[next] [prev] [prev-tail] [tail] [up]

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 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 68, 69, 70, 72, 73, 74, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 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, 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, 152 }

B grade: { 50, 54, 58, 63, 67, 71, 75, 76, 93 }

C grade: { 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 121, 148, 149, 150, 151, 153 }

F grade: { }

2.1.3 Maple

A grade: { 1, 3, 4, 5, 7, 8, 9, 10, 15, 16, 17, 30, 31, 35, 36, 37, 38, 39, 40, 41, 42, 46, 47, 51, 55, 59, 64, 68, 72, 73, 80, 84, 88, 92, 97, 101, 105, 109, 111, 112, 116, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 133, 134, 135, 136, 137, 138, 139 }

B grade: { 11, 12, 13, 14, 32, 33, 34, 43, 44, 45, 50, 54, 58, 60, 63, 67, 71, 79, 83, 87, 91, 96, 100, 104, 108, 110, 113, 114, 115, 117, 118, 130, 131 }

C grade: { 2, 48, 49, 52, 53, 56, 57, 61, 62, 65, 66, 69, 70, 74, 75, 76, 77, 78, 81, 82, 85, 86, 89, 90, 93, 94, 95, 98, 99, 102, 103, 106, 107, 147, 148, 149, 150, 151, 152, 153 }

F grade: { 6, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 140, 141, 142, 143, 144, 145, 146 }

2.1.4 Maxima

A grade: { 1, 2, 7, 8, 9, 10, 11, 12, 13, 30, 31, 35, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47, 60, 80, 84, 85, 86, 87, 88, 89, 90, 91, 92, 97, 101, 102, 103, 104, 105, 106, 107, 108, 109, 116, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 138, 139, 147, 148, 149, 150, 151, 152 }

B grade: { 14, 38, 39, 50, 52, 53, 54, 56, 57, 58, 63, 65, 66, 67, 69, 70, 71, 110, 113 }

C grade: { }

F grade: { 3, 4, 5, 6, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 48, 49, 51, 55, 59, 61, 62, 64, 68, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 93, 94, 95, 96, 98, 99, 100, 111, 112, 114, 115, 117, 118, 134, 135, 136, 137, 140, 141, 142, 143, 144, 145, 146, 153 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 30, 31, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 51, 55, 59, 60, 64, 67, 68, 71, 72, 80, 84, 88, 92, 97, 101, 105, 109, 116, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 137, 138, 139, 140, 143, 144, 145, 147 }

B grade: { 50, 54, 58, 63, 73, 79, 83, 87, 91, 96, 100, 104, 108, 110, 113, 134, 148, 149, 150, 151, 152 }

C grade: { 48, 49, 52, 53, 56, 57, 61, 62, 65, 66, 69, 70, 74, 75, 76, 77, 78, 81, 82, 85, 86, 89, 90, 93, 94, 95, 98, 99, 102, 103, 106, 107, 111, 112, 114, 115, 117, 118, 153 }

F grade: { 6, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 130, 135, 136, 141, 142, 146 }

2.1.6 Sympy

A grade: { 1, 3, 4, 5, 7, 8, 11, 12, 13, 14, 15, 16, 17, 30, 31, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 51, 60, 80, 119, 122, 123, 124, 128, 129 }

B grade: { 9, 10, 120, 121, 125, 131 }

C grade: { 19, 20, 21, 22, 26, 27, 28 }

F grade: { 2, 6, 18, 23, 24, 25, 29, 32, 33, 34, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 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, 126, 127, 130, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 11, 12, 13, 14, 15, 16, 17, 20, 26, 30, 31, 35, 36, 40, 42, 43, 44, 45, 46, 47, 51, 55, 59, 60, 64, 68, 72, 80, 84, 88, 92, 97, 101, 105, 109, 119, 120, 122, 123, 124, 126, 127, 128, 129, 131, 132, 133, 147, 148, 151, 152 }

B grade: { 7, 8, 9, 10, 125 }

C grade: { }

F grade: { 6, 18, 19, 21, 22, 23, 24, 25, 27, 28, 29, 32, 33, 34, 37, 38, 39, 41, 48, 49, 50, 52, 53, 54, 56, 57, 58, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 96, 98, 99, 100, 102, 103, 104, 106, 107, 108, 110, 111, 112, 113, 114, 115, 116, 117, 118, 121, 130, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 149, 150, 153 }

2.1.8 Mupad

A grade: { 31, 35, 36, 51, 55, 59, 64, 68, 72, 80, 84, 88, 92, 97, 101, 105, 109 }

B grade: { 1, 2, 14, 30, 38, 39, 40, 43, 44, 45, 47, 60, 110, 113, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 137, 138, 139, 147, 148, 149, 150, 151, 152 }

C grade: { }

F grade: { 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 37, 41, 42, 46, 48, 49, 50, 52, 53, 54, 56, 57, 58, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 96, 98, 99, 100, 102, 103, 104, 106, 107, 108, 111, 112, 114, 115, 116, 117, 118, 130, 135, 136, 140, 141, 142, 143, 144, 145, 146, 153 }

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 A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 37 46 37 45 60 37 230
normalized size 1 1.00 0.88 1.10 0.88 1.07 1.43 0.88 5.48
time (sec) N/A 0.041 0.018 0.039 0.313 0.444 3.823 0.115 0.686
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 40 140 40 58 0 40 58
normalized size 1 1.00 0.89 3.11 0.89 1.29 0.00 0.89 1.29
time (sec) N/A 0.042 0.045 0.294 0.311 0.483 0.000 0.122 0.632
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 86 211 0 76 129 88 -1
normalized size 1 1.00 0.60 1.47 0.00 0.53 0.90 0.61 -0.01
time (sec) N/A 0.080 0.087 0.050 0.000 0.457 7.248 0.264 0.000
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 74 163 0 65 102 75 -1
normalized size 1 1.00 0.64 1.41 0.00 0.56 0.88 0.65 -0.01
time (sec) N/A 0.042 0.062 0.046 0.000 0.450 2.455 0.247 0.000
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 59 116 0 49 71 62 -1
normalized size 1 1.00 0.67 1.32 0.00 0.56 0.81 0.70 -0.01
time (sec) N/A 0.029 0.045 0.041 0.000 0.690 0.992 0.246 0.000
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 288 288 171 0 0 0 0 0 -1
normalized size 1 1.00 0.59 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.167 2.872 0.268 0.000 0.645 0.000 0.000 0.000
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 54 67 58 44 53 105 -1
normalized size 1 1.00 0.95 1.18 1.02 0.77 0.93 1.84 -0.02
time (sec) N/A 0.019 0.041 0.040 0.369 0.617 4.595 0.262 0.000
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 67 69 68 58 83 198 -1
normalized size 1 1.00 0.79 0.81 0.80 0.68 0.98 2.33 -0.01
time (sec) N/A 0.028 0.051 0.041 0.334 0.629 5.128 0.257 0.000
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 78 117 109 68 352 282 -1
normalized size 1 1.00 0.69 1.04 0.96 0.60 3.12 2.50 -0.01
time (sec) N/A 0.039 0.067 0.043 0.339 0.839 6.502 0.278 0.000
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 141 141 89 167 132 80 575 361 -1
normalized size 1 1.00 0.63 1.18 0.94 0.57 4.08 2.56 -0.01
time (sec) N/A 0.050 0.075 0.046 0.339 0.795 9.155 0.263 0.000
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 83 230 167 79 124 137 -1
normalized size 1 1.00 0.67 1.85 1.35 0.64 1.00 1.10 -0.01
time (sec) N/A 0.067 0.119 0.052 0.338 0.476 11.608 0.246 0.000
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 72 180 139 68 97 102 -1
normalized size 1 1.00 0.73 1.82 1.40 0.69 0.98 1.03 -0.01
time (sec) N/A 0.051 0.101 0.045 0.341 0.492 3.563 0.252 0.000
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 60 132 111 56 70 64 -1
normalized size 1 1.00 0.81 1.78 1.50 0.76 0.95 0.86 -0.01
time (sec) N/A 0.036 0.091 0.043 0.339 0.442 1.239 0.227 0.000
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 43 84 77 41 39 41 35
normalized size 1 1.00 1.00 1.95 1.79 0.95 0.91 0.95 0.81
time (sec) N/A 0.010 0.024 0.042 0.335 0.442 1.058 0.182 0.658
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 86 57 0 148 60 54 -1
normalized size 1 1.00 1.46 0.97 0.00 2.51 1.02 0.92 -0.02
time (sec) N/A 0.033 0.066 0.039 0.000 0.599 5.543 0.247 0.000
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 101 100 0 198 82 83 -1
normalized size 1 1.00 1.11 1.10 0.00 2.18 0.90 0.91 -0.01
time (sec) N/A 0.046 0.106 0.042 0.000 0.596 11.583 0.228 0.000
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 114 150 0 228 148 108 -1
normalized size 1 1.00 0.96 1.26 0.00 1.92 1.24 0.91 -0.01
time (sec) N/A 0.060 0.131 0.041 0.000 0.634 19.727 0.248 0.000
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) F F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 211 211 170 0 0 0 0 0 -1
normalized size 1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.120 0.625 0.236 0.000 0.530 0.000 0.000 0.000
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) F C F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 181 181 158 0 0 0 75 0 -1
normalized size 1 1.00 0.87 0.00 0.00 0.00 0.41 0.00 -0.01
time (sec) N/A 0.088 0.463 0.237 0.000 0.599 150.302 0.000 0.000
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) F C A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 153 153 147 0 0 0 75 1 -1
normalized size 1 1.00 0.96 0.00 0.00 0.00 0.49 0.01 -0.01
time (sec) N/A 0.074 0.310 0.247 0.000 0.481 3.962 0.253 0.000
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 122 122 115 0 0 0 71 0 -1
normalized size 1 1.00 0.94 0.00 0.00 0.00 0.58 0.00 -0.01
time (sec) N/A 0.061 0.130 0.237 0.000 0.476 5.369 0.000 0.000
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 156 156 150 0 0 0 78 0 -1
normalized size 1 1.00 0.96 0.00 0.00 0.00 0.50 0.00 -0.01
time (sec) N/A 0.075 0.285 0.237 0.000 0.478 146.125 0.000 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 186 186 162 0 0 0 0 0 -1
normalized size 1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.090 0.342 0.233 0.000 0.549 0.000 0.000 0.000
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 216 216 171 0 0 0 0 0 -1
normalized size 1 1.00 0.79 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.108 0.615 0.237 0.000 0.437 0.000 0.000 0.000
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) F F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 326 326 139 0 0 0 0 0 -1
normalized size 1 1.00 0.43 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.192 0.160 0.234 0.000 0.549 0.000 0.000 0.000
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) F C A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 296 296 119 0 0 0 75 1 -1
normalized size 1 1.00 0.40 0.00 0.00 0.00 0.25 0.00 -0.00
time (sec) N/A 0.161 0.123 0.234 0.000 1.270 13.071 0.264 0.000
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 260 260 89 0 0 0 71 0 -1
normalized size 1 1.00 0.34 0.00 0.00 0.00 0.27 0.00 -0.00
time (sec) N/A 0.139 0.119 0.240 0.000 0.516 8.901 0.000 0.000
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 298 298 121 0 0 0 78 0 -1
normalized size 1 1.00 0.41 0.00 0.00 0.00 0.26 0.00 -0.00
time (sec) N/A 0.166 0.154 0.235 0.000 0.537 13.090 0.000 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 331 331 137 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 0.194 0.136 0.233 0.000 0.547 0.000 0.000 0.000
Problem 30 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 50 50 50 43 42 47 41 43 42
normalized size 1 1.00 1.00 0.86 0.84 0.94 0.82 0.86 0.84
time (sec) N/A 0.146 0.017 0.046 0.425 0.531 0.888 0.137 0.759
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 43 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 0.046 0.101 2.563 0.000 0.608 0.000 0.000 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 431 431 530 1631 0 0 0 0 -1
normalized size 1 1.00 1.23 3.78 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.485 0.205 1.991 0.000 0.607 0.000 0.000 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 283 283 354 837 0 0 0 0 -1
normalized size 1 1.00 1.25 2.96 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.295 0.135 1.325 0.000 0.457 0.000 0.000 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 93 263 0 0 0 0 -1
normalized size 1 1.00 0.95 2.68 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.067 0.034 0.796 0.000 0.566 0.000 0.000 0.000
Problem 35 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 43 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 0.044 0.101 1.336 0.000 0.495 0.000 0.000 0.000
Problem 36 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 43 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 0.041 0.890 1.260 0.000 0.571 0.000 0.000 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 34 41 38 33 158 0 -1
normalized size 1 1.00 0.92 1.11 1.03 0.89 4.27 0.00 -0.03
time (sec) N/A 0.024 0.064 0.185 0.340 0.517 2.700 0.000 0.000
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 20 20 81 13 32 0 19
normalized size 1 1.00 0.87 0.87 3.52 0.57 1.39 0.00 0.83
time (sec) N/A 0.009 0.017 0.177 0.324 0.825 0.360 0.000 0.120
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 20 20 57 13 32 0 19
normalized size 1 1.00 0.87 0.87 2.48 0.57 1.39 0.00 0.83
time (sec) N/A 0.007 0.017 0.177 0.318 0.489 0.199 0.000 0.061
Problem 40 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 16 16 18 15 12 10 42 26 16
normalized size 1 1.00 1.12 0.94 0.75 0.62 2.62 1.62 1.00
time (sec) N/A 0.003 0.009 0.038 0.321 0.760 0.143 0.128 0.039
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 19 21 42 8 34 0 -1
normalized size 1 1.00 0.90 1.00 2.00 0.38 1.62 0.00 -0.05
time (sec) N/A 0.031 0.017 0.186 0.419 0.794 0.925 0.000 0.000
Problem 42 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 36 36 31 56 40 42 160 62 -1
normalized size 1 1.00 0.86 1.56 1.11 1.17 4.44 1.72 -0.03
time (sec) N/A 0.021 0.054 0.312 0.325 0.551 6.606 0.137 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 20 65 17 17 26 19 25
normalized size 1 1.00 0.87 2.83 0.74 0.74 1.13 0.83 1.09
time (sec) N/A 0.008 0.018 0.434 0.322 0.444 0.390 0.130 0.542
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 20 54 17 17 49 19 25
normalized size 1 1.00 0.87 2.35 0.74 0.74 2.13 0.83 1.09
time (sec) N/A 0.007 0.016 0.440 0.318 0.394 0.303 0.137 0.072
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 18 51 15 15 24 15 21
normalized size 1 1.00 1.12 3.19 0.94 0.94 1.50 0.94 1.31
time (sec) N/A 0.003 0.009 0.045 0.322 0.674 0.131 0.113 0.071
Problem 46 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 19 19 19 35 14 14 27 15 -1
normalized size 1 1.00 1.00 1.84 0.74 0.74 1.42 0.79 -0.05
time (sec) N/A 0.033 0.019 0.386 0.310 0.469 4.571 0.113 0.000
Problem 47 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 16 16 18 15 12 10 42 26 16
normalized size 1 1.00 1.12 0.94 0.75 0.62 2.62 1.62 1.00
time (sec) N/A 0.003 0.001 0.036 0.317 0.589 0.140 0.113 0.002
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 403 403 363 8040 0 1973 0 0 -1
normalized size 1 1.00 0.90 19.95 0.00 4.90 0.00 0.00 -0.00
time (sec) N/A 0.517 1.078 65.269 0.000 0.755 0.000 0.000 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 305 305 272 7648 0 1557 0 0 -1
normalized size 1 1.00 0.89 25.08 0.00 5.10 0.00 0.00 -0.00
time (sec) N/A 0.405 0.698 6.247 0.000 0.672 0.000 0.000 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 198 198 555 1002 433 1117 0 0 -1
normalized size 1 1.00 2.80 5.06 2.19 5.64 0.00 0.00 -0.01
time (sec) N/A 0.234 7.922 1.216 0.523 0.696 0.000 0.000 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) 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 0.132 5.242 0.719 0.000 0.428 0.000 0.000 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 140 1532 309 322 0 0 -1
normalized size 1 1.00 0.91 9.95 2.01 2.09 0.00 0.00 -0.01
time (sec) N/A 0.238 0.485 6.712 0.382 0.572 0.000 0.000 0.000
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 110 1497 218 271 0 0 -1
normalized size 1 1.00 0.89 12.17 1.77 2.20 0.00 0.00 -0.01
time (sec) N/A 0.206 0.358 6.033 0.363 0.492 0.000 0.000 0.000
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 85 85 967 1489 448 202 0 0 -1
normalized size 1 1.00 11.38 17.52 5.27 2.38 0.00 0.00 -0.01
time (sec) N/A 0.125 18.752 0.509 0.471 0.630 0.000 0.000 0.000
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 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 -0.04
time (sec) N/A 0.120 0.735 1.638 0.000 0.635 0.000 0.000 0.000
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 155 155 137 1533 310 320 0 0 -1
normalized size 1 1.00 0.88 9.89 2.00 2.06 0.00 0.00 -0.01
time (sec) N/A 0.244 0.513 6.704 0.384 0.508 0.000 0.000 0.000
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 111 1498 219 269 0 0 -1
normalized size 1 1.00 0.90 12.08 1.77 2.17 0.00 0.00 -0.01
time (sec) N/A 0.208 0.391 5.480 0.369 0.711 0.000 0.000 0.000
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 86 86 847 1681 448 200 0 0 -1
normalized size 1 1.00 9.85 19.55 5.21 2.33 0.00 0.00 -0.01
time (sec) N/A 0.129 17.583 0.560 0.463 0.752 0.000 0.000 0.000
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 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 -0.04
time (sec) N/A 0.136 1.136 1.896 0.000 0.423 0.000 0.000 0.000
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 18 51 15 15 24 15 21
normalized size 1 1.00 1.12 3.19 0.94 0.94 1.50 0.94 1.31
time (sec) N/A 0.003 0.009 0.046 0.319 0.483 0.143 0.126 0.002
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 399 399 359 7906 0 1585 0 0 -1
normalized size 1 1.00 0.90 19.81 0.00 3.97 0.00 0.00 -0.00
time (sec) N/A 0.511 1.006 73.710 0.000 0.780 0.000 0.000 0.000
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 303 303 270 7538 0 1285 0 0 -1
normalized size 1 1.00 0.89 24.88 0.00 4.24 0.00 0.00 -0.00
time (sec) N/A 0.400 0.628 6.507 0.000 0.913 0.000 0.000 0.000
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 198 198 1648 1159 532 961 0 0 -1
normalized size 1 1.00 8.32 5.85 2.69 4.85 0.00 0.00 -0.01
time (sec) N/A 0.250 22.192 1.398 0.550 0.715 0.000 0.000 0.000
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) A F(-1) 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 0.134 5.129 1.301 0.000 0.482 0.000 0.000 0.000
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 136 1532 309 165 0 0 -1
normalized size 1 1.00 0.88 9.95 2.01 1.07 0.00 0.00 -0.01
time (sec) N/A 0.256 0.383 6.565 0.366 0.419 0.000 0.000 0.000
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 110 1497 218 143 0 0 -1
normalized size 1 1.00 0.89 12.17 1.77 1.16 0.00 0.00 -0.01
time (sec) N/A 0.222 0.234 5.463 0.344 0.434 0.000 0.000 0.000
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B A F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 85 85 929 1495 456 111 0 0 -1
normalized size 1 1.00 10.93 17.59 5.36 1.31 0.00 0.00 -0.01
time (sec) N/A 0.131 20.268 0.688 0.442 0.627 0.000 0.000 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 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 -0.04
time (sec) N/A 0.121 0.764 1.796 0.000 0.491 0.000 0.000 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 155 155 140 1533 310 166 0 0 -1
normalized size 1 1.00 0.90 9.89 2.00 1.07 0.00 0.00 -0.01
time (sec) N/A 0.261 0.381 6.618 0.374 0.766 0.000 0.000 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 110 1498 219 144 0 0 -1
normalized size 1 1.00 0.89 12.08 1.77 1.16 0.00 0.00 -0.01
time (sec) N/A 0.224 0.223 5.573 0.349 0.681 0.000 0.000 0.000
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B A F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 86 86 872 1753 456 112 0 0 -1
normalized size 1 1.00 10.14 20.38 5.30 1.30 0.00 0.00 -0.01
time (sec) N/A 0.134 15.673 0.700 0.473 0.547 0.000 0.000 0.000
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 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 -0.04
time (sec) N/A 0.119 0.746 2.062 0.000 0.830 0.000 0.000 0.000
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 64 52 0 58 0 0 -1
normalized size 1 1.00 1.64 1.33 0.00 1.49 0.00 0.00 -0.03
time (sec) N/A 0.032 0.031 0.379 0.000 0.604 0.000 0.000 0.000
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 105 732 0 93 0 0 -1
normalized size 1 1.00 1.42 9.89 0.00 1.26 0.00 0.00 -0.01
time (sec) N/A 0.061 0.026 1.344 0.000 0.451 0.000 0.000 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 356 758 0 125 0 0 -1
normalized size 1 1.00 3.30 7.02 0.00 1.16 0.00 0.00 -0.01
time (sec) N/A 0.088 0.118 0.628 0.000 0.584 0.000 0.000 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F C F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 299 299 600 7275 0 1448 0 0 -1
normalized size 1 1.00 2.01 24.33 0.00 4.84 0.00 0.00 -0.00
time (sec) N/A 0.209 5.494 47.255 0.000 0.597 0.000 0.000 0.000
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 229 229 375 5425 0 994 0 0 -1
normalized size 1 1.00 1.64 23.69 0.00 4.34 0.00 0.00 -0.00
time (sec) N/A 0.152 2.935 37.576 0.000 0.608 0.000 0.000 0.000
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 159 159 278 2414 0 596 0 0 -1
normalized size 1 1.00 1.75 15.18 0.00 3.75 0.00 0.00 -0.01
time (sec) N/A 0.097 1.942 4.748 0.000 0.640 0.000 0.000 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 132 178 0 334 0 0 -1
normalized size 1 1.00 1.78 2.41 0.00 4.51 0.00 0.00 -0.01
time (sec) N/A 0.042 0.070 0.564 0.000 0.935 0.000 0.000 0.000
Problem 80 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 0.038 6.652 1.394 0.000 0.580 0.000 0.000 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 355 355 305 6936 0 1335 0 0 -1
normalized size 1 1.00 0.86 19.54 0.00 3.76 0.00 0.00 -0.00
time (sec) N/A 0.461 5.808 60.801 0.000 0.626 0.000 0.000 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 267 267 229 6586 0 1103 0 0 -1
normalized size 1 1.00 0.86 24.67 0.00 4.13 0.00 0.00 -0.00
time (sec) N/A 0.373 4.871 6.160 0.000 0.930 0.000 0.000 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 174 174 288 350 0 851 0 0 -1
normalized size 1 1.00 1.66 2.01 0.00 4.89 0.00 0.00 -0.01
time (sec) N/A 0.231 4.520 0.363 0.000 1.138 0.000 0.000 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) 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 0.126 8.677 0.829 0.000 0.513 0.000 0.000 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 142 142 128 1555 129 291 0 0 -1
normalized size 1 1.00 0.90 10.95 0.91 2.05 0.00 0.00 -0.01
time (sec) N/A 0.228 5.757 6.865 1.943 0.726 0.000 0.000 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 102 1519 106 245 0 0 -1
normalized size 1 1.00 0.90 13.44 0.94 2.17 0.00 0.00 -0.01
time (sec) N/A 0.195 5.722 5.013 2.044 0.616 0.000 0.000 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 71 1381 80 187 0 0 -1
normalized size 1 1.00 0.90 17.48 1.01 2.37 0.00 0.00 -0.01
time (sec) N/A 0.118 1.945 0.579 1.992 0.675 0.000 0.000 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) 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 0.112 4.094 1.753 0.000 1.003 0.000 0.000 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 128 1570 129 291 0 0 -1
normalized size 1 1.00 0.88 10.83 0.89 2.01 0.00 0.00 -0.01
time (sec) N/A 0.220 5.813 6.790 1.950 0.615 0.000 0.000 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 102 1534 107 245 0 0 -1
normalized size 1 1.00 0.88 13.22 0.92 2.11 0.00 0.00 -0.01
time (sec) N/A 0.197 5.677 4.946 1.946 0.521 0.000 0.000 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 71 1351 80 187 0 0 -1
normalized size 1 1.00 0.87 16.48 0.98 2.28 0.00 0.00 -0.01
time (sec) N/A 0.119 1.852 0.457 1.948 0.551 0.000 0.000 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 25 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 -0.04
time (sec) N/A 0.116 4.104 1.658 0.000 0.641 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F C F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 299 299 600 7275 0 1448 0 0 -1
normalized size 1 1.00 2.01 24.33 0.00 4.84 0.00 0.00 -0.00
time (sec) N/A 0.209 6.055 49.104 0.000 1.067 0.000 0.000 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 229 229 375 5425 0 994 0 0 -1
normalized size 1 1.00 1.64 23.69 0.00 4.34 0.00 0.00 -0.00
time (sec) N/A 0.153 2.998 37.481 0.000 0.573 0.000 0.000 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 159 159 278 2415 0 596 0 0 -1
normalized size 1 1.00 1.75 15.19 0.00 3.75 0.00 0.00 -0.01
time (sec) N/A 0.100 2.184 4.685 0.000 0.521 0.000 0.000 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 132 178 0 334 0 0 -1
normalized size 1 1.00 1.81 2.44 0.00 4.58 0.00 0.00 -0.01
time (sec) N/A 0.043 0.085 0.550 0.000 0.475 0.000 0.000 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) 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 0.043 5.933 2.477 0.000 0.456 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 351 351 299 6864 0 1315 0 0 -1
normalized size 1 1.00 0.85 19.56 0.00 3.75 0.00 0.00 -0.00
time (sec) N/A 0.465 6.176 60.585 0.000 0.590 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 265 265 225 6514 0 1087 0 0 -1
normalized size 1 1.00 0.85 24.58 0.00 4.10 0.00 0.00 -0.00
time (sec) N/A 0.370 4.763 6.266 0.000 0.645 0.000 0.000 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 174 174 287 350 0 839 0 0 -1
normalized size 1 1.00 1.65 2.01 0.00 4.82 0.00 0.00 -0.01
time (sec) N/A 0.228 4.259 0.542 0.000 0.965 0.000 0.000 0.000
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) 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 0.121 8.874 1.064 0.000 0.470 0.000 0.000 0.000
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 142 142 128 1554 129 291 0 0 -1
normalized size 1 1.00 0.90 10.94 0.91 2.05 0.00 0.00 -0.01
time (sec) N/A 0.236 1.830 6.835 1.995 0.513 0.000 0.000 0.000
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 102 1518 106 245 0 0 -1
normalized size 1 1.00 0.90 13.43 0.94 2.17 0.00 0.00 -0.01
time (sec) N/A 0.206 1.793 5.278 2.041 0.556 0.000 0.000 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 71 1381 80 187 0 0 -1
normalized size 1 1.00 0.90 17.48 1.01 2.37 0.00 0.00 -0.01
time (sec) N/A 0.122 0.791 0.730 1.999 0.529 0.000 0.000 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) 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 0.110 4.133 2.008 0.000 0.456 0.000 0.000 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 128 1571 129 291 0 0 -1
normalized size 1 1.00 0.88 10.83 0.89 2.01 0.00 0.00 -0.01
time (sec) N/A 0.231 1.848 7.321 2.006 0.477 0.000 0.000 0.000
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 102 1535 107 245 0 0 -1
normalized size 1 1.00 0.88 13.23 0.92 2.11 0.00 0.00 -0.01
time (sec) N/A 0.201 1.700 5.235 2.029 0.490 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 71 1351 80 187 0 0 -1
normalized size 1 1.00 0.87 16.48 0.98 2.28 0.00 0.00 -0.01
time (sec) N/A 0.121 0.795 0.770 1.963 0.513 0.000 0.000 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 25 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 -0.04
time (sec) N/A 0.112 4.268 1.903 0.000 0.506 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 59 59 34 40 0 0 21
normalized size 1 1.00 1.90 1.90 1.10 1.29 0.00 0.00 0.68
time (sec) N/A 0.026 0.048 0.056 0.428 0.465 0.000 0.000 0.688
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 50 44 0 65 0 0 -1
normalized size 1 1.00 0.79 0.70 0.00 1.03 0.00 0.00 -0.02
time (sec) N/A 0.043 0.012 0.132 0.000 0.451 0.000 0.000 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 91 70 0 87 0 0 -1
normalized size 1 1.00 1.00 0.77 0.00 0.96 0.00 0.00 -0.01
time (sec) N/A 0.066 0.009 0.125 0.000 0.481 0.000 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 83 106 63 103 0 0 37
normalized size 1 1.00 1.84 2.36 1.40 2.29 0.00 0.00 0.82
time (sec) N/A 0.028 0.113 0.059 0.440 0.500 0.000 0.000 0.745
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 71 349 0 151 0 0 -1
normalized size 1 1.00 0.78 3.84 0.00 1.66 0.00 0.00 -0.01
time (sec) N/A 0.058 0.016 0.229 0.000 0.805 0.000 0.000 0.000
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 133 133 133 407 0 187 0 0 -1
normalized size 1 1.00 1.00 3.06 0.00 1.41 0.00 0.00 -0.01
time (sec) N/A 0.090 0.010 0.230 0.000 0.521 0.000 0.000 0.000
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 196 196 167 186 189 212 0 0 -1
normalized size 1 1.00 0.85 0.95 0.96 1.08 0.00 0.00 -0.01
time (sec) N/A 0.148 0.196 0.062 0.500 1.032 0.000 0.000 0.000
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F C F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 232 250 236 672 0 304 0 0 -1
normalized size 1 1.08 1.02 2.90 0.00 1.31 0.00 0.00 -0.00
time (sec) N/A 0.151 0.100 0.322 0.000 0.455 0.000 0.000 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F C F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 302 313 334 758 0 378 0 0 -1
normalized size 1 1.04 1.11 2.51 0.00 1.25 0.00 0.00 -0.00
time (sec) N/A 0.201 0.016 0.294 0.000 0.812 0.000 0.000 0.000
Problem 119 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 23 19 28 19 20 20
normalized size 1 1.00 1.00 0.92 0.76 1.12 0.76 0.80 0.80
time (sec) N/A 0.021 0.019 0.042 0.316 0.554 6.360 0.113 0.089
Problem 120 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 45 45 35 32 31 50 153 32 31
normalized size 1 1.00 0.78 0.71 0.69 1.11 3.40 0.71 0.69
time (sec) N/A 0.032 0.038 0.046 0.411 0.675 0.516 0.111 0.124
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 81 54 54 77 223 0 46
normalized size 1 1.00 1.27 0.84 0.84 1.20 3.48 0.00 0.72
time (sec) N/A 0.067 0.047 0.047 0.405 1.130 0.604 0.000 0.700
Problem 122 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 30 30 22 25 24 18 26 24 24
normalized size 1 1.00 0.73 0.83 0.80 0.60 0.87 0.80 0.80
time (sec) N/A 0.011 0.011 0.037 0.413 0.653 0.210 0.125 0.075
Problem 123 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 5 5 5 6 5 5 5 5 5
normalized size 1 1.00 1.00 1.20 1.00 1.00 1.00 1.00 1.00
time (sec) N/A 0.025 0.033 0.036 0.313 0.501 0.257 0.123 0.225
Problem 124 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 17 17 17 19 16 15 14 16 15
normalized size 1 1.00 1.00 1.12 0.94 0.88 0.82 0.94 0.88
time (sec) N/A 0.039 0.048 0.076 0.326 0.577 0.515 0.115 0.135
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 17 16 26 53 104 16
normalized size 1 1.00 1.00 0.94 0.89 1.44 2.94 5.78 0.89
time (sec) N/A 0.151 0.033 0.046 0.565 0.539 0.622 0.143 0.127
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 58 45 44 40 0 44 72
normalized size 1 1.00 0.85 0.66 0.65 0.59 0.00 0.65 1.06
time (sec) N/A 0.028 0.064 0.056 0.455 0.567 0.000 0.128 1.653
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 53 40 39 35 0 39 65
normalized size 1 1.00 0.90 0.68 0.66 0.59 0.00 0.66 1.10
time (sec) N/A 0.026 0.033 0.055 0.463 0.580 0.000 0.151 0.940
Problem 128 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 50 50 48 35 34 28 39 34 58
normalized size 1 1.00 0.96 0.70 0.68 0.56 0.78 0.68 1.16
time (sec) N/A 0.018 0.030 0.053 0.461 0.992 161.339 0.152 0.850
Problem 129 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 37 37 39 28 26 22 29 27 40
normalized size 1 1.00 1.05 0.76 0.70 0.59 0.78 0.73 1.08
time (sec) N/A 0.010 0.428 0.054 0.451 0.428 73.759 0.136 0.894
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 84 194 43 0 0 0 -1
normalized size 1 1.00 2.00 4.62 1.02 0.00 0.00 0.00 -0.02
time (sec) N/A 0.042 0.202 1.402 0.433 0.750 0.000 0.000 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 40 57 29 28 537 28 44
normalized size 1 1.00 0.98 1.39 0.71 0.68 13.10 0.68 1.07
time (sec) N/A 0.022 0.034 0.057 0.451 0.614 68.660 0.148 1.409
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 48 35 34 35 0 34 49
normalized size 1 1.00 0.96 0.70 0.68 0.70 0.00 0.68 0.98
time (sec) N/A 0.024 0.031 0.073 0.452 0.567 0.000 0.145 1.359
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 51 40 39 40 0 39 56
normalized size 1 1.00 0.86 0.68 0.66 0.68 0.00 0.66 0.95
time (sec) N/A 0.025 0.044 0.077 0.453 0.501 0.000 0.148 0.939
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 63 73 0 126 0 0 57
normalized size 1 1.00 1.00 1.16 0.00 2.00 0.00 0.00 0.90
time (sec) N/A 0.107 0.063 0.517 0.000 0.785 0.000 0.000 0.727
Problem 135 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 59 59 59 72 0 0 0 0 -1
normalized size 1 1.00 1.00 1.22 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.098 0.031 0.433 0.000 0.527 0.000 0.000 0.000
Problem 136 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 59 59 59 72 0 0 0 0 -1
normalized size 1 1.00 1.00 1.22 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.062 0.022 0.433 0.000 0.954 0.000 0.000 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 55 71 0 83 0 0 49
normalized size 1 1.00 1.00 1.29 0.00 1.51 0.00 0.00 0.89
time (sec) N/A 0.108 0.056 1.785 0.000 0.551 0.000 0.000 0.599
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 57 71 29 82 0 0 51
normalized size 1 1.00 1.00 1.25 0.51 1.44 0.00 0.00 0.89
time (sec) N/A 0.099 0.027 0.425 0.559 0.444 0.000 0.000 0.602
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 59 72 29 82 0 0 51
normalized size 1 1.00 1.00 1.22 0.49 1.39 0.00 0.00 0.86
time (sec) N/A 0.101 0.027 0.434 0.615 0.543 0.000 0.000 0.614
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 66 0 0 132 0 0 -1
normalized size 1 1.00 0.92 0.00 0.00 1.83 0.00 0.00 -0.01
time (sec) N/A 0.108 0.238 1.113 0.000 0.680 0.000 0.000 0.000
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 62 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 0.098 0.133 0.444 0.000 0.840 0.000 0.000 0.000
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 62 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 0.062 0.062 0.448 0.000 0.717 0.000 0.000 0.000
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 58 0 0 83 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 1.30 0.00 0.00 -0.02
time (sec) N/A 0.108 0.109 0.448 0.000 0.667 0.000 0.000 0.000
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 60 0 0 82 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 1.24 0.00 0.00 -0.02
time (sec) N/A 0.101 0.100 0.445 0.000 0.819 0.000 0.000 0.000
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 62 0 0 83 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 1.22 0.00 0.00 -0.01
time (sec) N/A 0.100 0.096 0.446 0.000 0.614 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 101 101 166 0 0 0 0 0 -1
normalized size 1 1.00 1.64 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.266 3.034 6.751 0.000 0.544 0.000 0.000 0.000
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-1) A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 48 48 61 1299 48 75 0 65 66
normalized size 1 1.00 1.27 27.06 1.00 1.56 0.00 1.35 1.38
time (sec) N/A 0.075 0.115 1.345 0.432 0.701 0.000 2.064 0.769
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A B F(-1) A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 103 103 146 1375 131 221 0 154 133
normalized size 1 1.00 1.42 13.35 1.27 2.15 0.00 1.50 1.29
time (sec) N/A 0.155 0.157 2.615 0.430 0.881 0.000 0.914 0.314
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A B F(-1) F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 180 180 89 1355 167 431 0 0 164
normalized size 1 1.00 0.49 7.53 0.93 2.39 0.00 0.00 0.91
time (sec) N/A 0.182 0.126 2.616 0.422 0.506 0.000 0.000 1.416
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A B F F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 180 180 89 1355 167 431 0 0 164
normalized size 1 1.00 0.49 7.53 0.93 2.39 0.00 0.00 0.91
time (sec) N/A 0.179 0.124 2.070 0.426 0.683 0.000 0.000 1.656
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A B F(-1) A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 103 103 145 842 169 276 0 154 135
normalized size 1 1.00 1.41 8.17 1.64 2.68 0.00 1.50 1.31
time (sec) N/A 0.145 0.160 1.876 0.452 0.647 0.000 0.137 0.819
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B F A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 47 47 57 885 47 131 0 66 67
normalized size 1 1.00 1.21 18.83 1.00 2.79 0.00 1.40 1.43
time (sec) N/A 0.079 0.116 0.980 0.417 0.607 0.000 0.126 0.697
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 116 896 0 246 0 0 -1
normalized size 1 1.00 0.71 5.50 0.00 1.51 0.00 0.00 -0.01
time (sec) N/A 0.572 0.299 0.701 0.000 0.616 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 [73] had the largest ratio of [1.333]

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 4 1.00 12 0.333
2 A 4 4 1.00 14 0.286
3 A 6 4 1.00 25 0.160
4 A 5 4 1.00 25 0.160
5 A 4 4 1.00 23 0.174
6 A 8 8 1.00 25 0.320
7 A 2 2 1.00 25 0.080
8 A 3 3 1.00 25 0.120
9 A 4 3 1.00 25 0.120
10 A 5 3 1.00 25 0.120
11 A 4 3 1.00 25 0.120
12 A 4 3 1.00 25 0.120
13 A 4 3 1.00 25 0.120
14 A 2 2 1.00 21 0.095
15 A 4 4 1.00 25 0.160
16 A 5 5 1.00 25 0.200
17 A 6 5 1.00 25 0.200
18 A 6 4 1.00 27 0.148
19 A 5 4 1.00 27 0.148
20 A 4 4 1.00 27 0.148
21 A 3 3 1.00 27 0.111
22 A 4 4 1.00 27 0.148
23 A 5 4 1.00 27 0.148
24 A 6 4 1.00 27 0.148
25 A 7 6 1.00 27 0.222
26 A 6 6 1.00 27 0.222
27 A 5 5 1.00 27 0.185
28 A 6 6 1.00 27 0.222
29 A 7 6 1.00 27 0.222
30 A 8 7 1.00 11 0.636
31 A 0 0 0.00 0 0.000
32 A 9 7 1.00 40 0.175
33 A 7 6 1.00 40 0.150
34 A 4 4 1.00 38 0.105
35 A 0 0 0.00 0 0.000
36 A 0 0 0.00 0 0.000
37 A 2 2 1.00 11 0.182
38 A 2 2 1.00 11 0.182
39 A 2 2 1.00 9 0.222
40 A 2 2 1.00 7 0.286
41 A 2 2 1.00 11 0.182
42 A 2 2 1.00 11 0.182
43 A 2 2 1.00 11 0.182
44 A 2 2 1.00 9 0.222
45 A 2 2 1.00 7 0.286
46 A 2 2 1.00 11 0.182
47 A 2 2 1.00 7 0.286
48 A 11 6 1.00 15 0.400
49 A 9 5 1.00 13 0.385
50 A 7 4 1.00 11 0.364
51 A 0 0 0.00 0 0.000
52 A 7 7 1.00 21 0.333
53 A 6 6 1.00 19 0.316
54 A 5 5 1.00 17 0.294
55 A 0 0 0.00 0 0.000
56 A 7 7 1.00 21 0.333
57 A 6 6 1.00 19 0.316
58 A 5 5 1.00 17 0.294
59 A 0 0 0.00 0 0.000
60 A 2 2 1.00 7 0.286
61 A 11 6 1.00 15 0.400
62 A 9 5 1.00 13 0.385
63 A 7 4 1.00 11 0.364
64 A 0 0 0.00 0 0.000
65 A 7 7 1.00 21 0.333
66 A 6 6 1.00 19 0.316
67 A 5 5 1.00 17 0.294
68 A 0 0 0.00 0 0.000
69 A 7 7 1.00 21 0.333
70 A 6 6 1.00 19 0.316
71 A 5 5 1.00 17 0.294
72 A 0 0 0.00 0 0.000
73 A 6 4 1.00 3 1.333
74 A 8 5 1.00 5 1.000
75 A 10 6 1.00 7 0.857
76 A 12 6 1.00 15 0.400
77 A 10 6 1.00 15 0.400
78 A 8 5 1.00 13 0.385
79 A 6 4 1.00 7 0.571
80 A 0 0 0.00 0 0.000
81 A 11 6 1.00 15 0.400
82 A 9 5 1.00 13 0.385
83 A 7 4 1.00 11 0.364
84 A 0 0 0.00 0 0.000
85 A 7 7 1.00 19 0.368
86 A 6 6 1.00 17 0.353
87 A 5 5 1.00 15 0.333
88 A 0 0 0.00 0 0.000
89 A 7 7 1.00 22 0.318
90 A 6 6 1.00 20 0.300
91 A 5 5 1.00 18 0.278
92 A 0 0 0.00 0 0.000
93 A 12 6 1.00 15 0.400
94 A 10 6 1.00 15 0.400
95 A 8 5 1.00 13 0.385
96 A 6 4 1.00 7 0.571
97 A 0 0 0.00 0 0.000
98 A 11 6 1.00 15 0.400
99 A 9 5 1.00 13 0.385
100 A 7 4 1.00 11 0.364
101 A 0 0 0.00 0 0.000
102 A 7 7 1.00 19 0.368
103 A 6 6 1.00 17 0.353
104 A 5 5 1.00 15 0.333
105 A 0 0 0.00 0 0.000
106 A 7 7 1.00 22 0.318
107 A 6 6 1.00 20 0.300
108 A 5 5 1.00 18 0.278
109 A 0 0 0.00 0 0.000
110 A 4 3 1.00 4 0.750
111 A 7 4 1.00 6 0.667
112 A 9 5 1.00 8 0.625
113 A 4 3 1.00 8 0.375
114 A 7 4 1.00 10 0.400
115 A 9 5 1.00 12 0.417
116 A 6 6 1.00 12 0.500
117 A 9 5 1.08 14 0.357
118 A 11 6 1.04 16 0.375
119 A 5 6 1.00 10 0.600
120 A 5 4 1.00 8 0.500
121 A 9 8 1.00 14 0.571
122 A 4 4 1.00 8 0.500
123 A 1 1 1.00 14 0.071
124 A 1 1 1.00 19 0.053
125 A 5 3 1.00 26 0.115
126 A 9 6 1.00 21 0.286
127 A 8 6 1.00 21 0.286
128 A 7 6 1.00 19 0.316
129 A 6 6 1.00 18 0.333
130 A 6 5 1.00 21 0.238
131 A 6 6 1.00 21 0.286
132 A 7 6 1.00 21 0.286
133 A 8 6 1.00 21 0.286
134 A 2 2 1.00 39 0.051
135 A 2 2 1.00 39 0.051
136 A 2 2 1.00 37 0.054
137 A 2 2 1.00 39 0.051
138 A 2 2 1.00 39 0.051
139 A 2 2 1.00 39 0.051
140 A 2 2 1.00 40 0.050
141 A 2 2 1.00 40 0.050
142 A 2 2 1.00 38 0.053
143 A 2 2 1.00 40 0.050
144 A 2 2 1.00 40 0.050
145 A 2 2 1.00 40 0.050
146 A 9 7 1.00 24 0.292
147 A 5 5 1.00 20 0.250
148 A 8 7 1.00 20 0.350
149 A 13 10 1.00 20 0.500
150 A 13 10 1.00 20 0.500
151 A 8 7 1.00 20 0.350
152 A 5 5 1.00 20 0.250
153 A 13 9 1.00 24 0.375

[next] [prev] [prev-tail] [front] [up]