Average Error: 0.0 → 0.1
Time: 3.5s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\log \left(\sqrt{\frac{1}{x} - 1} \cdot \sqrt{\frac{1}{x} - 1}\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\log \left(\sqrt{\frac{1}{x} - 1} \cdot \sqrt{\frac{1}{x} - 1}\right)
double f(double x) {
        double r24792 = 1.0;
        double r24793 = x;
        double r24794 = r24792 / r24793;
        double r24795 = r24794 - r24792;
        double r24796 = log(r24795);
        double r24797 = -r24796;
        return r24797;
}
↓
double f(double x) {
        double r24798 = 1.0;
        double r24799 = x;
        double r24800 = r24798 / r24799;
        double r24801 = r24800 - r24798;
        double r24802 = sqrt(r24801);
        double r24803 = r24802 * r24802;
        double r24804 = log(r24803);
        double r24805 = -r24804;
        return r24805;
}

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-sqrt0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))