;BY FEBRUARY 27 YOUR ROOT FINDING MUST HANDLE THE FOLLOWING DIFFERENTIABLE FUNCTIONS....
;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;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'':[]
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;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'':[]
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;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'':[]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;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'':[]
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;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'':[]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;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':[-0.71, 0.0, 0.71]
f'':[-0.41, 0.41]
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;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]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;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: VF
Summary of Roots:
f:[-6.28, -3.14, 0.0, 3.14, 6.28]
f':[-4.71, -1.57, 1.57, 4.71]
f'':[-6.28, -3.14, 0.0, 3.14, 6.28]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;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: VOCFOCOVOCOCOCOVOCOCOVOCFOCOVOCOCOCOVOCOCOC
Summary of Roots:
f:[-6.28, 0.0, 6.28]
f':[-3.14, 3.14]
f'':[-6.28, 0.0, 6.28]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;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: COVFOC
EVAL: f''(0.00)= 4.00000 RESULT: valid TREE: COVFOCOCOCOVFOC
Summary of Roots:
f:[-5.5, -3.93, -2.36, -0.79, 0.79, 2.36, 3.93, 5.5, 7.07]
f':[-6.28, -4.71, -3.14, -1.57, 0.0, 1.57, 3.14, 4.71, 6.28]
f'':[-5.5, -3.93, -2.36, -0.79, 0.79, 2.36, 3.93, 5.5, 7.07]
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