Average Error: 0.0 → 0.0
Time: 3.3s
Precision: binary64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\log \left(\sqrt[3]{\frac{1}{x} - 1} \cdot \left(\sqrt[3]{\frac{1}{x} - 1} \cdot \sqrt[3]{\frac{1}{x} - 1}\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\log \left(\sqrt[3]{\frac{1}{x} - 1} \cdot \left(\sqrt[3]{\frac{1}{x} - 1} \cdot \sqrt[3]{\frac{1}{x} - 1}\right)\right)
(FPCore (x) :precision binary64 (- (log (- (/ 1.0 x) 1.0))))
↓
(FPCore (x)
 :precision binary64
 (-
  (log
   (*
    (cbrt (- (/ 1.0 x) 1.0))
    (* (cbrt (- (/ 1.0 x) 1.0)) (cbrt (- (/ 1.0 x) 1.0)))))))
double code(double x) {
	return -log((1.0 / x) - 1.0);
}
↓
double code(double x) {
	return -log(cbrt((1.0 / x) - 1.0) * (cbrt((1.0 / x) - 1.0) * cbrt((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-cube-cbrt_binary640.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2021097 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1.0 x) 1.0))))