Average Error: 0.3 → 0.0
Time: 11.3s
Precision: 64
\[\log x - \log \left(\log x\right)\]
↓
\[\log \left(\frac{x}{\log x}\right)\]
\log x - \log \left(\log x\right)
↓
\log \left(\frac{x}{\log x}\right)
double f(double x) {
        double r3821596 = x;
        double r3821597 = log(r3821596);
        double r3821598 = log(r3821597);
        double r3821599 = r3821597 - r3821598;
        return r3821599;
}
↓
double f(double x) {
        double r3821600 = x;
        double r3821601 = log(r3821600);
        double r3821602 = r3821600 / r3821601;
        double r3821603 = log(r3821602);
        return r3821603;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))