Average Error: 0.2 → 0.0
Time: 9.8s
Precision: 64
Internal Precision: 128
\[\log x - \log \left(\log x\right)\]
↓
\[\log \left(\frac{1}{\frac{\log x}{x}}\right)\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  2. Initial simplification0.2

    \[\leadsto \log x - \log \left(\log x\right)\]
  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 clear-num0.0

    \[\leadsto \log \color{blue}{\left(\frac{1}{\frac{\log x}{x}}\right)}\]

  7. Final simplification0.0

    \[\leadsto \log \left(\frac{1}{\frac{\log x}{x}}\right)\]

Runtime

Time bar (total: 9.8s)Debug logProfile

herbie shell --seed 2018256 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))