Average Error: 0.0 → 0.0
Time: 9.1s
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 r134643 = 1.0;
        double r134644 = x;
        double r134645 = r134643 / r134644;
        double r134646 = r134645 - r134643;
        double r134647 = log(r134646);
        double r134648 = -r134647;
        return r134648;
}
↓
double f(double x) {
        double r134649 = 1.0;
        double r134650 = x;
        double r134651 = r134649 / r134650;
        double r134652 = r134651 - r134649;
        double r134653 = sqrt(r134652);
        double r134654 = log(r134653);
        double r134655 = r134654 + r134654;
        double r134656 = -r134655;
        return r134656;
}

Error

Bits error versus x

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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 2019138 
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))