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Chapter 2
detailed summary tables of results

 2.1 List of integrals sorted by grade for each CAS
  2.1.1 Rubi
  2.1.2 Mathematica
  2.1.3 Maple
  2.1.4 Maxima
  2.1.5 FriCAS
  2.1.6 Sympy
  2.1.7 Giac
  2.1.8 Mupad
 2.2 Detailed conclusion table per each integral for all CAS systems
 2.3 Detailed conclusion table specific for Rubi results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

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, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

B grade: { }

C grade: { 11, 40 }

F grade: { }

2.1.3 Maple

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, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 77, 78, 79, 83, 84, 85, 89, 90, 91, 95, 96, 97, 98, 102, 103, 104, 108, 109, 110, 114, 115, 116, 117, 118, 121, 122, 123, 124, 125, 126, 127, 128, 134, 135 }

B grade: { }

C grade: { 132, 133 }

F grade: { 74, 75, 76, 80, 81, 82, 86, 87, 88, 92, 93, 94, 99, 100, 101, 105, 106, 107, 111, 112, 113, 119, 120, 129, 130, 131, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 21, 22, 24, 26, 33, 35, 37, 49, 50, 58, 59, 65, 66, 72, 73, 79, 85, 91, 97, 98, 104, 110, 116, 117, 118, 121, 122, 123, 124, 125, 126, 127, 128, 134, 135 }

B grade: { }

C grade: { }

F grade: { 6, 17, 18, 20, 23, 25, 27, 28, 29, 30, 31, 32, 34, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 119, 120, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 8, 10, 12, 13, 14, 15, 16, 19, 21, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 58, 59, 65, 66, 72, 73, 117, 118, 121, 122, 128, 134, 135 }

B grade: { 7, 9, 11 }

C grade: { }

F grade: { 6, 17, 18, 20, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 119, 120, 123, 124, 125, 126, 127, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 58, 59, 65, 66, 72, 73, 79, 85, 91, 97, 98, 104, 110, 116, 117, 118, 121, 122, 124, 125, 126, 127, 128, 134, 135 }

B grade: { }

C grade: { }

F grade: { 6, 7, 8, 9, 10, 11, 17, 18, 19, 20, 21, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 119, 120, 123, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

2.1.7 Giac

A grade: { 4, 5, 8, 9, 10, 11, 16, 26, 37, 49, 50, 58, 59, 65, 66, 72, 73, 79, 85, 91, 97, 98, 104, 110, 116, 117, 118, 121, 122, 126, 127, 134, 135 }

B grade: { 7, 19, 21 }

C grade: { }

F grade: { 1, 2, 3, 6, 12, 13, 14, 15, 17, 18, 20, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 119, 120, 123, 124, 125, 128, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

2.1.8 Mupad

A grade: { 49, 50, 58, 59, 65, 66, 72, 73, 79, 85, 91, 97, 98, 104, 110, 116, 117, 118, 121, 122, 123, 124, 125, 126, 127, 128, 134, 135 }

B grade: { 4, 5 }

C grade: { }

F grade: { 1, 2, 3, 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, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 119, 120, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

2.2 Detailed conclusion table per each integral for all CAS systems

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 A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 50 69 68 61 70 0 -1
normalized size 1 1.00 0.69 0.96 0.94 0.85 0.97 0.00 -0.01
time (sec) N/A 0.044 0.036 0.025 0.320 0.419 1.767 0.000 0.000
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 49 58 59 59 61 0 -1
normalized size 1 1.00 0.73 0.87 0.88 0.88 0.91 0.00 -0.01
time (sec) N/A 0.026 0.017 0.021 0.320 0.417 0.882 0.000 0.000
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 41 50 48 52 48 0 -1
normalized size 1 1.00 0.79 0.96 0.92 1.00 0.92 0.00 -0.02
time (sec) N/A 0.035 0.024 0.021 0.343 0.408 0.442 0.000 0.000
Problem 4 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 44 44 40 39 39 48 37 68 36
normalized size 1 1.00 0.91 0.89 0.89 1.09 0.84 1.55 0.82
time (sec) N/A 0.016 0.011 0.020 0.311 0.434 0.196 0.141 1.653
Problem 5 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 25 26 25 37 20 35 23
normalized size 1 1.00 1.00 1.04 1.00 1.48 0.80 1.40 0.92
time (sec) N/A 0.008 0.008 0.018 0.294 0.415 0.131 0.114 0.070
Problem 6 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 43 43 43 94 0 0 0 0 -1
normalized size 1 1.00 1.00 2.19 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.060 0.003 0.171 0.000 0.413 0.000 0.000 0.000
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 30 22 90 0 56 -1
normalized size 1 1.00 1.00 1.11 0.81 3.33 0.00 2.07 -0.04
time (sec) N/A 0.021 0.002 0.022 0.316 0.467 0.000 0.128 0.000
Problem 8 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 33 33 28 37 27 36 0 50 -1
normalized size 1 1.00 0.85 1.12 0.82 1.09 0.00 1.52 -0.03
time (sec) N/A 0.014 0.008 0.024 0.308 0.422 0.000 0.144 0.000
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 51 43 117 0 84 -1
normalized size 1 1.00 1.00 0.94 0.80 2.17 0.00 1.56 -0.02
time (sec) N/A 0.032 0.010 0.020 0.333 0.437 0.000 0.124 0.000
Problem 10 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 56 56 40 56 49 49 0 77 -1
normalized size 1 1.00 0.71 1.00 0.88 0.88 0.00 1.38 -0.02
time (sec) N/A 0.020 0.013 0.022 0.309 0.421 0.000 0.150 0.000
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 49 70 63 129 0 107 -1
normalized size 1 1.00 0.64 0.91 0.82 1.68 0.00 1.39 -0.01
time (sec) N/A 0.045 0.013 0.029 0.297 0.445 0.000 0.125 0.000
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 75 103 99 99 114 0 -1
normalized size 1 1.00 0.64 0.88 0.85 0.85 0.97 0.00 -0.01
time (sec) N/A 0.188 0.068 0.382 0.335 0.421 3.029 0.000 0.000
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 96 96 72 87 109 92 90 0 -1
normalized size 1 1.00 0.75 0.91 1.14 0.96 0.94 0.00 -0.01
time (sec) N/A 0.165 0.047 0.376 0.331 0.409 1.859 0.000 0.000
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 59 72 70 82 76 0 -1
normalized size 1 1.00 0.74 0.90 0.88 1.02 0.95 0.00 -0.01
time (sec) N/A 0.123 0.063 0.375 0.328 0.418 0.864 0.000 0.000
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 53 59 81 73 51 0 -1
normalized size 1 1.00 0.90 1.00 1.37 1.24 0.86 0.00 -0.02
time (sec) N/A 0.092 0.032 0.079 0.341 0.413 0.434 0.000 0.000
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 34 36 32 59 32 62 -1
normalized size 1 1.00 1.00 1.06 0.94 1.74 0.94 1.82 -0.03
time (sec) N/A 0.045 0.015 0.093 0.321 0.411 0.186 0.132 0.000
Problem 17 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 60 60 60 151 0 0 0 0 -1
normalized size 1 1.00 1.00 2.52 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.097 0.006 0.171 0.000 0.406 0.000 0.000 0.000
Problem 18 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 50 50 75 107 0 0 0 0 -1
normalized size 1 1.00 1.50 2.14 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.100 0.213 0.237 0.000 0.463 0.000 0.000 0.000
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 43 67 39 67 0 98 -1
normalized size 1 1.00 1.00 1.56 0.91 1.56 0.00 2.28 -0.02
time (sec) N/A 0.080 0.034 0.360 0.307 0.416 0.000 0.171 0.000
Problem 20 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 99 99 125 144 0 0 0 0 -1
normalized size 1 1.00 1.26 1.45 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.163 0.531 0.478 0.000 0.421 0.000 0.000 0.000
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 64 99 71 85 0 148 -1
normalized size 1 1.00 0.75 1.16 0.84 1.00 0.00 1.74 -0.01
time (sec) N/A 0.138 0.065 0.451 0.313 0.427 0.000 0.251 0.000
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 195 195 120 172 165 151 196 0 -1
normalized size 1 1.00 0.62 0.88 0.85 0.77 1.01 0.00 -0.01
time (sec) N/A 0.366 0.076 0.484 0.346 0.411 5.446 0.000 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 110 141 0 142 160 0 -1
normalized size 1 1.00 0.67 0.87 0.00 0.87 0.98 0.00 -0.01
time (sec) N/A 0.298 0.070 0.382 0.000 0.446 3.154 0.000 0.000
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 93 116 116 124 128 0 -1
normalized size 1 1.00 0.70 0.88 0.88 0.94 0.97 0.00 -0.01
time (sec) N/A 0.221 0.060 0.379 0.330 0.420 1.802 0.000 0.000
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 80 88 0 112 92 0 -1
normalized size 1 1.00 0.82 0.91 0.00 1.15 0.95 0.00 -0.01
time (sec) N/A 0.153 0.048 0.081 0.000 0.407 0.872 0.000 0.000
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 58 55 57 90 54 98 -1
normalized size 1 1.00 1.00 0.95 0.98 1.55 0.93 1.69 -0.02
time (sec) N/A 0.081 0.017 0.099 0.311 0.398 0.427 0.176 0.000
Problem 27 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 83 83 83 204 0 0 0 0 -1
normalized size 1 1.00 1.00 2.46 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.112 0.007 0.161 0.000 0.413 0.000 0.000 0.000
Problem 28 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 84 84 117 162 0 0 0 0 -1
normalized size 1 1.00 1.39 1.93 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.159 0.127 0.231 0.000 0.417 0.000 0.000 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 93 93 80 149 0 0 0 0 -1
normalized size 1 1.00 0.86 1.60 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.168 0.345 0.366 0.000 0.464 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 NO TBD TBD TBD TBD TBD TBD
size 151 151 268 228 0 0 0 0 -1
normalized size 1 1.00 1.77 1.51 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.277 2.250 0.540 0.000 0.427 0.000 0.000 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 159 159 107 210 0 0 0 0 -1
normalized size 1 1.00 0.67 1.32 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.286 0.691 0.467 0.000 0.428 0.000 0.000 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 276 276 165 242 0 208 269 0 -1
normalized size 1 1.00 0.60 0.88 0.00 0.75 0.97 0.00 -0.00
time (sec) N/A 0.856 0.106 0.482 0.000 0.412 15.202 0.000 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 244 244 148 210 201 189 241 0 -1
normalized size 1 1.00 0.61 0.86 0.82 0.77 0.99 0.00 -0.00
time (sec) N/A 0.657 0.091 0.480 0.346 0.425 8.860 0.000 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 194 194 133 172 0 176 190 0 -1
normalized size 1 1.00 0.69 0.89 0.00 0.91 0.98 0.00 -0.01
time (sec) N/A 0.504 0.075 0.385 0.000 0.440 5.557 0.000 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 112 140 143 154 158 0 -1
normalized size 1 1.00 0.69 0.86 0.88 0.95 0.98 0.00 -0.01
time (sec) N/A 0.363 0.075 0.380 0.335 0.425 3.079 0.000 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 94 105 0 138 104 0 -1
normalized size 1 1.00 0.85 0.95 0.00 1.25 0.95 0.00 -0.01
time (sec) N/A 0.239 0.048 0.095 0.000 0.414 1.779 0.000 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 67 65 73 112 65 125 -1
normalized size 1 1.00 1.00 0.97 1.09 1.67 0.97 1.87 -0.01
time (sec) N/A 0.125 0.020 0.095 0.308 0.407 0.829 0.239 0.000
Problem 38 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 97 97 97 257 0 0 0 0 -1
normalized size 1 1.00 1.00 2.65 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.122 0.009 0.159 0.000 0.418 0.000 0.000 0.000
Problem 39 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 120 120 161 217 0 0 0 0 -1
normalized size 1 1.00 1.34 1.81 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.188 0.247 0.235 0.000 0.428 0.000 0.000 0.000
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 113 208 0 0 0 0 -1
normalized size 1 1.00 1.05 1.93 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.207 0.281 0.369 0.000 0.420 0.000 0.000 0.000
Problem 41 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 223 223 355 372 0 0 0 0 -1
normalized size 1 1.00 1.59 1.67 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.393 2.641 0.485 0.000 0.432 0.000 0.000 0.000
Problem 42 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 55 55 40 40 0 0 0 0 -1
normalized size 1 1.00 0.73 0.73 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.100 0.013 0.195 0.000 0.414 0.000 0.000 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 33 33 0 0 0 0 -1
normalized size 1 1.00 0.77 0.77 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.083 0.113 0.191 0.000 0.441 0.000 0.000 0.000
Problem 44 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 41 41 31 31 0 0 0 0 -1
normalized size 1 1.00 0.76 0.76 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.084 0.010 0.164 0.000 0.402 0.000 0.000 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 24 24 0 0 0 0 -1
normalized size 1 1.00 0.83 0.83 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.068 0.077 0.157 0.000 0.402 0.000 0.000 0.000
Problem 46 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 27 27 22 22 0 0 0 0 -1
normalized size 1 1.00 0.81 0.81 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.067 0.007 0.127 0.000 0.416 0.000 0.000 0.000
Problem 47 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 14 14 14 13 0 0 0 0 -1
normalized size 1 1.00 1.00 0.93 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.038 0.022 0.161 0.000 0.396 0.000 0.000 0.000
Problem 48 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 9 9 9 10 0 0 0 0 -1
normalized size 1 1.00 1.00 1.11 0.00 0.00 0.00 0.00 -0.11
time (sec) N/A 0.018 0.009 0.100 0.000 0.398 0.000 0.000 0.000
Problem 49 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 13 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 -0.08
time (sec) N/A 0.014 0.190 0.265 0.000 0.431 0.000 0.000 0.000
Problem 50 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 13 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 -0.08
time (sec) N/A 0.015 0.869 0.364 0.000 0.392 0.000 0.000 0.000
Problem 51 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 82 82 85 104 0 0 0 0 -1
normalized size 1 1.00 1.04 1.27 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.081 0.295 0.208 0.000 0.399 0.000 0.000 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 78 78 0 0 0 0 -1
normalized size 1 1.00 1.11 1.11 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.066 0.042 0.196 0.000 0.397 0.000 0.000 0.000
Problem 53 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 68 68 60 80 0 0 0 0 -1
normalized size 1 1.00 0.88 1.18 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.066 0.213 0.171 0.000 0.386 0.000 0.000 0.000
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 56 54 0 0 0 0 -1
normalized size 1 1.00 1.00 0.96 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.049 0.028 0.155 0.000 0.388 0.000 0.000 0.000
Problem 55 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 54 54 49 56 0 0 0 0 -1
normalized size 1 1.00 0.91 1.04 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.047 0.174 0.137 0.000 0.394 0.000 0.000 0.000
Problem 56 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 37 37 32 28 0 0 0 0 -1
normalized size 1 1.00 0.86 0.76 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.025 0.004 0.165 0.000 0.452 0.000 0.000 0.000
Problem 57 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 34 34 31 30 0 0 0 0 -1
normalized size 1 1.00 0.91 0.88 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.083 0.051 0.093 0.000 0.403 0.000 0.000 0.000
Problem 58 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 13 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 -0.08
time (sec) N/A 0.013 0.786 0.245 0.000 0.409 0.000 0.000 0.000
Problem 59 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 13 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 -0.08
time (sec) N/A 0.014 5.059 0.355 0.000 0.430 0.000 0.000 0.000
Problem 60 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 97 97 102 120 0 0 0 0 -1
normalized size 1 1.00 1.05 1.24 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.354 0.157 0.168 0.000 0.472 0.000 0.000 0.000
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 69 82 0 0 0 0 -1
normalized size 1 1.00 0.84 1.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.304 0.221 0.156 0.000 0.468 0.000 0.000 0.000
Problem 62 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 81 81 64 81 0 0 0 0 -1
normalized size 1 1.00 0.79 1.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.253 0.160 0.138 0.000 0.436 0.000 0.000 0.000
Problem 63 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 63 63 62 43 0 0 0 0 -1
normalized size 1 1.00 0.98 0.68 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.171 0.053 0.168 0.000 0.459 0.000 0.000 0.000
Problem 64 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 50 50 47 42 0 0 0 0 -1
normalized size 1 1.00 0.94 0.84 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.083 0.022 0.092 0.000 0.434 0.000 0.000 0.000
Problem 65 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 13 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 -0.08
time (sec) N/A 0.013 0.564 0.236 0.000 0.413 0.000 0.000 0.000
Problem 66 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 13 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 -0.08
time (sec) N/A 0.014 5.316 0.350 0.000 0.441 0.000 0.000 0.000
Problem 67 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 155 155 156 169 0 0 0 0 -1
normalized size 1 1.00 1.01 1.09 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.320 0.368 0.191 0.000 0.423 0.000 0.000 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 141 141 105 114 0 0 0 0 -1
normalized size 1 1.00 0.74 0.81 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.283 0.422 0.181 0.000 0.433 0.000 0.000 0.000
Problem 69 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 138 138 99 115 0 0 0 0 -1
normalized size 1 1.00 0.72 0.83 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.306 0.330 0.137 0.000 0.421 0.000 0.000 0.000
Problem 70 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 95 95 84 60 0 0 0 0 -1
normalized size 1 1.00 0.88 0.63 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.163 0.132 0.169 0.000 0.421 0.000 0.000 0.000
Problem 71 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 76 76 69 61 0 0 0 0 -1
normalized size 1 1.00 0.91 0.80 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.150 0.063 0.102 0.000 0.434 0.000 0.000 0.000
Problem 72 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 13 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 -0.08
time (sec) N/A 0.013 1.910 0.243 0.000 0.878 0.000 0.000 0.000
Problem 73 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 13 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 -0.08
time (sec) N/A 0.014 9.338 0.367 0.000 0.394 0.000 0.000 0.000
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 182 182 161 0 0 0 0 0 -1
normalized size 1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.324 0.048 180.000 0.000 0.000 0.000 0.000 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 139 139 101 0 0 0 0 0 -1
normalized size 1 1.00 0.73 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.262 0.039 180.000 0.000 0.000 0.000 0.000 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 120 120 101 0 0 0 0 0 -1
normalized size 1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.244 0.037 180.000 0.000 0.000 0.000 0.000 0.000
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 93 93 52 75 0 0 0 0 -1
normalized size 1 1.00 0.56 0.81 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.191 0.035 0.295 0.000 0.000 0.000 0.000 0.000
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 53 53 45 42 0 0 0 0 -1
normalized size 1 1.00 0.85 0.79 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.107 0.053 0.301 0.000 0.000 0.000 0.000 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 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 -0.07
time (sec) N/A 0.014 0.369 0.358 0.000 0.000 0.000 0.000 0.000
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 330 330 152 0 0 0 0 0 -1
normalized size 1 1.00 0.46 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.713 0.130 180.000 0.000 0.000 0.000 0.000 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 199 199 102 0 0 0 0 0 -1
normalized size 1 1.00 0.51 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.487 0.038 180.000 0.000 0.000 0.000 0.000 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 179 179 102 0 0 0 0 0 -1
normalized size 1 1.00 0.57 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.371 0.038 180.000 0.000 0.000 0.000 0.000 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 122 122 52 102 0 0 0 0 -1
normalized size 1 1.00 0.43 0.84 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.219 0.023 0.348 0.000 0.000 0.000 0.000 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 81 81 47 65 0 0 0 0 -1
normalized size 1 1.00 0.58 0.80 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.119 0.030 0.338 0.000 0.000 0.000 0.000 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 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 -0.07
time (sec) N/A 0.015 0.340 0.346 0.000 0.000 0.000 0.000 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 379 379 152 0 0 0 0 0 -1
normalized size 1 1.00 0.40 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.996 0.126 180.000 0.000 0.000 0.000 0.000 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 247 247 101 0 0 0 0 0 -1
normalized size 1 1.00 0.41 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.711 0.039 180.000 0.000 0.000 0.000 0.000 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 210 210 101 0 0 0 0 0 -1
normalized size 1 1.00 0.48 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.551 0.038 180.000 0.000 0.000 0.000 0.000 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 152 152 52 136 0 0 0 0 -1
normalized size 1 1.00 0.34 0.89 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.337 0.036 0.354 0.000 0.000 0.000 0.000 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 94 94 45 78 0 0 0 0 -1
normalized size 1 1.00 0.48 0.83 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.184 0.052 0.339 0.000 0.000 0.000 0.000 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 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 -0.07
time (sec) N/A 0.013 0.343 0.355 0.000 0.000 0.000 0.000 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 163 163 151 0 0 0 0 0 -1
normalized size 1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.204 0.112 180.000 0.000 0.000 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 109 109 99 0 0 0 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.148 0.081 180.000 0.000 0.000 0.000 0.000 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 105 105 99 0 0 0 0 0 -1
normalized size 1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.143 0.077 180.000 0.000 0.000 0.000 0.000 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 63 63 52 37 0 0 0 0 -1
normalized size 1 1.00 0.83 0.59 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.077 0.022 0.206 0.000 0.000 0.000 0.000 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 43 43 47 24 0 0 0 0 -1
normalized size 1 1.00 1.09 0.56 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.047 0.029 0.193 0.000 0.000 0.000 0.000 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 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 -0.07
time (sec) N/A 0.013 0.333 0.352 0.000 0.000 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 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 -0.07
time (sec) N/A 0.015 1.713 0.607 0.000 0.000 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 188 188 216 0 0 0 0 0 -1
normalized size 1 1.00 1.15 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.185 0.306 180.000 0.000 0.000 0.000 0.000 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 138 138 126 0 0 0 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.133 0.041 180.000 0.000 0.000 0.000 0.000 0.000
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 130 130 140 0 0 0 0 0 -1
normalized size 1 1.00 1.08 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.122 0.142 180.000 0.000 0.000 0.000 0.000 0.000
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 84 84 78 80 0 0 0 0 -1
normalized size 1 1.00 0.93 0.95 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.066 0.028 0.359 0.000 0.000 0.000 0.000 0.000
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 64 64 69 65 0 0 0 0 -1
normalized size 1 1.00 1.08 1.02 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.110 0.073 0.355 0.000 0.000 0.000 0.000 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 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 -0.07
time (sec) N/A 0.013 0.419 0.355 0.000 0.000 0.000 0.000 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 223 223 343 0 0 0 0 0 -1
normalized size 1 1.00 1.54 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.584 0.363 180.000 0.000 0.000 0.000 0.000 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 167 167 174 0 0 0 0 0 -1
normalized size 1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.441 0.434 180.000 0.000 0.000 0.000 0.000 0.000
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 161 161 225 0 0 0 0 0 -1
normalized size 1 1.00 1.40 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.372 0.157 180.000 0.000 0.000 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 118 118 98 119 0 0 0 0 -1
normalized size 1 1.00 0.83 1.01 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.223 0.185 0.332 0.000 0.000 0.000 0.000 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 84 84 105 81 0 0 0 0 -1
normalized size 1 1.00 1.25 0.96 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.117 0.107 0.321 0.000 0.000 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 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 -0.07
time (sec) N/A 0.014 0.423 0.358 0.000 0.000 0.000 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 285 285 334 0 0 0 0 0 -1
normalized size 1 1.00 1.17 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.544 0.754 180.000 0.000 0.000 0.000 0.000 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 229 229 210 0 0 0 0 0 -1
normalized size 1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.428 0.735 180.000 0.000 0.000 0.000 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 222 222 221 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.434 0.397 180.000 0.000 0.000 0.000 0.000 0.000
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 147 147 118 147 0 0 0 0 -1
normalized size 1 1.00 0.80 1.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.212 0.346 0.342 0.000 0.000 0.000 0.000 0.000
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 112 112 111 105 0 0 0 0 -1
normalized size 1 1.00 0.99 0.94 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.189 0.200 0.328 0.000 0.000 0.000 0.000 0.000
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 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 -0.07
time (sec) N/A 0.014 0.421 0.350 0.000 0.000 0.000 0.000 0.000
Problem 117 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 54 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 0.110 0.877 1.324 0.000 0.489 0.000 0.000 0.000
Problem 118 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 54 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 0.106 0.787 1.188 0.000 0.434 0.000 0.000 0.000
Problem 119 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 137 137 123 0 0 0 0 0 -1
normalized size 1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.100 0.041 1.206 0.000 0.440 0.000 0.000 0.000
Problem 120 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 60 60 55 0 0 0 0 0 -1
normalized size 1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.020 0.023 1.201 0.000 0.444 0.000 0.000 0.000
Problem 121 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 13 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 -0.08
time (sec) N/A 0.015 0.424 1.011 0.000 0.442 0.000 0.000 0.000
Problem 122 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 13 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 -0.08
time (sec) N/A 0.014 0.447 0.992 0.000 0.407 0.000 0.000 0.000
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) F(-1) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 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 -0.07
time (sec) N/A 0.015 1.118 0.375 0.000 0.000 0.000 0.000 0.000
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 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 -0.07
time (sec) N/A 0.014 1.120 0.243 0.000 0.000 0.000 0.000 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 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 -0.07
time (sec) N/A 0.013 1.414 0.246 0.000 0.000 0.000 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 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 -0.07
time (sec) N/A 0.014 1.287 0.245 0.000 0.000 0.000 0.000 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 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 -0.07
time (sec) N/A 0.015 1.205 0.237 0.000 0.000 0.000 0.000 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 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 -0.07
time (sec) N/A 0.018 0.793 0.155 0.000 0.477 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 173 173 145 0 0 0 0 0 -1
normalized size 1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.216 0.155 180.000 0.000 0.459 0.000 0.000 0.000
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 99 0 0 0 0 0 -1
normalized size 1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.174 0.069 180.000 0.000 0.428 0.000 0.000 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 97 0 0 0 0 0 -1
normalized size 1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.145 0.075 180.000 0.000 0.499 0.000 0.000 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 59 38 0 0 0 0 -1
normalized size 1 1.00 1.00 0.64 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.084 0.017 0.161 0.000 0.422 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 45 40 0 0 0 0 -1
normalized size 1 1.00 0.92 0.82 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.047 0.027 0.142 0.000 0.424 0.000 0.000 0.000
Problem 134 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 13 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 -0.08
time (sec) N/A 0.015 0.289 0.161 0.000 0.419 0.000 0.000 0.000
Problem 135 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 13 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 -0.08
time (sec) N/A 0.016 1.125 0.254 0.000 0.462 0.000 0.000 0.000
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 213 213 215 0 0 0 0 0 -1
normalized size 1 1.00 1.01 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.605 0.420 180.000 0.000 0.000 0.000 0.000 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 145 145 127 0 0 0 0 0 -1
normalized size 1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.432 0.099 0.382 0.000 0.000 0.000 0.000 0.000
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 102 102 101 0 0 0 0 0 -1
normalized size 1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.250 0.241 0.365 0.000 0.000 0.000 0.000 0.000
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 282 282 215 0 0 0 0 0 -1
normalized size 1 1.00 0.76 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.862 0.313 180.000 0.000 0.000 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 179 179 129 0 0 0 0 0 -1
normalized size 1 1.00 0.72 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.478 0.107 0.395 0.000 0.000 0.000 0.000 0.000
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 135 135 251 0 0 0 0 0 -1
normalized size 1 1.00 1.86 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.255 1.110 0.394 0.000 0.000 0.000 0.000 0.000
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 327 327 215 0 0 0 0 0 -1
normalized size 1 1.00 0.66 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.250 0.497 180.000 0.000 0.000 0.000 0.000 0.000
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 223 223 115 0 0 0 0 0 -1
normalized size 1 1.00 0.52 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.751 0.077 0.378 0.000 0.000 0.000 0.000 0.000
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 155 155 282 0 0 0 0 0 -1
normalized size 1 1.00 1.82 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.406 3.646 0.371 0.000 0.000 0.000 0.000 0.000
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 194 194 196 0 0 0 0 0 -1
normalized size 1 1.00 1.01 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.350 0.234 180.000 0.000 0.000 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 107 107 108 0 0 0 0 0 -1
normalized size 1 1.00 1.01 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.179 0.068 0.372 0.000 0.000 0.000 0.000 0.000
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 88 88 101 0 0 0 0 0 -1
normalized size 1 1.00 1.15 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.104 0.103 0.362 0.000 0.000 0.000 0.000 0.000
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 226 226 290 0 0 0 0 0 -1
normalized size 1 1.00 1.28 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.324 0.409 180.000 0.000 0.000 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 135 135 134 0 0 0 0 0 -1
normalized size 1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.162 0.115 0.379 0.000 0.000 0.000 0.000 0.000
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 116 116 137 0 0 0 0 0 -1
normalized size 1 1.00 1.18 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.256 0.246 0.378 0.000 0.000 0.000 0.000 0.000
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 271 271 340 0 0 0 0 0 -1
normalized size 1 1.00 1.25 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.899 1.622 180.000 0.000 0.000 0.000 0.000 0.000
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 183 183 200 0 0 0 0 0 -1
normalized size 1 1.00 1.09 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.517 0.746 0.378 0.000 0.000 0.000 0.000 0.000
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 143 143 181 0 0 0 0 0 -1
normalized size 1 1.00 1.27 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.273 0.602 0.363 0.000 0.000 0.000 0.000 0.000
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 346 346 417 0 0 0 0 0 -1
normalized size 1 1.00 1.21 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.033 1.740 180.000 0.000 0.000 0.000 0.000 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 219 219 208 0 0 0 0 0 -1
normalized size 1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.506 1.220 0.374 0.000 0.000 0.000 0.000 0.000
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 178 178 210 0 0 0 0 0 -1
normalized size 1 1.00 1.18 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.447 0.631 0.372 0.000 0.000 0.000 0.000 0.000

2.3 Detailed conclusion table specific for Rubi results

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 [30] had the largest ratio of [1.000]

Table 2.1:Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 4 3 1.00 8 0.375
2 A 4 3 1.00 8 0.375
3 A 4 3 1.00 8 0.375
4 A 3 3 1.00 6 0.500
5 A 2 2 1.00 4 0.500
6 A 5 5 1.00 8 0.625
7 A 4 4 1.00 8 0.500
8 A 2 2 1.00 8 0.250
9 A 5 5 1.00 8 0.625
10 A 3 3 1.00 8 0.375
11 A 6 5 1.00 8 0.625
12 A 7 5 1.00 10 0.500
13 A 6 4 1.00 10 0.400
14 A 5 5 1.00 10 0.500
15 A 4 4 1.00 8 0.500
16 A 3 3 1.00 6 0.500
17 A 6 6 1.00 10 0.600
18 A 7 5 1.00 10 0.500
19 A 3 3 1.00 10 0.300
20 A 9 7 1.00 10 0.700
21 A 5 5 1.00 10 0.500
22 A 14 7 1.00 10 0.700
23 A 11 5 1.00 10 0.500
24 A 9 7 1.00 10 0.700
25 A 6 5 1.00 8 0.625
26 A 4 3 1.00 6 0.500
27 A 7 7 1.00 10 0.700
28 A 9 6 1.00 10 0.600
29 A 7 7 1.00 10 0.700
30 A 14 10 1.00 10 1.000
31 A 10 9 1.00 10 0.900
32 A 23 4 1.00 10 0.400
33 A 19 6 1.00 10 0.600
34 A 14 4 1.00 10 0.400
35 A 11 6 1.00 10 0.600
36 A 7 4 1.00 8 0.500
37 A 5 3 1.00 6 0.500
38 A 8 7 1.00 10 0.700
39 A 11 7 1.00 10 0.700
40 A 8 8 1.00 10 0.800
41 A 19 10 1.00 10 1.000
42 A 7 3 1.00 10 0.300
43 A 6 3 1.00 10 0.300
44 A 6 3 1.00 10 0.300
45 A 5 3 1.00 10 0.300
46 A 5 3 1.00 10 0.300
47 A 4 4 1.00 8 0.500
48 A 2 2 1.00 6 0.333
49 A 0 0 0.00 0 0.000
50 A 0 0 0.00 0 0.000
51 A 6 2 1.00 10 0.200
52 A 5 2 1.00 10 0.200
53 A 5 2 1.00 10 0.200
54 A 4 2 1.00 10 0.200
55 A 4 2 1.00 10 0.200
56 A 2 2 1.00 8 0.250
57 A 3 3 1.00 6 0.500
58 A 0 0 0.00 0 0.000
59 A 0 0 0.00 0 0.000
60 A 14 5 1.00 10 0.500
61 A 12 6 1.00 10 0.600
62 A 10 6 1.00 10 0.600
63 A 7 7 1.00 8 0.875
64 A 4 4 1.00 6 0.667
65 A 0 0 0.00 0 0.000
66 A 0 0 0.00 0 0.000
67 A 12 4 1.00 10 0.400
68 A 9 4 1.00 10 0.400
69 A 10 6 1.00 10 0.600
70 A 5 5 1.00 8 0.625
71 A 5 4 1.00 6 0.667
72 A 0 0 0.00 0 0.000
73 A 0 0 0.00 0 0.000
74 A 19 7 1.00 12 0.583
75 A 14 7 1.00 12 0.583
76 A 14 7 1.00 12 0.583
77 A 9 7 1.00 10 0.700
78 A 7 6 1.00 8 0.750
79 A 0 0 0.00 0 0.000
80 A 41 10 1.00 12 0.833
81 A 25 10 1.00 12 0.833
82 A 22 10 1.00 12 0.833
83 A 11 10 1.00 10 1.000
84 A 8 7 1.00 8 0.875
85 A 0 0 0.00 0 0.000
86 A 44 10 1.00 12 0.833
87 A 27 9 1.00 12 0.750
88 A 24 10 1.00 12 0.833
89 A 12 9 1.00 10 0.900
90 A 9 7 1.00 8 0.875
91 A 0 0 0.00 0 0.000
92 A 18 6 1.00 12 0.500
93 A 13 6 1.00 12 0.500
94 A 13 6 1.00 12 0.500
95 A 8 7 1.00 10 0.700
96 A 6 5 1.00 8 0.625
97 A 0 0 0.00 0 0.000
98 A 0 0 0.00 0 0.000
99 A 17 5 1.00 12 0.417
100 A 12 5 1.00 12 0.417
101 A 12 5 1.00 12 0.417
102 A 6 5 1.00 10 0.500
103 A 7 6 1.00 8 0.750
104 A 0 0 0.00 0 0.000
105 A 34 8 1.00 12 0.667
106 A 24 9 1.00 12 0.750
107 A 22 9 1.00 12 0.750
108 A 11 10 1.00 10 1.000
109 A 8 7 1.00 8 0.875
110 A 0 0 0.00 0 0.000
111 A 32 7 1.00 12 0.583
112 A 21 7 1.00 12 0.583
113 A 22 9 1.00 12 0.750
114 A 9 8 1.00 10 0.800
115 A 9 7 1.00 8 0.875
116 A 0 0 0.00 0 0.000
117 A 0 0 0.00 0 0.000
118 A 0 0 0.00 0 0.000
119 A 2 2 1.00 10 0.200
120 A 2 2 1.00 8 0.250
121 A 0 0 0.00 0 0.000
122 A 0 0 0.00 0 0.000
123 A 0 0 0.00 0 0.000
124 A 0 0 0.00 0 0.000
125 A 0 0 0.00 0 0.000
126 A 0 0 0.00 0 0.000
127 A 0 0 0.00 0 0.000
128 A 0 0 0.00 0 0.000
129 A 12 4 1.00 10 0.400
130 A 9 4 1.00 10 0.400
131 A 9 4 1.00 10 0.400
132 A 6 5 1.00 8 0.625
133 A 4 3 1.00 6 0.500
134 A 0 0 0.00 0 0.000
135 A 0 0 0.00 0 0.000
136 A 14 7 1.00 16 0.438
137 A 9 7 1.00 14 0.500
138 A 7 6 1.00 12 0.500
139 A 22 10 1.00 16 0.625
140 A 11 10 1.00 14 0.714
141 A 8 7 1.00 12 0.583
142 A 24 10 1.00 16 0.625
143 A 12 9 1.00 14 0.643
144 A 9 7 1.00 12 0.583
145 A 13 6 1.00 16 0.375
146 A 8 7 1.00 14 0.500
147 A 6 5 1.00 12 0.417
148 A 12 5 1.00 16 0.312
149 A 6 5 1.00 14 0.357
150 A 7 6 1.00 12 0.500
151 A 22 9 1.00 16 0.562
152 A 11 10 1.00 14 0.714
153 A 8 7 1.00 12 0.583
154 A 22 9 1.00 16 0.562
155 A 9 8 1.00 14 0.571
156 A 9 7 1.00 12 0.583

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