Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\log \left(\left(\frac{\sqrt{1}}{\sqrt{x}} + \sqrt{1}\right) \cdot \left(\frac{\sqrt{1}}{\sqrt{x}} - \sqrt{1}\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\log \left(\left(\frac{\sqrt{1}}{\sqrt{x}} + \sqrt{1}\right) \cdot \left(\frac{\sqrt{1}}{\sqrt{x}} - \sqrt{1}\right)\right)
double f(double x) {
        double r13988 = 1.0;
        double r13989 = x;
        double r13990 = r13988 / r13989;
        double r13991 = r13990 - r13988;
        double r13992 = log(r13991);
        double r13993 = -r13992;
        return r13993;
}
↓
double f(double x) {
        double r13994 = 1.0;
        double r13995 = sqrt(r13994);
        double r13996 = x;
        double r13997 = sqrt(r13996);
        double r13998 = r13995 / r13997;
        double r13999 = r13998 + r13995;
        double r14000 = r13998 - r13995;
        double r14001 = r13999 * r14000;
        double r14002 = log(r14001);
        double r14003 = -r14002;
        return r14003;
}

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

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

  4. Applied add-sqr-sqrt0.0

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

  5. Applied add-sqr-sqrt0.0

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

  6. Applied times-frac0.0

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

  7. Applied difference-of-squares0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))