Error

Derivation

1. Initial program 0.3

   \[\log x - \log \left(\log x\right)\]
2. Using strategy rm

3. Applied add-log-exp0.3

   \[\leadsto \log x - \color{blue}{\log \left(e^{\log \left(\log x\right)}\right)}\]

4. Applied diff-log0.0

   \[\leadsto \color{blue}{\log \left(\frac{x}{e^{\log \left(\log x\right)}}\right)}\]

5. Simplified0.0

   \[\leadsto \log \color{blue}{\left(\frac{x}{\log x}\right)}\]

6. Final simplification0.0

   \[\leadsto \log \left(\frac{x}{\log x}\right)\]

Reproduce

herbie shell --seed 2019088 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))