Average Error: 0.3 → 0.0
Time: 19.0s
Precision: binary64
Cost: 448
\[\log x - \log \log x\]
↓
\[\log \left(-\frac{x}{-\log x}\right)\]
\log x - \log \log x
↓
\log \left(-\frac{x}{-\log x}\right)
(FPCore (x) :precision binary64 (- (log x) (log (log x))))
↓
(FPCore (x) :precision binary64 (log (- (/ x (- (log x))))))
double code(double x) {
	return log(x) - log(log(x));
}
↓
double code(double x) {
	return log(-(x / -log(x)));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs
Alternative 1
Accuracy0.0
Cost512
\[\log \left(\frac{-1}{\frac{\log x}{-x}}\right)\]
Alternative 2
Accuracy0.3
Cost384
\[\log x - \log \log x\]

Derivation

  1. Initial program 0.3

    \[\log x - \log \log x\]
  2. Using strategy rm

  3. Applied diff-log_binary64_11930.0

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

  5. Applied frac-2neg_binary64_11120.0

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

  7. Applied neg-sub0_binary64_10960.0

    \[\leadsto \log \left(\frac{\color{blue}{0 - x}}{-\log x}\right)\]

  8. Applied div-sub_binary64_11060.0

    \[\leadsto \log \color{blue}{\left(\frac{0}{-\log x} - \frac{x}{-\log x}\right)}\]

  9. Simplified0.0

    \[\leadsto \log \left(\color{blue}{0} - \frac{x}{-\log x}\right)\]

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020322 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  :precision binary64
  (- (log x) (log (log x))))