# Model tp099
# Source version 1
# Simple APM canonicalizer version 1.3
# AMPL backend version 1.1
param a_1 := 0;
param a_2 := 50;
param a_3 := 50;
param a_4 := 75;
param a_5 := 75;
param a_6 := 75;
param a_7 := 100;
param a_8 := 100;
param b := 32;
param t_1 := 0;
param t_2 := 25;
param t_3 := 50;
param t_4 := 100;
param t_5 := 150;
param t_6 := 200;
param t_7 := 290;
param t_8 := 380;
param s_1 := 0;
param q_1 := 0;
param r_1 := 0;
var x_1 >= 0, <= 1.58;
let x_1 := 0.5;
var x_2 >= 0, <= 1.58;
let x_2 := 0.5;
var x_3 >= 0, <= 1.58;
let x_3 := 0.5;
var x_4 >= 0, <= 1.58;
let x_4 := 0.5;
var x_5 >= 0, <= 1.58;
let x_5 := 0.5;
var x_6 >= 0, <= 1.58;
let x_6 := 0.5;
var x_7 >= 0, <= 1.58;
let x_7 := 0.5;
var s_2 = s_1 + (t_2 - t_1)*(a_2*sin(x_1) - b);
var s_3 = s_2 + (t_3 - t_2)*(a_3*sin(x_2) - b);
var s_4 = s_3 + (t_4 - t_3)*(a_4*sin(x_3) - b);
var s_5 = s_4 + (t_5 - t_4)*(a_5*sin(x_4) - b);
var s_6 = s_5 + (t_6 - t_5)*(a_6*sin(x_5) - b);
var s_7 = s_6 + (t_7 - t_6)*(a_7*sin(x_6) - b);
var s_8 = s_7 + (t_8 - t_7)*(a_8*sin(x_7) - b);
var q_2 = q_1 + 0.5*(t_2 - t_1)^2*(a_2*sin(x_1) - b) + (t_2 - t_1)*s_1;
var q_3 = q_2 + 0.5*(t_3 - t_2)^2*(a_3*sin(x_2) - b) + (t_3 - t_2)*s_2;
var q_4 = q_3 + 0.5*(t_4 - t_3)^2*(a_4*sin(x_3) - b) + (t_4 - t_3)*s_3;
var q_5 = q_4 + 0.5*(t_5 - t_4)^2*(a_5*sin(x_4) - b) + (t_5 - t_4)*s_4;
var q_6 = q_5 + 0.5*(t_6 - t_5)^2*(a_6*sin(x_5) - b) + (t_6 - t_5)*s_5;
var q_7 = q_6 + 0.5*(t_7 - t_6)^2*(a_7*sin(x_6) - b) + (t_7 - t_6)*s_6;
var q_8 = q_7 + 0.5*(t_8 - t_7)^2*(a_8*sin(x_7) - b) + (t_8 - t_7)*s_7;
var c_1 = q_8 - 100000;
var c_2 = s_8 - 1000;
var r_2 = r_1 + a_2*(t_2 - t_1)*cos(x_1);
var r_3 = r_2 + a_3*(t_3 - t_2)*cos(x_2);
var r_4 = r_3 + a_4*(t_4 - t_3)*cos(x_3);
var r_5 = r_4 + a_5*(t_5 - t_4)*cos(x_4);
var r_6 = r_5 + a_6*(t_6 - t_5)*cos(x_5);
var r_7 = r_6 + a_7*(t_7 - t_6)*cos(x_6);
var r_8 = r_7 + a_8*(t_8 - t_7)*cos(x_7);
var mf = -r_8^2;
var myminfun = mf;
var myabsdevnod0_0 = abs(myminfun + 831079891.5101075);
var myreldevnod0_0 = abs(myminfun/831079891.5101075 + 1);
var myabsdevnod0_1 = abs(x_1 - 0.542467816212317);
var myreldevnod0_1 = abs(x_1/0.542467816212317 - 1);
var myabsdevnod0_2 = abs(x_2 - 0.5290214242019767);
var myreldevnod0_2 = abs(x_2/0.5290214242019767 - 1);
var myabsdevnod0_3 = abs(x_3 - 0.5084491553164001);
var myreldevnod0_3 = abs(x_3/0.5084491553164001 - 1);
var myabsdevnod0_4 = abs(x_4 - 0.4802688509618159);
var myreldevnod0_4 = abs(x_4/0.4802688509618159 - 1);
var myabsdevnod0_5 = abs(x_5 - 0.4512363497966467);
var myreldevnod0_5 = abs(x_5/0.4512363497966467 - 1);
var myabsdevnod0_6 = abs(x_6 - 0.4091830824209853);
var myreldevnod0_6 = abs(x_6/0.4091830824209853 - 1);
var myabsdevnod0_7 = abs(x_7 - 0.3527878917811228);
var myreldevnod0_7 = abs(x_7/0.3527878917811228 - 1);
var myabsdevnod1_0 = (1/2)*(abs(myabsdevnod0_0 - myabsdevnod0_1) + (myabsdevnod0_0 + myabsdevnod0_1));
var myreldevnod1_0 = (1/2)*(abs(myreldevnod0_0 - myreldevnod0_1) + (myreldevnod0_0 + myreldevnod0_1));
var myabsdevnod1_2 = (1/2)*(abs(myabsdevnod0_2 - myabsdevnod0_3) + (myabsdevnod0_2 + myabsdevnod0_3));
var myreldevnod1_2 = (1/2)*(abs(myreldevnod0_2 - myreldevnod0_3) + (myreldevnod0_2 + myreldevnod0_3));
var myabsdevnod1_4 = (1/2)*(abs(myabsdevnod0_4 - myabsdevnod0_5) + (myabsdevnod0_4 + myabsdevnod0_5));
var myreldevnod1_4 = (1/2)*(abs(myreldevnod0_4 - myreldevnod0_5) + (myreldevnod0_4 + myreldevnod0_5));
var myabsdevnod1_6 = (1/2)*(abs(myabsdevnod0_6 - myabsdevnod0_7) + (myabsdevnod0_6 + myabsdevnod0_7));
var myreldevnod1_6 = (1/2)*(abs(myreldevnod0_6 - myreldevnod0_7) + (myreldevnod0_6 + myreldevnod0_7));
var myabsdevnod2_0 = (1/2)*(abs(myabsdevnod1_0 - myabsdevnod1_2) + (myabsdevnod1_0 + myabsdevnod1_2));
var myreldevnod2_0 = (1/2)*(abs(myreldevnod1_0 - myreldevnod1_2) + (myreldevnod1_0 + myreldevnod1_2));
var myabsdevnod2_4 = (1/2)*(abs(myabsdevnod1_4 - myabsdevnod1_6) + (myabsdevnod1_4 + myabsdevnod1_6));
var myreldevnod2_4 = (1/2)*(abs(myreldevnod1_4 - myreldevnod1_6) + (myreldevnod1_4 + myreldevnod1_6));
var myabsdevnod3_0 = (1/2)*(abs(myabsdevnod2_0 - myabsdevnod2_4) + (myabsdevnod2_0 + myabsdevnod2_4));
var myreldevnod3_0 = (1/2)*(abs(myreldevnod2_0 - myreldevnod2_4) + (myreldevnod2_0 + myreldevnod2_4));
var zmyabsdevmax = myabsdevnod3_0;
var zmyreldevmax = myreldevnod3_0;
minimize obj: myminfun;
subject to ce_1: c_1 = 0;
subject to ce_2: c_2 = 0;
solve;
display x_1;
display x_2;
display x_3;
display x_4;
display x_5;
display x_6;
display x_7;
display myminfun;
display zmyabsdevmax;
display zmyreldevmax;
# End Model