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 | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 49 | 91 | 36 | 114 | 13 | 0 | 29 | 15 | 71 |
N.S. |
1 | 0.62 | 1.15 | 0.46 | 1.44 | 0.16 | 0.00 | 0.37 | 0.19 | 0.90 |
time (sec) |
N/A | 0.193 | 0.537 | 0.128 | 0.036 | 0.065 | 0.000 | 0.125 | 0.180 | 21.998 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 71 | 39 | 31 | 83 | 13 | 0 | 23 | 15 | 59 |
N.S. |
1 | 1.06 | 0.58 | 0.46 | 1.24 | 0.19 | 0.00 | 0.34 | 0.22 | 0.88 |
time (sec) |
N/A | 0.212 | 1.012 | 0.102 | 0.034 | 0.059 | 0.000 | 0.107 | 0.184 | 21.879 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 88 | 23 | 52 | 13 | 0 | 22 | 14 | 33 |
N.S. |
1 | 1.00 | 2.44 | 0.64 | 1.44 | 0.36 | 0.00 | 0.61 | 0.39 | 0.92 |
time (sec) |
N/A | 0.179 | 0.451 | 0.102 | 0.035 | 0.063 | 0.000 | 0.140 | 0.175 | 21.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 45 | 454 | 26 | 96 | 11 | 0 | 28 | 11 | 109 |
N.S. |
1 | 0.60 | 6.05 | 0.35 | 1.28 | 0.15 | 0.00 | 0.37 | 0.15 | 1.45 |
time (sec) |
N/A | 0.196 | 1.013 | 0.083 | 0.037 | 0.062 | 0.000 | 0.133 | 0.169 | 21.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 45 | 178 | 28 | 99 | 17 | 0 | 43 | 17 | 112 |
N.S. |
1 | 0.60 | 2.37 | 0.37 | 1.32 | 0.23 | 0.00 | 0.57 | 0.23 | 1.49 |
time (sec) |
N/A | 0.207 | 0.386 | 0.086 | 0.035 | 0.061 | 0.000 | 0.129 | 0.182 | 21.739 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 37 | 22 | 86 | 13 | 0 | 30 | 15 | 33 |
N.S. |
1 | 1.00 | 0.95 | 0.56 | 2.21 | 0.33 | 0.00 | 0.77 | 0.38 | 0.85 |
time (sec) |
N/A | 0.188 | 1.016 | 0.086 | 0.040 | 0.062 | 0.000 | 0.126 | 0.176 | 23.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 49 | 39 | 24 | 117 | 15 | 0 | 31 | 15 | 35 |
N.S. |
1 | 0.62 | 0.49 | 0.30 | 1.48 | 0.19 | 0.00 | 0.39 | 0.19 | 0.44 |
time (sec) |
N/A | 0.201 | 1.018 | 0.089 | 0.045 | 0.061 | 0.000 | 0.112 | 0.176 | 23.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 49 | 39 | 24 | 148 | 15 | 0 | 31 | 15 | 35 |
N.S. |
1 | 0.62 | 0.49 | 0.30 | 1.87 | 0.19 | 0.00 | 0.39 | 0.19 | 0.44 |
time (sec) |
N/A | 0.202 | 1.013 | 0.088 | 0.039 | 0.061 | 0.000 | 0.132 | 0.182 | 21.851 |
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 | 79 | 49 | 39 | 36 | 13 | 13 | 0 | 29 | 15 | 0 |
N.S. |
1 | 0.62 | 0.49 | 0.46 | 0.16 | 0.16 | 0.00 | 0.37 | 0.19 | 0.00 |
time (sec) |
N/A | 0.200 | 1.012 | 2.171 | 0.034 | 0.063 | 0.000 | 0.126 | 0.174 | 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 | 79 | 49 | 39 | 36 | 13 | 13 | 0 | 29 | 15 | 0 |
N.S. |
1 | 0.62 | 0.49 | 0.46 | 0.16 | 0.16 | 0.00 | 0.37 | 0.19 | 0.00 |
time (sec) |
N/A | 0.200 | 1.012 | 1.787 | 0.034 | 0.064 | 0.000 | 0.129 | 0.184 | 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 | 79 | 49 | 39 | 36 | 13 | 13 | 0 | 29 | 15 | 0 |
N.S. |
1 | 0.62 | 0.49 | 0.46 | 0.16 | 0.16 | 0.00 | 0.37 | 0.19 | 0.00 |
time (sec) |
N/A | 0.199 | 1.011 | 1.297 | 0.039 | 0.064 | 0.000 | 0.133 | 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 | 74 | 50 | 36 | 33 | 10 | 10 | 0 | 20 | 12 | 0 |
N.S. |
1 | 0.68 | 0.49 | 0.45 | 0.14 | 0.14 | 0.00 | 0.27 | 0.16 | 0.00 |
time (sec) |
N/A | 0.193 | 0.010 | 1.067 | 0.034 | 0.061 | 0.000 | 0.112 | 0.176 | 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 | 77 | 47 | 38 | 36 | 14 | 14 | 0 | 29 | 14 | 0 |
N.S. |
1 | 0.61 | 0.49 | 0.47 | 0.18 | 0.18 | 0.00 | 0.38 | 0.18 | 0.00 |
time (sec) |
N/A | 0.200 | 1.014 | 1.509 | 0.034 | 0.062 | 0.000 | 0.125 | 0.184 | 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 | 74 | 44 | 37 | 34 | 15 | 15 | 0 | 26 | 15 | 0 |
N.S. |
1 | 0.59 | 0.50 | 0.46 | 0.20 | 0.20 | 0.00 | 0.35 | 0.20 | 0.00 |
time (sec) |
N/A | 0.198 | 1.011 | 1.812 | 0.033 | 0.063 | 0.000 | 0.133 | 0.172 | 0.000 |
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 | 77 | 47 | 37 | 34 | 13 | 13 | 0 | 30 | 15 | 33 |
N.S. |
1 | 0.61 | 0.48 | 0.44 | 0.17 | 0.17 | 0.00 | 0.39 | 0.19 | 0.43 |
time (sec) |
N/A | 0.200 | 1.011 | 2.569 | 0.036 | 0.064 | 0.000 | 0.135 | 0.185 | 21.224 |
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 | 79 | 49 | 39 | 35 | 15 | 15 | 0 | 31 | 15 | 35 |
N.S. |
1 | 0.62 | 0.49 | 0.44 | 0.19 | 0.19 | 0.00 | 0.39 | 0.19 | 0.44 |
time (sec) |
N/A | 0.206 | 1.012 | 2.948 | 0.033 | 0.062 | 0.000 | 0.105 | 0.176 | 21.130 |
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 | 79 | 49 | 39 | 35 | 15 | 15 | 0 | 31 | 15 | 35 |
N.S. |
1 | 0.62 | 0.49 | 0.44 | 0.19 | 0.19 | 0.00 | 0.39 | 0.19 | 0.44 |
time (sec) |
N/A | 0.203 | 1.013 | 5.086 | 0.035 | 0.065 | 0.000 | 0.117 | 0.172 | 21.674 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 78 | 113 | 42 | 114 | 35 | 0 | 67 | 37 | 0 |
N.S. |
1 | 0.66 | 0.95 | 0.35 | 0.96 | 0.29 | 0.00 | 0.56 | 0.31 | 0.00 |
time (sec) |
N/A | 0.234 | 0.890 | 0.121 | 0.036 | 0.067 | 0.000 | 0.116 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 73 | 113 | 31 | 83 | 35 | 0 | 45 | 37 | 46 |
N.S. |
1 | 1.06 | 1.64 | 0.45 | 1.20 | 0.51 | 0.00 | 0.65 | 0.54 | 0.67 |
time (sec) |
N/A | 0.215 | 0.773 | 0.105 | 0.036 | 0.064 | 0.000 | 0.126 | 0.174 | 20.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 60 | 23 | 52 | 35 | 0 | 44 | 36 | 36 |
N.S. |
1 | 1.00 | 1.58 | 0.61 | 1.37 | 0.92 | 0.00 | 1.16 | 0.95 | 0.95 |
time (sec) |
N/A | 0.181 | 1.027 | 0.103 | 0.035 | 0.065 | 0.000 | 0.132 | 0.182 | 20.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 74 | 60 | 54 | 152 | 32 | 0 | 65 | 32 | 0 |
N.S. |
1 | 0.46 | 0.38 | 0.34 | 0.95 | 0.20 | 0.00 | 0.41 | 0.20 | 0.00 |
time (sec) |
N/A | 0.222 | 1.029 | 0.100 | 0.038 | 0.064 | 0.000 | 0.107 | 0.179 | 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 | 161 | 73 | 62 | 59 | 156 | 38 | 0 | 85 | 38 | 0 |
N.S. |
1 | 0.45 | 0.39 | 0.37 | 0.97 | 0.24 | 0.00 | 0.53 | 0.24 | 0.00 |
time (sec) |
N/A | 0.230 | 1.029 | 0.116 | 0.036 | 0.062 | 0.000 | 0.129 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 72 | 61 | 59 | 220 | 39 | 0 | 86 | 39 | 0 |
N.S. |
1 | 0.44 | 0.38 | 0.36 | 1.36 | 0.24 | 0.00 | 0.53 | 0.24 | 0.00 |
time (sec) |
N/A | 0.230 | 1.026 | 0.100 | 0.037 | 0.063 | 0.000 | 0.128 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 74 | 266 | 52 | 253 | 39 | 0 | 85 | 39 | 0 |
N.S. |
1 | 0.46 | 1.65 | 0.32 | 1.57 | 0.24 | 0.00 | 0.53 | 0.24 | 0.00 |
time (sec) |
N/A | 0.230 | 0.596 | 0.104 | 0.039 | 0.062 | 0.000 | 0.130 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 59 | 41 | 148 | 35 | 0 | 68 | 37 | 151 |
N.S. |
1 | 1.00 | 1.44 | 1.00 | 3.61 | 0.85 | 0.00 | 1.66 | 0.90 | 3.68 |
time (sec) |
N/A | 0.181 | 1.020 | 0.104 | 0.039 | 0.063 | 0.000 | 0.124 | 0.184 | 20.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 75 | 61 | 44 | 179 | 37 | 0 | 69 | 37 | 151 |
N.S. |
1 | 0.89 | 0.73 | 0.52 | 2.13 | 0.44 | 0.00 | 0.82 | 0.44 | 1.80 |
time (sec) |
N/A | 0.203 | 1.022 | 0.108 | 0.040 | 0.064 | 0.000 | 0.112 | 0.168 | 20.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 78 | 61 | 44 | 210 | 37 | 0 | 69 | 37 | 151 |
N.S. |
1 | 0.47 | 0.37 | 0.26 | 1.26 | 0.22 | 0.00 | 0.41 | 0.22 | 0.90 |
time (sec) |
N/A | 0.231 | 1.022 | 0.111 | 0.041 | 0.063 | 0.000 | 0.126 | 0.172 | 21.563 |
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 | 167 | 75 | 61 | 58 | 35 | 35 | 0 | 67 | 37 | 0 |
N.S. |
1 | 0.45 | 0.37 | 0.35 | 0.21 | 0.21 | 0.00 | 0.40 | 0.22 | 0.00 |
time (sec) |
N/A | 0.224 | 1.023 | 2.145 | 0.033 | 0.078 | 0.000 | 0.128 | 0.180 | 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 | 167 | 75 | 61 | 58 | 35 | 35 | 0 | 67 | 37 | 0 |
N.S. |
1 | 0.45 | 0.37 | 0.35 | 0.21 | 0.21 | 0.00 | 0.40 | 0.22 | 0.00 |
time (sec) |
N/A | 0.227 | 1.025 | 1.793 | 0.034 | 0.067 | 0.000 | 0.129 | 0.171 | 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 | 167 | 75 | 61 | 58 | 35 | 35 | 0 | 67 | 37 | 0 |
N.S. |
1 | 0.45 | 0.37 | 0.35 | 0.21 | 0.21 | 0.00 | 0.40 | 0.22 | 0.00 |
time (sec) |
N/A | 0.218 | 1.021 | 1.253 | 0.033 | 0.067 | 0.000 | 0.132 | 0.183 | 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 | 162 | 78 | 59 | 56 | 32 | 32 | 0 | 64 | 35 | 0 |
N.S. |
1 | 0.48 | 0.36 | 0.35 | 0.20 | 0.20 | 0.00 | 0.40 | 0.22 | 0.00 |
time (sec) |
N/A | 0.222 | 1.019 | 1.034 | 0.040 | 0.062 | 0.000 | 0.109 | 0.179 | 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 | 165 | 73 | 61 | 58 | 37 | 37 | 0 | 67 | 37 | 0 |
N.S. |
1 | 0.44 | 0.37 | 0.35 | 0.22 | 0.22 | 0.00 | 0.41 | 0.22 | 0.00 |
time (sec) |
N/A | 0.224 | 1.021 | 1.522 | 0.038 | 0.065 | 0.000 | 0.130 | 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 | 163 | 71 | 61 | 58 | 37 | 37 | 0 | 65 | 37 | 0 |
N.S. |
1 | 0.44 | 0.37 | 0.36 | 0.23 | 0.23 | 0.00 | 0.40 | 0.23 | 0.00 |
time (sec) |
N/A | 0.225 | 1.022 | 1.764 | 0.033 | 0.063 | 0.000 | 0.113 | 0.181 | 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 | 165 | 73 | 61 | 58 | 37 | 37 | 0 | 69 | 37 | 0 |
N.S. |
1 | 0.44 | 0.37 | 0.35 | 0.22 | 0.22 | 0.00 | 0.42 | 0.22 | 0.00 |
time (sec) |
N/A | 0.227 | 1.020 | 2.506 | 0.036 | 0.065 | 0.000 | 0.137 | 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 | 163 | 71 | 61 | 58 | 37 | 37 | 0 | 68 | 37 | 0 |
N.S. |
1 | 0.44 | 0.37 | 0.36 | 0.23 | 0.23 | 0.00 | 0.42 | 0.23 | 0.00 |
time (sec) |
N/A | 0.224 | 1.023 | 3.015 | 0.034 | 0.061 | 0.000 | 0.124 | 0.188 | 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 | 165 | 73 | 61 | 58 | 37 | 37 | 0 | 70 | 37 | 0 |
N.S. |
1 | 0.44 | 0.37 | 0.35 | 0.22 | 0.22 | 0.00 | 0.42 | 0.22 | 0.00 |
time (sec) |
N/A | 0.224 | 1.017 | 5.102 | 0.036 | 0.063 | 0.000 | 0.112 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 107 | 83 | 53 | 145 | 57 | 0 | 105 | 59 | 0 |
N.S. |
1 | 0.67 | 0.52 | 0.33 | 0.91 | 0.36 | 0.00 | 0.66 | 0.37 | 0.00 |
time (sec) |
N/A | 0.257 | 1.036 | 0.195 | 0.036 | 0.063 | 0.000 | 0.134 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 88 | 83 | 42 | 114 | 57 | 0 | 105 | 59 | 0 |
N.S. |
1 | 0.74 | 0.70 | 0.35 | 0.96 | 0.48 | 0.00 | 0.88 | 0.50 | 0.00 |
time (sec) |
N/A | 0.240 | 1.037 | 0.148 | 0.042 | 0.067 | 0.000 | 0.114 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 73 | 83 | 31 | 83 | 57 | 0 | 67 | 59 | 0 |
N.S. |
1 | 1.06 | 1.20 | 0.45 | 1.20 | 0.83 | 0.00 | 0.97 | 0.86 | 0.00 |
time (sec) |
N/A | 0.213 | 1.034 | 0.115 | 0.035 | 0.064 | 0.000 | 0.132 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 82 | 23 | 52 | 57 | 0 | 66 | 58 | 36 |
N.S. |
1 | 1.00 | 2.16 | 0.61 | 1.37 | 1.50 | 0.00 | 1.74 | 1.53 | 0.95 |
time (sec) |
N/A | 0.179 | 1.034 | 0.109 | 0.035 | 0.069 | 0.000 | 0.128 | 0.165 | 22.417 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 98 | 82 | 75 | 206 | 55 | 0 | 104 | 55 | 0 |
N.S. |
1 | 0.39 | 0.33 | 0.30 | 0.82 | 0.22 | 0.00 | 0.41 | 0.22 | 0.00 |
time (sec) |
N/A | 0.244 | 1.039 | 0.102 | 0.041 | 0.068 | 0.000 | 0.113 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 97 | 85 | 81 | 214 | 61 | 0 | 124 | 61 | 0 |
N.S. |
1 | 0.38 | 0.34 | 0.32 | 0.85 | 0.24 | 0.00 | 0.49 | 0.24 | 0.00 |
time (sec) |
N/A | 0.245 | 1.036 | 0.107 | 0.043 | 0.073 | 0.000 | 0.141 | 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 | 252 | 99 | 85 | 82 | 282 | 61 | 0 | 126 | 61 | 0 |
N.S. |
1 | 0.39 | 0.34 | 0.33 | 1.12 | 0.24 | 0.00 | 0.50 | 0.24 | 0.00 |
time (sec) |
N/A | 0.248 | 1.047 | 0.119 | 0.041 | 0.069 | 0.000 | 0.111 | 0.176 | 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 | 252 | 99 | 85 | 82 | 313 | 61 | 0 | 127 | 61 | 0 |
N.S. |
1 | 0.39 | 0.34 | 0.33 | 1.24 | 0.24 | 0.00 | 0.50 | 0.24 | 0.00 |
time (sec) |
N/A | 0.249 | 1.038 | 0.165 | 0.043 | 0.068 | 0.000 | 0.129 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 96 | 85 | 81 | 342 | 61 | 0 | 125 | 61 | 0 |
N.S. |
1 | 0.38 | 0.34 | 0.32 | 1.36 | 0.24 | 0.00 | 0.50 | 0.24 | 0.00 |
time (sec) |
N/A | 0.246 | 1.030 | 0.219 | 0.041 | 0.068 | 0.000 | 0.142 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 98 | 268 | 72 | 374 | 61 | 0 | 123 | 61 | 0 |
N.S. |
1 | 0.39 | 1.07 | 0.29 | 1.49 | 0.24 | 0.00 | 0.49 | 0.24 | 0.00 |
time (sec) |
N/A | 0.250 | 0.856 | 0.366 | 0.046 | 0.071 | 0.000 | 0.112 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 81 | 58 | 210 | 57 | 0 | 106 | 59 | 231 |
N.S. |
1 | 1.00 | 1.98 | 1.41 | 5.12 | 1.39 | 0.00 | 2.59 | 1.44 | 5.63 |
time (sec) |
N/A | 0.183 | 1.030 | 0.651 | 0.047 | 0.067 | 0.000 | 0.126 | 0.164 | 19.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 75 | 83 | 68 | 241 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.89 | 0.99 | 0.81 | 2.87 | 0.70 | 0.00 | 1.27 | 0.70 | 2.75 |
time (sec) |
N/A | 0.202 | 1.033 | 1.181 | 0.053 | 0.070 | 0.000 | 0.133 | 0.165 | 19.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 103 | 83 | 66 | 272 | 59 | 0 | 107 | 59 | 231 |
N.S. |
1 | 0.80 | 0.65 | 0.52 | 2.12 | 0.46 | 0.00 | 0.84 | 0.46 | 1.80 |
time (sec) |
N/A | 0.221 | 1.029 | 2.158 | 0.050 | 0.070 | 0.000 | 0.145 | 0.174 | 19.603 |
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 | 255 | 101 | 83 | 80 | 57 | 57 | 0 | 105 | 59 | 0 |
N.S. |
1 | 0.40 | 0.33 | 0.31 | 0.22 | 0.22 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.247 | 1.030 | 2.179 | 0.036 | 0.072 | 0.000 | 0.126 | 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 | 252 | 98 | 83 | 80 | 56 | 56 | 0 | 104 | 59 | 0 |
N.S. |
1 | 0.39 | 0.33 | 0.32 | 0.22 | 0.22 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.243 | 1.025 | 1.769 | 0.038 | 0.064 | 0.000 | 0.113 | 0.180 | 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 | 252 | 98 | 83 | 80 | 56 | 56 | 0 | 104 | 59 | 0 |
N.S. |
1 | 0.39 | 0.33 | 0.32 | 0.22 | 0.22 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.234 | 1.026 | 1.283 | 0.037 | 0.069 | 0.000 | 0.121 | 0.173 | 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 | 247 | 101 | 81 | 78 | 53 | 53 | 0 | 101 | 57 | 0 |
N.S. |
1 | 0.41 | 0.33 | 0.32 | 0.21 | 0.21 | 0.00 | 0.41 | 0.23 | 0.00 |
time (sec) |
N/A | 0.243 | 1.027 | 1.106 | 0.034 | 0.066 | 0.000 | 0.142 | 0.173 | 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 | 251 | 97 | 83 | 80 | 59 | 59 | 0 | 105 | 59 | 0 |
N.S. |
1 | 0.39 | 0.33 | 0.32 | 0.24 | 0.24 | 0.00 | 0.42 | 0.24 | 0.00 |
time (sec) |
N/A | 0.243 | 1.028 | 1.522 | 0.038 | 0.073 | 0.000 | 0.114 | 0.180 | 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 | 251 | 97 | 83 | 80 | 59 | 59 | 0 | 103 | 59 | 0 |
N.S. |
1 | 0.39 | 0.33 | 0.32 | 0.24 | 0.24 | 0.00 | 0.41 | 0.24 | 0.00 |
time (sec) |
N/A | 0.238 | 1.029 | 1.766 | 0.034 | 0.071 | 0.000 | 0.121 | 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 | 249 | 95 | 83 | 80 | 59 | 59 | 0 | 107 | 59 | 0 |
N.S. |
1 | 0.38 | 0.33 | 0.32 | 0.24 | 0.24 | 0.00 | 0.43 | 0.24 | 0.00 |
time (sec) |
N/A | 0.239 | 1.031 | 2.497 | 0.034 | 0.071 | 0.000 | 0.144 | 0.175 | 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 | 251 | 97 | 83 | 80 | 59 | 59 | 0 | 106 | 59 | 0 |
N.S. |
1 | 0.39 | 0.33 | 0.32 | 0.24 | 0.24 | 0.00 | 0.42 | 0.24 | 0.00 |
time (sec) |
N/A | 0.241 | 1.031 | 3.093 | 0.038 | 0.077 | 0.000 | 0.135 | 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 | 248 | 94 | 83 | 80 | 59 | 59 | 0 | 107 | 59 | 0 |
N.S. |
1 | 0.38 | 0.33 | 0.32 | 0.24 | 0.24 | 0.00 | 0.43 | 0.24 | 0.00 |
time (sec) |
N/A | 0.242 | 1.026 | 5.523 | 0.033 | 0.067 | 0.000 | 0.130 | 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 | 169 | 81 | 67 | 64 | 95 | 45 | 0 | 79 | 73 | 0 |
N.S. |
1 | 0.48 | 0.40 | 0.38 | 0.56 | 0.27 | 0.00 | 0.47 | 0.43 | 0.00 |
time (sec) |
N/A | 0.237 | 1.036 | 0.122 | 0.034 | 0.068 | 0.000 | 0.115 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 68 | 167 | 47 | 36 | 33 | 0 | 59 | 61 | 0 |
N.S. |
1 | 0.54 | 1.31 | 0.37 | 0.28 | 0.26 | 0.00 | 0.46 | 0.48 | 0.00 |
time (sec) |
N/A | 0.222 | 0.575 | 0.128 | 0.035 | 0.067 | 0.000 | 0.124 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 74 | 113 | 34 | 42 | 22 | 0 | 33 | 48 | 64 |
N.S. |
1 | 0.99 | 1.51 | 0.45 | 0.56 | 0.29 | 0.00 | 0.44 | 0.64 | 0.85 |
time (sec) |
N/A | 0.215 | 0.499 | 0.102 | 0.035 | 0.067 | 0.000 | 0.124 | 0.175 | 19.846 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 51 | 22 | 15 | 13 | 0 | 22 | 37 | 33 |
N.S. |
1 | 1.00 | 1.16 | 0.50 | 0.34 | 0.30 | 0.00 | 0.50 | 0.84 | 0.75 |
time (sec) |
N/A | 0.178 | 0.186 | 0.098 | 0.034 | 0.067 | 0.000 | 0.145 | 0.171 | 19.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 55 | 134 | 31 | 43 | 18 | 0 | 32 | 45 | 48 |
N.S. |
1 | 0.69 | 1.68 | 0.39 | 0.54 | 0.22 | 0.00 | 0.40 | 0.56 | 0.60 |
time (sec) |
N/A | 0.191 | 0.285 | 0.105 | 0.036 | 0.071 | 0.000 | 0.112 | 0.173 | 20.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 65 | 175 | 44 | 73 | 33 | 0 | 50 | 61 | 75 |
N.S. |
1 | 0.52 | 1.40 | 0.35 | 0.58 | 0.26 | 0.00 | 0.40 | 0.49 | 0.60 |
time (sec) |
N/A | 0.223 | 0.307 | 0.108 | 0.037 | 0.085 | 0.000 | 0.130 | 0.178 | 20.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 79 | 162 | 58 | 104 | 45 | 0 | 65 | 78 | 0 |
N.S. |
1 | 0.48 | 0.98 | 0.35 | 0.63 | 0.27 | 0.00 | 0.39 | 0.47 | 0.00 |
time (sec) |
N/A | 0.239 | 0.589 | 0.119 | 0.040 | 0.080 | 0.000 | 0.125 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 93 | 192 | 71 | 135 | 58 | 0 | 78 | 89 | 0 |
N.S. |
1 | 0.45 | 0.92 | 0.34 | 0.65 | 0.28 | 0.00 | 0.38 | 0.43 | 0.00 |
time (sec) |
N/A | 0.248 | 0.738 | 0.144 | 0.051 | 0.069 | 0.000 | 0.118 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 162 | 140 | 86 | 122 | 108 | 0 | 169 | 88 | 0 |
N.S. |
1 | 0.58 | 0.51 | 0.31 | 0.44 | 0.39 | 0.00 | 0.61 | 0.32 | 0.00 |
time (sec) |
N/A | 0.317 | 1.079 | 3.038 | 0.130 | 0.075 | 0.000 | 0.124 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 163 | 131 | 77 | 109 | 123 | 0 | 146 | 81 | 0 |
N.S. |
1 | 0.68 | 0.55 | 0.32 | 0.45 | 0.51 | 0.00 | 0.61 | 0.34 | 0.00 |
time (sec) |
N/A | 0.344 | 1.043 | 2.164 | 0.120 | 0.089 | 0.000 | 0.135 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 153 | 128 | 74 | 106 | 106 | 0 | 143 | 78 | 0 |
N.S. |
1 | 0.65 | 0.54 | 0.31 | 0.45 | 0.45 | 0.00 | 0.61 | 0.33 | 0.00 |
time (sec) |
N/A | 0.333 | 1.047 | 1.808 | 0.129 | 0.080 | 0.000 | 0.132 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 146 | 109 | 47 | 98 | 304 | 0 | 124 | 65 | 0 |
N.S. |
1 | 0.72 | 0.54 | 0.23 | 0.49 | 1.50 | 0.00 | 0.61 | 0.32 | 0.00 |
time (sec) |
N/A | 0.309 | 1.031 | 1.277 | 0.131 | 0.116 | 0.000 | 0.145 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 143 | 109 | 47 | 98 | 299 | 0 | 122 | 67 | 0 |
N.S. |
1 | 0.71 | 0.54 | 0.23 | 0.49 | 1.48 | 0.00 | 0.60 | 0.33 | 0.00 |
time (sec) |
N/A | 0.320 | 1.029 | 1.076 | 0.118 | 0.093 | 0.000 | 0.116 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 161 | 133 | 93 | 106 | 103 | 0 | 131 | 84 | 0 |
N.S. |
1 | 0.68 | 0.56 | 0.39 | 0.45 | 0.43 | 0.00 | 0.55 | 0.35 | 0.00 |
time (sec) |
N/A | 0.364 | 1.037 | 1.538 | 0.122 | 0.076 | 0.000 | 0.140 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 158 | 140 | 94 | 106 | 143 | 0 | 125 | 96 | 0 |
N.S. |
1 | 0.65 | 0.58 | 0.39 | 0.44 | 0.59 | 0.00 | 0.51 | 0.40 | 0.00 |
time (sec) |
N/A | 0.341 | 1.042 | 1.862 | 0.118 | 0.075 | 0.000 | 0.133 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 178 | 151 | 105 | 119 | 129 | 0 | 137 | 107 | 0 |
N.S. |
1 | 0.64 | 0.54 | 0.38 | 0.43 | 0.46 | 0.00 | 0.49 | 0.38 | 0.00 |
time (sec) |
N/A | 0.365 | 1.049 | 2.621 | 0.126 | 0.077 | 0.000 | 0.121 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 105 | 93 | 77 | 145 | 103 | 0 | 116 | 201 | 0 |
N.S. |
1 | 0.54 | 0.47 | 0.39 | 0.74 | 0.53 | 0.00 | 0.59 | 1.03 | 0.00 |
time (sec) |
N/A | 0.268 | 1.044 | 0.148 | 0.041 | 0.066 | 0.000 | 0.134 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 91 | 81 | 65 | 114 | 91 | 0 | 92 | 187 | 0 |
N.S. |
1 | 0.59 | 0.53 | 0.42 | 0.74 | 0.59 | 0.00 | 0.60 | 1.21 | 0.00 |
time (sec) |
N/A | 0.250 | 1.042 | 0.106 | 0.044 | 0.072 | 0.000 | 0.129 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 80 | 192 | 54 | 55 | 69 | 0 | 62 | 170 | 0 |
N.S. |
1 | 0.69 | 1.66 | 0.47 | 0.47 | 0.59 | 0.00 | 0.53 | 1.47 | 0.00 |
time (sec) |
N/A | 0.241 | 0.756 | 0.100 | 0.036 | 0.072 | 0.000 | 0.145 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 71 | 119 | 31 | 43 | 36 | 0 | 32 | 28 | 42 |
N.S. |
1 | 1.73 | 2.90 | 0.76 | 1.05 | 0.88 | 0.00 | 0.78 | 0.68 | 1.02 |
time (sec) |
N/A | 0.212 | 0.502 | 0.090 | 0.037 | 0.070 | 0.000 | 0.122 | 0.167 | 20.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 143 | 23 | 16 | 26 | 0 | 24 | 25 | 34 |
N.S. |
1 | 1.00 | 3.76 | 0.61 | 0.42 | 0.68 | 0.00 | 0.63 | 0.66 | 0.89 |
time (sec) |
N/A | 0.181 | 0.555 | 0.084 | 0.039 | 0.066 | 0.000 | 0.132 | 0.176 | 20.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 84 | 74 | 70 | 88 | 90 | 0 | 87 | 198 | 0 |
N.S. |
1 | 0.57 | 0.50 | 0.48 | 0.60 | 0.61 | 0.00 | 0.59 | 1.35 | 0.00 |
time (sec) |
N/A | 0.242 | 1.042 | 0.112 | 0.036 | 0.071 | 0.000 | 0.136 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 98 | 97 | 92 | 117 | 119 | 0 | 120 | 228 | 0 |
N.S. |
1 | 0.52 | 0.52 | 0.49 | 0.62 | 0.63 | 0.00 | 0.64 | 1.21 | 0.00 |
time (sec) |
N/A | 0.263 | 1.038 | 0.115 | 0.036 | 0.070 | 0.000 | 0.135 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 117 | 111 | 104 | 148 | 134 | 0 | 109 | 245 | 0 |
N.S. |
1 | 0.51 | 0.48 | 0.45 | 0.64 | 0.58 | 0.00 | 0.47 | 1.06 | 0.00 |
time (sec) |
N/A | 0.280 | 1.046 | 0.126 | 0.043 | 0.073 | 0.000 | 0.119 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 193 | 235 | 85 | 137 | 503 | 0 | 177 | 278 | 0 |
N.S. |
1 | 0.70 | 0.85 | 0.31 | 0.50 | 1.83 | 0.00 | 0.64 | 1.01 | 0.00 |
time (sec) |
N/A | 0.384 | 1.125 | 2.983 | 0.128 | 0.087 | 0.000 | 0.141 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 200 | 235 | 89 | 149 | 512 | 0 | 185 | 265 | 0 |
N.S. |
1 | 0.71 | 0.84 | 0.32 | 0.53 | 1.83 | 0.00 | 0.66 | 0.95 | 0.00 |
time (sec) |
N/A | 0.377 | 1.103 | 2.203 | 0.114 | 0.088 | 0.000 | 0.144 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 191 | 235 | 87 | 146 | 503 | 0 | 176 | 278 | 0 |
N.S. |
1 | 0.69 | 0.85 | 0.32 | 0.53 | 1.82 | 0.00 | 0.64 | 1.01 | 0.00 |
time (sec) |
N/A | 0.373 | 1.070 | 1.861 | 0.118 | 0.087 | 0.000 | 0.142 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 200 | 237 | 90 | 147 | 514 | 0 | 176 | 267 | 0 |
N.S. |
1 | 0.72 | 0.86 | 0.32 | 0.53 | 1.86 | 0.00 | 0.64 | 0.96 | 0.00 |
time (sec) |
N/A | 0.378 | 1.079 | 1.268 | 0.113 | 0.092 | 0.000 | 0.115 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 207 | 235 | 88 | 145 | 499 | 0 | 177 | 278 | 0 |
N.S. |
1 | 0.76 | 0.86 | 0.32 | 0.53 | 1.83 | 0.00 | 0.65 | 1.02 | 0.00 |
time (sec) |
N/A | 0.392 | 1.074 | 1.080 | 0.121 | 0.110 | 0.000 | 0.146 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 316 | 215 | 260 | 115 | 148 | 201 | 0 | 201 | 290 | 0 |
N.S. |
1 | 0.68 | 0.82 | 0.36 | 0.47 | 0.64 | 0.00 | 0.64 | 0.92 | 0.00 |
time (sec) |
N/A | 0.414 | 1.091 | 1.561 | 0.121 | 0.081 | 0.000 | 0.148 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 212 | 266 | 116 | 150 | 242 | 0 | 184 | 309 | 0 |
N.S. |
1 | 0.68 | 0.85 | 0.37 | 0.48 | 0.77 | 0.00 | 0.59 | 0.98 | 0.00 |
time (sec) |
N/A | 0.413 | 1.102 | 1.832 | 0.127 | 0.079 | 0.000 | 0.120 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 86 | 206 | 42 | 53 | 69 | 0 | 43 | 68 | 53 |
N.S. |
1 | 0.72 | 1.73 | 0.35 | 0.45 | 0.58 | 0.00 | 0.36 | 0.57 | 0.45 |
time (sec) |
N/A | 0.239 | 0.970 | 0.099 | 0.038 | 0.067 | 0.000 | 0.120 | 0.182 | 18.720 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 73 | 232 | 31 | 43 | 58 | 0 | 32 | 57 | 42 |
N.S. |
1 | 1.06 | 3.36 | 0.45 | 0.62 | 0.84 | 0.00 | 0.46 | 0.83 | 0.61 |
time (sec) |
N/A | 0.213 | 0.911 | 0.100 | 0.037 | 0.068 | 0.000 | 0.128 | 0.174 | 19.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 267 | 23 | 16 | 48 | 0 | 24 | 47 | 34 |
N.S. |
1 | 1.00 | 7.03 | 0.61 | 0.42 | 1.26 | 0.00 | 0.63 | 1.24 | 0.89 |
time (sec) |
N/A | 0.184 | 0.924 | 0.092 | 0.052 | 0.068 | 0.000 | 0.112 | 0.188 | 18.842 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 116 | 96 | 92 | 132 | 178 | 0 | 109 | 372 | 0 |
N.S. |
1 | 0.52 | 0.43 | 0.41 | 0.59 | 0.80 | 0.00 | 0.49 | 1.67 | 0.00 |
time (sec) |
N/A | 0.272 | 1.057 | 0.122 | 0.054 | 0.069 | 0.000 | 0.143 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 132 | 119 | 114 | 163 | 207 | 0 | 143 | 404 | 0 |
N.S. |
1 | 0.49 | 0.44 | 0.42 | 0.61 | 0.77 | 0.00 | 0.53 | 1.50 | 0.00 |
time (sec) |
N/A | 0.297 | 1.059 | 0.138 | 0.050 | 0.070 | 0.000 | 0.117 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 254 | 226 | 107 | 197 | 734 | 0 | 207 | 481 | 0 |
N.S. |
1 | 0.70 | 0.62 | 0.29 | 0.54 | 2.01 | 0.00 | 0.57 | 1.32 | 0.00 |
time (sec) |
N/A | 0.448 | 1.162 | 4.622 | 0.140 | 0.083 | 0.000 | 0.141 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 243 | 218 | 105 | 195 | 723 | 0 | 205 | 492 | 0 |
N.S. |
1 | 0.68 | 0.61 | 0.29 | 0.54 | 2.01 | 0.00 | 0.57 | 1.37 | 0.00 |
time (sec) |
N/A | 0.434 | 1.154 | 3.004 | 0.136 | 0.089 | 0.000 | 0.147 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 368 | 254 | 229 | 109 | 195 | 734 | 0 | 207 | 481 | 0 |
N.S. |
1 | 0.69 | 0.62 | 0.30 | 0.53 | 1.99 | 0.00 | 0.56 | 1.31 | 0.00 |
time (sec) |
N/A | 0.443 | 1.191 | 2.218 | 0.150 | 0.084 | 0.000 | 0.127 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 241 | 221 | 107 | 193 | 723 | 0 | 199 | 492 | 0 |
N.S. |
1 | 0.67 | 0.61 | 0.30 | 0.54 | 2.01 | 0.00 | 0.55 | 1.37 | 0.00 |
time (sec) |
N/A | 0.423 | 1.162 | 1.787 | 0.133 | 0.087 | 0.000 | 0.140 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 254 | 219 | 112 | 191 | 734 | 0 | 198 | 481 | 0 |
N.S. |
1 | 0.71 | 0.61 | 0.31 | 0.53 | 2.04 | 0.00 | 0.55 | 1.34 | 0.00 |
time (sec) |
N/A | 0.442 | 1.139 | 1.257 | 0.125 | 0.083 | 0.000 | 0.146 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 269 | 211 | 110 | 189 | 719 | 0 | 199 | 492 | 0 |
N.S. |
1 | 0.77 | 0.60 | 0.31 | 0.54 | 2.05 | 0.00 | 0.57 | 1.40 | 0.00 |
time (sec) |
N/A | 0.466 | 1.148 | 1.043 | 0.122 | 0.090 | 0.000 | 0.126 | 0.181 | 0.000 |