Average Error: 0.0 → 0.0
Time: 1.6s
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{\frac{\frac{1}{x - 1}}{x - 1} - \frac{x}{1 + x} \cdot \frac{x}{1 + x}}{\frac{1}{x - 1} - \frac{x}{1 + x}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{\frac{\frac{1}{x - 1}}{x - 1} - \frac{x}{1 + x} \cdot \frac{x}{1 + x}}{\frac{1}{x - 1} - \frac{x}{1 + x}}
(FPCore (x) :precision binary64 (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (/
  (- (/ (/ 1.0 (- x 1.0)) (- x 1.0)) (* (/ x (+ 1.0 x)) (/ x (+ 1.0 x))))
  (- (/ 1.0 (- x 1.0)) (/ 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 / (x - 1.0)) / (x - 1.0)) - ((x / (1.0 + x)) * (x / (1.0 + x)))) / ((1.0 / (x - 1.0)) - (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

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020233 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))