Average Error: 0.0 → 0.0
Time: 2.4s
Precision: binary64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[\left(-\log \left(\sqrt{1} + \frac{\sqrt{1}}{\sqrt{x}}\right)\right) - \log \left(\frac{\sqrt{1}}{\sqrt{x}} - \sqrt{1}\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
\left(-\log \left(\sqrt{1} + \frac{\sqrt{1}}{\sqrt{x}}\right)\right) - \log \left(\frac{\sqrt{1}}{\sqrt{x}} - \sqrt{1}\right)
(FPCore (x) :precision binary64 (- (log (- (/ 1.0 x) 1.0))))
↓
(FPCore (x)
 :precision binary64
 (-
  (- (log (+ (sqrt 1.0) (/ (sqrt 1.0) (sqrt x)))))
  (log (- (/ (sqrt 1.0) (sqrt x)) (sqrt 1.0)))))
double code(double x) {
	return ((double) -(((double) log(((double) ((1.0 / x) - 1.0))))));
}
↓
double code(double x) {
	return ((double) (((double) -(((double) log(((double) (((double) sqrt(1.0)) + (((double) sqrt(1.0)) / ((double) sqrt(x))))))))) - ((double) log(((double) ((((double) sqrt(1.0)) / ((double) sqrt(x))) - ((double) sqrt(1.0))))))));
}

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. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020198 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1.0 x) 1.0))))