Average Error: 0.0 → 0.0
Time: 11.8s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\left(\log \left(\frac{1}{\sqrt{x}} + 1\right) + \log \left(\frac{1}{\sqrt{x}} - 1\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\left(\log \left(\frac{1}{\sqrt{x}} + 1\right) + \log \left(\frac{1}{\sqrt{x}} - 1\right)\right)
double f(double x) {
        double r240636 = 1.0;
        double r240637 = x;
        double r240638 = r240636 / r240637;
        double r240639 = r240638 - r240636;
        double r240640 = log(r240639);
        double r240641 = -r240640;
        return r240641;
}
↓
double f(double x) {
        double r240642 = 1.0;
        double r240643 = x;
        double r240644 = sqrt(r240643);
        double r240645 = r240642 / r240644;
        double r240646 = r240645 + r240642;
        double r240647 = log(r240646);
        double r240648 = r240645 - r240642;
        double r240649 = log(r240648);
        double r240650 = r240647 + r240649;
        double r240651 = -r240650;
        return r240651;
}

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 *-un-lft-identity0.0

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

  4. Applied add-sqr-sqrt0.0

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

  5. Applied *-un-lft-identity0.0

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

  6. Applied times-frac0.0

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

  7. Applied difference-of-squares0.0

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

  8. Applied log-prod0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019146 
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))