Average Error: 0.0 → 0.0
Time: 1.7s
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(1 + x\right) + \frac{x}{1 + x}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(1 + x\right) + \frac{x}{1 + x}
(FPCore (x) :precision binary64 (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (+ (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ 1.0 x)) (/ x (+ 1.0 x))))
double code(double x) {
	return ((double) ((1.0 / ((double) (x - 1.0))) + (x / ((double) (x + 1.0)))));
}
↓
double code(double x) {
	return ((double) (((double) ((1.0 / ((double) (((double) (x * x)) - ((double) (1.0 * 1.0))))) * ((double) (1.0 + x)))) + (x / ((double) (1.0 + x)))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 0.0 bits

    \[\frac{1}{x - 1} + \frac{x}{x + 1}\]
  2. Using strategy rm

  3. Applied flip--Error: 0.0 bits

    \[\leadsto \frac{1}{\color{blue}{\frac{x \cdot x - 1 \cdot 1}{x + 1}}} + \frac{x}{x + 1}\]

  4. Applied associate-/r/Error: 0.0 bits

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

  5. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020203 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))