Average Error: 0.3 → 0.0
Time: 10.5s
Precision: 64
\[\log x - \log \left(\log x\right)\]
↓
\[\log \left(\frac{1}{\sqrt{\log x}} \cdot \frac{x}{\sqrt{\log x}}\right)\]
\log x - \log \left(\log x\right)
↓
\log \left(\frac{1}{\sqrt{\log x}} \cdot \frac{x}{\sqrt{\log x}}\right)
double f(double x) {
        double r78362 = x;
        double r78363 = log(r78362);
        double r78364 = log(r78363);
        double r78365 = r78363 - r78364;
        return r78365;
}
↓
double f(double x) {
        double r78366 = 1.0;
        double r78367 = x;
        double r78368 = log(r78367);
        double r78369 = sqrt(r78368);
        double r78370 = r78366 / r78369;
        double r78371 = r78367 / r78369;
        double r78372 = r78370 * r78371;
        double r78373 = log(r78372);
        return r78373;
}

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 add-sqr-sqrt0.0

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

  6. Applied *-un-lft-identity0.0

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

  7. Applied times-frac0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))