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

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

double f(double wj, double x) {
        double r8899 = wj;
        double r8900 = exp(r8899);
        double r8901 = r8899 * r8900;
        double r8902 = x;
        double r8903 = r8901 - r8902;
        double r8904 = r8900 + r8901;
        double r8905 = r8903 / r8904;
        double r8906 = r8899 - r8905;
        return r8906;
}

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2019173 +o rules:numerics
(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

atab-pick-alt: contract violation expected: alt? given: '(#<alt (λ (wj x) (- wj (/ (- (/ wj 1) (/ x (exp wj))) (+ wj 1))))>) in: the range of the #:picking-func argument of (-> alt-table? #:only-fresh boolean? #:picking-func (-> (listof alt?) alt?) (values alt? alt-table?)) contract from: /data/pavpan/nightlies/herbie/no-costs-2/src/core/alt-table.rkt blaming: /data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt (assuming the contract is correct) at: /data/pavpan/nightlies/herbie/no-costs-2/src/core/alt-table.rkt:13.3		L	C
raise-blame-error16	/opt/racket-7.0/collects/racket/contract/private/blame.rkt	347	0
(unnamed)	/data/pavpan/nightlies/herbie/no-costs-2/src/core/alt-table.rkt	59	0
(unnamed)	/opt/racket-7.0/collects/racket/contract/private/arrow-val-first.rkt	388	18
choose-best-alt!	/data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt	110	0
run-iter!	/data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt	319	0
for-loop	/data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt	353	4
run-improve43	/data/pavpan/nightlies/herbie/no-costs-2/src/mainloop.rkt	338	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

could not determine a ground truth for program body (more)

Reproduce

Backtrace