Average Error: 0.0 → 0.0
Time: 7.5s
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 r464220 = 1.0;
        double r464221 = x;
        double r464222 = r464220 / r464221;
        double r464223 = r464222 - r464220;
        double r464224 = log(r464223);
        double r464225 = -r464224;
        return r464225;
}
↓
double f(double x) {
        double r464226 = 1.0;
        double r464227 = x;
        double r464228 = r464226 / r464227;
        double r464229 = r464228 - r464226;
        double r464230 = sqrt(r464229);
        double r464231 = log(r464230);
        double r464232 = r464231 + r464231;
        double r464233 = -r464232;
        return r464233;
}

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 
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1.0 x) 1.0))))