Commit 77e7f380 authored by Heiko Becker's avatar Heiko Becker
Browse files

Add FPTaylor input files

parent 8b9d6c33
Variables
real s1 in [0.0, 1.0],
real s2 in [-0.5, 0.5],
real s3 in [0, 0.5],
real s4 in [0, 0.5];
Definitions
r1 rnd64= (-1828.6) * s1 + (-1028.6) * s2 + (-2008.0) * s3 + (-104.0) * s4
;
Expressions
ballbeam = r1
;
Variables
real s1 in [-10.0, 10.0],
real s2 in [-10.0, 10.0],
real s3 in [-10.0, 10.0],
real s4 in [-10.0, 10.0],
real y1 in [-10.0, 10.0],
real y2 in [-10.0, 10.0];
Expressions
out1 rnd64= (-0.0429) * s1 + (-0.9170) * s2 + (-0.3299) * s3 + (-0.8206) * s4,
out2 rnd64= 2.4908 * s1 + 0.0751 * s2 + 1.7481 * s3 + (-1.1433) * s4,
state1 rnd64= 0.9670 * s1 + (-0.0019) * s2 + 0.0187 * s3 + (-0.0088) * s4 + 0.0447 * y1,
state2 rnd64= (-0.0078) * s1 + 0.9052 * s2 + (-0.0181) * s3 + (-0.0392) * s4 + (-0.0003) * y1 + 0.0020 * y2,
state3 rnd64= (-0.0830) * s1 + 0.0222 * s2 + 0.8620 * s3 + 0.0978 * s4 + 0.0170 * y1 + 0.0058 * y2,
state4 rnd64= (-0.0133) * s1 + 0.0243 * s2 + (-0.0043) * s3 + 0.9824 * s4 + 0.0127 * y1 + 0.0059 * y2
;
Variables
real s1 in [-1.0, 1.0],
real s2 in [-1.0, 1.0],
real s3 in [-1.0, 1.0],
real s4 in [-1.0, 1.0],
real y1 in [-1.0, 1.0],
real y2 in [-1.0, 1.0];
Expressions
out1 rnd64= (-0.058300) * s1 + (-0.908300) * s2 + (-0.325800) * s3 + (-0.872100) * s4,
out2 rnd64= (2.463800) * s1 + (0.050400) * s2 + (1.709900) * s3 + (-1.165300) * s4,
state1 rnd64= (0.934292) * s1 + (0.008415) * s2 + (-0.014106) * s3 + (0.023954) * s4 + (0.077400) * y1 + (-0.010300) * y2,
state2 rnd64= (-0.006769) * s1 + (0.884924) * s2 + (-0.016066) * s3 + (-0.044019) * s4 + (-0.002200) * y1 + (0.022700) * y2,
state3 rnd64= (-0.092148) * s1 + (-0.011039) * s2 + (0.853511) * s3 + (0.107537) * s4 + (0.026700) * y1 + (0.039800) * y2,
state4 rnd64= (-0.036410) * s1 + (0.030194) * s2 + (-0.027155) * s3 + (1.004619) * s4 + (0.035600) * y1 + (0.000100) * y2
;
Variables
real s1 in [-1.0, 1.0],
real s2 in [-1.0, 1.0],
real y1 in [-1.0, 1.0];
Expressions
out1 rnd64= (-3.025300) * s1 + (-12.608900) * s2,
state1 rnd64= (0.961270) * s1 + (-0.095962) * s2 + (0.013200) * y1,
state2 rnd64= (-0.058217) * s1 + (0.727430) * s2 + (0.102100) * y1
;
Variables
real u in [0.0, 1.0];
Definitions
r1 rnd64= (1 - u) * (1 - u) * (1 - u) / 6.0,
r2 rnd64= (3 * u*u*u - 6 * u*u + 4) / 6.0,
r3 rnd64= (-3 * u*u*u + 3*u*u + 3*u + 1) / 6.0,
r4 rnd64= -u*u*u / 6.0
;
Expressions
bspline0 = r1,
bspline1 = r2,
bspline2 = r3,
bspline3 = r4
;
Variables
real k in [1.3806503e-23, 1.3806503e-23];
real T in [300.0, 300.0];
real a in [0.401, 0.401];
real b in [42.7e-6, 42.7e-6];
real N in [1000, 1000];
real p in [3.5e7, 3.5e7];
real V in [0.1, 0.5];
Definitions
res rnd64= (p + a * (N / V) * (N / V)) * (V - N * b) - k * N * T;
Expressions
carbon_gas = res;
Variables
real s1 in [-1.0, 1.0],
real s2 in [-1.0, 1.0],
real s3 in [-1.0, 1.0],
real y1 in [-1.0, 1.0];
Expressions
out1 rnd64= (-0.112900) * s1 + (-0.021100) * s2 + (-0.009300) * s3,
state1 rnd64= (0.960883) * s1 + (0.000949) * s2 + (-0.000004) * s3 + (0.039000) * y1,
state2 rnd64= (-0.602449) * s1 + (0.899089) * s2 + (-0.013648) * s3 + (0.370000) * y1,
state3 rnd64= (-0.009134) * s1 + (-0.011434) * s2 + (-0.002232) * s3 + (-0.017500) * y1
;
Variables
real u0 in [-100, 100],
real v0 in [20, 20000],
real T0 in [-30, 50];
Definitions
u rnd64= u0,
v rnd64= v0,
T rnd64= T0,
t1 = rnd64(rnd64(rnd64(331.4) + rnd64(rnd64(0.6) * T))),
r rnd64= rnd64(rnd64(-t1) * v) / ((t1 + u) * (t1 + u))
;
Expressions
doppler1 = r
;
Variables
real x1 in [0, 6],
real x2 in [0, 6],
real x3 in [1, 5],
real x4 in [0, 6],
real x5 in [1, 5],
real x6 in [0, 10];
Expressions
floudas1 rnd64= -25 * ((x1 - 2) * (x1 - 2)) - ((x2 - 2) * (x2 - 2)) - ((x3 - 1) * (x3 - 1))
- ((x4 - 4) * (x4 - 4)) - ((x5 - 1) * (x5 - 1)) - ((x6 - 4) * (x6 - 4));
Variables
real x1 in [0, 3],
real x2 in [0, 4];
Expressions
floudas2 rnd64= -x1 - x2;
Variables
real x1 in [0, 1],
real x2 in [0, 1],
real x3 in [0, 1],
real x4 in [0, 1],
real x5 in [0, 1],
real x6 in [0, 1],
real x7 in [0, 1],
real x8 in [0, 1],
real x9 in [0, 1],
real x10 in [0, 1];
Expressions
floudas26 rnd64= 48*x1 + 42*x2 + 48*x3 + 45*x4 + 44*x5 + 41*x6 + 47*x7 + 42*x8 + 45*x9 + 46*x10 -
50*(x1*x1 + x2*x2 + x3*x3 + x4*x4 + x5*x5 + x6*x6 + x7*x7 + x8*x8 + x9*x9 + x10*x10);
Variables
real x1 in [0, 6],
real x2 in [0, 6],
real x3 in [1, 5],
real x4 in [0, 6],
real x5 in [1, 5],
real x6 in [0, 10];
Expressions
floudas33 rnd64= (-1) * (25 * (x1 - 2)*(x1 - 2)) - (x2 - 2)* (x2 - 2) - (x3 - 1)*(x3 - 1) -
(x4 - 4)*(x4 - 4) - (x5 - 1)*(x5 - 1) - (x6 - 4)* (x6 - 4);
Variables
real x1 in [0, 2],
real x2 in [0, 2],
real x3 in [0, 3];
Expressions
floudas34 rnd64= -2 * x1 + x2 - x3;
Variables
real x1 in [0, 3],
real x2 in [0, 4];
Expressions
floudas46 rnd64= (-1 * x1) - x2;
Variables
real x1 in [0, 2],
real x2 in [0, 3];
Expressions
floudas47 rnd64= -12 * x1 - 7 * x2 + x2 * x2;
Variables
real x1_0 in [-5, 5],
real x2_0 in [-5, 5];
Definitions
x1 rnd64= x1_0,
x2 rnd64= x2_0,
t1 rnd64= x1*x1 + x2,
t2 = rnd64(rnd64(x1 + rnd64(x2*x2))),
r rnd64= (t1 - 11)*(t1 - 11) + rnd64(rnd64(t2 - 7)*rnd64(t2 - 7))
;
Expressions
himmilbeauLet = r
;
Variables
real s1 in [-50, 50],
real s2 in [-10, 10],
real s3 in [-0.785, 0.785],
real s4 in [-0.785, 0.785];
Definitions
r rnd64= 1.0000 * s1 + 1.6567 * s2 + (-18.6854) * s3 + (-3.4594) * s4
;
Expressions
invertedPendulum = r
;
Variables
real x1_0 in [4, 6.36],
real x2_0 in [4, 6.36],
real x3_0 in [4, 6.36],
real x4_0 in [4, 6.36],
real x5_0 in [4, 6.36],
real x6_0 in [4, 6.36];
Definitions
x1 rnd64= x1_0,
x2 rnd64= x2_0,
x3 rnd64= x3_0,
x4 rnd64= x4_0,
x5 rnd64= x5_0,
x6 rnd64= x6_0,
t0 = rnd64(rnd64(rnd64(rnd64(rnd64(rnd64(-1 * x1) + x2) + x3) - x4) + x5) + x6),
r0 rnd64= (((((x2 * x5) + (x3 * x6)) - (x2 * x3)) - (x5 * x6)) + rnd64(x1 * t0)),
t1 = rnd64(rnd64(rnd64(rnd64(-1 * x1) + x2) + x3) - x4),
r1 rnd64= ((((((((x1 * x4) * t1) + (x2 * ((rnd64(x1 - x2) + x3) + x4))) + (x3 * ((rnd64(x1 + x2) - x3) + x4))) - ((x2 * x3) * x4)) - (x1 * x3)) - rnd64(x1 * x2)) - x4),
t2 = rnd64(rnd64(rnd64(rnd64(rnd64(rnd64(-1 * x1) + x2) + x3) - x4) + x5) + x6),
t3 = rnd64(rnd64(rnd64(rnd64(rnd64(x1 - x2) + x3) + x4) - x5) + x6),
r2 rnd64= ((((((((x1 * x4) * t2) + ((x2 * x5) * t3)) + ((x3 * x6) * ((((rnd64(x1 + x2) - x3) + x4) + x5) - x6))) - ((x2 * x3) * x4)) - ((x1 * x3) * x5)) - (rnd64(x1 * x2) * x6)) - ((x4 * x5) * x6))
;
Expressions
kepler0 = r0,
kepler1 = r1,
kepler2 = r2;
Base path: /home/hbecker/Git_Repos/FPTaylor
Config file: /home/hbecker/Git_Repos/FPTaylor/default.cfg
default-rnd = rnd64
nlopt-cc = gcc -std=c99 -O3
opt-exact = true
develop = false
log-append-date = start
uncertainty = false
rel-error = false
opt-approx = false
proof-record = false
find-bounds = true
proof-dir = proofs
opt-f-abs-tol = 0.01
fail-on-exception = true
print-opt-lower-bounds = true
bb-compile = {base}/b_and_b/compile.sh {base} {input} {out}
z3-python-lib =
opt-x-abs-tol = 0.01
export-error-bounds =
opt-f-rel-tol = 0.01
opt-x-rel-tol = 0.0
rel-error-threshold = 0.0001
bb-alg = opt0
log-base-dir = log
intermediate-opt = false
z3-interval-bounds = true
opt-max-iters = 1000000
abs-error = true
z3-bin =
maxima-simplification = false
debug = true
export-error-bounds-data =
fp-power2-model = true
opt = bb
default-var-type = float64
verbosity = 2
ulp-error = false
opt-timeout = 10000
nlopt-lib = -lnlopt -lm
tmp-base-dir = tmp
unique-indices = false
z3-seed = 0
tmp-date = false
z3-python-cmd = python
const-approx-real-vars = false
eval_const_expr: (-(100))
result: -100
eval_const_expr: 100
result: 100
eval_const_expr: 0
result: 0
eval_const_expr: 100
result: 100
eval_const_expr: (-(100))
result: -100
eval_const_expr: 20
result: 20
eval_const_expr: 20000
result: 20000
eval_const_expr: 0
result: 0
eval_const_expr: 20000
result: 20000
eval_const_expr: 20
result: 20
eval_const_expr: (-(30))
result: -30
eval_const_expr: 50
result: 50
eval_const_expr: 0
result: 0
eval_const_expr: 50
result: 50
eval_const_expr: (-(30))
result: -30
|tasks| = 1
Processing: doppler1
*************************************
Taylor form for: rnd64((rnd64((rnd64((-(rnd64(rnd64((rnd64((1657/5)) + rnd64((rnd64((3/5)) * rnd64(T0))))))))) * rnd64(v0))) / rnd64((rnd64((rnd64(rnd64(rnd64((rnd64((1657/5)) + rnd64((rnd64((3/5)) * rnd64(T0))))))) + rnd64(rnd64(u0)))) * rnd64((rnd64(rnd64(rnd64((rnd64((1657/5)) + rnd64((rnd64((3/5)) * rnd64(T0))))))) + rnd64(rnd64(u0))))))))
Conservative bound: [-158.719144, -0.029442]
Simplified rounding: rnd64((rnd64(((-(rnd[64,ne,1.00,-53,0]((rnd64((1657/5)) + rnd64((rnd64((3/5)) * rnd64(T0))))))) * rnd64(v0))) / rnd64((rnd[64,ne,1.00,-53,0]((rnd[64,ne,1.00,-53,0]((rnd64((1657/5)) + rnd64((rnd64((3/5)) * rnd64(T0))))) + rnd64(u0))) * rnd[64,ne,1.00,-53,0]((rnd[64,ne,1.00,-53,0]((rnd64((1657/5)) + rnd64((rnd64((3/5)) * rnd64(T0))))) + rnd64(u0)))))))
Building Taylor forms...
const_rnd_form
precise_const_rnd_form
Inexact constant: (1657/5); err = (1024/5)
const_rnd_form
precise_const_rnd_form
Inexact constant: (3/5); err = (1/5)
var_rnd_form
mul_form
rounded_form
add_form
rounded_form
neg_form
var_rnd_form
mul_form
rounded_form
const_rnd_form
precise_const_rnd_form
Inexact constant: (1657/5); err = (1024/5)
const_rnd_form
precise_const_rnd_form
Inexact constant: (3/5); err = (1/5)
var_rnd_form
mul_form
rounded_form
add_form
rounded_form
var_rnd_form
add_form
rounded_form
const_rnd_form
precise_const_rnd_form
Inexact constant: (1657/5); err = (1024/5)
const_rnd_form
precise_const_rnd_form
Inexact constant: (3/5); err = (1/5)
var_rnd_form
mul_form
rounded_form
add_form
rounded_form
var_rnd_form
add_form
rounded_form
mul_form
rounded_form
div_form
inv_form
mul_form
rounded_form
Simplifying Taylor forms...
success
v0 = (((-(((1657/5) + ((3/5) * T0)))) * v0) * (1 / ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))))
-1 (58): exp = -53: (2486717035483741/309485009821345068724781056)
1 (24): exp = -53: ((((((((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((((((1657/5) + ((3/5) * T0)) + u0) * (1024/5)) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))))))) + (((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((((((1657/5) + ((3/5) * T0)) + u0) * (T0 * (1/5))) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)))))))) + (((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((((((1657/5) + ((3/5) * T0)) + u0) * (1024/5)) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)))))))) + (((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((((((1657/5) + ((3/5) * T0)) + u0) * (T0 * (1/5))) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)))))))) + ((1 / ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))) * (v0 * (-((1024/5)))))) + ((1 / ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))) * (v0 * (-((T0 * (1/5)))))))
2 (26): exp = -53: (((((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((((((1657/5) + ((3/5) * T0)) + u0) * ((3/5) * floor_power2(T0))) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))))))) + (((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((((((1657/5) + ((3/5) * T0)) + u0) * ((3/5) * floor_power2(T0))) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)))))))) + ((1 / ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))) * (v0 * (-(((3/5) * floor_power2(T0)))))))
3 (28): exp = -53: (((((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((((((1657/5) + ((3/5) * T0)) + u0) * floor_power2((((3/5) * T0) + interval(-3.24185123190545780801e-15, 3.24185123190545780801e-15)))) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))))))) + (((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((((((1657/5) + ((3/5) * T0)) + u0) * floor_power2((((3/5) * T0) + interval(-3.24185123190545780801e-15, 3.24185123190545780801e-15)))) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)))))))) + ((1 / ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))) * (v0 * (-(floor_power2((((3/5) * T0) + interval(-3.24185123190545780801e-15, 3.24185123190545780801e-15))))))))
4 (30): exp = -53: (((((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((((((1657/5) + ((3/5) * T0)) + u0) * floor_power2((((1657/5) + ((3/5) * T0)) + interval(-2.77555756156289166660e-14, 2.77555756156289166660e-14)))) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))))))) + (((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((((((1657/5) + ((3/5) * T0)) + u0) * floor_power2((((1657/5) + ((3/5) * T0)) + interval(-2.77555756156289166660e-14, 2.77555756156289166660e-14)))) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)))))))) + ((1 / ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))) * (v0 * (-(floor_power2((((1657/5) + ((3/5) * T0)) + interval(-2.77555756156289166660e-14, 2.77555756156289166660e-14))))))))
5 (9): exp = -53: ((1 / ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))) * ((-(((1657/5) + ((3/5) * T0)))) * floor_power2(v0)))
6 (11): exp = -53: ((1 / ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))) * floor_power2((((-(((1657/5) + ((3/5) * T0)))) * v0) + interval(-1.78092847136213132150e-09, 1.78092847136213132150e-09))))
7 (32): exp = -53: ((((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((((((1657/5) + ((3/5) * T0)) + u0) * floor_power2(u0)) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))))))) + (((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((((((1657/5) + ((3/5) * T0)) + u0) * floor_power2(u0)) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))))))))
8 (33): exp = -53: ((((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((((((1657/5) + ((3/5) * T0)) + u0) * floor_power2(((((1657/5) + ((3/5) * T0)) + u0) + interval(-6.32827124036339354259e-14, 6.32827124036339354259e-14)))) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))))))) + (((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((((((1657/5) + ((3/5) * T0)) + u0) * floor_power2(((((1657/5) + ((3/5) * T0)) + u0) + interval(-6.32827124036339354259e-14, 6.32827124036339354259e-14)))) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0))))))))
9 (36): exp = -53: (((-(((1657/5) + ((3/5) * T0)))) * v0) * (-((floor_power2((((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) + interval(-8.46248404684502588932e-11, 8.46248404684502588932e-11))) / (((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)) * ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)))))))
10 (40): exp = -53: floor_power2(((((-(((1657/5) + ((3/5) * T0)))) * v0) * (1 / ((((1657/5) + ((3/5) * T0)) + u0) * (((1657/5) + ((3/5) * T0)) + u0)))) + interval(-3.94993705872679559268e-13, 3.94993705872679559268e-13)))
Corresponding original subexpressions:
1: rnd64(0)
2: rnd64(T0)
3: rnd64((rnd64((3/5)) * rnd64(T0)))
4: rnd[64,ne,1.00,-53,0]((rnd64((1657/5)) + rnd64((rnd64((3/5)) * rnd64(T0)))))
5: rnd64(v0)
6: rnd64(((-(rnd[64,ne,1.00,-53,0]((rnd64((1657/5)) + rnd64((rnd64((3/5)) * rnd64(T0))))))) * rnd64(v0)))
7: rnd64(u0)
8: rnd[64,ne,1.00,-53,0]((rnd[64,ne,1.00,-53,0]((rnd64((1657/5)) + rnd64((rnd64((3/5)) * rnd64(T0))))) + rnd64(u0)))
9: rnd64((rnd[64,ne,1.00,-53,0]((rnd[64,ne,1.00,-53,0]((rnd64((1657/5)) + rnd64((rnd64((3/5)) * rnd64(T0))))) + rnd64(u0))) * rnd[64,ne,1.00,-53,0]((rnd[64,ne,1.00,-53,0]((rnd64((1657/5)) + rnd64((rnd64((3/5)) * rnd64(T0))))) + rnd64(u0)))))
10: rnd64((rnd64(((-(rnd[64,ne,1.00,-53,0]((rnd64((1657/5)) + rnd64((rnd64((3/5)) * rnd64(T0))))))) * rnd64(v0))) / rnd64((rnd[64,ne,1.00,-53,0]((rnd[64,ne,1.00,-53,0]((rnd64((1657/5)) + rnd64((rnd64((3/5)) * rnd64(T0))))) + rnd64(u0))) * rnd[64,ne,1.00,-53,0]((rnd[64,ne,1.00,-53,0]((rnd64((1657/5)) + rnd64((rnd64((3/5)) * rnd64(T0))))) + rnd64(u0)))))))
bb_opt: x_abs_tol = 1.000000e-02, f_rel_tol = 1.000000e-02, f_abs_tol = 1.000000e-02, iters = 1000000
iterations(min = 427, max = 23): 427
min = -1.389561e+02 (lower_min = -1.375714e+02)
max = -3.169713e-02 (lower_max = -3.967690e-02)
subopt = 1.384675e+00 (1.0%)
bounds: [-1.389561e+02, -3.169713e-02]
Computing absolute errors
bb_opt: x_abs_tol = 1.000000e-02, f_rel_tol = 1.000000e-02, f_abs_tol = 1.000000e-02, iters = 1000000
iterations(min = 0, max = 0): 0
min = 8.035016e-12 (lower_min = 8.035016e-12)
max = 8.035016e-12 (lower_max = 8.035016e-12)
subopt = 0.000000e+00 (0.0%)
rmin(result = 8.035016e-12, lower = 8.035016e-12), rmax(result = 8.035016e-12, lower = 8.035016e-12)
-1: exp = -53: 8.035016e-12 (low = 8.035016e-12, subopt = 0.0%)
Solving the exact optimization problem
bb_opt: x_abs_tol = 1.000000e-02, f_rel_tol = 1.000000e-02, f_abs_tol = 1.000000e-02, iters = 1000000
iterations(min = 0, max = 7313): 7313
min = 0.000000e+00 (lower_min = 0.000000e+00)
max = 1.096961e+03 (lower_max = 1.088234e+03)
subopt = 8.726599e+00 (0.8%)
exact bound (exp = -53): 1.096961e+03 (low = 1.088234e+03, subopt = 0.8%)
total2: 8.920660e-28 (low = 8.920660e-28, subopt = 0.0%)
exact total: 1.217871e-13 (low = 1.208183e-13, subopt = 0.8%)
Elapsed time: 1.36586
*************************************
-------------------------------------------------------------------------------
Problem: doppler1
Optimization lower bounds for error models:
The absolute error model (exact): 1.208183e-13 (suboptimality = 0.8%)
Bounds (without rounding): [-1.389561e+02, -3.169713e-02]
Bounds (floating-point): [-1.38956107612810029650e+02, -3.16971265341684516059e-02]
Absolute error (exact): 1.217871e-13
Elapsed time: 1.37
Base path: /home/hbecker/Git_Repos/FPTaylor
Config file: /home/hbecker/Git_Repos/FPTaylor/default.cfg
default-rnd = rnd64
nlopt-cc = gcc -std=c99 -O3
opt-exact = true
develop = false
log-append-date = start
uncertainty = false
rel-error = false
opt-approx = false
proof-record = false
find-bounds = true
proof-dir = proofs
opt-f-abs-tol = 0.01
fail-on-exception = true
print-opt-lower-bounds = true
bb-compile = {base}/b_and_b/compile.sh {base} {input} {out}
z3-python-lib =
opt-x-abs-tol = 0.01
export-error-bounds =
opt-f-rel-tol = 0.01
opt-x-rel-tol = 0.0
rel-error-threshold = 0.0001
bb-alg = opt0
log-base-dir = log
intermediate-opt = false
z3-interval-bounds = true
opt-max-iters = 1000000
abs-error = true
z3-bin =
maxima-simplification = false
debug = true
export-error-bounds-data =
fp-power2-model = true
opt = bb
default-var-type = float64
verbosity = 2
ulp-error = false
opt-timeout = 10000
nlopt-lib = -lnlopt -lm
tmp-base-dir = tmp
unique-indices = false
z3-seed = 0
tmp-date = false
z3-python-cmd = python
const-approx-real-vars = false
eval_const_expr: (-(5))
result: -5
eval_const_expr: 5
result: 5
eval_const_expr: 0
result: 0
eval_const_expr: 5
result: 5
eval_const_expr: (-(5))
result: -5
eval_const_expr: (-(5))
result: -5
eval_const_expr: 5
result: 5
eval_const_expr: 0
result: 0
eval_const_expr: 5
result: 5
eval_const_expr: (-(5))
result: -5
|tasks| = 1
Processing: himmilbeauLet
*************************************
Taylor form for: rnd64((rnd64((rnd64((rnd64(rnd64((rnd64((rnd64(rnd64(x1_0)) * rnd64(rnd64(x1_0)))) + rnd64(rnd64(x2_0))))) - rnd64(11))) * rnd64((rnd64(rnd64((rnd64((rnd64(rnd64(x1_0)) * rnd64(rnd64(x1_0)))) + rnd64(rnd64(x2_0))))) - rnd64(11))))) + rnd64((rnd64((rnd64(rnd64((rnd64(x1_0) + rnd64((rnd64(x2_0) * rnd64(x2_0)))))) - 7)) * rnd64((rnd64(rnd64((rnd64(x1_0) + rnd64((rnd64(x2_0) * rnd64(x2_0)))))) - 7))))))
Conservative bound: [-0.000000, 890.000000]
Simplified rounding: rnd[64,ne,1.00,-53,0]((rnd64((rnd[64,ne,1.00,-53,0]((rnd[64,ne,1.00,-53,0]((rnd64((rnd64(x1_0) * rnd64(x1_0))) + rnd64(x2_0))) - 11)) * rnd[64,ne,1.00,-53,0]((rnd[64,ne,1.00,-53,0]((rnd64((rnd64(x1_0) * rnd64(x1_0))) + rnd64(x2_0))) - 11)))) + rnd64((rnd[64,ne,1.00,-53,0]((rnd[64,ne,1.00,-53,0]((rnd64(x1_0) + rnd64((rnd64(x2_0) * rnd64(x2_0))))) - 7)) * rnd[64,ne,1.00,-53,0]((rnd[64,ne,1.00,-53,0]((rnd64(x1_0) + rnd64((rnd64(x2_0) * rnd64(x2_0))))) - 7))))))
Building Taylor forms...
var_rnd_form
var_rnd_form
mul_form
rounded_form
var_rnd_form
add_form
rounded_form
const_form
sub_form
rounded_form
var_rnd_form
var_rnd_form
mul_form
rounded_form
var_rnd_form
add_form
rounded_form
const_form
sub_form
rounded_form
mul_form
rounded_form
var_rnd_form
var_rnd_form
var_rnd_form
mul_form
rounded_form
add_form
rounded_form
const_form
sub_form
rounded_form
var_rnd_form
var_rnd_form
var_rnd_form
mul_form
rounded_form
add_form
rounded_form
const_form
sub_form
rounded_form
mul_form
rounded_form
add_form
rounded_form
Simplifying Taylor forms...
success
v0 = (((((x1_0 * x1_0) + x2_0) - 11) * (((x1_0 * x1_0) + x2_0) - 11)) + (((x1_0 + (x2_0 * x2_0)) - 7) * ((x1_0 + (x2_0 * x2_0)) - 7)))
-1 (68): exp = -53: (2511284557840387/1237940039285380274899124224)
1 (12): exp = -53: (((((((((x1_0 * x1_0) + x2_0) - 11) * (x1_0 * floor_power2(x1_0))) + ((((x1_0 * x1_0) + x2_0) - 11) * (x1_0 * floor_power2(x1_0)))) + ((((x1_0 * x1_0) + x2_0) - 11) * (x1_0 * floor_power2(x1_0)))) + ((((x1_0 * x1_0) + x2_0) - 11) * (x1_0 * floor_power2(x1_0)))) + (((x1_0 + (x2_0 * x2_0)) - 7) * floor_power2(x1_0))) + (((x1_0 + (x2_0 * x2_0)) - 7) * floor_power2(x1_0)))
2 (14): exp = -53: (((((x1_0 * x1_0) + x2_0) - 11) * floor_power2(((x1_0 * x1_0) + interval(-4.44089209850062695056e-15, 4.44089209850062695056e-15)))) + ((((x1_0 * x1_0) + x2_0) - 11) * floor_power2(((x1_0 * x1_0) + interval(-4.44089209850062695056e-15, 4.44089209850062695056e-15)))))
3 (16): exp = -53: (((((((((x1_0 * x1_0) + x2_0) - 11) * floor_power2(x2_0)) + ((((x1_0 * x1_0) + x2_0) - 11) * floor_power2(x2_0))) + (((x1_0 + (x2_0 * x2_0)) - 7) * (x2_0 * floor_power2(x2_0)))) + (((x1_0 + (x2_0 * x2_0)) - 7) * (x2_0 * floor_power2(x2_0)))) + (((x1_0 + (x2_0 * x2_0)) - 7) * (x2_0 * floor_power2(x2_0)))) + (((x1_0 + (x2_0 * x2_0)) - 7) * (x2_0 * floor_power2(x2_0))))
4 (17): exp = -53: (((((x1_0 * x1_0) + x2_0) - 11) * floor_power2((((x1_0 * x1_0) + x2_0) + interval(-6.66133814775094003140e-15, 6.66133814775094003140e-15)))) + ((((x1_0 * x1_0) + x2_0) - 11) * floor_power2((((x1_0 * x1_0) + x2_0) + interval(-6.66133814775094003140e-15, 6.66133814775094003140e-15)))))
5 (19): exp = -53: (((((x1_0 * x1_0) + x2_0) - 11) * floor_power2(((((x1_0 * x1_0) + x2_0) - 11) + interval(-8.43769498715119128494e-15, 8.43769498715119128494e-15)))) + ((((x1_0 * x1_0) + x2_0) - 11) * floor_power2(((((x1_0 * x1_0) + x2_0) - 11) + interval(-8.43769498715119128494e-15, 8.43769498715119128494e-15)))))
6 (22): exp = -53: floor_power2((((((x1_0 * x1_0) + x2_0) - 11) * (((x1_0 * x1_0) + x2_0) - 11)) + interval(-3.88133969408954928480e-13, 3.88133969408954928480e-13)))
7 (38): exp = -53: ((((x1_0 + (x2_0 * x2_0)) - 7) * floor_power2(((x2_0 * x2_0) + interval(-4.44089209850062695056e-15, 4.44089209850062695056e-15)))) + (((x1_0 + (x2_0 * x2_0)) - 7) * floor_power2(((x2_0 * x2_0) + interval(-4.44089209850062695056e-15, 4.44089209850062695056e-15)))))
8 (40): exp = -53: ((((x1_0 + (x2_0 * x2_0)) - 7) * floor_power2(((x1_0 + (x2_0 * x2_0)) + interval(-6.66133814775094003140e-15, 6.66133814775094003140e-15)))) + (((x1_0 + (x2_0 * x2_0)) - 7) * floor_power2(((x1_0 + (x2_0 * x2_0)) + interval(-6.66133814775094003140e-15, 6.66133814775094003140e-15)))))
9 (42): exp = -53: ((((x1_0 + (x2_0 * x2_0)) - 7) * floor_power2((((x1_0 + (x2_0 * x2_0)) - 7) + interval(-8.43769498715119128494e-15, 8.43769498715119128494e-15)))) + (((x1_0 + (x2_0 * x2_0)) - 7) * floor_power2((((x1_0 + (x2_0 * x2_0)) - 7) + interval(-8.43769498715119128494e-15, 8.43769498715119128494e-15)))))
10 (45): exp = -53: floor_power2(((((x1_0 + (x2_0 * x2_0)) - 7) * ((x1_0 + (x2_0 * x2_0)) - 7)) + interval(-4.69846384021366550830e-13, 4.69846384021366550830e-13)))
11 (47): exp = -53: floor_power2(((((((x1_0 * x1_0) + x2_0) - 11) * (((x1_0 * x1_0) + x2_0) - 11)) + (((x1_0 + (x2_0 * x2_0)) - 7) * ((x1_0 + (x2_0 * x2_0)) - 7))) + interval(-9.43245481721534006486e-13, 9.43245481721534006486e-13)))