Average Error: 0.0 → 0.0
Time: 6.2s
Precision: binary64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[\left(-\log \left(\sqrt{\frac{1}{x} - 1}\right)\right) - \log \left(\sqrt{\frac{1}{x} - 1}\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
\left(-\log \left(\sqrt{\frac{1}{x} - 1}\right)\right) - \log \left(\sqrt{\frac{1}{x} - 1}\right)
double code(double x) {
	return ((double) -(((double) log(((double) ((1.0 / x) - 1.0))))));
}
↓
double code(double x) {
	return ((double) (((double) -(((double) log(((double) sqrt(((double) ((1.0 / x) - 1.0)))))))) - ((double) log(((double) sqrt(((double) ((1.0 / x) - 1.0))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[-\log \left(\frac{1}{x} - 1\right)\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied log-prod0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020196 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1.0 x) 1.0))))