Average Error: 0.0 → 0.0
Time: 15.5s
Precision: 64
\[-\log \left(\frac{1.0}{x} - 1.0\right)\]
↓
\[-\left(\log \left(\sqrt{\frac{1.0}{x} - 1.0}\right) + \log \left(\sqrt{\frac{1.0}{x} - 1.0}\right)\right)\]
-\log \left(\frac{1.0}{x} - 1.0\right)
↓
-\left(\log \left(\sqrt{\frac{1.0}{x} - 1.0}\right) + \log \left(\sqrt{\frac{1.0}{x} - 1.0}\right)\right)
double f(double x) {
        double r364392 = 1.0;
        double r364393 = x;
        double r364394 = r364392 / r364393;
        double r364395 = r364394 - r364392;
        double r364396 = log(r364395);
        double r364397 = -r364396;
        return r364397;
}
↓
double f(double x) {
        double r364398 = 1.0;
        double r364399 = x;
        double r364400 = r364398 / r364399;
        double r364401 = r364400 - r364398;
        double r364402 = sqrt(r364401);
        double r364403 = log(r364402);
        double r364404 = r364403 + r364403;
        double r364405 = -r364404;
        return r364405;
}

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

    \[-\log \left(\frac{1.0}{x} - 1.0\right)\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto -\log \color{blue}{\left(\sqrt{\frac{1.0}{x} - 1.0} \cdot \sqrt{\frac{1.0}{x} - 1.0}\right)}\]

  4. Applied log-prod0.0

    \[\leadsto -\color{blue}{\left(\log \left(\sqrt{\frac{1.0}{x} - 1.0}\right) + \log \left(\sqrt{\frac{1.0}{x} - 1.0}\right)\right)}\]

  5. Final simplification0.0

    \[\leadsto -\left(\log \left(\sqrt{\frac{1.0}{x} - 1.0}\right) + \log \left(\sqrt{\frac{1.0}{x} - 1.0}\right)\right)\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1.0 x) 1.0))))