`fpbracketed-root``f``a``b`procedure- f
- (flonum -> flonum)
- a
- flonum
- b
- flonum

Uses the Brent-Dekker method to find a floating-point root of

`f`(a flonum`x`for which`(f x)`is very near a zero crossing) between`a`and`b`. The values`(f a)`and`(f b)`must have opposite signs, but a and b may be in any order.Examples:

> (define (f x) (+ 1.0 (* (+ x 3.0) (sqr (- x 1.0))))) > (define x0 (fpbracketed-root f -4.0 2.0)) > (f (fpprev x0)) -7.105427357601002e-15 > (f x0) 6.661338147750939e-16 > (fpbracketed-root f -1.0 2.0) +nan.0

Caveats:

- There is no guarantee that
`fpbracketed-root`will find any particular root. Moreover, future updates to its implementation could make it find different ones. - There is currently no guarantee that it will find the closest
`x`to an exact root. - It currently runs for at most 5000 iterations.

It usually requires far fewer iterations, especially if the initial bounds

`a`and`b`are tight.