Average Error: 0.0 → 0.0
Time: 17.8s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\log \left(\left(\sqrt{1} + \sqrt{\frac{1}{x}}\right) \cdot \left(\frac{\sqrt{1}}{\sqrt{x}} - \sqrt{1}\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\log \left(\left(\sqrt{1} + \sqrt{\frac{1}{x}}\right) \cdot \left(\frac{\sqrt{1}}{\sqrt{x}} - \sqrt{1}\right)\right)
double f(double x) {
        double r817354 = 1.0;
        double r817355 = x;
        double r817356 = r817354 / r817355;
        double r817357 = r817356 - r817354;
        double r817358 = log(r817357);
        double r817359 = -r817358;
        return r817359;
}
↓
double f(double x) {
        double r817360 = 1.0;
        double r817361 = sqrt(r817360);
        double r817362 = x;
        double r817363 = r817360 / r817362;
        double r817364 = sqrt(r817363);
        double r817365 = r817361 + r817364;
        double r817366 = sqrt(r817362);
        double r817367 = r817361 / r817366;
        double r817368 = r817367 - r817361;
        double r817369 = r817365 * r817368;
        double r817370 = log(r817369);
        double r817371 = -r817370;
        return r817371;
}

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. Using strategy rm

  9. Applied sqrt-undiv0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1.0 x) 1.0))))