Average Error: 0.0 → 0.0
Time: 7.7s
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 r325212 = 1.0;
        double r325213 = x;
        double r325214 = r325212 / r325213;
        double r325215 = r325214 - r325212;
        double r325216 = log(r325215);
        double r325217 = -r325216;
        return r325217;
}
↓
double f(double x) {
        double r325218 = 1.0;
        double r325219 = x;
        double r325220 = r325218 / r325219;
        double r325221 = r325220 - r325218;
        double r325222 = sqrt(r325221);
        double r325223 = log(r325222);
        double r325224 = r325223 + r325223;
        double r325225 = -r325224;
        return r325225;
}

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 2019169 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1.0 x) 1.0))))