A grade: { 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35 }
B grade: { 21 }
C grade: { }
A grade: { 2, 3, 5, 7, 9, 10, 11, 12, 13, 15, 16, 17, 18, 22, 23, 24, 27, 28, 29, 30, 31, 32, 34, 35 }
B grade: { 8, 14, 19, 20, 33 }
C grade: { 1, 4, 6, 21, 25, 26 }
F grade: { }
A grade: { 1, 3, 4, 5, 10, 12, 20, 21, 22, 23, 25, 27, 30, 32, 33, 35 }
B grade: { 2, 11, 17, 19, 24, 26 }
F grade: { 9, 15, 16, 18, 28, 29, 31, 34 }
A grade: { 1, 3, 5, 7, 8, 10, 11, 12, 19, 20, 22, 33, 34 }
B grade: { 23 }
C grade: { 4 }
F grade: { 2, 6, 9, 13, 14, 15, 16, 17, 18, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 35 }
A grade: { 1, 2, 3, 4, 5, 9, 12, 15, 16, 17, 18, 19, 22 }
B grade: { 6, 10, 11, 13, 14, 20, 21, 23, 24, 26, 33 }
C grade: { }
F grade: { 7, 8, 25, 27, 28, 29, 30, 31, 32, 34, 35 }
C grade: { }
F grade: { 2, 4, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35 }
A grade: { 1, 3, 5, 6, 10, 11, 12, 21, 22, 23 }
B grade: { 2, 17, 19, 20, 24, 26 }
C grade: { 4 }
F grade: { 7, 8, 9, 13, 14, 15, 16, 18, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35 }
A grade: { }
B grade: { 1, 2, 3, 5, 6, 21, 22, 23, 26 }
C grade: { }
F grade: { 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35 }
Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)
Problem 1 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | A | A | A | B | A | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 77 | 21 | 20 | 25 | 61 | 18 | 16 |
normalized size | 1 | 1.00 | 3.50 | 0.95 | 0.91 | 1.14 | 2.77 | 0.82 | 0.73 |
time (sec) | N/A | 0.135 | 0.069 | 0.077 | 1.119 | 0.410 | 6.726 | 0.176 | 0.141 |
Problem 2 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | A | F | B | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 24 | 50 | 0 | 44 | 0 | 147 | 49 |
normalized size | 1 | 1.00 | 0.75 | 1.56 | 0.00 | 1.38 | 0.00 | 4.59 | 1.53 |
time (sec) | N/A | 0.156 | 0.024 | 0.014 | 0.000 | 0.411 | 0.000 | 0.243 | 0.622 |
Problem 3 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | A | A | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 16 | 16 | 23 | 20 | 14 | 15 | 14 |
normalized size | 1 | 1.00 | 0.64 | 0.64 | 0.92 | 0.80 | 0.56 | 0.60 | 0.56 |
time (sec) | N/A | 0.014 | 0.012 | 0.019 | 0.527 | 0.407 | 0.378 | 0.170 | 0.163 |
Problem 4 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 68 | 42 | 112 | 46 | 0 | 43 | -1 |
normalized size | 1 | 1.00 | 1.17 | 0.72 | 1.93 | 0.79 | 0.00 | 0.74 | -0.02 |
time (sec) | N/A | 0.082 | 0.022 | 0.021 | 1.378 | 0.446 | 0.000 | 0.175 | 0.000 |
Problem 5 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | B | A | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 26 | 42 | 56 | 67 | 838 | 32 | 88 |
normalized size | 1 | 1.00 | 0.52 | 0.84 | 1.12 | 1.34 | 16.76 | 0.64 | 1.76 |
time (sec) | N/A | 0.026 | 0.044 | 0.130 | 0.494 | 0.411 | 5.674 | 0.168 | 0.269 |
Problem 6 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | C | F | B | A | A | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 334 | 334 | 30 | 36 | 0 | 1058 | 26 | 248 | 313 |
normalized size | 1 | 1.00 | 0.09 | 0.11 | 0.00 | 3.17 | 0.08 | 0.74 | 0.94 |
time (sec) | N/A | 0.347 | 0.006 | 0.033 | 0.000 | 0.445 | 2.810 | 0.197 | 0.262 |
Problem 7 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | F | A | C | A | F(-2) | F | F | F |
verified | N/A | N/A | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 0 | 430 | 171 | 366 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 1.48 | 0.59 | 1.26 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.049 | 1.110 | 0.170 | 1.299 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 8 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | F | B | C | A | F(-2) | F | F | F |
verified | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 0 | 654 | 198 | 378 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 2.12 | 0.64 | 1.23 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.043 | 0.600 | 0.016 | 1.280 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 9 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | A | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 84 | 0 | 0 | 66 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.059 | 0.046 | 0.041 | 0.000 | 0.416 | 0.000 | 0.000 | 0.000 |
Problem 10 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | B | A | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 34 | 51 | 101 | 112 | 51 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.83 | 1.24 | 2.46 | 2.73 | 1.24 | -0.02 |
time (sec) | N/A | 0.193 | 0.066 | 0.005 | 1.424 | 0.410 | 21.078 | 0.186 | 0.000 |
Problem 11 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | A | B | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 71 | 175 | 63 | 112 | 0 | 67 | -1 |
normalized size | 1 | 1.00 | 0.97 | 2.40 | 0.86 | 1.53 | 0.00 | 0.92 | -0.01 |
time (sec) | N/A | 0.108 | 0.069 | 0.174 | 1.296 | 0.407 | 0.000 | 0.811 | 0.000 |
Problem 12 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 52 | 60 | 77 | 110 | 0 | 79 | -1 |
normalized size | 1 | 1.00 | 0.71 | 0.82 | 1.05 | 1.51 | 0.00 | 1.08 | -0.01 |
time (sec) | N/A | 0.271 | 0.083 | 0.009 | 1.471 | 0.408 | 0.000 | 0.715 | 0.000 |
Problem 13 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | C | F | B | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 365 | 357 | 109 | 0 | 5235 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 0.30 | 0.00 | 14.34 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.859 | 0.493 | 0.045 | 0.000 | 8.433 | 0.000 | 0.000 | 0.000 |
Problem 14 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | C | F | B | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 337 | 337 | 2581 | 105 | 0 | 4535 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 7.66 | 0.31 | 0.00 | 13.46 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.621 | 6.376 | 0.020 | 0.000 | 4.999 | 0.000 | 0.000 | 0.000 |
Problem 15 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | A | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 74 | 0 | 0 | 56 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.73 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.071 | 0.042 | 0.087 | 0.000 | 0.854 | 0.000 | 0.000 | 0.000 |
Problem 16 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | A | F | F(-2) | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 112 | 0 | 0 | 73 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.62 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.191 | 0.087 | 0.221 | 0.000 | 1.215 | 0.000 | 0.000 | 0.000 |
Problem 17 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | A | F | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 85 | 298 | 0 | 81 | 0 | 188 | -1 |
normalized size | 1 | 1.00 | 1.02 | 3.59 | 0.00 | 0.98 | 0.00 | 2.27 | -0.01 |
time (sec) | N/A | 0.100 | 0.045 | 0.015 | 0.000 | 2.797 | 0.000 | 0.679 | 0.000 |
Problem 18 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | A | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 98 | 0 | 0 | 122 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.02 | 0.00 | 0.00 | 1.27 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.084 | 0.202 | 0.057 | 0.000 | 2.856 | 0.000 | 0.000 | 0.000 |
Problem 19 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | A | A | A | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 112 | 49 | 36 | 34 | 65 | 75 | -1 |
normalized size | 1 | 1.00 | 4.48 | 1.96 | 1.44 | 1.36 | 2.60 | 3.00 | -0.04 |
time (sec) | N/A | 0.075 | 0.130 | 0.031 | 1.211 | 0.394 | 3.975 | 0.249 | 0.000 |
Problem 20 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | A | A | B | F | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 126 | 33 | 35 | 55 | 0 | 74 | -1 |
normalized size | 1 | 1.00 | 5.04 | 1.32 | 1.40 | 2.20 | 0.00 | 2.96 | -0.04 |
time (sec) | N/A | 0.051 | 0.116 | 0.120 | 1.087 | 0.432 | 0.000 | 0.246 | 0.000 |
Problem 21 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | B | C | A | F(-1) | B | F | A | B |
verified | N/A | NO | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 786 | 478 | 95 | 0 | 219 | 0 | 104 | 307 |
normalized size | 1 | 7.28 | 4.43 | 0.88 | 0.00 | 2.03 | 0.00 | 0.96 | 2.84 |
time (sec) | N/A | 1.117 | 6.357 | 0.141 | 0.000 | 0.561 | 0.000 | 0.204 | 1.247 |
Problem 22 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | B | A | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 56 | 27 | 40 | 46 | 66 | 30 | 26 |
normalized size | 1 | 1.00 | 1.93 | 0.93 | 1.38 | 1.59 | 2.28 | 1.03 | 0.90 |
time (sec) | N/A | 0.020 | 0.042 | 0.084 | 0.434 | 0.444 | 0.692 | 0.179 | 0.278 |
Problem 23 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | B | B | F | A | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 20 | 43 | 68 | 0 | 21 | 19 |
normalized size | 1 | 1.00 | 1.00 | 0.77 | 1.65 | 2.62 | 0.00 | 0.81 | 0.73 |
time (sec) | N/A | 0.013 | 0.019 | 0.052 | 0.977 | 0.415 | 0.000 | 0.217 | 0.162 |
Problem 24 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | B | F | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 147 | 121 | 366 | 0 | 859 | 0 | 377 | -1 |
normalized size | 1 | 1.34 | 1.10 | 3.33 | 0.00 | 7.81 | 0.00 | 3.43 | -0.01 |
time (sec) | N/A | 0.607 | 0.134 | 0.180 | 0.000 | 0.461 | 0.000 | 0.591 | 0.000 |
Problem 25 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | A | F | F | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 54 | 75 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.35 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) | N/A | 0.081 | 1.930 | 0.161 | 0.000 | 0.471 | 0.000 | 0.000 | 0.000 |
Problem 26 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | B | F | B | B |
verified | N/A | NO | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 349 | 910 | 392 | 0 | 452 | 0 | 301 | 608 |
normalized size | 1 | 1.89 | 4.92 | 2.12 | 0.00 | 2.44 | 0.00 | 1.63 | 3.29 |
time (sec) | N/A | 0.976 | 0.580 | 0.211 | 0.000 | 0.471 | 0.000 | 0.386 | 2.183 |
Problem 27 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | F | F | F(-1) | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 102 | 83 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.146 | 0.019 | 0.065 | 0.000 | 0.416 | 0.000 | 0.000 | 0.000 |
Problem 28 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 122 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.203 | 0.095 | 4.107 | 0.000 | 0.411 | 0.000 | 0.000 | 0.000 |
Problem 29 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | F | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 395 | 395 | 347 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.537 | 0.248 | 6.564 | 0.000 | 0.427 | 0.000 | 0.000 | 0.000 |
Problem 30 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | F | F | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 981 | 981 | 868 | 730 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.88 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.252 | 0.557 | 0.094 | 0.000 | 0.417 | 0.000 | 0.000 | 0.000 |
Problem 31 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 555 | 555 | 1076 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.712 | 1.576 | 0.113 | 0.000 | 0.416 | 0.000 | 0.000 | 0.000 |
Problem 32 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | F | F | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 313 | 303 | 252 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.377 | 0.105 | 0.025 | 0.000 | 0.424 | 0.000 | 0.000 | 0.000 |
Problem 33 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | A | A | B | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 262 | 113 | 84 | 220 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.28 | 1.41 | 1.05 | 2.75 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.083 | 0.256 | 0.172 | 1.009 | 0.454 | 0.000 | 0.000 | 0.000 |
Problem 34 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | A | F | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 44 | 0 | 31 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.77 | 0.00 | 0.54 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) | N/A | 0.076 | 0.059 | 0.592 | 1.151 | 0.435 | 0.000 | 0.000 | 0.000 |
Problem 35 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 131 | 171 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.08 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.109 | 0.218 | 0.382 | 0.000 | 0.436 | 0.000 | 0.000 | 0.000 |
The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [29] had the largest ratio of [1.154]
# | grade |
|
|
|
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) | |||||||||||
1 | A | 1 | 1 | 1.00 | 12 | 0.083 | |||||||||||
2 | A | 4 | 3 | 1.00 | 19 | 0.158 | |||||||||||
3 | A | 2 | 2 | 1.00 | 6 | 0.333 | |||||||||||
4 | A | 5 | 5 | 1.00 | 10 | 0.500 | |||||||||||
5 | A | 3 | 2 | 1.00 | 7 | 0.286 | |||||||||||
6 | A | 22 | 9 | 1.00 | 8 | 1.125 | |||||||||||
7 | F | 0 | 0 | N/A | 0 | N/A | |||||||||||
8 | F | 0 | 0 | N/A | 0 | N/A | |||||||||||
9 | A | 4 | 3 | 1.00 | 19 | 0.158 | |||||||||||
10 | A | 6 | 3 | 1.00 | 25 | 0.120 | |||||||||||
11 | A | 5 | 2 | 1.00 | 19 | 0.105 | |||||||||||
12 | A | 6 | 3 | 1.00 | 21 | 0.143 | |||||||||||
13 | A | 20 | 8 | 1.00 | 28 | 0.286 | |||||||||||
14 | A | 22 | 9 | 1.00 | 21 | 0.429 | |||||||||||
15 | A | 2 | 1 | 1.00 | 27 | 0.037 | |||||||||||
16 | A | 3 | 2 | 1.00 | 36 | 0.056 | |||||||||||
17 | A | 7 | 5 | 1.00 | 17 | 0.294 | |||||||||||
18 | A | 7 | 5 | 1.00 | 17 | 0.294 | |||||||||||
19 | A | 6 | 6 | 1.00 | 25 | 0.240 | |||||||||||
20 | A | 7 | 7 | 1.00 | 14 | 0.500 | |||||||||||
21 | B | 45 | 7 | 7.28 | 9 | 0.778 | |||||||||||
22 | A | 3 | 3 | 1.00 | 8 | 0.375 | |||||||||||
23 | A | 2 | 2 | 1.00 | 10 | 0.200 | |||||||||||
24 | A | 11 | 7 | 1.34 | 16 | 0.438 | |||||||||||
25 | A | 5 | 5 | 1.00 | 11 | 0.454 | |||||||||||
26 | A | 31 | 12 | 1.89 | 16 | 0.750 | |||||||||||
27 | A | 12 | 10 | 1.00 | 16 | 0.625 | |||||||||||
28 | A | 13 | 12 | 1.00 | 12 | 1.000 | |||||||||||
29 | A | 28 | 15 | 1.00 | 13 | 1.154 | |||||||||||
30 | A | 44 | 10 | 1.00 | 18 | 0.556 | |||||||||||
31 | A | 35 | 16 | 1.00 | 18 | 0.889 | |||||||||||
32 | A | 21 | 7 | 1.00 | 14 | 0.500 | |||||||||||
33 | A | 7 | 4 | 1.00 | 5 | 0.800 | |||||||||||
34 | A | 5 | 5 | 1.00 | 8 | 0.625 | |||||||||||
35 | A | 10 | 7 | 1.00 | 14 | 0.500 | |||||||||||