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Derivation

1. Initial program 0.3

   \[\log x - \log \left(\log x\right)\]

2. Initial simplification0.3

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

4. Applied diff-log0.0

   \[\leadsto \color{blue}{\log \left(\frac{x}{\log x}\right)}\]
5. Using strategy rm

6. Applied add-sqr-sqrt0.0

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

7. Applied log-prod0.0

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

8. Final simplification0.0

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

Runtime

Time bar (total: 9.9s)Debug logProfile

herbie shell --seed 2018286 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))