Average Error: 0.0 → 0.5
Time: 1.4s
Precision: binary64
\[-\log \left(\frac{1}{x} - 1\right) \]
↓
\[x + \log x \]
-\log \left(\frac{1}{x} - 1\right)
↓
x + \log x

(FPCore (x) :precision binary64 (- (log (- (/ 1.0 x) 1.0))))
↓
(FPCore (x) :precision binary64 (+ x (log x)))
double code(double x) {
	return -log((1.0 / x) - 1.0);
}
↓
double code(double x) {
	return x + log(x);
}

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. Taylor expanded in x around 0 0.5

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

  3. Final simplification0.5

    \[\leadsto x + \log x \]

Reproduce

herbie shell --seed 2022081 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1.0 x) 1.0))))