## Chapter 2detailed summary tables of results

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 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 }

#### 2.1.2 Mathematica

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, 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, 125, 126, 127, 128, 129, 130, 131, 137, 138, 139, 140, 141, 142, 143, 144, 145 }

B grade: { 135, 136 }

C grade: { 40, 41, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 132, 133, 134 }

#### 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, 51, 64, 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, 131, 132, 133, 134, 143, 144, 145 }

B grade: { 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130 }

C grade: { 135, 136, 137, 138, 139, 140, 141, 142 }

F grade: { 40, 41 }

#### 2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 37, 38, 39, 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, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145 }

F grade: { 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 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, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130 }

#### 2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 47, 48, 49, 50, 51, 52, 53, 54, 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, 125, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145 }

B grade: { 37, 38, 39, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124 }

F grade: { 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 46, 68, 73, 126, 127, 128, 129, 130 }

#### 2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 39, 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, 111, 112, 115, 118, 119, 123, 124 }

B grade: { 64, 110, 113, 114, 116, 117, 120, 121, 122 }

C grade: { 133, 134, 135, 136, 141, 142 }

F grade: { 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 125, 126, 127, 128, 129, 130, 131, 132, 137, 138, 139, 140, 143, 144, 145 }

#### 2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 47, 48, 49, 50, 51, 52, 53, 54, 61, 62, 63, 64, 65, 66, 67, 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, 125, 132, 133, 134, 139, 140 }

B grade: { 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 55, 56, 57, 58, 59, 60, 68, 69, 70, 71, 72, 73, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 141, 142, 143, 144, 145 }

F grade: { 40, 41, 135, 136, 137, 138 }

B 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, 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 }

F grade: { 40, 41 }

### 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 74 74 74 61 60 64 68 64 62 normalized size 1 1.00 1.00 0.82 0.81 0.86 0.92 0.86 0.84 time (sec) N/A 0.082 0.015 0.000 0.452 0.663 0.071 0.286 0.036
 Problem 2 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 74 74 74 61 60 64 68 64 62 normalized size 1 1.00 1.00 0.82 0.81 0.86 0.92 0.86 0.84 time (sec) N/A 0.057 0.011 0.003 0.465 0.607 0.072 0.227 0.030
 Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A A A A A A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 69 69 69 58 57 61 65 61 59 normalized size 1 1.00 1.00 0.84 0.83 0.88 0.94 0.88 0.86 time (sec) N/A 0.036 0.012 0.000 0.455 0.519 0.069 0.377 0.029
 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 65 65 65 60 55 55 63 60 57 normalized size 1 1.00 1.00 0.92 0.85 0.85 0.97 0.92 0.88 time (sec) N/A 0.040 0.015 0.002 0.604 0.749 0.157 0.372 0.036
 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 63 63 63 57 55 62 58 57 56 normalized size 1 1.00 1.00 0.90 0.87 0.98 0.92 0.90 0.89 time (sec) N/A 0.051 0.022 0.006 0.680 0.822 0.175 0.299 0.037
 Problem 6 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 63 63 58 58 55 62 61 58 56 normalized size 1 1.00 0.92 0.92 0.87 0.98 0.97 0.92 0.89 time (sec) N/A 0.048 0.038 0.010 0.752 0.502 0.294 0.290 0.035
 Problem 7 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 63 63 60 57 56 62 63 56 55 normalized size 1 1.00 0.95 0.90 0.89 0.98 1.00 0.89 0.87 time (sec) N/A 0.051 0.045 0.007 0.659 0.742 0.521 0.369 0.033
 Problem 8 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 63 63 62 58 56 62 63 57 56 normalized size 1 1.00 0.98 0.92 0.89 0.98 1.00 0.90 0.89 time (sec) N/A 0.051 0.027 0.006 0.752 0.722 1.755 0.288 0.048
 Problem 9 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 63 63 63 60 56 62 66 57 56 normalized size 1 1.00 1.00 0.95 0.89 0.98 1.05 0.90 0.89 time (sec) N/A 0.052 0.054 0.007 0.739 0.571 5.698 0.259 0.777
 Problem 10 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 68 68 68 63 59 62 70 60 60 normalized size 1 1.00 1.00 0.93 0.87 0.91 1.03 0.88 0.88 time (sec) N/A 0.048 0.045 0.006 0.874 0.659 15.378 0.390 0.790
 Problem 11 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 159 159 159 142 143 154 168 154 141 normalized size 1 1.00 1.00 0.89 0.90 0.97 1.06 0.97 0.89 time (sec) N/A 0.214 0.044 0.001 1.134 0.469 0.093 0.406 0.817
 Problem 12 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 159 159 159 142 143 154 163 154 141 normalized size 1 1.00 1.00 0.89 0.90 0.97 1.03 0.97 0.89 time (sec) N/A 0.143 0.036 0.001 1.182 0.549 0.094 0.306 0.068
 Problem 13 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 154 154 154 139 140 151 165 151 138 normalized size 1 1.00 1.00 0.90 0.91 0.98 1.07 0.98 0.90 time (sec) N/A 0.111 0.029 0.002 0.629 0.554 0.093 0.300 0.070
 Problem 14 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 150 150 150 149 138 138 156 149 135 normalized size 1 1.00 1.00 0.99 0.92 0.92 1.04 0.99 0.90 time (sec) N/A 0.107 0.038 0.004 0.843 0.582 0.306 0.364 0.799
 Problem 15 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 145 145 145 147 137 145 156 147 135 normalized size 1 1.00 1.00 1.01 0.94 1.00 1.08 1.01 0.93 time (sec) N/A 0.121 0.091 0.007 0.734 0.647 0.322 0.282 0.797
 Problem 16 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 149 149 139 148 139 145 153 148 135 normalized size 1 1.00 0.93 0.99 0.93 0.97 1.03 0.99 0.91 time (sec) N/A 0.123 0.094 0.007 0.622 0.684 0.460 0.395 0.792
 Problem 17 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 149 149 151 146 140 145 160 146 137 normalized size 1 1.00 1.01 0.98 0.94 0.97 1.07 0.98 0.92 time (sec) N/A 0.137 0.077 0.009 0.681 0.752 0.719 0.284 0.059
 Problem 18 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 148 148 130 144 139 145 153 142 134 normalized size 1 1.00 0.88 0.97 0.94 0.98 1.03 0.96 0.91 time (sec) N/A 0.142 0.081 0.008 0.624 0.919 2.349 0.377 0.058
 Problem 19 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 143 143 142 144 138 145 155 140 136 normalized size 1 1.00 0.99 1.01 0.97 1.01 1.08 0.98 0.95 time (sec) N/A 0.147 0.077 0.009 0.612 0.760 7.809 0.292 0.054
 Problem 20 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 149 149 144 148 140 145 158 141 136 normalized size 1 1.00 0.97 0.99 0.94 0.97 1.06 0.95 0.91 time (sec) N/A 0.143 0.092 0.009 0.688 0.594 27.402 0.396 0.057
 Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 339 339 460 1622 0 0 0 5304 2588 normalized size 1 1.00 1.36 4.78 0.00 0.00 0.00 15.65 7.63 time (sec) N/A 1.856 0.572 0.065 0.000 0.000 0.000 5.749 0.958
 Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 278 278 377 1171 0 0 0 3519 2696 normalized size 1 1.00 1.36 4.21 0.00 0.00 0.00 12.66 9.70 time (sec) N/A 0.466 0.420 0.054 0.000 0.000 0.000 5.025 1.527
 Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 270 270 360 1327 0 0 0 3843 1890 normalized size 1 1.00 1.33 4.91 0.00 0.00 0.00 14.23 7.00 time (sec) N/A 0.835 0.366 0.050 0.000 0.000 0.000 5.566 2.001
 Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 223 223 240 728 0 0 0 2369 5594 normalized size 1 1.00 1.08 3.26 0.00 0.00 0.00 10.62 25.09 time (sec) N/A 0.213 0.359 0.040 0.000 0.000 0.000 5.359 1.885
 Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 211 211 234 616 0 0 0 1616 3942 normalized size 1 1.00 1.11 2.92 0.00 0.00 0.00 7.66 18.68 time (sec) N/A 0.266 0.209 0.025 0.000 0.000 0.000 4.372 2.306
 Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 229 229 285 488 0 0 0 2336 2258 normalized size 1 1.00 1.24 2.13 0.00 0.00 0.00 10.20 9.86 time (sec) N/A 0.259 0.445 0.037 0.000 0.000 0.000 5.075 1.493
 Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 260 260 315 811 0 0 0 3507 2588 normalized size 1 1.00 1.21 3.12 0.00 0.00 0.00 13.49 9.95 time (sec) N/A 0.471 1.080 0.040 0.000 0.000 0.000 5.393 1.022
 Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 288 288 377 1054 0 0 0 3353 3563 normalized size 1 1.00 1.31 3.66 0.00 0.00 0.00 11.64 12.37 time (sec) N/A 0.474 0.889 0.056 0.000 0.000 0.000 5.872 1.172
 Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 412 412 444 1429 0 0 0 5219 4754 normalized size 1 1.00 1.08 3.47 0.00 0.00 0.00 12.67 11.54 time (sec) N/A 1.334 1.382 0.062 0.000 0.000 0.000 8.471 1.774
 Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 347 347 358 831 0 0 0 3228 3278 normalized size 1 1.00 1.03 2.39 0.00 0.00 0.00 9.30 9.45 time (sec) N/A 0.618 0.894 0.044 0.000 0.000 0.000 5.369 1.613
 Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 356 356 378 1119 0 0 0 4440 3835 normalized size 1 1.00 1.06 3.14 0.00 0.00 0.00 12.47 10.77 time (sec) N/A 0.902 1.039 0.055 0.000 0.000 0.000 7.049 1.671
 Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 317 317 335 1344 0 0 0 3013 3198 normalized size 1 1.00 1.06 4.24 0.00 0.00 0.00 9.50 10.09 time (sec) N/A 0.415 1.249 0.177 0.000 0.000 0.000 5.173 1.595
 Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 368 368 393 1813 0 0 0 5158 4707 normalized size 1 1.00 1.07 4.93 0.00 0.00 0.00 14.02 12.79 time (sec) N/A 0.867 1.224 0.151 0.000 0.000 0.000 7.849 1.675
 Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 403 403 458 1603 0 0 0 6022 8129 normalized size 1 1.00 1.14 3.98 0.00 0.00 0.00 14.94 20.17 time (sec) N/A 0.932 1.473 0.063 0.000 0.000 0.000 6.553 1.838
 Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 514 514 559 2398 0 0 0 9015 8684 normalized size 1 1.00 1.09 4.67 0.00 0.00 0.00 17.54 16.89 time (sec) N/A 1.486 2.027 0.085 0.000 0.000 0.000 11.545 2.468
 Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 534 534 655 2512 0 0 0 6938 10595 normalized size 1 1.00 1.23 4.70 0.00 0.00 0.00 12.99 19.84 time (sec) N/A 1.992 2.470 0.096 0.000 0.000 0.000 7.565 2.773
 Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B A B F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 399 399 296 5520 611 3898 0 7808 2443 normalized size 1 1.00 0.74 13.83 1.53 9.77 0.00 19.57 6.12 time (sec) N/A 0.425 0.919 0.013 1.706 1.909 0.000 1.131 3.280
 Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B A B F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 260 260 185 2187 344 1603 0 3203 1314 normalized size 1 1.00 0.71 8.41 1.32 6.17 0.00 12.32 5.05 time (sec) N/A 0.223 0.277 0.010 1.731 1.041 0.000 0.725 1.810
 Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B A B A B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 137 137 90 585 155 444 3735 914 527 normalized size 1 1.00 0.66 4.27 1.13 3.24 27.26 6.67 3.85 time (sec) N/A 0.088 0.104 0.005 0.815 1.338 2.575 0.533 1.075
 Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A C F F F F F F veriﬁed N/A Yes NO TBD TBD TBD TBD TBD TBD size 368 368 438 0 0 0 0 0 -1 normalized size 1 1.00 1.19 0.00 0.00 0.00 0.00 0.00 -0.00 time (sec) N/A 0.622 0.474 0.035 0.000 1.068 0.000 0.000 0.000
 Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A C F F F F(-1) F F veriﬁed N/A Yes NO TBD TBD TBD TBD TBD TBD size 685 670 242 0 0 0 0 0 -1 normalized size 1 0.98 0.35 0.00 0.00 0.00 0.00 0.00 -0.00 time (sec) N/A 2.378 0.327 0.031 0.000 1.106 0.000 0.000 0.000
 Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 356 356 378 1119 0 0 0 4440 3835 normalized size 1 1.00 1.06 3.14 0.00 0.00 0.00 12.47 10.77 time (sec) N/A 0.924 1.038 0.000 0.000 0.000 0.000 7.038 0.004
 Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 356 356 378 1119 0 0 0 4440 3835 normalized size 1 1.00 1.06 3.14 0.00 0.00 0.00 12.47 10.77 time (sec) N/A 0.371 0.425 0.036 0.000 0.000 0.000 7.135 1.551
 Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 356 356 378 1119 0 0 0 4439 3835 normalized size 1 1.00 1.06 3.14 0.00 0.00 0.00 12.47 10.77 time (sec) N/A 0.370 0.154 0.039 0.000 0.000 0.000 6.896 1.474
 Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 356 356 378 1119 0 0 0 4439 3835 normalized size 1 1.00 1.06 3.14 0.00 0.00 0.00 12.47 10.77 time (sec) N/A 0.356 0.154 0.034 0.000 0.000 0.000 7.311 1.389
 Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 356 356 378 1119 0 0 0 4439 3835 normalized size 1 1.00 1.06 3.14 0.00 0.00 0.00 12.47 10.77 time (sec) N/A 0.359 0.153 0.033 0.000 0.000 0.000 6.836 1.414
 Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F(-2) A F(-1) A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 273 273 260 622 0 900 0 306 2972 normalized size 1 1.00 0.95 2.28 0.00 3.30 0.00 1.12 10.89 time (sec) N/A 0.854 0.199 0.007 0.000 1.846 0.000 1.868 1.604
 Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F(-2) A F(-1) A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 203 203 193 474 0 677 0 214 2295 normalized size 1 1.00 0.95 2.33 0.00 3.33 0.00 1.05 11.31 time (sec) N/A 0.424 0.143 0.006 0.000 1.957 0.000 2.005 1.626
 Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F(-2) A F(-1) A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 144 144 136 321 0 473 0 141 1689 normalized size 1 1.00 0.94 2.23 0.00 3.28 0.00 0.98 11.73 time (sec) N/A 0.272 0.099 0.006 0.000 1.504 0.000 1.987 1.300
 Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F(-2) A F(-1) A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 103 103 100 211 0 318 0 99 1081 normalized size 1 1.00 0.97 2.05 0.00 3.09 0.00 0.96 10.50 time (sec) N/A 0.179 0.066 0.004 0.000 1.337 0.000 1.780 1.830
 Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A A F(-2) A F(-1) A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 97 97 178 165 0 309 0 97 3927 normalized size 1 1.00 1.84 1.70 0.00 3.19 0.00 1.00 40.48 time (sec) N/A 0.200 0.137 0.009 0.000 1.410 0.000 1.903 8.881
 Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F(-2) A F(-1) A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 118 118 203 227 0 399 0 135 4437 normalized size 1 1.00 1.72 1.92 0.00 3.38 0.00 1.14 37.60 time (sec) N/A 0.285 0.150 0.010 0.000 1.643 0.000 1.777 7.857
 Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F(-2) A F(-1) A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 174 174 314 356 0 609 0 212 6187 normalized size 1 1.00 1.80 2.05 0.00 3.50 0.00 1.22 35.56 time (sec) N/A 0.407 0.345 0.012 0.000 2.538 0.000 1.719 9.917
 Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F(-2) A F(-1) A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 244 244 416 523 0 834 0 313 9141 normalized size 1 1.00 1.70 2.14 0.00 3.42 0.00 1.28 37.46 time (sec) N/A 0.573 0.348 0.013 0.000 5.313 0.000 1.941 13.829
 Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F B F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 369 369 456 1450 0 15467 0 7243 23332 normalized size 1 1.00 1.24 3.93 0.00 41.92 0.00 19.63 63.23 time (sec) N/A 4.577 0.509 0.035 0.000 35.653 0.000 5.025 4.912
 Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F B F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 282 282 365 1035 0 9364 0 5461 15674 normalized size 1 1.00 1.29 3.67 0.00 33.21 0.00 19.37 55.58 time (sec) N/A 3.590 0.492 0.030 0.000 8.048 0.000 4.755 3.359
 Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F B F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 219 219 258 676 0 5788 0 4086 10209 normalized size 1 1.00 1.18 3.09 0.00 26.43 0.00 18.66 46.62 time (sec) N/A 0.637 0.326 0.027 0.000 4.487 0.000 3.908 3.360
 Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F B F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 213 213 253 563 0 5930 0 3988 10170 normalized size 1 1.00 1.19 2.64 0.00 27.84 0.00 18.72 47.75 time (sec) N/A 0.839 0.302 0.025 0.000 2.258 0.000 5.936 3.515
 Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F B F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 267 267 284 727 0 9850 0 3813 15505 normalized size 1 1.00 1.06 2.72 0.00 36.89 0.00 14.28 58.07 time (sec) N/A 1.065 0.339 0.027 0.000 10.542 0.000 3.442 4.763
 Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F B F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 329 329 394 1121 0 15830 0 6718 23019 normalized size 1 1.00 1.20 3.41 0.00 48.12 0.00 20.42 69.97 time (sec) N/A 1.942 0.551 0.033 0.000 38.588 0.000 7.015 6.247
 Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F(-2) B F(-1) A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 320 320 309 1167 0 2111 0 424 3499 normalized size 1 1.00 0.97 3.65 0.00 6.60 0.00 1.32 10.93 time (sec) N/A 1.233 0.497 0.024 0.000 1.656 0.000 1.952 1.333
 Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F(-2) B F(-1) A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 236 236 236 832 0 1455 0 279 2450 normalized size 1 1.00 1.00 3.53 0.00 6.17 0.00 1.18 10.38 time (sec) N/A 0.440 0.356 0.017 0.000 1.014 0.000 1.865 1.811
 Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F(-2) B F(-1) A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 165 165 175 336 0 970 0 195 1651 normalized size 1 1.00 1.06 2.04 0.00 5.88 0.00 1.18 10.01 time (sec) N/A 0.287 0.249 0.015 0.000 1.056 0.000 1.838 2.717
 Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A A F(-2) B B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 123 123 130 205 0 650 474 140 342 normalized size 1 1.00 1.06 1.67 0.00 5.28 3.85 1.14 2.78 time (sec) N/A 0.184 0.102 0.012 0.000 0.890 38.035 2.167 0.378
 Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F(-2) B F(-1) A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 166 166 268 462 0 1103 0 227 8706 normalized size 1 1.00 1.61 2.78 0.00 6.64 0.00 1.37 52.45 time (sec) N/A 0.394 0.445 0.017 0.000 3.256 0.000 2.001 11.849
 Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F(-2) B F(-1) A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 234 234 403 722 0 1764 0 287 11879 normalized size 1 1.00 1.72 3.09 0.00 7.54 0.00 1.23 50.76 time (sec) N/A 0.725 0.658 0.023 0.000 7.130 0.000 1.846 12.979
 Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F(-2) B F(-1) A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 329 329 592 1078 0 2567 0 535 15905 normalized size 1 1.00 1.80 3.28 0.00 7.80 0.00 1.63 48.34 time (sec) N/A 1.157 1.216 0.029 0.000 16.734 0.000 1.888 21.016
 Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 550 550 648 2558 0 0 0 8957 33799 normalized size 1 1.00 1.18 4.65 0.00 0.00 0.00 16.29 61.45 time (sec) N/A 13.227 2.131 0.056 0.000 0.000 0.000 9.044 4.104
 Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F B F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 436 436 511 1977 0 12597 0 7496 25862 normalized size 1 1.00 1.17 4.53 0.00 28.89 0.00 17.19 59.32 time (sec) N/A 5.541 1.542 0.052 0.000 17.362 0.000 8.250 2.648
 Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F B F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 362 362 414 1300 0 8951 0 6208 19494 normalized size 1 1.00 1.14 3.59 0.00 24.73 0.00 17.15 53.85 time (sec) N/A 2.498 1.103 0.043 0.000 8.443 0.000 6.811 6.543
 Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F B F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 346 346 382 1182 0 8991 0 6356 19589 normalized size 1 1.00 1.10 3.42 0.00 25.99 0.00 18.37 56.62 time (sec) N/A 1.896 1.081 0.040 0.000 8.489 0.000 6.973 6.552
 Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F B F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 399 399 444 1575 0 13111 0 7182 28164 normalized size 1 1.00 1.11 3.95 0.00 32.86 0.00 18.00 70.59 time (sec) N/A 2.203 1.319 0.048 0.000 19.288 0.000 7.093 6.862
 Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad grade A A A B F F(-1) F(-1) B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD TBD size 575 575 548 2180 0 0 0 8660 36097 normalized size 1 1.00 0.95 3.79 0.00 0.00 0.00 15.06 62.78 time (sec) N/A 9.906 1.797 0.065 0.000 0.000 0.000 8.591 7.370
 Problem 74 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 68 68 62 56 58 82 61 63 57 normalized size 1 1.00 0.91 0.82 0.85 1.21 0.90 0.93 0.84 time (sec) N/A 0.126 0.028 0.017 0.602 0.785 0.172 0.362 0.056
 Problem 75 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 61 61 61 51 53 77 56 58 53 normalized size 1 1.00 1.00 0.84 0.87 1.26 0.92 0.95 0.87 time (sec) N/A 0.118 0.027 0.016 0.719 0.829 0.171 0.323 0.039
 Problem 76 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 54 54 54 46 48 72 48 53 47 normalized size 1 1.00 1.00 0.85 0.89 1.33 0.89 0.98 0.87 time (sec) N/A 0.108 0.024 0.016 1.075 0.708 0.173 0.367 0.897
 Problem 77 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 49 49 49 41 43 67 44 45 43 normalized size 1 1.00 1.00 0.84 0.88 1.37 0.90 0.92 0.88 time (sec) N/A 0.086 0.022 0.015 0.514 0.901 0.174 0.390 0.038
 Problem 78 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 42 36 38 57 36 40 37 normalized size 1 1.00 1.00 0.86 0.90 1.36 0.86 0.95 0.88 time (sec) N/A 0.049 0.017 0.016 0.522 1.045 0.166 0.354 0.049
 Problem 79 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 44 38 44 71 41 47 40 normalized size 1 1.00 1.00 0.86 1.00 1.61 0.93 1.07 0.91 time (sec) N/A 0.077 0.022 0.016 0.724 0.901 0.183 0.377 0.041
 Problem 80 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 55 55 50 45 53 92 51 53 50 normalized size 1 1.00 0.91 0.82 0.96 1.67 0.93 0.96 0.91 time (sec) N/A 0.104 0.025 0.017 0.792 0.980 0.205 0.374 0.044
 Problem 81 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 64 64 56 50 56 97 56 66 55 normalized size 1 1.00 0.88 0.78 0.88 1.52 0.88 1.03 0.86 time (sec) N/A 0.111 0.027 0.019 0.679 1.053 0.213 0.341 0.919
 Problem 82 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 70 70 71 56 58 79 68 58 58 normalized size 1 1.00 1.01 0.80 0.83 1.13 0.97 0.83 0.83 time (sec) N/A 0.085 0.044 0.012 1.639 1.087 0.210 0.331 0.952
 Problem 83 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 57 57 58 49 51 74 54 51 50 normalized size 1 1.00 1.02 0.86 0.89 1.30 0.95 0.89 0.88 time (sec) N/A 0.082 0.048 0.012 1.621 0.865 0.207 0.314 0.054
 Problem 84 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 56 56 57 46 48 69 54 48 48 normalized size 1 1.00 1.02 0.82 0.86 1.23 0.96 0.86 0.86 time (sec) N/A 0.073 0.042 0.013 1.635 0.909 0.210 0.306 0.918
 Problem 85 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 49 49 50 41 43 64 48 43 42 normalized size 1 1.00 1.02 0.84 0.88 1.31 0.98 0.88 0.86 time (sec) N/A 0.066 0.038 0.011 1.633 0.914 0.207 0.340 0.068
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 Problem 86 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 48 48 46 38 40 59 46 40 40 normalized size 1 1.00 0.96 0.79 0.83