Average Error: 29.2 → 0.0
Time: 2.0s
Precision: 64
\[\frac{x}{x + 1} - \frac{x + 1}{x - 1}\]
↓
\[\frac{\frac{-1}{x} - 3}{x - 1 \cdot \frac{1}{x}}\]
\frac{x}{x + 1} - \frac{x + 1}{x - 1}
↓
\frac{\frac{-1}{x} - 3}{x - 1 \cdot \frac{1}{x}}
double code(double x) {
	return ((x / (x + 1.0)) - ((x + 1.0) / (x - 1.0)));
}
↓
double code(double x) {
	return (((-1.0 / x) - 3.0) / (x - (1.0 * (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 29.2

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

  3. Applied clear-num29.2

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

  4. Applied frac-sub28.9

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

  5. Simplified28.9

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

  6. Taylor expanded around 0 0.0

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

  7. Simplified0.0

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

  8. Taylor expanded around 0 0.0

    \[\leadsto \frac{\frac{-1}{x} - 3}{\color{blue}{x - 1 \cdot \frac{1}{x}}}\]

  9. Final simplification0.0

    \[\leadsto \frac{\frac{-1}{x} - 3}{x - 1 \cdot \frac{1}{x}}\]

Reproduce

herbie shell --seed 2020071 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))