Average Error: 0.3 → 0.0
Time: 2.6s
Precision: 64
\[\log x - \log \left(\log x\right)\]
↓
\[\log \left(\frac{-1 \cdot x}{\log \left(\frac{1}{x}\right)}\right)\]
\log x - \log \left(\log x\right)
↓
\log \left(\frac{-1 \cdot x}{\log \left(\frac{1}{x}\right)}\right)
double f(double x) {
        double r114583 = x;
        double r114584 = log(r114583);
        double r114585 = log(r114584);
        double r114586 = r114584 - r114585;
        return r114586;
}
↓
double f(double x) {
        double r114587 = -1.0;
        double r114588 = x;
        double r114589 = r114587 * r114588;
        double r114590 = 1.0;
        double r114591 = r114590 / r114588;
        double r114592 = log(r114591);
        double r114593 = r114589 / r114592;
        double r114594 = log(r114593);
        return r114594;
}

Error

Bits error versus x

Try it out

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 frac-2neg0.0

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

  6. Simplified0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  :precision binary64
  (- (log x) (log (log x))))