Average Error: 0.0 → 0.3
Time: 9.8s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\left(\frac{-1}{2} \cdot \left(x \cdot x\right) - \left(x + \log x\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\left(\frac{-1}{2} \cdot \left(x \cdot x\right) - \left(x + \log x\right)\right)
double f(double x) {
        double r307330 = 1.0;
        double r307331 = x;
        double r307332 = r307330 / r307331;
        double r307333 = r307332 - r307330;
        double r307334 = log(r307333);
        double r307335 = -r307334;
        return r307335;
}
↓
double f(double x) {
        double r307336 = -0.5;
        double r307337 = x;
        double r307338 = r307337 * r307337;
        double r307339 = r307336 * r307338;
        double r307340 = log(r307337);
        double r307341 = r307337 + r307340;
        double r307342 = r307339 - r307341;
        double r307343 = -r307342;
        return r307343;
}

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. Taylor expanded around 0 0.3

    \[\leadsto -\color{blue}{\left(-\left(x + \left(\frac{1}{2} \cdot {x}^{2} + \log x\right)\right)\right)}\]

  3. Simplified0.3

    \[\leadsto -\color{blue}{\left(\frac{-1}{2} \cdot \left(x \cdot x\right) - \left(\log x + x\right)\right)}\]

  4. Final simplification0.3

    \[\leadsto -\left(\frac{-1}{2} \cdot \left(x \cdot x\right) - \left(x + \log x\right)\right)\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))