A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34 }
B grade: { }
C grade: { }
F grade: { }
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34 }
B grade: { }
C grade: { }
F grade: { }
A grade: { 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34 }
B grade: { }
C grade: { }
A grade: { 4, 9, 14, 15, 19, 23, 27, 28, 31, 34 }
B grade: { }
C grade: { 1, 2, 3, 6, 7, 8, 11, 12, 13, 16, 17, 18, 20, 21, 22, 24, 25, 26, 29, 30, 32, 33 }
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34 }
B grade: { }
C grade: { }
F grade: { }
A grade: { 3, 4, 8, 9, 13, 14, 15, 18, 19, 22, 23, 26, 27, 28, 31, 34 }
C grade: { }
F grade: { 1, 2, 5, 6, 7, 10, 11, 16, 17, 20, 21, 24, 29, 30, 32, 33 }
A grade: { 4, 9, 14, 15, 19, 23, 27, 28, 31, 34 }
B grade: { }
C grade: { 1, 2, 3, 6, 7, 8, 11, 12, 13, 16, 17, 18, 20, 21, 22, 24, 25, 26, 29, 30, 32, 33 }
A grade: { 4, 9, 14, 15, 19, 23, 27, 28, 31, 34 }
C grade: { }
F grade: { 1, 2, 5, 6, 7, 10, 16, 17, 18, 20, 21, 22, 24, 25, 26, 29, 30, 32, 33 }
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 | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 249 | 160 | 204 | 1556 | 173 | 0 | 225 | -1 |
normalized size | 1 | 1.00 | 0.64 | 0.82 | 6.25 | 0.69 | 0.00 | 0.90 | -0.00 |
time (sec) | N/A | 0.252 | 0.702 | 0.029 | 3.799 | 1.431 | 0.000 | 0.464 | 0.000 |
Problem 2 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 112 | 99 | 578 | 119 | 0 | 181 | -1 |
normalized size | 1 | 1.00 | 0.91 | 0.80 | 4.70 | 0.97 | 0.00 | 1.47 | -0.01 |
time (sec) | N/A | 0.041 | 0.302 | 0.024 | 2.652 | 0.995 | 0.000 | 0.619 | 0.000 |
Problem 3 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | A | C | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 85 | 81 | 112 | 103 | 88 | 135 | 99 |
normalized size | 1 | 1.00 | 0.87 | 0.83 | 1.14 | 1.05 | 0.90 | 1.38 | 1.01 |
time (sec) | N/A | 0.028 | 0.172 | 0.027 | 0.695 | 1.163 | 0.497 | 0.519 | 0.058 |
Problem 4 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.06 |
time (sec) | N/A | 0.009 | 3.695 | 0.126 | 0.000 | 0.843 | 0.000 | 0.000 | 0.000 |
Problem 5 | 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 | 111 | 111 | 110 | 0 | 0 | 115 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 0.00 | 0.00 | 1.04 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.094 | 3.347 | 0.325 | 0.000 | 1.276 | 0.000 | 0.000 | 0.000 |
Problem 6 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 251 | 164 | 202 | 1556 | 178 | 0 | 227 | -1 |
normalized size | 1 | 1.00 | 0.65 | 0.80 | 6.20 | 0.71 | 0.00 | 0.90 | -0.00 |
time (sec) | N/A | 0.218 | 0.713 | 0.023 | 4.554 | 1.315 | 0.000 | 0.511 | 0.000 |
Problem 7 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 116 | 98 | 578 | 125 | 0 | 183 | -1 |
normalized size | 1 | 1.00 | 0.94 | 0.79 | 4.66 | 1.01 | 0.00 | 1.48 | -0.01 |
time (sec) | N/A | 0.046 | 0.316 | 0.023 | 2.501 | 0.881 | 0.000 | 0.473 | 0.000 |
Problem 8 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | A | C | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 88 | 79 | 112 | 106 | 94 | 137 | 105 |
normalized size | 1 | 1.00 | 0.89 | 0.80 | 1.13 | 1.07 | 0.95 | 1.38 | 1.06 |
time (sec) | N/A | 0.024 | 0.175 | 0.023 | 0.768 | 1.204 | 0.486 | 0.453 | 0.053 |
Problem 9 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) | N/A | 0.009 | 3.488 | 0.095 | 0.000 | 1.276 | 0.000 | 0.000 | 0.000 |
Problem 10 | 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 | 111 | 111 | 114 | 0 | 0 | 123 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 0.00 | 0.00 | 1.11 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.092 | 4.122 | 0.320 | 0.000 | 0.533 | 0.000 | 0.000 | 0.000 |
Problem 11 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 67 | 59 | 159 | 59 | 0 | 75 | 64 |
normalized size | 1 | 1.00 | 0.82 | 0.72 | 1.94 | 0.72 | 0.00 | 0.91 | 0.78 |
time (sec) | N/A | 0.035 | 0.141 | 0.025 | 1.757 | 1.341 | 0.000 | 0.431 | 0.104 |
Problem 12 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | B | C | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 39 | 30 | 125 | 32 | 155 | 65 | 32 |
normalized size | 1 | 1.00 | 0.95 | 0.73 | 3.05 | 0.78 | 3.78 | 1.59 | 0.78 |
time (sec) | N/A | 0.014 | 0.048 | 0.025 | 1.549 | 0.787 | 1.102 | 0.495 | 0.483 |
Problem 13 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | A | C | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 20 | 70 | 22 | 29 | 39 | 19 |
normalized size | 1 | 1.00 | 1.00 | 0.83 | 2.92 | 0.92 | 1.21 | 1.62 | 0.79 |
time (sec) | N/A | 0.006 | 0.024 | 0.021 | 0.890 | 0.572 | 0.434 | 0.714 | 0.041 |
Problem 14 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.06 |
time (sec) | N/A | 0.009 | 11.043 | 0.123 | 0.000 | 1.252 | 0.000 | 0.000 | 0.000 |
Problem 15 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) | N/A | 0.026 | 12.206 | 0.111 | 0.000 | 0.775 | 0.000 | 0.000 | 0.000 |
Problem 16 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 248 | 170 | 191 | 1603 | 178 | 0 | 212 | -1 |
normalized size | 1 | 1.00 | 0.69 | 0.77 | 6.46 | 0.72 | 0.00 | 0.85 | -0.00 |
time (sec) | N/A | 0.241 | 0.661 | 0.058 | 4.252 | 0.958 | 0.000 | 0.670 | 0.000 |
Problem 17 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 116 | 95 | 608 | 124 | 0 | 170 | -1 |
normalized size | 1 | 1.00 | 0.92 | 0.75 | 4.83 | 0.98 | 0.00 | 1.35 | -0.01 |
time (sec) | N/A | 0.067 | 0.268 | 0.042 | 2.635 | 1.018 | 0.000 | 0.635 | 0.000 |
Problem 18 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | A | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 97 | 72 | 124 | 93 | 83 | 122 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.72 | 1.24 | 0.93 | 0.83 | 1.22 | -0.01 |
time (sec) | N/A | 0.051 | 0.103 | 0.039 | 1.347 | 0.707 | 0.935 | 0.524 | 0.000 |
Problem 19 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) | N/A | 0.029 | 6.397 | 0.170 | 0.000 | 1.748 | 0.000 | 0.000 | 0.000 |
Problem 20 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 248 | 175 | 199 | 1603 | 187 | 0 | 214 | -1 |
normalized size | 1 | 1.00 | 0.71 | 0.80 | 6.46 | 0.75 | 0.00 | 0.86 | -0.00 |
time (sec) | N/A | 0.242 | 0.659 | 0.045 | 5.432 | 0.957 | 0.000 | 0.674 | 0.000 |
Problem 21 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 122 | 99 | 608 | 133 | 0 | 172 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.79 | 4.83 | 1.06 | 0.00 | 1.37 | -0.01 |
time (sec) | N/A | 0.076 | 0.283 | 0.044 | 2.609 | 0.887 | 0.000 | 0.632 | 0.000 |
Problem 22 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | A | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 100 | 76 | 124 | 96 | 88 | 124 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.76 | 1.24 | 0.96 | 0.88 | 1.24 | -0.01 |
time (sec) | N/A | 0.056 | 0.108 | 0.042 | 1.160 | 1.199 | 0.969 | 0.770 | 0.000 |
Problem 23 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) | N/A | 0.029 | 6.689 | 0.170 | 0.000 | 0.899 | 0.000 | 0.000 | 0.000 |
Problem 24 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 77 | 64 | 169 | 57 | 0 | 64 | -1 |
normalized size | 1 | 1.00 | 0.91 | 0.75 | 1.99 | 0.67 | 0.00 | 0.75 | -0.01 |
time (sec) | N/A | 0.070 | 0.148 | 0.046 | 1.758 | 0.808 | 0.000 | 1.351 | 0.000 |
Problem 25 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | B | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 41 | 35 | 137 | 37 | 121 | 54 | -1 |
normalized size | 1 | 1.00 | 0.89 | 0.76 | 2.98 | 0.80 | 2.63 | 1.17 | -0.02 |
time (sec) | N/A | 0.033 | 0.058 | 0.038 | 1.572 | 0.686 | 1.551 | 0.614 | 0.000 |
Problem 26 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | A | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 26 | 20 | 34 | 19 | 22 | 26 | -1 |
normalized size | 1 | 1.00 | 0.96 | 0.74 | 1.26 | 0.70 | 0.81 | 0.96 | -0.04 |
time (sec) | N/A | 0.015 | 0.013 | 0.042 | 1.280 | 0.797 | 0.792 | 0.972 | 0.000 |
Problem 27 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) | N/A | 0.029 | 10.427 | 0.188 | 0.000 | 0.749 | 0.000 | 0.000 | 0.000 |
Problem 28 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.052 | 10.646 | 0.217 | 0.000 | 0.723 | 0.000 | 0.000 | 0.000 |
Problem 29 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 285 | 187 | 396 | 2255 | 230 | 0 | 565 | -1 |
normalized size | 1 | 1.00 | 0.66 | 1.39 | 7.91 | 0.81 | 0.00 | 1.98 | -0.00 |
time (sec) | N/A | 0.274 | 1.266 | 0.035 | 6.331 | 1.044 | 0.000 | 1.229 | 0.000 |
Problem 30 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 129 | 182 | 693 | 136 | 0 | 325 | -1 |
normalized size | 1 | 1.00 | 0.92 | 1.30 | 4.95 | 0.97 | 0.00 | 2.32 | -0.01 |
time (sec) | N/A | 0.058 | 0.561 | 0.026 | 2.776 | 0.833 | 0.000 | 0.495 | 0.000 |
Problem 31 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) | N/A | 0.012 | 6.271 | 0.179 | 0.000 | 0.547 | 0.000 | 0.000 | 0.000 |
Problem 32 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 291 | 215 | 378 | 2344 | 257 | 0 | 536 | -1 |
normalized size | 1 | 1.00 | 0.74 | 1.30 | 8.05 | 0.88 | 0.00 | 1.84 | -0.00 |
time (sec) | N/A | 0.364 | 1.160 | 0.047 | 7.831 | 1.055 | 0.000 | 0.775 | 0.000 |
Problem 33 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 139 | 170 | 735 | 149 | 0 | 304 | -1 |
normalized size | 1 | 1.00 | 0.93 | 1.13 | 4.90 | 0.99 | 0.00 | 2.03 | -0.01 |
time (sec) | N/A | 0.094 | 0.412 | 0.042 | 1.687 | 0.911 | 0.000 | 0.736 | 0.000 |
Problem 34 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) | N/A | 0.040 | 6.589 | 0.303 | 0.000 | 0.838 | 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 [24] had the largest ratio of [.4667]
# | grade |
|
|
|
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) | |||||||||||
1 | A | 8 | 6 | 1.00 | 15 | 0.400 | |||||||||||
2 | A | 4 | 4 | 1.00 | 13 | 0.308 | |||||||||||
3 | A | 3 | 3 | 1.00 | 11 | 0.273 | |||||||||||
4 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
5 | A | 5 | 4 | 1.00 | 32 | 0.125 | |||||||||||
6 | A | 8 | 6 | 1.00 | 16 | 0.375 | |||||||||||
7 | A | 4 | 4 | 1.00 | 14 | 0.286 | |||||||||||
8 | A | 3 | 3 | 1.00 | 12 | 0.250 | |||||||||||
9 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
10 | A | 5 | 4 | 1.00 | 34 | 0.118 | |||||||||||
11 | A | 6 | 6 | 1.00 | 13 | 0.462 | |||||||||||
12 | A | 3 | 3 | 1.00 | 11 | 0.273 | |||||||||||
13 | A | 2 | 2 | 1.00 | 9 | 0.222 | |||||||||||
14 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
15 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
16 | A | 10 | 7 | 1.00 | 17 | 0.412 | |||||||||||
17 | A | 6 | 5 | 1.00 | 15 | 0.333 | |||||||||||
18 | A | 5 | 4 | 1.00 | 13 | 0.308 | |||||||||||
19 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
20 | A | 10 | 7 | 1.00 | 18 | 0.389 | |||||||||||
21 | A | 6 | 5 | 1.00 | 16 | 0.312 | |||||||||||
22 | A | 5 | 4 | 1.00 | 14 | 0.286 | |||||||||||
23 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
24 | A | 8 | 7 | 1.00 | 15 | 0.467 | |||||||||||
25 | A | 5 | 4 | 1.00 | 13 | 0.308 | |||||||||||
26 | A | 4 | 3 | 1.00 | 11 | 0.273 | |||||||||||
27 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
28 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
29 | A | 8 | 6 | 1.00 | 19 | 0.316 | |||||||||||
30 | A | 4 | 4 | 1.00 | 17 | 0.235 | |||||||||||
31 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
32 | A | 10 | 7 | 1.00 | 21 | 0.333 | |||||||||||
33 | A | 6 | 5 | 1.00 | 19 | 0.263 | |||||||||||
34 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||