Average Error: 0.0 → 0.1
Time: 13.4s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\left(\log \left(\sqrt{\frac{1}{x} - 1}\right) + \log \left(\sqrt{\sqrt{\frac{1}{x}} + \sqrt{1}} \cdot \sqrt{\sqrt{\frac{1}{x}} - \sqrt{1}}\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\left(\log \left(\sqrt{\frac{1}{x} - 1}\right) + \log \left(\sqrt{\sqrt{\frac{1}{x}} + \sqrt{1}} \cdot \sqrt{\sqrt{\frac{1}{x}} - \sqrt{1}}\right)\right)
double f(double x) {
        double r21706 = 1.0;
        double r21707 = x;
        double r21708 = r21706 / r21707;
        double r21709 = r21708 - r21706;
        double r21710 = log(r21709);
        double r21711 = -r21710;
        return r21711;
}
↓
double f(double x) {
        double r21712 = 1.0;
        double r21713 = x;
        double r21714 = r21712 / r21713;
        double r21715 = r21714 - r21712;
        double r21716 = sqrt(r21715);
        double r21717 = log(r21716);
        double r21718 = sqrt(r21714);
        double r21719 = sqrt(r21712);
        double r21720 = r21718 + r21719;
        double r21721 = sqrt(r21720);
        double r21722 = r21718 - r21719;
        double r21723 = sqrt(r21722);
        double r21724 = r21721 * r21723;
        double r21725 = log(r21724);
        double r21726 = r21717 + r21725;
        double r21727 = -r21726;
        return r21727;
}

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. Using strategy rm

  6. Applied add-sqr-sqrt0.0

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

  7. Applied add-sqr-sqrt0.0

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

  8. Applied difference-of-squares0.0

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

  9. Applied sqrt-prod0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))