Average Error: 0.3 → 0.0
Time: 8.5s
Precision: 64
Internal Precision: 576
\[\log x - \log \left(\log x\right)\]
↓
\[\log \left(\frac{x}{\log x}\right)\]

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. 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. Final simplification0.0

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

Runtime

Time bar (total: 8.5s)Debug logProfile

herbie shell --seed 2018249 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))