Average Error: 0.0 → 0.0
Time: 4.6s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\log \left(\left(\sqrt{\frac{1}{x}} + \sqrt{1}\right) \cdot \left(\sqrt{\frac{1}{x}} - \sqrt{1}\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\log \left(\left(\sqrt{\frac{1}{x}} + \sqrt{1}\right) \cdot \left(\sqrt{\frac{1}{x}} - \sqrt{1}\right)\right)
double f(double x) {
        double r29641 = 1.0;
        double r29642 = x;
        double r29643 = r29641 / r29642;
        double r29644 = r29643 - r29641;
        double r29645 = log(r29644);
        double r29646 = -r29645;
        return r29646;
}
↓
double f(double x) {
        double r29647 = 1.0;
        double r29648 = x;
        double r29649 = r29647 / r29648;
        double r29650 = sqrt(r29649);
        double r29651 = sqrt(r29647);
        double r29652 = r29650 + r29651;
        double r29653 = r29650 - r29651;
        double r29654 = r29652 * r29653;
        double r29655 = log(r29654);
        double r29656 = -r29655;
        return r29656;
}

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

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

  4. Applied add-sqr-sqrt0.0

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

  5. Applied difference-of-squares0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020033 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))