Average Error: 0.0 → 0.0
Time: 2.2s
Precision: binary64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\left(\log \left(\sqrt{\frac{1}{x} - 1}\right) + \log \left(\left|\sqrt[3]{\frac{1}{x} - 1}\right| \cdot \sqrt{\sqrt[3]{\frac{1}{x} - 1}}\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\left(\log \left(\sqrt{\frac{1}{x} - 1}\right) + \log \left(\left|\sqrt[3]{\frac{1}{x} - 1}\right| \cdot \sqrt{\sqrt[3]{\frac{1}{x} - 1}}\right)\right)
(FPCore (x) :precision binary64 (- (log (- (/ 1.0 x) 1.0))))
↓
(FPCore (x)
 :precision binary64
 (-
  (+
   (log (sqrt (- (/ 1.0 x) 1.0)))
   (log (* (fabs (cbrt (- (/ 1.0 x) 1.0))) (sqrt (cbrt (- (/ 1.0 x) 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) sqrt(((double) ((1.0 / x) - 1.0)))))) + ((double) log(((double) (((double) fabs(((double) cbrt(((double) ((1.0 / x) - 1.0)))))) * ((double) sqrt(((double) cbrt(((double) ((1.0 / x) - 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-sqrt_binary640.0

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

  4. Applied log-prod_binary640.0

    \[\leadsto -\color{blue}{\left(\log \left(\sqrt{\frac{1}{x} - 1}\right) + \log \left(\sqrt{\frac{1}{x} - 1}\right)\right)}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt_binary640.0

    \[\leadsto -\left(\log \left(\sqrt{\frac{1}{x} - 1}\right) + \log \left(\sqrt{\color{blue}{\left(\sqrt[3]{\frac{1}{x} - 1} \cdot \sqrt[3]{\frac{1}{x} - 1}\right) \cdot \sqrt[3]{\frac{1}{x} - 1}}}\right)\right)\]

  7. Applied sqrt-prod_binary640.0

    \[\leadsto -\left(\log \left(\sqrt{\frac{1}{x} - 1}\right) + \log \color{blue}{\left(\sqrt{\sqrt[3]{\frac{1}{x} - 1} \cdot \sqrt[3]{\frac{1}{x} - 1}} \cdot \sqrt{\sqrt[3]{\frac{1}{x} - 1}}\right)}\right)\]

  8. Simplified0.0

    \[\leadsto -\left(\log \left(\sqrt{\frac{1}{x} - 1}\right) + \log \left(\color{blue}{\left|\sqrt[3]{\frac{1}{x} - 1}\right|} \cdot \sqrt{\sqrt[3]{\frac{1}{x} - 1}}\right)\right)\]

  9. Final simplification0.0

    \[\leadsto -\left(\log \left(\sqrt{\frac{1}{x} - 1}\right) + \log \left(\left|\sqrt[3]{\frac{1}{x} - 1}\right| \cdot \sqrt{\sqrt[3]{\frac{1}{x} - 1}}\right)\right)\]

Reproduce

herbie shell --seed 2020210 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1.0 x) 1.0))))