Average Error: 0.0 → 0.0
Time: 8.3s
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 r351159 = 1.0;
        double r351160 = x;
        double r351161 = r351159 / r351160;
        double r351162 = r351161 - r351159;
        double r351163 = log(r351162);
        double r351164 = -r351163;
        return r351164;
}
↓
double f(double x) {
        double r351165 = 1.0;
        double r351166 = x;
        double r351167 = r351165 / r351166;
        double r351168 = r351167 - r351165;
        double r351169 = sqrt(r351168);
        double r351170 = log(r351169);
        double r351171 = r351170 + r351170;
        double r351172 = -r351171;
        return r351172;
}

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 2019172 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1.0 x) 1.0))))