52ac791d-9b34-4f78-afc7-47ea6cdbdfd0 3 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

The hyperfast Golden-Ratio search [min/max]

x f x 4^2 x 3^* - 7 x 2^* - 2 - : a b G 32 / b * 12 / a * - 12 / 5 sqrt * a b - (* + : 21 line

TOL 1012 -^:

Code adapted from Valery Ochov Mathcad 11 f a b test TOL Extrema y1 y2 ≥ max in range ≡ y1 y2 ≤ min in range ≡ x1 a b G eval : y1 x1 f eval : x2 b a G eval : y2 x2 f eval : 41 line iter 0 : iter 1000 < a b - abs TOL ≤ break test b x2 : x2 x1 : y2 y1 : x1 a b G eval : y1 x1 f eval : 51 line a x1 : x1 x2 : y1 y2 : x2 b a G eval : y2 x2 f eval : 51 line if iter iter 1 + : 21 line if while a b + 2 / iter 21 mat 61 line :

1. All modules/functions in "Symbolic" optimiz. 2. Once in target: shrink the range 3. respect the search y1≥y2≡"max in range" y1≤y2≡"min in range"

t0 1 time :

X f 1.5 - 1 - y1 y2 ≤ TOL Extrema 1 el f 0.5 - 0.5 y1 y2 ≥ TOL Extrema 1 el f 2.5 3 y1 y2 ≤ TOL Extrema 1 el 31 mat :

1 time t0 - 0.4 s *

x f X 1 el X 1 el f + 15 red X 2 el X 2 el f + 15 red X 3 el X 3 el f + 15 red 3 5 mat 2 1 sys

X 1.265564 - 2.816018 108 -^* - 2.765564 31 mat

data 1021324354627 0.3 8 0.4 9 0.4 10 0.38 11412 0.45 13 0.5 - 14 0.48 - 15 0.45 16617 0.6 18 0.62 - 19 0.6 - 20 0.55 21822 0.6 23 0.65 24 0.61 25 0.59 252 mat :

Locate exact value in vector V x FindIdx j 1 : V j el x ≠ j j 1 + : while j 2 / V j el 21 mat 31 line :

key 0.5 - :

data key FindIdx 13 0.5 - 21 mat

data 13 row 13 0.5 - 12 mat

data key FindIndex 8121 mat

data 000000000000000 0.8482 0.8688 0.8378 0.8078 0.7786 0.8029 0.7743 0.7466 0.7196 0.7464 0.7198 0.694 0.6689 0.6972 0.6724 0.6483 0 0.6542 0.6309 000000000000000000000000000000000000000000000000000000224 mat :

key 0.7466 :

data key FindIdx 23 0.7466 21 mat

data rows 22