Re: Differentiable Forth

On Wed, 17 Jul 2024 15:26:54 +0000, ahmed wrote:
..

>
>
: dlf7() dldup dldup dl* dlcos dl* ; \ f7(x) = x*cos(x^2),
: der_f7() ( f: x --y)  \ its deriv: d/dx(f7) = x*cos(x^2)-2*x*sin(x^2)
    fdup fdup f* ( f: x x^2)
    fsincos ( f: x s c )
    frot ( f: s c x)
    ftuck ( f: s x c x)
    f* ( f: s x cx)
    -frot ( f: cx s x)
    f* 2e f* f-
;
>
cr 1e der_f7() f.   \ -1.14263966374765  ok calculated at 1e
cr 1e der dlf7() f. \ -1.14263966374765  ok
>

There is an error in der_f7() analytic formula.
the correct version is hereafter:
: dlf7() dldup dldup dl* dlcos dl* ; \ f7(x) = x*cos(x^2),
: der_f7() ( f: x --y)  \ its deriv: d/dx(f7) = cos(x^2)-2*x^2*sin(x^2)
    fdup f* ( f: x^2)
    fdup fsincos ( f: x^2 s c )
    -frot ( f:  c x^2 s )
    f* 2e f* ( f: c 2s*x^2)
    f-
;
cr 2e der_f7() f.   \ 5.40077634159981  ok calculated at 2e
cr 2e der dlf7() f. \ 5.40077634159981  ok
cr cr cr