1
2log2h = <float64ne> (_log2h);
3log2m = <float64ne> (_log2m);
4log2l = <float64ne> (_log2l);
5
6Log2hml = log2h + log2m + log2l; #MAPLE
7
8logih = <float64ne> (_logih);
9logim = <float64ne> (_logim);
10logil = <float64ne> (_logil);
11
12Logihml = logih + logim + logil; #MAPLE
13
14
15accPolyC14 = <float64ne> (_accPolyC14);
16accPolyC13 = <float64ne> (_accPolyC13);
17accPolyC12 = <float64ne> (_accPolyC12);
18accPolyC11 = <float64ne> (_accPolyC11);
19accPolyC10 = <float64ne> (_accPolyC10);
20
21accPolyC9h = <float64ne> (_accPolyC9h);
22accPolyC9l = <float64ne> (_accPolyC9l);
23AccPolyC9hl = accPolyC9h + accPolyC9l; #MAPLE
24accPolyC8h = <float64ne> (_accPolyC8h);
25accPolyC8l = <float64ne> (_accPolyC8l);
26AccPolyC8hl = accPolyC8h + accPolyC8l; #MAPLE
27accPolyC7h = <float64ne> (_accPolyC7h);
28accPolyC7l = <float64ne> (_accPolyC7l);
29AccPolyC7hl = accPolyC7h + accPolyC7l; #MAPLE
30accPolyC6h = <float64ne> (_accPolyC6h);
31accPolyC6l = <float64ne> (_accPolyC6l);
32AccPolyC6hl = accPolyC6h + accPolyC6l; #MAPLE
33accPolyC5h = <float64ne> (_accPolyC5h);
34accPolyC5l = <float64ne> (_accPolyC5l);
35AccPolyC5hl = accPolyC5h + accPolyC5l; #MAPLE
36accPolyC4h = <float64ne> (_accPolyC4h);
37accPolyC4l = <float64ne> (_accPolyC4l);
38AccPolyC4hl = accPolyC4h + accPolyC4l; #MAPLE
39accPolyC3h = <float64ne> (_accPolyC3h);
40accPolyC3l = <float64ne> (_accPolyC3l);
41AccPolyC3hl = accPolyC3h + accPolyC3l; #MAPLE
42
43E = 1; #MAPLE
44
45zh = <float64ne> (Z);
46zl = Z - zh; #MAPLE
47
48highPoly <float64ne> = accPolyC10 + zh * (accPolyC11 + zh * (accPolyC12 + zh * (accPolyC13 + zh * accPolyC14)));
49
50T1hl = zh * highPoly; #MAPLE
51
52T2 = AccPolyC9hl + T1hl; #MAPLE
53T3 = Z * T2hl; #MAPLE
54T4 = AccPolyC8hl + T3hl; #MAPLE
55T5 = Z * T4hl; #MAPLE
56T6 = AccPolyC7hl + T5hl; #MAPLE
57T7 = Z * T6hl; #MAPLE
58T8 = AccPolyC6hl + T7hl; #MAPLE
59T9 = Z * T8hl; #MAPLE
60T10 = AccPolyC5hl + T9hl; #MAPLE
61T11 = Z * T10hl; #MAPLE
62T12 = AccPolyC4hl + T11hl; #MAPLE
63T13 = Z * T12hl; #MAPLE
64T14 = AccPolyC3hl + T13hl; #MAPLE
65
66
67ZSquare = Z * Z; #MAPLE
68ZCube = Z * ZSquarehml; #MAPLE
69HigherPolyMultZ = T14hl * ZCubehml; #MAPLE
70ZSquareHalfhml = -0.5 * ZSquarehml; #MAPLE
71PolyWithSquare = ZSquareHalfhml + HigherPolyMultZhml; #MAPLE
72Poly = Z + PolyWithSquarehml; #MAPLE
73Logy = Logihml + Polyhml; #MAPLE
74Log2edhml = E * Log2hml; #MAPLE
75Logover = Log2edhml + Logyhml; #MAPLE
76
77
78#Mathematical definition of the logarithm
79
80MHighPoly = accPolyC10 + Z * (accPolyC11 + Z * (accPolyC12 + Z * (accPolyC13 + Z * accPolyC14))); #MAPLE
81MT1 = Z * MHighPoly; #MAPLE
82MT2 = AccPolyC9hl + MT1; #MAPLE
83MT3 = Z * MT2; #MAPLE
84MT4 = AccPolyC8hl + MT3; #MAPLE
85MT5 = Z * MT4; #MAPLE
86MT6 = AccPolyC7hl + MT5; #MAPLE
87MT7 = Z * MT6; #MAPLE
88MT8 = AccPolyC6hl + MT7; #MAPLE
89MT9 = Z * MT8; #MAPLE
90MT10 = AccPolyC5hl + MT9; #MAPLE
91MT11 = Z * MT10; #MAPLE
92MT12 = AccPolyC4hl + MT11; #MAPLE
93MT13 = Z * MT12; #MAPLE
94MT14 = AccPolyC3hl + MT13; #MAPLE
95MZSquare = Z * Z; #MAPLE
96MZCube = Z * MZSquare; #MAPLE
97MHigherPolyMultZ = MT14 * MZCube; #MAPLE
98MZSquareHalf = -0.5 * MZSquare; #MAPLE
99MPolyWithSquare = MZSquareHalf + MHigherPolyMultZ; #MAPLE
100MPoly = Z + MPolyWithSquare; #MAPLE
101MLogy = MLogi + MLog1pZ; #MAPLE
102MLog2E = E * MLog2; #MAPLE
103MLog = MLog2E + MLogy; #MAPLE
104
105
106#Useful additional definitions
107
108delta1 = highPoly - MHighPoly; #MAPLE
109delta2 = T1hl - MT1; #MAPLE
110delta3 = T2hl - MT2; #MAPLE
111delta4 = T3hl - MT3; #MAPLE
112delta5 = T4hl - MT4; #MAPLE
113delta6 = T5hl - MT5; #MAPLE
114delta7 = T6hl - MT6; #MAPLE
115delta8 = T7hl - MT7; #MAPLE
116delta9 = T8hl - MT8; #MAPLE
117delta10 = T9hl - MT9; #MAPLE
118delta11 = T10hl - MT10; #MAPLE
119delta12 = T11hl - MT11; #MAPLE
120delta13 = T12hl - MT12; #MAPLE
121delta14 = T13hl - MT13; #MAPLE
122delta15 = T14hl - MT14; #MAPLE
123delta16 = ZSquarehml - MZSquare; #MAPLE
124delta17 = ZCubehml - MZCube; #MAPLE
125delta18 = HigherPolyMultZhml - MHigherPolyMultZ; #MAPLE
126delta19 = ZSquareHalfhml - MZSquareHalf; #MAPLE
127delta20 = PolyWithSquarehml - MPolyWithSquare; #MAPLE
128delta21 = Polyhml - MPoly; #MAPLE
129delta22 = Logyhml - MLogy; #MAPLE
130delta23 = Log2edhml - MLog2E; #MAPLE
131delta24 = Loghml - MLog; #MAPLE
132delta25 = Logihml - MLogi; #MAPLE
133delta26 = Polyhml - MLog1pZ; #MAPLE
134
135
136#End additional definitions
137
138{
139(T2hl - T2) / T2 in [-1b-103,1b-103]
140/\ (T3hl - T3) / T3 in [-1b-102,1b-102]
141/\ (T4hl - T4) / T4 in [-1b-103,1b-103]
142/\ (T5hl - T5) / T5 in [-1b-102,1b-102]
143/\ (T6hl - T6) / T6 in [-1b-103,1b-103]
144/\ (T7hl - T7) / T7 in [-1b-102,1b-102]
145/\ (T8hl - T8) / T8 in [-1b-103,1b-103]
146/\ (T9hl - T9) / T9 in [-1b-102,1b-102]
147/\ (T10hl - T10) / T10 in [-1b-103,1b-103]
148/\ (T11hl - T11) / T11 in [-1b-102,1b-102]
149/\ (T12hl - T12) / T12 in [-1b-103,1b-103]
150/\ (T13hl - T13) / T13 in [-1b-102,1b-102]
151/\ (T14hl - T14) / T14 in [-1b-103,1b-103]
152/\ (ZSquarehml - ZSquare) / ZSquare in [-1b-149,1b-149]
153/\ (ZCubehml - ZCube) / ZCube in [-1b-144,1b-144]
154/\ (HigherPolyMultZhml - HigherPolyMultZ) / HigherPolyMultZ in [-1b-141,1b-141]
155/\ (PolyWithSquarehml - PolyWithSquare) / PolyWithSquare in [-1b-137,1b-137]
156/\ (Polyhml - Poly) / Poly in [-1b-134,1b-134]
157/\ (Logyhml - Logy) / Logy in [-1b-128,1b-128]
158/\ (Loghml - Logover) / Logover in [-1b-123,1b-123]
159/\ (Log2hml - MLog2) / MLog2 in [-1b-126,1b-126]
160/\ (Logihml - MLogi) / MLogi in [-1b-159,1b-159]
161/\ (MPoly - MLog1pZ) / MLog1pZ in [-_epsilonApproxAccurate,_epsilonApproxAccurate]
162/\ Z in [_zmin,_zmax]
163/\ ((logh + logm + logl) - Loghml) / Loghml in [-1b-159,1b-159]
164->
165((logh + logm + logl) - MLog) / MLog in [-5735b-132,5735b-132]
166}
167
168MLog1pZ -> MPoly * (1 / (((MPoly - MLog1pZ) / MLog1pZ) + 1));
169MLog2 -> Log2hml * (1 / (((Log2hml - MLog2) / MLog2) + 1));
170MLogi -> Logihml * (1 / (((Logihml - MLogi) / MLogi) + 1));
171
172T2hl -> (T2 * ((T2hl - T2) / T2)) + T2;
173T3hl -> (T3 * ((T3hl - T3) / T3)) + T3;
174T4hl -> (T4 * ((T4hl - T4) / T4)) + T4;
175T5hl -> (T5 * ((T5hl - T5) / T5)) + T5;
176T6hl -> (T6 * ((T6hl - T6) / T6)) + T6;
177T7hl -> (T7 * ((T7hl - T7) / T7)) + T7;
178T8hl -> (T8 * ((T8hl - T8) / T8)) + T8;
179T9hl -> (T9 * ((T9hl - T9) / T9)) + T9;
180T10hl -> (T10 * ((T10hl - T10) / T10)) + T10;
181T11hl -> (T11 * ((T11hl - T11) / T11)) + T11;
182T12hl -> (T12 * ((T12hl - T12) / T12)) + T12;
183T13hl -> (T13 * ((T13hl - T13) / T13)) + T13;
184T14hl -> (T14 * ((T14hl - T14) / T14)) + T14;
185
186ZSquarehml -> (ZSquare * ((ZSquarehml - ZSquare) / ZSquare)) + ZSquare;
187ZCubehml -> (ZCube * ((ZCubehml - ZCube) / ZCube)) + ZCube;
188HigherPolyMultZhml -> (HigherPolyMultZ * ((HigherPolyMultZhml - HigherPolyMultZ) / HigherPolyMultZ)) + HigherPolyMultZ;
189PolyWithSquarehml -> (PolyWithSquare * ((PolyWithSquarehml - PolyWithSquare) / PolyWithSquare)) + PolyWithSquare;
190Polyhml -> (Poly * ((Polyhml - Poly) / Poly)) + Poly;
191Logyhml -> (Logy * ((Logyhml - Logy) / Logy)) + Logy;
192
193
194delta3 -> delta2 + (T2 * ((T2hl - T2) / T2));
195delta4 -> Z * delta3 + T3 * ((T3hl - T3) / T3);
196delta5 -> delta4 + (T4 * ((T4hl - T4) / T4));
197delta6 -> Z * delta5 + T5 * ((T5hl - T5) / T5);
198delta7 -> delta6 + (T6 * ((T6hl - T6) / T6));
199delta8 -> Z * delta7 + T7 * ((T7hl - T7) / T7);
200delta9 -> delta8 + (T8 * ((T8hl - T8) / T8));
201delta10 -> Z * delta9 + T9 * ((T9hl - T9) / T9);
202delta11 -> delta10 + (T10 * ((T10hl - T10) / T10));
203delta12 -> Z * delta11 + T11 * ((T11hl - T11) / T11);
204delta13 -> delta12 + (T12 * ((T12hl - T12) / T12));
205delta14 -> Z * delta13 + T13 * ((T13hl - T13) / T13);
206delta15 -> delta14 + (T14 * ((T14hl - T14) / T14));
207delta16 -> Z*Z*((ZSquarehml - ZSquare) / ZSquare);
208delta17 -> Z * delta16 + ZCube * ((ZCubehml - ZCube) / ZCube);
209delta18 -> delta15 * delta17 + delta15 * MZCube + delta17 * MT14 +
210		HigherPolyMultZ * ((HigherPolyMultZhml - HigherPolyMultZ) / HigherPolyMultZ);
211delta20 -> delta19 + delta18 + PolyWithSquare * ((PolyWithSquarehml - PolyWithSquare) / PolyWithSquare);
212delta21 -> delta20 + Poly * ((Polyhml - Poly) / Poly);
213delta22 -> delta25 + delta26 + Logy * ((Logyhml - Logy) / Logy);
214delta26 -> delta21 + MLog1pZ * ((MPoly - MLog1pZ) / MLog1pZ);
215delta24 -> delta23 + delta22 + Logover * ((Loghml - Logover) / Logover);
216
217((logh + logm + logl) - MLog) / MLog -> ((Loghml - MLog) / MLog) + ((((logh + logm + logl) - Loghml) / Loghml) * (((Loghml - MLog) / MLog) + 1));