;BY FEBRUARY 27 YOUR ROOT FINDING MUST HANDLE THE FOLLOWING...
;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;CONTINUOUS, no roots
PARS: f(x) = 2 RESULT: valid TREE: C
EVAL: f(1.00) = 2.00000 RESULT: valid TREE: C
EVAL: f'(1.00) = 0.00000 RESULT: valid TREE: C
EVAL: f''(1.00)= 0.00000 RESULT: valid TREE: C
>Summary of Roots:
f:[]
f':[]
f'':[]
>Analysis over the closed interval [-10.00,10.00]:
x f(x) f'(x) f"(x) Feature
----------------End of Analysis---------------------------------
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;CONTINUOUS, no roots
PARS: f(x) = sin(3) RESULT: valid TREE: C
EVAL: f(12.00) = 0.14112 RESULT: valid TREE: C
EVAL: f'(12.00) = 0.00000 RESULT: valid TREE: C
EVAL: f''(12.00)= 0.00000 RESULT: valid TREE: C
>Summary of Roots:
f:[]
f':[]
f'':[]
>Analysis over the closed interval [-10.00,10.00]:
x f(x) f'(x) f"(x) Feature
----------------End of Analysis---------------------------------
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;CONTINUOUS, 1 root: {0.0}
PARS: f(x) = x RESULT: valid TREE: V
EVAL: f(3.00) = 3.00000 RESULT: valid TREE: V
EVAL: f'(3.00) = 1.00000 RESULT: valid TREE: C
EVAL: f''(3.00)= 0.00000 RESULT: valid TREE: C
>Summary of Roots:
f:[0.0]
f':[]
f'':[]
>Analysis over the closed interval [-10.00,10.00]:
x f(x) f'(x) f"(x) Feature
0.00 0.00 1.00 0.00 ?
----------------End of Analysis---------------------------------
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;CONTINUOUS, 1 root: {0.75}
PARS: f(x) = 4*x-3 RESULT: valid TREE: COVOC
EVAL: f(12.00) = 45.00000 RESULT: valid TREE: COVOC
EVAL: f'(12.00) = 4.00000 RESULT: valid TREE: C
EVAL: f''(12.00)= 0.00000 RESULT: valid TREE: C
>Summary of Roots:
f:[0.75]
f':[]
f'':[]
>Analysis over the closed interval [-10.00,10.00]:
x f(x) f'(x) f"(x) Feature
0.75 0.00 4.00 0.00 ?
----------------End of Analysis---------------------------------
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;CONTINUOUS, 2 (equal) roots: {0.0}
PARS: f(x) = x^2 RESULT: valid TREE: VOC
EVAL: f(-1.00) = 1.00000 RESULT: valid TREE: VOC
EVAL: f'(-1.00) = -2.00000 RESULT: valid TREE: COV
EVAL: f''(-1.00)= 2.00000 RESULT: valid TREE: C
>Summary of Roots:
f:[0.0]
f':[0.0]
f'':[]
>Analysis over the closed interval [-10.00,10.00]:
x f(x) f'(x) f"(x) Feature
0.00 0.00 0.00 2.00 ?
----------------End of Analysis---------------------------------
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;CONTINUOUS, 4 roots: {-1.0, 0.0, 1.0}
PARS: f(x) = x^4-x^2 RESULT: valid TREE: VOCOVOC
EVAL: f(0.00) = 0.00000 RESULT: valid TREE: VOCOVOC
EVAL: f'(0.00) = 0.00000 RESULT: valid TREE: COVOCOCOV
EVAL: f''(0.00)= -2.00000 RESULT: valid TREE: COCOVOCOC
>Summary of Roots:
f:[-1.0, 0.0, 1.0]
f':[-0.707, 0.0, 0.707]
f'':[-0.408, 0.408]
>Analysis over the closed interval [-5.00, 5.00]:
x f(x) f'(x) f"(x) Feature
-1.00 0.00 -2.00 10.00 ?
-0.71 -0.25 0.00 4.00 ?
-0.41 -0.14 0.54 0.00 ?
0.00 0.00 0.00 -2.00 ?
0.41 -0.14 -0.54 0.00 ?
0.71 -0.25 0.00 4.00 ?
1.00 0.00 2.00 10.00 ?
----------------End of Analysis---------------------------------
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;CONTINUOUS, 6 (equal) roots: {0.0}
PARS: f(x) = x^6 RESULT: valid TREE: VOC
EVAL: f(0.00) = 0.00000 RESULT: valid TREE: VOC
EVAL: f'(0.00) = 0.00000 RESULT: valid TREE: COVOC
EVAL: f''(0.00)= 0.00000 RESULT: valid TREE: COCOVOC
>Summary of Roots:
f:[0.0]
f':[0.0]
f'':[0.0]
>Analysis over the closed interval [-9.95, 9.95]:
x f(x) f'(x) f"(x) Feature
0.00 0.00 0.00 0.00 ?
----------------End of Analysis---------------------------------
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;CONTINUOUS, 5 roots: {-6.28, -3.14, 0.0, 3.14, 6.28}
PARS: f(x) = sin(x) RESULT: valid TREE: VF
EVAL: f(0.00) = 0.00000 RESULT: valid TREE: VF
EVAL: f'(0.00) = 1.00000 RESULT: valid TREE: VF
EVAL: f''(0.00)= -0.00000 RESULT: valid TREE: COVF
>Summary of Roots:
f:[-6.283, -3.142, 0.0, 3.142, 6.283]
f':[-4.712, -1.571, 1.571, 4.712]
f'':[-6.283, -3.142, 0.0, 3.142, 6.283]
>Analysis over the closed interval [-7.00, 7.00]:
x f(x) f'(x) f"(x) Feature
-6.28 0.00 1.00 0.00 ?
-4.71 1.00 0.00 -1.00 ?
-3.14 0.00 -1.00 0.00 ?
-1.57 -1.00 0.00 1.00 ?
0.00 0.00 1.00 0.00 ?
1.57 1.00 0.00 -1.00 ?
3.14 0.00 -1.00 0.00 ?
4.71 -1.00 0.00 1.00 ?
6.28 0.00 1.00 0.00 ?
----------------End of Analysis---------------------------------
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;CONTINUOUS, 3 roots: {-6.28, 0.0, 6.28}
PARS: f(x) = sin(x/2) RESULT: valid TREE: VOCF
EVAL: f(0.00) = 0.00000 RESULT: valid TREE: VOCF
EVAL: f'(0.00) = 0.50000 RESULT: valid TREE: VOCFOCOVOCOC
EVAL: f''(0.00)= 0.00000 RESULT: valid TREE: COVOCFOCOVOCOCOCOVOCOCOVOCFOCOVOCOCOCOVOCOCOC
>Summary of Roots:
f:[-6.283, 0.0, 6.283]
f':[-3.142, 3.142]
f'':[-6.283, 0.0, 6.283]
>Analysis over the closed interval [-7.00, 7.00]:
x f(x) f'(x) f"(x) Feature
-6.28 0.00 -0.50 0.00 ?
-3.14 -1.00 0.00 0.25 ?
0.00 0.00 0.50 0.00 ?
3.14 1.00 0.00 -0.25 ?
6.28 0.00 -0.50 0.00 ?
----------------End of Analysis---------------------------------
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;CONTINUOUS, 9 roots: {-5.5, -3.93, -2.36, -0.79, 0.79, 2.36, 3.93, 5.5, 7.07}
PARS: f(x) = cos(2*x) RESULT: valid TREE: COVF
EVAL: f(0.00) = 1.00000 RESULT: valid TREE: COVF
EVAL: f'(0.00) = -0.00000 RESULT: valid TREE: COCOVFOC
EVAL: f''(0.00)= -4.00000 RESULT: valid TREE: COCOVFOCOCOCOCOVFOC
>Summary of Roots:
f:[-5.498, -3.927, -2.356, -0.785, 0.785, 2.356, 3.927, 5.498, 7.069]
f':[-6.283, -4.712, -3.142, -1.571, 0.0, 1.571, 3.142, 4.712, 6.283]
f'':[-5.498, -3.927, -2.356, -0.785, 0.785, 2.356, 3.927, 5.498, 7.069]
>Analysis over the closed interval [-7.00, 7.00]:
x f(x) f'(x) f"(x) Feature
-6.28 1.00 0.00 -4.00 ?
-5.50 0.00 -2.00 0.00 ?
-4.71 -1.00 0.00 4.00 ?
-3.93 0.00 2.00 0.00 ?
-3.14 1.00 0.00 -4.00 ?
-2.36 0.00 -2.00 0.00 ?
-1.57 -1.00 0.00 4.00 ?
-0.79 0.00 2.00 0.00 ?
0.00 1.00 0.00 -4.00 ?
0.79 0.00 -2.00 0.00 ?
1.57 -1.00 0.00 4.00 ?
2.36 0.00 2.00 0.00 ?
3.14 1.00 0.00 -4.00 ?
3.93 0.00 -2.00 0.00 ?
4.71 -1.00 0.00 4.00 ?
5.50 0.00 2.00 0.00 ?
6.28 1.00 0.00 -4.00 ?
7.07 0.00 -2.00 0.00 ?
----------------End of Analysis---------------------------------
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