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 | 17 | 17 | 17 | 16 | 15 | 15 | 14 | 15 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.82 | 0.88 | 1.00 | 0.88 |
time (sec) |
N/A | 0.318 | 0.048 | 0.050 | 0.031 | 0.071 | 0.055 | 0.113 | 0.166 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 11 | 10 | 10 | 8 | 10 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 1.00 | 0.83 |
time (sec) |
N/A | 0.278 | 0.025 | 0.029 | 0.033 | 0.073 | 0.036 | 0.132 | 0.155 | 0.102 |
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 | 27 | 22 | 20 | 19 | 21 | 26 | 19 | 20 | 19 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.70 | 0.78 | 0.96 | 0.70 | 0.74 | 0.70 |
time (sec) |
N/A | 0.268 | 0.056 | 0.182 | 0.027 | 0.074 | 0.086 | 0.113 | 0.158 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 7 | 5 | 4 | 16 | 8 | 6 | 8 | 6 |
N.S. |
1 | 1.00 | 1.40 | 1.00 | 0.80 | 3.20 | 1.60 | 1.20 | 1.60 | 1.20 |
time (sec) |
N/A | 0.297 | 0.010 | 0.180 | 0.026 | 0.080 | 0.312 | 0.129 | 0.166 | 0.027 |
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 | 21 | 24 | 24 | 18 | 16 | 24 | 17 | 19 | 27 | 19 |
N.S. |
1 | 1.14 | 1.14 | 0.86 | 0.76 | 1.14 | 0.81 | 0.90 | 1.29 | 0.90 |
time (sec) |
N/A | 0.291 | 0.035 | 0.030 | 0.028 | 0.079 | 0.043 | 0.131 | 0.166 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 22 | 20 | 19 | 21 | 24 | 19 | 20 | 19 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.70 | 0.78 | 0.89 | 0.70 | 0.74 | 0.70 |
time (sec) |
N/A | 0.270 | 0.085 | 0.266 | 0.028 | 0.071 | 0.088 | 0.114 | 0.163 | 0.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 28 | 39 | 52 | 0 | 41 | 89 | 78 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.15 | 1.53 | 0.00 | 1.21 | 2.62 | 2.29 |
time (sec) |
N/A | 0.437 | 0.026 | 0.529 | 0.033 | 0.114 | 0.000 | 0.119 | 0.161 | 1.175 |
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 | 26 | 20 | 18 | 16 | 18 | 14 | 16 | 25 | 10 |
N.S. |
1 | 1.00 | 0.77 | 0.69 | 0.62 | 0.69 | 0.54 | 0.62 | 0.96 | 0.38 |
time (sec) |
N/A | 0.291 | 0.086 | 0.062 | 0.031 | 0.074 | 0.041 | 0.132 | 0.159 | 0.034 |
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 | 15 | 10 | 14 | 13 | 13 | 12 | 13 | 15 | 13 |
N.S. |
1 | 1.00 | 0.67 | 0.93 | 0.87 | 0.87 | 0.80 | 0.87 | 1.00 | 0.87 |
time (sec) |
N/A | 0.307 | 0.040 | 0.041 | 0.027 | 0.070 | 0.053 | 0.105 | 0.167 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 22 | 15 | 17 | 14 | 22 | 17 | 15 | 14 |
N.S. |
1 | 1.00 | 0.81 | 0.56 | 0.63 | 0.52 | 0.81 | 0.63 | 0.56 | 0.52 |
time (sec) |
N/A | 0.291 | 0.037 | 0.036 | 0.031 | 0.070 | 0.399 | 0.112 | 0.158 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 22 | 15 | 17 | 14 | 22 | 17 | 15 | 14 |
N.S. |
1 | 1.00 | 0.81 | 0.56 | 0.63 | 0.52 | 0.81 | 0.63 | 0.56 | 0.52 |
time (sec) |
N/A | 0.291 | 0.039 | 0.033 | 0.033 | 0.073 | 0.510 | 0.138 | 0.165 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 56 | 50 | 48 | 62 | 58 | 49 | 57 | 49 |
N.S. |
1 | 1.00 | 0.90 | 0.81 | 0.77 | 1.00 | 0.94 | 0.79 | 0.92 | 0.79 |
time (sec) |
N/A | 0.369 | 0.226 | 0.110 | 0.105 | 0.076 | 0.877 | 0.135 | 0.162 | 0.468 |
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 | 19 | 12 | 12 | 19 | 11 | 10 | 11 | 12 | 11 |
N.S. |
1 | 1.00 | 0.63 | 0.63 | 1.00 | 0.58 | 0.53 | 0.58 | 0.63 | 0.58 |
time (sec) |
N/A | 0.332 | 0.037 | 0.035 | 0.028 | 0.100 | 0.033 | 0.119 | 0.162 | 0.111 |
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 | 32 | 32 | 19 | 16 | 28 | 16 | 15 | 16 | 17 | 16 |
N.S. |
1 | 1.00 | 0.59 | 0.50 | 0.88 | 0.50 | 0.47 | 0.50 | 0.53 | 0.50 |
time (sec) |
N/A | 0.352 | 0.040 | 0.035 | 0.033 | 0.066 | 0.035 | 0.132 | 0.164 | 0.113 |
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 | 11 | 0 | 11 | 11 | 10 | 10 | 8 | 10 | 11 | 10 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.91 | 0.91 | 0.73 | 0.91 | 1.00 | 0.91 |
time (sec) |
N/A | 0.000 | 0.050 | 0.159 | 0.080 | 0.076 | 0.158 | 0.111 | 0.155 | 0.156 |
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 | 9 | 9 | 9 | 7 | 6 | 6 | 5 | 6 | 7 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.67 | 0.67 | 0.56 | 0.67 | 0.78 | 0.67 |
time (sec) |
N/A | 0.261 | 0.010 | 0.049 | 0.029 | 0.074 | 0.043 | 0.110 | 0.161 | 0.021 |
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 | 9 | 0 | 9 | 15 | 9 | 18 | 12 | 16 | 9 | 9 |
N.S. |
1 | 0.00 | 1.00 | 1.67 | 1.00 | 2.00 | 1.33 | 1.78 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.025 | 0.062 | 0.073 | 0.091 | 0.075 | 0.149 | 0.162 | 0.186 |
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 | 28 | 26 | 22 | 21 | 21 | 22 | 21 | 23 | 21 |
N.S. |
1 | 1.12 | 1.04 | 0.88 | 0.84 | 0.84 | 0.88 | 0.84 | 0.92 | 0.84 |
time (sec) |
N/A | 0.287 | 0.027 | 0.068 | 0.026 | 0.070 | 0.044 | 0.132 | 0.154 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 43 | 40 | 34 | 33 | 33 | 37 | 33 | 36 | 33 |
N.S. |
1 | 1.08 | 1.00 | 0.85 | 0.82 | 0.82 | 0.92 | 0.82 | 0.90 | 0.82 |
time (sec) |
N/A | 0.302 | 0.035 | 0.122 | 0.027 | 0.091 | 0.053 | 0.129 | 0.162 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 56 | 53 | 46 | 45 | 45 | 51 | 45 | 49 | 45 |
N.S. |
1 | 1.06 | 1.00 | 0.87 | 0.85 | 0.85 | 0.96 | 0.85 | 0.92 | 0.85 |
time (sec) |
N/A | 0.320 | 0.037 | 0.237 | 0.026 | 0.068 | 0.062 | 0.136 | 0.169 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 26 | 45 | 80 | 60 | 29 | 16 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 1.41 | 2.50 | 1.88 | 0.91 | 0.50 | 0.78 |
time (sec) |
N/A | 0.293 | 0.064 | 0.060 | 0.112 | 0.078 | 0.593 | 0.120 | 0.167 | 0.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 28 | 27 | 85 | 58 | 27 | 18 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.79 | 2.50 | 1.71 | 0.79 | 0.53 | 0.91 |
time (sec) |
N/A | 0.296 | 0.064 | 0.053 | 0.117 | 0.076 | 0.617 | 0.137 | 0.169 | 0.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 51 | 50 | 42 | 63 | 107 | 78 | 44 | 14 | 43 |
N.S. |
1 | 0.96 | 0.94 | 0.79 | 1.19 | 2.02 | 1.47 | 0.83 | 0.26 | 0.81 |
time (sec) |
N/A | 0.303 | 0.071 | 0.033 | 0.111 | 0.077 | 0.985 | 0.116 | 0.161 | 0.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 55 | 54 | 46 | 47 | 115 | 75 | 45 | 16 | 47 |
N.S. |
1 | 0.96 | 0.95 | 0.81 | 0.82 | 2.02 | 1.32 | 0.79 | 0.28 | 0.82 |
time (sec) |
N/A | 0.308 | 0.067 | 0.037 | 0.116 | 0.073 | 0.855 | 0.135 | 0.155 | 0.135 |
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 | 27 | 20 | 18 | 17 | 21 | 24 | 17 | 20 | 19 |
N.S. |
1 | 1.00 | 0.74 | 0.67 | 0.63 | 0.78 | 0.89 | 0.63 | 0.74 | 0.70 |
time (sec) |
N/A | 0.272 | 0.050 | 0.165 | 0.031 | 0.078 | 0.090 | 0.115 | 0.157 | 0.100 |
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 | 10 | 10 | 10 | 9 | 8 | 8 | 19 | 8 | 10 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 1.90 | 0.80 | 1.00 | 0.80 |
time (sec) |
N/A | 0.262 | 0.034 | 0.033 | 0.108 | 0.075 | 0.051 | 0.114 | 0.158 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 18 | 17 | 17 | 19 | 18 | 20 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.80 | 1.70 | 1.70 | 1.90 | 1.80 | 2.00 | 1.70 |
time (sec) |
N/A | 0.261 | 0.047 | 0.034 | 0.026 | 0.074 | 0.052 | 0.126 | 0.156 | 0.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 10 | 14 | 21 | 15 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 0.56 | 0.78 | 1.17 | 0.83 | 0.00 |
time (sec) |
N/A | 0.272 | 3.813 | 0.029 | 0.031 | 0.069 | 0.767 | 0.110 | 0.170 | 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 | 47 | 47 | 19 | 18 | 26 | 42 | 17 | 33 | 25 | 17 |
N.S. |
1 | 1.00 | 0.40 | 0.38 | 0.55 | 0.89 | 0.36 | 0.70 | 0.53 | 0.36 |
time (sec) |
N/A | 0.359 | 0.078 | 0.042 | 0.107 | 0.074 | 0.058 | 0.145 | 0.162 | 0.288 |
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 | 44 | 54 | 24 | 21 | 21 | 21 | 20 | 21 | 22 | 21 |
N.S. |
1 | 1.23 | 0.55 | 0.48 | 0.48 | 0.48 | 0.45 | 0.48 | 0.50 | 0.48 |
time (sec) |
N/A | 0.391 | 0.023 | 0.037 | 0.031 | 0.071 | 0.034 | 0.130 | 0.163 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 57 | 26 | 23 | 30 | 23 | 24 | 23 | 27 | 23 |
N.S. |
1 | 1.10 | 0.50 | 0.44 | 0.58 | 0.44 | 0.46 | 0.44 | 0.52 | 0.44 |
time (sec) |
N/A | 0.411 | 0.038 | 0.044 | 0.031 | 0.064 | 0.036 | 0.123 | 0.157 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 45 | 23 | 22 | 35 | 24 | 22 | 43 | 22 |
N.S. |
1 | 1.00 | 1.36 | 0.70 | 0.67 | 1.06 | 0.73 | 0.67 | 1.30 | 0.67 |
time (sec) |
N/A | 0.284 | 0.100 | 0.037 | 0.106 | 0.080 | 0.321 | 0.139 | 0.161 | 0.132 |
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 | 50 | 54 | 33 | 39 | 37 | 32 | 36 | 53 | 35 | 32 |
N.S. |
1 | 1.08 | 0.66 | 0.78 | 0.74 | 0.64 | 0.72 | 1.06 | 0.70 | 0.64 |
time (sec) |
N/A | 0.321 | 0.055 | 0.025 | 0.033 | 0.070 | 0.699 | 0.127 | 0.157 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 48 | 62 | 61 | 50 | 61 | 75 | 61 | 38 |
N.S. |
1 | 1.00 | 0.59 | 0.77 | 0.75 | 0.62 | 0.75 | 0.93 | 0.75 | 0.47 |
time (sec) |
N/A | 0.362 | 0.067 | 0.056 | 0.032 | 0.073 | 6.508 | 0.134 | 0.159 | 0.109 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 46 | 54 | 45 | 44 | 44 | 49 | 44 | 49 | 44 |
N.S. |
1 | 0.84 | 0.98 | 0.82 | 0.80 | 0.80 | 0.89 | 0.80 | 0.89 | 0.80 |
time (sec) |
N/A | 0.451 | 0.054 | 0.622 | 0.033 | 0.070 | 0.061 | 0.126 | 0.158 | 0.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 55 | 27 | 26 | 43 | 26 | 26 | 54 | 26 |
N.S. |
1 | 1.00 | 1.57 | 0.77 | 0.74 | 1.23 | 0.74 | 0.74 | 1.54 | 0.74 |
time (sec) |
N/A | 0.521 | 0.116 | 0.087 | 0.107 | 0.077 | 15.408 | 0.120 | 0.166 | 0.148 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 24 | 29 | 24 | 23 | 23 | 24 | 23 | 27 | 24 |
N.S. |
1 | 0.75 | 0.91 | 0.75 | 0.72 | 0.72 | 0.75 | 0.72 | 0.84 | 0.75 |
time (sec) |
N/A | 0.602 | 0.094 | 0.161 | 0.033 | 0.072 | 0.062 | 0.137 | 0.162 | 0.127 |
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 | 5 | 5 | 5 | 4 | 3 | 3 | 3 | 3 | 5 | 3 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.60 | 0.60 | 0.60 | 0.60 | 1.00 | 0.60 |
time (sec) |
N/A | 0.253 | 0.008 | 0.021 | 0.032 | 0.073 | 0.236 | 0.145 | 0.169 | 0.017 |
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 | 7 | 7 | 7 | 5 | 4 | 4 | 5 | 0 | 7 | 4 |
N.S. |
1 | 1.00 | 1.00 | 0.71 | 0.57 | 0.57 | 0.71 | 0.00 | 1.00 | 0.57 |
time (sec) |
N/A | 0.308 | 0.018 | 0.032 | 0.027 | 0.066 | 0.393 | 0.000 | 0.163 | 0.025 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 25 | 23 | 17 | 16 | 19 | 17 | 24 | 24 | 8 |
N.S. |
1 | 1.14 | 1.05 | 0.77 | 0.73 | 0.86 | 0.77 | 1.09 | 1.09 | 0.36 |
time (sec) |
N/A | 0.297 | 0.036 | 0.066 | 0.032 | 0.067 | 0.039 | 0.140 | 0.163 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4 | 4 | 4 | 4 | 7 | 3 | 15 | 3 | 4 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.75 | 0.75 | 3.75 | 0.75 | 1.00 | 0.75 |
time (sec) |
N/A | 0.243 | 0.005 | 0.021 | 0.110 | 0.095 | 0.042 | 0.138 | 0.157 | 0.011 |
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 | 13 | 13 | 11 | 10 | 10 | 10 | 10 | 17 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.77 | 0.77 | 0.77 | 0.77 | 1.31 | 0.92 |
time (sec) |
N/A | 0.253 | 0.024 | 0.031 | 0.033 | 0.080 | 0.028 | 0.130 | 0.153 | 0.039 |
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 | 6 | 6 | 6 | 6 | 19 | 15 | 15 | 16 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 3.17 | 2.50 | 2.50 | 2.67 | 2.83 | 2.50 |
time (sec) |
N/A | 0.246 | 0.002 | 0.025 | 0.027 | 0.070 | 0.046 | 0.127 | 0.161 | 0.031 |
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 | 15 | 11 | 11 | 10 | 10 | 10 | 10 | 18 | 12 |
N.S. |
1 | 1.00 | 0.73 | 0.73 | 0.67 | 0.67 | 0.67 | 0.67 | 1.20 | 0.80 |
time (sec) |
N/A | 0.256 | 0.054 | 0.033 | 0.028 | 0.062 | 0.028 | 0.107 | 0.161 | 0.125 |
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 | 22 | 22 | 23 | 18 | 21 | 18 | 15 | 17 | 21 | 17 |
N.S. |
1 | 1.00 | 1.05 | 0.82 | 0.95 | 0.82 | 0.68 | 0.77 | 0.95 | 0.77 |
time (sec) |
N/A | 0.316 | 0.056 | 0.092 | 0.031 | 0.068 | 0.044 | 0.119 | 0.160 | 0.031 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 27 | 30 | 23 | 24 | 25 | 26 | 30 | 31 | 22 |
N.S. |
1 | 0.87 | 0.97 | 0.74 | 0.77 | 0.81 | 0.84 | 0.97 | 1.00 | 0.71 |
time (sec) |
N/A | 0.316 | 0.051 | 0.159 | 0.039 | 0.070 | 0.056 | 0.139 | 0.161 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 21 | 23 | 22 | 21 | 29 | 0 | 34 | 21 |
N.S. |
1 | 0.95 | 0.95 | 1.05 | 1.00 | 0.95 | 1.32 | 0.00 | 1.55 | 0.95 |
time (sec) |
N/A | 0.303 | 0.123 | 0.075 | 0.103 | 0.073 | 0.123 | 0.000 | 0.149 | 0.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 26 | 23 | 39 | 40 | 25 | 39 | 0 | 44 | 0 |
N.S. |
1 | 0.76 | 0.68 | 1.15 | 1.18 | 0.74 | 1.15 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.310 | 0.143 | 0.052 | 0.104 | 0.075 | 0.145 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 0 | 0 | 28 | 0 | 0 | 42 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.22 | 0.00 | 0.00 | 1.83 | 1.17 |
time (sec) |
N/A | 0.306 | 0.371 | 0.000 | 0.000 | 0.072 | 0.000 | 0.000 | 0.153 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 41 | 51 | 74 | 35 | 54 | 35 | 39 | 50 |
N.S. |
1 | 1.00 | 0.62 | 0.77 | 1.12 | 0.53 | 0.82 | 0.53 | 0.59 | 0.76 |
time (sec) |
N/A | 0.568 | 0.242 | 0.075 | 0.033 | 0.069 | 4.743 | 0.115 | 0.146 | 0.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 20 | 19 | 25 | 20 | 20 | 30 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.67 | 1.58 | 2.08 | 1.67 | 1.67 | 2.50 | 1.58 |
time (sec) |
N/A | 0.262 | 0.050 | 0.035 | 0.028 | 0.073 | 0.050 | 0.128 | 0.162 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 13 | 12 | 0 | 11 | 8 | 54 | 12 | 11 |
N.S. |
1 | 1.00 | 0.81 | 0.75 | 0.00 | 0.69 | 0.50 | 3.38 | 0.75 | 0.69 |
time (sec) |
N/A | 0.355 | 0.081 | 0.065 | 0.000 | 0.068 | 0.049 | 0.129 | 0.159 | 0.130 |
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 | 16 | 16 | 14 | 13 | 13 | 10 | 13 | 15 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.81 | 0.81 | 0.62 | 0.81 | 0.94 | 0.88 |
time (sec) |
N/A | 0.306 | 0.151 | 0.057 | 0.029 | 0.061 | 0.035 | 0.127 | 0.165 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 23 | 74 | 33 | 27 | 33 | 45 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.70 | 2.24 | 1.00 | 0.82 | 1.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.284 | 0.055 | 0.049 | 0.031 | 0.076 | 0.379 | 0.126 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 9 | 8 | 0 | 8 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.73 | 0.00 | 0.73 | 0.73 | 0.73 | 0.73 |
time (sec) |
N/A | 0.304 | 0.030 | 0.057 | 0.028 | 0.000 | 0.069 | 0.131 | 0.147 | 0.154 |
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 | 6 | 6 | 6 | 6 | 5 | 5 | 5 | 5 | 6 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.83 | 1.00 | 0.83 |
time (sec) |
N/A | 0.293 | 0.020 | 0.023 | 0.031 | 0.064 | 0.038 | 0.130 | 0.146 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 17 | 19 | 18 | 14 | 0 | 11 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.00 | 0.95 | 0.74 | 0.00 | 0.58 | 1.11 |
time (sec) |
N/A | 0.276 | 0.030 | 0.031 | 0.051 | 0.094 | 0.147 | 0.000 | 0.147 | 0.104 |
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 | 19 | 19 | 16 | 16 | 36 | 15 | 12 | 20 | 16 | 15 |
N.S. |
1 | 1.00 | 0.84 | 0.84 | 1.89 | 0.79 | 0.63 | 1.05 | 0.84 | 0.79 |
time (sec) |
N/A | 0.442 | 0.134 | 0.050 | 0.052 | 0.071 | 0.036 | 0.135 | 0.153 | 0.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 41 | 60 | 63 | 0 | 97 | 1392 | 59 | 62 |
N.S. |
1 | 1.09 | 0.73 | 1.07 | 1.12 | 0.00 | 1.73 | 24.86 | 1.05 | 1.11 |
time (sec) |
N/A | 0.405 | 0.140 | 0.174 | 0.034 | 0.000 | 0.066 | 0.136 | 0.149 | 0.195 |
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 | 15 | 12 | 12 | 13 | 13 | 10 | 13 | 11 | 11 |
N.S. |
1 | 1.00 | 0.80 | 0.80 | 0.87 | 0.87 | 0.67 | 0.87 | 0.73 | 0.73 |
time (sec) |
N/A | 0.250 | 0.042 | 0.056 | 0.033 | 0.076 | 0.040 | 0.113 | 0.160 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 12 | 12 | 11 | 10 | 11 | 10 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.86 | 0.79 | 0.71 | 0.79 | 0.71 | 0.79 |
time (sec) |
N/A | 0.249 | 0.006 | 0.055 | 0.026 | 0.070 | 0.059 | 0.135 | 0.163 | 0.123 |
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 | 12 | 11 | 11 | 8 | 11 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 0.73 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.245 | 0.005 | 0.050 | 0.025 | 0.085 | 0.039 | 0.108 | 0.161 | 0.119 |
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 | 20 | 20 | 20 | 17 | 20 | 17 | 17 | 20 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 1.00 | 0.85 | 0.85 | 1.00 | 0.85 | 0.85 |
time (sec) |
N/A | 0.245 | 0.021 | 0.062 | 0.024 | 0.067 | 0.059 | 0.130 | 0.159 | 0.122 |
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 | 32 | 32 | 19 | 16 | 34 | 16 | 15 | 16 | 19 | 16 |
N.S. |
1 | 1.00 | 0.59 | 0.50 | 1.06 | 0.50 | 0.47 | 0.50 | 0.59 | 0.50 |
time (sec) |
N/A | 0.325 | 0.092 | 0.053 | 0.031 | 0.065 | 0.036 | 0.110 | 0.158 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 28 | 27 | 40 | 36 | 27 | 45 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.82 | 1.21 | 1.09 | 0.82 | 1.36 | 0.79 |
time (sec) |
N/A | 0.254 | 0.025 | 0.201 | 0.030 | 0.084 | 0.040 | 0.132 | 0.162 | 0.165 |
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 | 21 | 21 | 21 | 12 | 11 | 11 | 10 | 11 | 10 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.57 | 0.52 | 0.52 | 0.48 | 0.52 | 0.48 | 0.52 |
time (sec) |
N/A | 0.251 | 0.005 | 0.066 | 0.026 | 0.070 | 0.058 | 0.132 | 0.160 | 0.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 9 | 8 | 0 | 0 | 0 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.73 | 0.00 | 0.00 | 0.00 | 0.73 | 0.73 |
time (sec) |
N/A | 0.284 | 0.003 | 0.029 | 0.063 | 0.000 | 0.000 | 0.000 | 0.157 | 0.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 10 | 16 | 0 | 0 | 0 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.33 | 0.00 | 0.00 | 0.00 | 0.75 | 0.75 |
time (sec) |
N/A | 0.603 | 0.178 | 0.070 | 0.060 | 0.000 | 0.000 | 0.000 | 0.163 | 0.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 10 | 9 | 0 | 0 | 0 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.75 | 0.00 | 0.00 | 0.00 | 0.75 | 0.75 |
time (sec) |
N/A | 0.434 | 0.014 | 0.033 | 0.061 | 0.000 | 0.000 | 0.000 | 0.162 | 0.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 12 | 14 | 0 | 15 | 14 | 55 | 14 |
N.S. |
1 | 1.00 | 1.12 | 0.75 | 0.88 | 0.00 | 0.94 | 0.88 | 3.44 | 0.88 |
time (sec) |
N/A | 0.583 | 0.257 | 0.000 | 0.059 | 0.000 | 0.776 | 0.157 | 0.168 | 0.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 19 | 21 | 0 | 15 | 21 | 55 | 21 |
N.S. |
1 | 1.00 | 1.08 | 0.73 | 0.81 | 0.00 | 0.58 | 0.81 | 2.12 | 0.81 |
time (sec) |
N/A | 0.424 | 0.024 | 0.000 | 0.061 | 0.000 | 0.233 | 0.156 | 0.167 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 10 | 12 | 0 | 14 | 12 | 55 | 12 |
N.S. |
1 | 1.00 | 1.14 | 0.71 | 0.86 | 0.00 | 1.00 | 0.86 | 3.93 | 0.86 |
time (sec) |
N/A | 0.499 | 0.245 | 0.002 | 0.064 | 0.000 | 0.354 | 0.147 | 0.175 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 16 | 23 | 0 | 0 | 0 | 63 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.15 | 0.00 | 0.00 | 0.00 | 3.15 | 0.75 |
time (sec) |
N/A | 0.973 | 1.211 | 0.105 | 0.074 | 0.000 | 0.000 | 0.000 | 0.168 | 0.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 16 | 18 | 0 | 19 | 18 | 21 | 18 |
N.S. |
1 | 1.00 | 1.10 | 0.80 | 0.90 | 0.00 | 0.95 | 0.90 | 1.05 | 0.90 |
time (sec) |
N/A | 0.601 | 0.678 | 0.000 | 0.067 | 0.000 | 0.470 | 0.134 | 0.155 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 9 | 8 | 0 | 12 | 8 | 27 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.69 | 0.62 | 0.00 | 0.92 | 0.62 | 2.08 | 0.62 |
time (sec) |
N/A | 0.313 | 0.029 | 0.025 | 0.025 | 0.000 | 0.092 | 0.117 | 0.153 | 0.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 9 | 8 | 0 | 0 | 0 | 27 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.69 | 0.62 | 0.00 | 0.00 | 0.00 | 2.08 | 0.62 |
time (sec) |
N/A | 0.329 | 0.003 | 0.039 | 0.060 | 0.000 | 0.000 | 0.000 | 0.164 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 13 | 8 | 10 | 0 | 10 | 10 | 11 | 10 |
N.S. |
1 | 1.00 | 1.18 | 0.73 | 0.91 | 0.00 | 0.91 | 0.91 | 1.00 | 0.91 |
time (sec) |
N/A | 0.387 | 0.081 | 0.000 | 0.055 | 0.000 | 0.237 | 0.136 | 0.160 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 10 | 16 | 0 | 0 | 0 | 45 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.33 | 0.00 | 0.00 | 0.00 | 3.75 | 0.75 |
time (sec) |
N/A | 0.790 | 0.188 | 0.042 | 0.063 | 0.000 | 0.000 | 0.000 | 0.169 | 0.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 10 | 16 | 0 | 0 | 0 | 45 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.33 | 0.00 | 0.00 | 0.00 | 3.75 | 0.75 |
time (sec) |
N/A | 0.442 | 0.016 | 0.046 | 0.071 | 0.000 | 0.000 | 0.000 | 0.177 | 0.146 |
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 | 31 | 34 | 31 | 23 | 24 | 27 | 22 | 28 | 31 | 22 |
N.S. |
1 | 1.10 | 1.00 | 0.74 | 0.77 | 0.87 | 0.71 | 0.90 | 1.00 | 0.71 |
time (sec) |
N/A | 0.368 | 0.036 | 0.161 | 0.032 | 0.073 | 0.055 | 0.124 | 0.158 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 11 | 8 | 10 | 10 | 7 | 10 | 19 | 10 |
N.S. |
1 | 1.00 | 1.22 | 0.89 | 1.11 | 1.11 | 0.78 | 1.11 | 2.11 | 1.11 |
time (sec) |
N/A | 0.310 | 5.719 | 0.005 | 0.055 | 0.068 | 0.209 | 0.127 | 0.164 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 15 | 10 | 12 | 0 | 12 | 12 | 19 | 12 |
N.S. |
1 | 1.00 | 1.15 | 0.77 | 0.92 | 0.00 | 0.92 | 0.92 | 1.46 | 0.92 |
time (sec) |
N/A | 0.352 | 0.107 | 0.004 | 0.059 | 0.000 | 0.240 | 0.127 | 0.154 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 13 | 9 | 14 | 11 | 8 | 11 | 18 | 11 |
N.S. |
1 | 1.00 | 1.18 | 0.82 | 1.27 | 1.00 | 0.73 | 1.00 | 1.64 | 1.00 |
time (sec) |
N/A | 0.318 | 0.025 | 0.003 | 0.061 | 0.065 | 0.210 | 0.105 | 0.156 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 15 | 11 | 18 | 13 | 10 | 13 | 24 | 13 |
N.S. |
1 | 1.00 | 1.15 | 0.85 | 1.38 | 1.00 | 0.77 | 1.00 | 1.85 | 1.00 |
time (sec) |
N/A | 0.334 | 0.104 | 0.004 | 0.073 | 0.070 | 0.249 | 0.144 | 0.156 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 11 | 9 | 11 | 11 | 8 | 11 | 11 | 11 |
N.S. |
1 | 1.00 | 1.22 | 1.00 | 1.22 | 1.22 | 0.89 | 1.22 | 1.22 | 1.22 |
time (sec) |
N/A | 0.356 | 0.078 | 0.003 | 0.052 | 0.061 | 0.200 | 0.107 | 0.155 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 13 | 11 | 13 | 13 | 10 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.18 | 1.00 | 1.18 | 1.18 | 0.91 | 1.18 | 1.18 | 1.18 |
time (sec) |
N/A | 0.390 | 0.089 | 0.003 | 0.053 | 0.064 | 0.244 | 0.122 | 0.156 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 11 | 9 | 11 | 20 | 10 | 11 | 11 | 11 |
N.S. |
1 | 1.00 | 1.22 | 1.00 | 1.22 | 2.22 | 1.11 | 1.22 | 1.22 | 1.22 |
time (sec) |
N/A | 0.377 | 0.031 | 0.003 | 0.050 | 0.070 | 0.397 | 0.110 | 0.161 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 13 | 11 | 13 | 22 | 12 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.18 | 1.00 | 1.18 | 2.00 | 1.09 | 1.18 | 1.18 | 1.18 |
time (sec) |
N/A | 0.419 | 0.033 | 0.004 | 0.052 | 0.067 | 0.476 | 0.130 | 0.152 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 37 | 58 | 46 | 78 | 46 | 37 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.61 | 1.28 | 2.17 | 1.28 | 1.03 | 0.00 |
time (sec) |
N/A | 0.472 | 0.122 | 0.488 | 0.075 | 0.076 | 0.388 | 0.226 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 241 | 36 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.00 | 6.51 | 0.97 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.378 | 0.027 | 0.059 | 0.083 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 50 | 298 | 50 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.00 | 5.96 | 1.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.372 | 0.036 | 0.283 | 0.129 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 219 | 38 | 0 | 105 | 0 | 11 | 58 |
N.S. |
1 | 1.00 | 1.00 | 5.92 | 1.03 | 0.00 | 2.84 | 0.00 | 0.30 | 1.57 |
time (sec) |
N/A | 0.280 | 0.013 | 0.085 | 0.083 | 0.000 | 0.704 | 0.000 | 0.161 | 0.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 267 | 42 | 0 | 0 | 0 | 11 | 71 |
N.S. |
1 | 1.00 | 1.00 | 6.51 | 1.02 | 0.00 | 0.00 | 0.00 | 0.27 | 1.73 |
time (sec) |
N/A | 0.279 | 0.013 | 0.141 | 0.089 | 0.000 | 0.000 | 0.000 | 0.169 | 0.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 52 | 0 | 0 | 0 | 0 | 0 | 19 | 77 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 1.48 |
time (sec) |
N/A | 0.310 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.284 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 56 | 0 | 0 | 0 | 0 | 0 | 19 | 94 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 1.68 |
time (sec) |
N/A | 0.305 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 74 | 0 | 0 | 89 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 1.11 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.360 | 0.318 | 0.000 | 0.000 | 0.073 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | F(-2) | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 0 | 21 | 0 | 0 | 0 | 49 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 1.24 | 0.00 | 0.00 | 0.00 | 2.88 | 0.82 |
time (sec) |
N/A | 1.182 | 0.769 | 0.000 | 0.058 | 0.000 | 0.000 | 0.000 | 0.157 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | F | F | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 0 | 16 | 21 | 18 | 0 | 0 | 64 | 18 |
N.S. |
1 | 0.00 | 0.00 | 0.89 | 1.17 | 1.00 | 0.00 | 0.00 | 3.56 | 1.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.106 | 0.073 | 0.093 | 0.000 | 0.000 | 0.167 | 0.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 11 | 10 | 13 | 27 | 76 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.91 | 1.18 | 2.45 | 6.91 | 1.00 | 0.91 |
time (sec) |
N/A | 0.398 | 0.005 | 0.234 | 0.034 | 0.069 | 2.598 | 0.122 | 0.158 | 1.277 |
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 | 20 | 20 | 20 | 20 | 20 | 21 | 0 | 21 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.00 | 1.05 | 0.00 | 1.05 | 0.95 | 0.95 |
time (sec) |
N/A | 0.528 | 0.004 | 2.811 | 0.035 | 0.077 | 0.000 | 0.137 | 0.155 | 4.188 |