Average Error: 0.0 → 0.0
Time: 9.8s
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 r11085 = 1.0;
        double r11086 = x;
        double r11087 = r11085 / r11086;
        double r11088 = r11087 - r11085;
        double r11089 = log(r11088);
        double r11090 = -r11089;
        return r11090;
}
↓
double f(double x) {
        double r11091 = 1.0;
        double r11092 = x;
        double r11093 = r11091 / r11092;
        double r11094 = r11093 - r11091;
        double r11095 = sqrt(r11094);
        double r11096 = log(r11095);
        double r11097 = r11096 + r11096;
        double r11098 = -r11097;
        return r11098;
}

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

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))