Average Error: 0.0 → 0.0
Time: 13.5s
Precision: 64
\[-\log \left(\frac{1.0}{x} - 1.0\right)\]
↓
\[-\left(\log \left(\sqrt{\frac{1.0}{x} - 1.0}\right) + \log \left(\sqrt{\frac{1.0}{x} - 1.0}\right)\right)\]
-\log \left(\frac{1.0}{x} - 1.0\right)
↓
-\left(\log \left(\sqrt{\frac{1.0}{x} - 1.0}\right) + \log \left(\sqrt{\frac{1.0}{x} - 1.0}\right)\right)
double f(double x) {
        double r392880 = 1.0;
        double r392881 = x;
        double r392882 = r392880 / r392881;
        double r392883 = r392882 - r392880;
        double r392884 = log(r392883);
        double r392885 = -r392884;
        return r392885;
}
↓
double f(double x) {
        double r392886 = 1.0;
        double r392887 = x;
        double r392888 = r392886 / r392887;
        double r392889 = r392888 - r392886;
        double r392890 = sqrt(r392889);
        double r392891 = log(r392890);
        double r392892 = r392891 + r392891;
        double r392893 = -r392892;
        return r392893;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[-\log \left(\frac{1.0}{x} - 1.0\right)\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto -\log \color{blue}{\left(\sqrt{\frac{1.0}{x} - 1.0} \cdot \sqrt{\frac{1.0}{x} - 1.0}\right)}\]

  4. Applied log-prod0.0

    \[\leadsto -\color{blue}{\left(\log \left(\sqrt{\frac{1.0}{x} - 1.0}\right) + \log \left(\sqrt{\frac{1.0}{x} - 1.0}\right)\right)}\]

  5. Final simplification0.0

    \[\leadsto -\left(\log \left(\sqrt{\frac{1.0}{x} - 1.0}\right) + \log \left(\sqrt{\frac{1.0}{x} - 1.0}\right)\right)\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1.0 x) 1.0))))