27 | 27 | 27 | 85 | 0 |
N.S. |
1 | 0.00 | 1.07 | 0.93 | 0.93 | 0.90 | 0.90 | 0.90 | 2.83 | 0.00 |
time (sec) |
N/A | 0.000 | 0.325 | 0.679 | 0.193 | 0.072 | 0.101 | 0.143 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 33 | 209 | 223 | 324 | 187 | 227 | 113 | 0 |
N.S. |
1 | 0.00 | 1.00 | 6.33 | 6.76 | 9.82 | 5.67 | 6.88 | 3.42 | 0.00 |
time (sec) |
N/A | 0.000 | 0.111 | 11.937 | 0.150 | 0.080 | 5.607 | 0.134 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 38 | 37 | 38 | 35 | 54 | 37 | 83 | 32 |
N.S. |
1 | 0.00 | 1.09 | 1.06 | 1.09 | 1.00 | 1.54 | 1.06 | 2.37 | 0.91 |
time (sec) |
N/A | 0.000 | 0.056 | 1.964 | 0.154 | 0.072 | 0.553 | 0.164 | 0.206 | 0.827 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 28 | 117 | 119 | 139 | 132 | 149 | 0 |
N.S. |
1 | 0.00 | 1.03 | 0.93 | 3.90 | 3.97 | 4.63 | 4.40 | 4.97 | 0.00 |
time (sec) |
N/A | 0.000 | 0.102 | 27.446 | 0.101 | 0.072 | 0.288 | 0.162 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 63 | 25 | 24 | 23 | 23 | 24 | 0 | 28 | 23 |
N.S. |
1 | 1.91 | 0.76 | 0.73 | 0.70 | 0.70 | 0.73 | 0.00 | 0.85 | 0.70 |
time (sec) |
N/A | 2.966 | 2.872 | 4.319 | 0.195 | 0.073 | 0.198 | 0.000 | 0.218 | 0.738 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 35 | 51 | 33 | 43 | 42 | 118 | 60 | 97 |
N.S. |
1 | 0.00 | 1.03 | 1.50 | 0.97 | 1.26 | 1.24 | 3.47 | 1.76 | 2.85 |
time (sec) |
N/A | 0.000 | 0.192 | 0.043 | 0.358 | 0.078 | 1.769 | 0.624 | 0.248 | 0.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 29 | 55 | 26 | 0 | 40 | 52 | 45 |
N.S. |
1 | 0.00 | 1.00 | 1.12 | 2.12 | 1.00 | 0.00 | 1.54 | 2.00 | 1.73 |
time (sec) |
N/A | 0.000 | 10.099 | 4.507 | 0.555 | 0.073 | 0.000 | 0.174 | 0.216 | 0.597 |
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 | 27 | 51 | 37 | 27 | 38 | 34 | 31 | 39 | 44 | 32 |
N.S. |
1 | 1.89 | 1.37 | 1.00 | 1.41 | 1.26 | 1.15 | 1.44 | 1.63 | 1.19 |
time (sec) |
N/A | 1.541 | 0.590 | 0.555 | 0.146 | 0.066 | 0.054 | 0.114 | 0.222 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 35 | 35 | 33 | 48 | 36 | 34 | 0 | 58 | 34 |
N.S. |
1 | 1.03 | 1.03 | 0.97 | 1.41 | 1.06 | 1.00 | 0.00 | 1.71 | 1.00 |
time (sec) |
N/A | 1.762 | 0.692 | 0.064 | 0.143 | 0.072 | 1.006 | 0.000 | 0.245 | 0.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 18 | 16 | 13 | 20 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.38 | 1.23 | 1.00 | 1.54 | 0.92 | 0.62 | 0.92 | 0.92 | 0.92 |
time (sec) |
N/A | 0.467 | 0.036 | 0.064 | 0.055 | 0.058 | 0.034 | 0.113 | 0.231 | 0.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 63 | 24 | 27 | 21 | 35 | 29 | 0 | 35 | 24 |
N.S. |
1 | 2.33 | 0.89 | 1.00 | 0.78 | 1.30 | 1.07 | 0.00 | 1.30 | 0.89 |
time (sec) |
N/A | 0.274 | 0.254 | 0.452 | 0.234 | 0.069 | 11.850 | 0.000 | 0.267 | 0.527 |
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 | 8 | 8 | 8 | 8 | 7 | 7 | 7 | 7 | 8 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.88 | 0.88 | 0.88 | 0.88 | 1.00 | 0.88 |
time (sec) |
N/A | 0.136 | 0.000 | 0.069 | 0.030 | 0.052 | 0.016 | 0.111 | 0.219 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 48 | 50 | 52 | 52 | 61 | 52 | 215 | 172 |
N.S. |
1 | 0.00 | 1.55 | 1.61 | 1.68 | 1.68 | 1.97 | 1.68 | 6.94 | 5.55 |
time (sec) |
N/A | 0.000 | 9.389 | 1.523 | 0.108 | 0.069 | 0.127 | 0.317 | 200.031 | 0.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 34 | 25 | 33 | 29 | 0 | 37 | 34 |
N.S. |
1 | 0.00 | 0.00 | 1.31 | 0.96 | 1.27 | 1.12 | 0.00 | 1.42 | 1.31 |
time (sec) |
N/A | 0.000 | 0.000 | 1.393 | 0.165 | 0.072 | 0.127 | 0.000 | 0.219 | 0.723 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 29 | 42 | 0 | 40 | 32 | 72 | 127 | 66 |
N.S. |
1 | 0.00 | 0.78 | 1.14 | 0.00 | 1.08 | 0.86 | 1.95 | 3.43 | 1.78 |
time (sec) |
N/A | 0.000 | 0.190 | 4.160 | 0.000 | 0.069 | 0.759 | 0.438 | 200.038 | 0.817 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 10 | 10 | 10 | 9 | 9 | 8 | 9 | 10 | 9 |
N.S. |
1 | 0.45 | 0.45 | 0.45 | 0.41 | 0.41 | 0.36 | 0.41 | 0.45 | 0.41 |
time (sec) |
N/A | 0.167 | 0.005 | 0.075 | 0.030 | 0.066 | 0.038 | 0.109 | 0.205 | 0.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 71 | 145 | 67 | 67 | 67 | 68 | 73 | 571 | 68 |
N.S. |
1 | 2.37 | 4.83 | 2.23 | 2.23 | 2.23 | 2.27 | 2.43 | 19.03 | 2.27 |
time (sec) |
N/A | 0.800 | 0.197 | 1.215 | 0.036 | 0.124 | 12.668 | 0.141 | 0.265 | 0.870 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 74 | 29 | 25 | 24 | 24 | 20 | 0 | 29 | 24 |
N.S. |
1 | 2.47 | 0.97 | 0.83 | 0.80 | 0.80 | 0.67 | 0.00 | 0.97 | 0.80 |
time (sec) |
N/A | 0.379 | 0.340 | 0.558 | 0.075 | 0.069 | 0.182 | 0.000 | 0.214 | 0.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 20 | 22 | 21 | 21 | 19 | 21 | 33 | 23 |
N.S. |
1 | 0.00 | 0.83 | 0.92 | 0.88 | 0.88 | 0.79 | 0.88 | 1.38 | 0.96 |
time (sec) |
N/A | 0.000 | 0.197 | 2.175 | 0.079 | 0.060 | 0.070 | 0.117 | 0.208 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 12 | 15 | 12 | 12 | 12 | 12 | 11 | 11 |
N.S. |
1 | 0.00 | 0.71 | 0.88 | 0.71 | 0.71 | 0.71 | 0.71 | 0.65 | 0.65 |
time (sec) |
N/A | 0.000 | 0.055 | 0.219 | 0.072 | 0.070 | 0.074 | 0.142 | 0.225 | 0.456 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 44 | 312 | 40 | 46 | 87 | 34 | 44 |
N.S. |
1 | 0.00 | 1.00 | 2.20 | 15.60 | 2.00 | 2.30 | 4.35 | 1.70 | 2.20 |
time (sec) |
N/A | 0.000 | 0.599 | 0.767 | 0.086 | 0.070 | 2.638 | 0.144 | 0.217 | 0.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 69 | 81 | 66 | 64 | 75 | 80 | 0 | 0 |
N.S. |
1 | 0.00 | 2.46 | 2.89 | 2.36 | 2.29 | 2.68 | 2.86 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.054 | 9.160 | 0.151 | 0.076 | 0.278 | 63.889 | 0.463 | 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 | 17 | 17 | 17 | 17 | 16 | 16 | 14 | 16 | 15 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.94 | 0.94 | 0.82 | 0.94 | 0.88 | 0.82 |
time (sec) |
N/A | 0.172 | 0.000 | 0.102 | 0.033 | 0.061 | 0.018 | 0.108 | 0.248 | 0.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | A | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 30 | 64 | 64 | 36 | 76 | 78 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.91 | 1.94 | 1.94 | 1.09 | 2.30 | 2.36 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 6.541 | 0.263 | 0.079 | 0.250 | 0.438 | 0.331 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 26 | 28 | 23 | 0 | 0 | 26 | 28 |
N.S. |
1 | 0.00 | 1.00 | 1.18 | 1.27 | 1.05 | 0.00 | 0.00 | 1.18 | 1.27 |
time (sec) |
N/A | 0.000 | 0.150 | 0.863 | 0.079 | 0.069 | 0.000 | 0.000 | 0.204 | 0.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 48 | 48 | 43 | 41 | 40 | 39 | 41 | 41 | 48 |
N.S. |
1 | 2.53 | 2.53 | 2.26 | 2.16 | 2.11 | 2.05 | 2.16 | 2.16 | 2.53 |
time (sec) |
N/A | 0.231 | 0.006 | 0.125 | 0.030 | 0.053 | 0.043 | 0.121 | 0.216 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 97 | 46 | 50 | 117 | 73 | 54 | 79 | 69 | 59 |
N.S. |
1 | 3.23 | 1.53 | 1.67 | 3.90 | 2.43 | 1.80 | 2.63 | 2.30 | 1.97 |
time (sec) |
N/A | 0.786 | 1.779 | 0.905 | 0.084 | 0.068 | 0.093 | 0.115 | 0.204 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 48 | 38 | 98 | 40 | 41 | 329 | 70 | 54 |
N.S. |
1 | 0.00 | 1.78 | 1.41 | 3.63 | 1.48 | 1.52 | 12.19 | 2.59 | 2.00 |
time (sec) |
N/A | 0.000 | 0.795 | 34.270 | 0.229 | 0.077 | 18.045 | 3.270 | 0.268 | 0.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 230 | 114 | 148 | 302 | 141 | 168 | 144 | 217 | 217 |
N.S. |
1 | 7.93 | 3.93 | 5.10 | 10.41 | 4.86 | 5.79 | 4.97 | 7.48 | 7.48 |
time (sec) |
N/A | 0.835 | 0.056 | 14.346 | 0.044 | 0.067 | 0.166 | 0.124 | 0.212 | 1.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | B | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 211 | 57 | 66 | 0 | 69 | 88 | 99 | 125 | 110 |
N.S. |
1 | 8.79 | 2.38 | 2.75 | 0.00 | 2.88 | 3.67 | 4.12 | 5.21 | 4.58 |
time (sec) |
N/A | 0.968 | 5.847 | 4.272 | 0.000 | 0.078 | 0.138 | 0.138 | 0.230 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 25 | 27 | 33 | 28 | 24 | 30 | 30 | 29 |
N.S. |
1 | 0.00 | 1.09 | 1.17 | 1.43 | 1.22 | 1.04 | 1.30 | 1.30 | 1.26 |
time (sec) |
N/A | 0.000 | 0.174 | 0.503 | 0.165 | 0.061 | 0.160 | 0.129 | 0.193 | 1.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 15 | 35 | 17 | 14 | 14 | 17 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 2.19 | 1.06 | 0.88 | 0.88 | 1.06 | 0.88 |
time (sec) |
N/A | 0.199 | 0.005 | 0.132 | 0.027 | 0.064 | 0.050 | 0.111 | 0.203 | 0.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 41 | 27 | 23 | 103 | 14 | 20 | 42 | 15 | 14 |
N.S. |
1 | 2.73 | 1.80 | 1.53 | 6.87 | 0.93 | 1.33 | 2.80 | 1.00 | 0.93 |
time (sec) |
N/A | 0.301 | 0.020 | 0.358 | 0.036 | 0.069 | 0.061 | 0.116 | 0.219 | 0.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 302 | 76 | 32 | 0 | 0 | 220 | 0 |
N.S. |
1 | 0.00 | 1.00 | 10.41 | 2.62 | 1.10 | 0.00 | 0.00 | 7.59 | 0.00 |
time (sec) |
N/A | 0.000 | 0.191 | 0.096 | 0.224 | 0.076 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 221 | 44 | 29 | 84 | 35 | 0 | 37 | 65 | 0 |
N.S. |
1 | 6.14 | 1.22 | 0.81 | 2.33 | 0.97 | 0.00 | 1.03 | 1.81 | 0.00 |
time (sec) |
N/A | 1.065 | 0.086 | 47.934 | 0.455 | 0.077 | 0.000 | 0.354 | 0.249 | 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 | 28 | 32 | 28 | 26 | 25 | 25 | 24 | 26 | 26 | 26 |
N.S. |
1 | 1.14 | 1.00 | 0.93 | 0.89 | 0.89 | 0.86 | 0.93 | 0.93 | 0.93 |
time (sec) |
N/A | 0.183 | 0.008 | 0.172 | 0.037 | 0.066 | 0.066 | 0.119 | 0.222 | 0.457 |
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 | 27 | 20 | 21 | 19 | 32 | 24 | 17 | 18 | 22 | 14 |
N.S. |
1 | 0.74 | 0.78 | 0.70 | 1.19 | 0.89 | 0.63 | 0.67 | 0.81 | 0.52 |
time (sec) |
N/A | 0.271 | 0.036 | 0.153 | 0.031 | 0.084 | 0.060 | 0.114 | 0.225 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 20 | 19 | 18 | 0 | 17 | 19 | 17 | 16 | 13 |
N.S. |
1 | 1.25 | 1.19 | 1.12 | 0.00 | 1.06 | 1.19 | 1.06 | 1.00 | 0.81 |
time (sec) |
N/A | 0.242 | 0.011 | 0.220 | 0.000 | 0.068 | 0.080 | 0.118 | 0.253 | 0.435 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 243 | 27 | 27 | 73 | 26 | 26 | 56 | 29 | 26 |
N.S. |
1 | 7.15 | 0.79 | 0.79 | 2.15 | 0.76 | 0.76 | 1.65 | 0.85 | 0.76 |
time (sec) |
N/A | 2.475 | 0.105 | 8.562 | 0.177 | 0.070 | 0.125 | 0.135 | 0.233 | 0.423 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 83 | 37 | 27 | 0 | 35 | 22 | 0 | 40 | 0 |
N.S. |
1 | 2.86 | 1.28 | 0.93 | 0.00 | 1.21 | 0.76 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 6.058 | 2.287 | 1.697 | 0.000 | 0.070 | 0.158 | 0.000 | 0.224 | 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 | 17 | 15 | 15 | 16 | 15 | 23 | 10 | 16 | 24 | 15 |
N.S. |
1 | 0.88 | 0.88 | 0.94 | 0.88 | 1.35 | 0.59 | 0.94 | 1.41 | 0.88 |
time (sec) |
N/A | 0.241 | 0.009 | 0.066 | 0.040 | 0.061 | 0.039 | 0.110 | 0.239 | 0.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 50 | 51 | 25 | 55 | 44 | 54 | 57 | 57 | 51 |
N.S. |
1 | 2.63 | 2.68 | 1.32 | 2.89 | 2.32 | 2.84 | 3.00 | 3.00 | 2.68 |
time (sec) |
N/A | 0.248 | 0.022 | 0.142 | 0.035 | 0.057 | 0.886 | 0.111 | 0.232 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 29 | 25 | 52 | 1065 | 263 | 357 | 428 | 471 | 428 |
N.S. |
1 | 1.16 | 1.00 | 2.08 | 42.60 | 10.52 | 14.28 | 17.12 | 18.84 | 17.12 |
time (sec) |
N/A | 1.340 | 0.078 | 40.185 | 0.076 | 0.073 | 0.538 | 0.124 | 0.226 | 3.241 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 19 | 20 | 20 | 19 | 17 | 172 | 31 | 31 |
N.S. |
1 | 0.00 | 0.86 | 0.91 | 0.91 | 0.86 | 0.77 | 7.82 | 1.41 | 1.41 |
time (sec) |
N/A | 0.000 | 0.074 | 2.826 | 0.160 | 0.067 | 0.081 | 0.164 | 0.217 | 0.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | F | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 79 | 82 | 93 | 87 | 205 | 318 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.55 | 2.65 | 3.00 | 2.81 | 6.61 | 10.26 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 3.216 | 0.215 | 0.078 | 0.353 | 3.690 | 200.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 36 | 33 | 32 | 32 | 29 | 0 | 36 | 32 |
N.S. |
1 | 0.00 | 1.50 | 1.38 | 1.33 | 1.33 | 1.21 | 0.00 | 1.50 | 1.33 |
time (sec) |
N/A | 0.000 | 0.247 | 0.172 | 0.071 | 0.067 | 0.201 | 0.000 | 0.231 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 26 | 22 | 19 | 18 | 18 | 17 | 36 | 32 | 18 |
N.S. |
1 | 1.18 | 1.00 | 0.86 | 0.82 | 0.82 | 0.77 | 1.64 | 1.45 | 0.82 |
time (sec) |
N/A | 0.470 | 0.034 | 0.102 | 0.054 | 0.069 | 0.069 | 0.116 | 0.209 | 0.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 76 | 28 | 28 | 37 | 33 | 31 | 37 | 83 | 40 |
N.S. |
1 | 3.30 | 1.22 | 1.22 | 1.61 | 1.43 | 1.35 | 1.61 | 3.61 | 1.74 |
time (sec) |
N/A | 1.010 | 0.253 | 0.677 | 0.145 | 0.072 | 0.149 | 0.187 | 200.019 | 0.491 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 17 | 36 | 76 | 20 | 0 | 0 | 50 |
N.S. |
1 | 0.00 | 0.95 | 0.77 | 1.64 | 3.45 | 0.91 | 0.00 | 0.00 | 2.27 |
time (sec) |
N/A | 0.000 | 4.052 | 0.664 | 0.584 | 0.076 | 0.241 | 0.000 | 0.664 | 1.188 |
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 | 7 | 3 | 3 | 4 | 3 | 3 | 2 | 3 | 3 | 3 |
N.S. |
1 | 0.43 | 0.43 | 0.57 | 0.43 | 0.43 | 0.29 | 0.43 | 0.43 | 0.43 |
time (sec) |
N/A | 0.127 | 0.000 | 0.045 | 0.029 | 0.059 | 0.017 | 0.116 | 0.258 | 0.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 32 | 31 | 37 | 31 | 159 | 31 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.19 | 1.15 | 1.37 | 1.15 | 5.89 | 1.15 | 0.00 |
time (sec) |
N/A | 0.000 | 0.092 | 193.500 | 0.089 | 0.066 | 0.175 | 0.248 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 17 | 16 | 0 | 15 | 10 | 15 | 17 | 15 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 0.00 | 0.88 | 0.59 | 0.88 | 1.00 | 0.88 |
time (sec) |
N/A | 0.000 | 0.375 | 0.199 | 0.000 | 0.065 | 0.124 | 0.132 | 0.222 | 0.654 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 66 | 26 | 39 | 0 | 37 | 41 | 61 | 43 | 23 |
N.S. |
1 | 2.87 | 1.13 | 1.70 | 0.00 | 1.61 | 1.78 | 2.65 | 1.87 | 1.00 |
time (sec) |
N/A | 0.709 | 0.830 | 0.554 | 0.000 | 0.076 | 0.104 | 0.135 | 0.241 | 0.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 726 | 21 | 22 | 19 | 21 | 19 | 24 | 21 | 21 |
N.S. |
1 | 31.57 | 0.91 | 0.96 | 0.83 | 0.91 | 0.83 | 1.04 | 0.91 | 0.91 |
time (sec) |
N/A | 4.053 | 0.338 | 0.521 | 0.279 | 0.070 | 0.106 | 0.124 | 0.230 | 0.531 |
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 | 19 | 20 | 13 | 13 | 17 | 17 | 12 | 17 | 13 | 16 |
N.S. |
1 | 1.05 | 0.68 | 0.68 | 0.89 | 0.89 | 0.63 | 0.89 | 0.68 | 0.84 |
time (sec) |
N/A | 0.156 | 0.001 | 0.087 | 0.027 | 0.055 | 0.021 | 0.106 | 0.213 | 0.167 |
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 | 24 | 17 | 17 | 16 | 15 | 15 | 14 | 17 | 17 | 15 |
N.S. |
1 | 0.71 | 0.71 | 0.67 | 0.62 | 0.62 | 0.58 | 0.71 | 0.71 | 0.62 |
time (sec) |
N/A | 0.163 | 0.002 | 0.097 | 0.031 | 0.072 | 0.046 | 0.118 | 0.216 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 20 | 20 | 19 | 23 | 17 | 23 | 23 | 19 |
N.S. |
1 | 0.00 | 0.77 | 0.77 | 0.73 | 0.88 | 0.65 | 0.88 | 0.88 | 0.73 |
time (sec) |
N/A | 0.000 | 0.088 | 0.242 | 0.067 | 0.071 | 0.083 | 0.120 | 0.277 | 0.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 10 | 11 | 32 | 10 | 8 | 27 | 10 | 10 |
N.S. |
1 | 1.00 | 0.83 | 0.92 | 2.67 | 0.83 | 0.67 | 2.25 | 0.83 | 0.83 |
time (sec) |
N/A | 0.194 | 0.024 | 0.073 | 0.036 | 0.065 | 0.048 | 0.104 | 0.239 | 0.474 |
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 | 18 | 21 | 21 | 10 | 9 | 9 | 7 | 9 | 10 | 9 |
N.S. |
1 | 1.17 | 1.17 | 0.56 | 0.50 | 0.50 | 0.39 | 0.50 | 0.56 | 0.50 |
time (sec) |
N/A | 0.164 | 0.012 | 0.064 | 0.035 | 0.067 | 0.032 | 0.107 | 0.219 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | C | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 54 | 25 | 46 | 96 | 42 | 48 | 46 | 52 | 22 |
N.S. |
1 | 2.35 | 1.09 | 2.00 | 4.17 | 1.83 | 2.09 | 2.00 | 2.26 | 0.96 |
time (sec) |
N/A | 0.522 | 1.309 | 0.528 | 0.161 | 0.067 | 0.087 | 0.116 | 0.234 | 0.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 42 | 0 | 41 | 0 | 0 | 26 | 23 |
N.S. |
1 | 0.00 | 1.00 | 1.62 | 0.00 | 1.58 | 0.00 | 0.00 | 1.00 | 0.88 |
time (sec) |
N/A | 0.000 | 0.137 | 33.504 | 0.000 | 0.070 | 0.000 | 0.000 | 0.257 | 0.719 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 13 | 13 | 14 | 38 | 19 | 12 | 13 | 17 | 13 |
N.S. |
1 | 0.81 | 0.81 | 0.88 | 2.38 | 1.19 | 0.75 | 0.81 | 1.06 | 0.81 |
time (sec) |
N/A | 0.247 | 0.006 | 0.176 | 0.042 | 0.074 | 0.054 | 0.112 | 0.221 | 0.501 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 427 | 48 | 65 | 43 | 56 | 50 | 95 | 256790 |
N.S. |
1 | 0.00 | 12.94 | 1.45 | 1.97 | 1.30 | 1.70 | 1.52 | 2.88 | 7781.52 |
time (sec) |
N/A | 0.000 | 0.516 | 0.319 | 0.030 | 0.075 | 2.047 | 0.133 | 0.203 | 18.276 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | A | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 317 | 37 | 37 | 0 | 39 | 217 | 32 |
N.S. |
1 | 0.00 | 1.00 | 10.23 | 1.19 | 1.19 | 0.00 | 1.26 | 7.00 | 1.03 |
time (sec) |
N/A | 0.000 | 0.124 | 0.279 | 0.255 | 0.087 | 0.000 | 0.254 | 200.020 | 1.233 |
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 | 11 | 11 | 11 | 11 | 10 | 10 | 7 | 10 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.91 | 0.91 | 0.64 | 0.91 | 1.00 | 0.91 |
time (sec) |
N/A | 0.226 | 0.013 | 0.078 | 0.028 | 0.069 | 0.046 | 0.116 | 0.263 | 0.500 |
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 | 26 | 27 | 16 | 14 | 25 | 13 | 14 | 13 | 14 | 13 |
N.S. |
1 | 1.04 | 0.62 | 0.54 | 0.96 | 0.50 | 0.54 | 0.50 | 0.54 | 0.50 |
time (sec) |
N/A | 0.212 | 0.022 | 0.112 | 0.031 | 0.063 | 0.039 | 0.115 | 0.284 | 0.026 |