Average Error: 0.0 → 0.0
Time: 16.2s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\left(\log \left(\frac{\sqrt{1}}{\sqrt{x}} + \sqrt{1}\right) + \log \left(\frac{\sqrt{1}}{\sqrt{x}} - \sqrt{1}\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\left(\log \left(\frac{\sqrt{1}}{\sqrt{x}} + \sqrt{1}\right) + \log \left(\frac{\sqrt{1}}{\sqrt{x}} - \sqrt{1}\right)\right)
double f(double x) {
        double r28274 = 1.0;
        double r28275 = x;
        double r28276 = r28274 / r28275;
        double r28277 = r28276 - r28274;
        double r28278 = log(r28277);
        double r28279 = -r28278;
        return r28279;
}
↓
double f(double x) {
        double r28280 = 1.0;
        double r28281 = sqrt(r28280);
        double r28282 = x;
        double r28283 = sqrt(r28282);
        double r28284 = r28281 / r28283;
        double r28285 = r28284 + r28281;
        double r28286 = log(r28285);
        double r28287 = r28284 - r28281;
        double r28288 = log(r28287);
        double r28289 = r28286 + r28288;
        double r28290 = -r28289;
        return r28290;
}

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. Applied log-prod0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))