Average Error: 0.0 → 0.0
Time: 2.6s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\left(\log \left(\frac{\sqrt{1}}{\sqrt{x}} + \sqrt{1}\right) + \log \left(\frac{\sqrt{1}}{\sqrt{x}} - \sqrt{1}\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\left(\log \left(\frac{\sqrt{1}}{\sqrt{x}} + \sqrt{1}\right) + \log \left(\frac{\sqrt{1}}{\sqrt{x}} - \sqrt{1}\right)\right)
double f(double x) {
        double r18884 = 1.0;
        double r18885 = x;
        double r18886 = r18884 / r18885;
        double r18887 = r18886 - r18884;
        double r18888 = log(r18887);
        double r18889 = -r18888;
        return r18889;
}
↓
double f(double x) {
        double r18890 = 1.0;
        double r18891 = sqrt(r18890);
        double r18892 = x;
        double r18893 = sqrt(r18892);
        double r18894 = r18891 / r18893;
        double r18895 = r18894 + r18891;
        double r18896 = log(r18895);
        double r18897 = r18894 - r18891;
        double r18898 = log(r18897);
        double r18899 = r18896 + r18898;
        double r18900 = -r18899;
        return r18900;
}

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

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

  4. Applied add-sqr-sqrt0.0

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

  5. Applied add-sqr-sqrt0.0

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

  6. Applied times-frac0.0

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

  7. Applied difference-of-squares0.0

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

  8. Applied log-prod0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020049 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))