Average Error: 0.0 → 0.0
Time: 3.8s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\left(\log \left(\sqrt{\sqrt{\frac{1}{x}} + \sqrt{1}} \cdot \sqrt{\sqrt{\frac{1}{x}} - \sqrt{1}}\right) + \log \left(\sqrt{\frac{1}{x} - 1}\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\left(\log \left(\sqrt{\sqrt{\frac{1}{x}} + \sqrt{1}} \cdot \sqrt{\sqrt{\frac{1}{x}} - \sqrt{1}}\right) + \log \left(\sqrt{\frac{1}{x} - 1}\right)\right)
double f(double x) {
        double r32681 = 1.0;
        double r32682 = x;
        double r32683 = r32681 / r32682;
        double r32684 = r32683 - r32681;
        double r32685 = log(r32684);
        double r32686 = -r32685;
        return r32686;
}
↓
double f(double x) {
        double r32687 = 1.0;
        double r32688 = x;
        double r32689 = r32687 / r32688;
        double r32690 = sqrt(r32689);
        double r32691 = sqrt(r32687);
        double r32692 = r32690 + r32691;
        double r32693 = sqrt(r32692);
        double r32694 = r32690 - r32691;
        double r32695 = sqrt(r32694);
        double r32696 = r32693 * r32695;
        double r32697 = log(r32696);
        double r32698 = r32689 - r32687;
        double r32699 = sqrt(r32698);
        double r32700 = log(r32699);
        double r32701 = r32697 + r32700;
        double r32702 = -r32701;
        return r32702;
}

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

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

  7. Applied add-sqr-sqrt0.0

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

  8. Applied difference-of-squares0.0

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

  9. Applied sqrt-prod0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))