Average Error: 0.0 → 0.0
Time: 2.9s
Precision: binary64
\[-\log \left(\frac{1}{x} - 1\right) \]
↓
\[\begin{array}{l} t_0 := \log \left(\sqrt{\frac{1}{x} - 1}\right)\\ -\left(t_0 + t_0\right) \end{array} \]
-\log \left(\frac{1}{x} - 1\right)
↓
\begin{array}{l}
t_0 := \log \left(\sqrt{\frac{1}{x} - 1}\right)\\
-\left(t_0 + t_0\right)
\end{array}

(FPCore (x) :precision binary64 (- (log (- (/ 1.0 x) 1.0))))
↓
(FPCore (x)
 :precision binary64
 (let* ((t_0 (log (sqrt (- (/ 1.0 x) 1.0))))) (- (+ t_0 t_0))))
double code(double x) {
	return -log((1.0 / x) - 1.0);
}
↓
double code(double x) {
	double t_0 = log(sqrt((1.0 / x) - 1.0));
	return -(t_0 + t_0);
}

Error

Bits error versus x

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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. Applied add-sqr-sqrt_binary640.0

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

  3. Applied log-prod_binary640.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2021275 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1.0 x) 1.0))))