Average Error: 0.0 → 0.0
Time: 2.2s
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 r9143 = 1.0;
        double r9144 = x;
        double r9145 = r9143 / r9144;
        double r9146 = r9145 - r9143;
        double r9147 = log(r9146);
        double r9148 = -r9147;
        return r9148;
}
↓
double f(double x) {
        double r9149 = 1.0;
        double r9150 = x;
        double r9151 = r9149 / r9150;
        double r9152 = r9151 - r9149;
        double r9153 = sqrt(r9152);
        double r9154 = r9153 * r9153;
        double r9155 = log(r9154);
        double r9156 = -r9155;
        return r9156;
}

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

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

Reproduce

herbie shell --seed 2020027 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))