Average Error: 0.0 → 0.0
Time: 803.0ms
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{-1 + x \cdot x} \cdot \left(1 + x\right) + \frac{x}{1 + x}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{-1 + x \cdot x} \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 (+ -1.0 (* x x))) (+ 1.0 x)) (/ x (+ 1.0 x))))
double code(double x) {
	return (1.0 / (x - 1.0)) + (x / (x + 1.0));
}
↓
double code(double x) {
	return ((1.0 / (-1.0 + (x * x))) * (1.0 + x)) + (x / (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 0.0

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

  3. Applied flip--_binary640.0

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

  4. Applied associate-/r/_binary640.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020224 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))