Average Error: 0.3 → 0.0
Time: 15.1s
Precision: 64
Internal Precision: 576
\[\log x - \log \left(\log x\right)\]
↓
\[\log \left(\frac{\frac{x}{\sqrt{\log x}}}{\sqrt{\log x}}\right)\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

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

  3. Applied diff-log0.0

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

  5. Applied add-sqr-sqrt0.0

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

  6. Applied associate-/r*0.0

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

  7. Final simplification0.0

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

Runtime

Time bar (total: 15.1s)Debug logProfile

herbie shell --seed 2018251 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))