Average Error: 0.0 → 0.4
Time: 7.4s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\left(x \cdot \left(x \cdot \frac{-1}{2}\right) - \left(x + \log x\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\left(x \cdot \left(x \cdot \frac{-1}{2}\right) - \left(x + \log x\right)\right)
double f(double x) {
        double r146278 = 1.0;
        double r146279 = x;
        double r146280 = r146278 / r146279;
        double r146281 = r146280 - r146278;
        double r146282 = log(r146281);
        double r146283 = -r146282;
        return r146283;
}
↓
double f(double x) {
        double r146284 = x;
        double r146285 = -0.5;
        double r146286 = r146284 * r146285;
        double r146287 = r146284 * r146286;
        double r146288 = log(r146284);
        double r146289 = r146284 + r146288;
        double r146290 = r146287 - r146289;
        double r146291 = -r146290;
        return r146291;
}

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 0.4

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

  3. Simplified0.4

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2019151 
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))