\[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]

wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}

double f(double wj, double x) {
        double r8006 = wj;
        double r8007 = exp(r8006);
        double r8008 = r8006 * r8007;
        double r8009 = x;
        double r8010 = r8008 - r8009;
        double r8011 = r8007 + r8008;
        double r8012 = r8010 / r8011;
        double r8013 = r8006 - r8012;
        return r8013;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019191 
(FPCore (wj x)
  :name "Jmat.Real.lambertw, newton loop step"

  :herbie-target
  (- wj (- (/ wj (+ wj 1.0)) (/ x (+ (exp wj) (* wj (exp wj))))))

  (- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj))))))

Backtrace

get-representation: Unknown representation #f		L	C
loop	/data/pavpan/nightlies/herbie/interface2/src/points.rkt	122	4
prepare-points	/data/pavpan/nightlies/herbie/interface2/src/points.rkt	146	0
setup-prog!34	/data/pavpan/nightlies/herbie/interface2/src/mainloop.rkt	67	0
run-improve43	/data/pavpan/nightlies/herbie/interface2/src/mainloop.rkt	339	0
(unnamed)	/opt/racket-7.0/collects/racket/private/more-scheme.rkt	261	28
run	/opt/racket-7.0/share/pkgs/profile-lib/main.rkt	39	2
profile-thunk16	/opt/racket-7.0/share/pkgs/profile-lib/main.rkt	9	0
(unnamed)	/opt/racket-7.0/collects/racket/private/more-scheme.rkt	261	28