Average Error: 0.0 → 0.0
Time: 18.4s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\left(\log \left(\sqrt{\frac{1}{x} - 1}\right) + \log \left(\sqrt{\frac{1}{x} - 1}\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\left(\log \left(\sqrt{\frac{1}{x} - 1}\right) + \log \left(\sqrt{\frac{1}{x} - 1}\right)\right)
double f(double x) {
        double r234149 = 1.0;
        double r234150 = x;
        double r234151 = r234149 / r234150;
        double r234152 = r234151 - r234149;
        double r234153 = log(r234152);
        double r234154 = -r234153;
        return r234154;
}
↓
double f(double x) {
        double r234155 = 1.0;
        double r234156 = x;
        double r234157 = r234155 / r234156;
        double r234158 = r234157 - r234155;
        double r234159 = sqrt(r234158);
        double r234160 = log(r234159);
        double r234161 = r234160 + r234160;
        double r234162 = -r234161;
        return r234162;
}

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

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

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))