Average Error: 0.0 → 0.0
Time: 9.4s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[\left(-2\right) \cdot \log \left(\sqrt{\frac{1}{x} - 1}\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
\left(-2\right) \cdot \log \left(\sqrt{\frac{1}{x} - 1}\right)
double f(double x) {
        double r34423 = 1.0;
        double r34424 = x;
        double r34425 = r34423 / r34424;
        double r34426 = r34425 - r34423;
        double r34427 = log(r34426);
        double r34428 = -r34427;
        return r34428;
}
↓
double f(double x) {
        double r34429 = 2.0;
        double r34430 = -r34429;
        double r34431 = 1.0;
        double r34432 = x;
        double r34433 = r34431 / r34432;
        double r34434 = r34433 - r34431;
        double r34435 = sqrt(r34434);
        double r34436 = log(r34435);
        double r34437 = r34430 * r34436;
        return r34437;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))