Average Error: 14.5 → 0.5
Time: 3.5s
Precision: binary64
Cost: 448
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{-2}{-1 + x \cdot x}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{-2}{-1 + x \cdot x}
(FPCore (x) :precision binary64 (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))
↓
(FPCore (x) :precision binary64 (/ -2.0 (+ -1.0 (* x x))))
double code(double x) {
	return (1.0 / (x + 1.0)) - (1.0 / (x - 1.0));
}
↓
double code(double x) {
	return -2.0 / (-1.0 + (x * x));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error1.0
Cost776
\[\begin{array}{l} \mathbf{if}\;x \leq -1.0247328982238428 \lor \neg \left(x \leq 1.0121555451085444\right):\\ \;\;\;\;\frac{-2}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 + \left(x \cdot x\right) \cdot 2\\ \end{array}\]
Alternative 2
Error1.1
Cost648
\[\begin{array}{l} \mathbf{if}\;x \leq -1.0247328982238428 \lor \neg \left(x \leq 1.0121555451085444\right):\\ \;\;\;\;\frac{-2}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array}\]
Alternative 3
Error15.8
Cost706
\[\begin{array}{l} \mathbf{if}\;x \leq -1.0247328982238428:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 1.0121555451085444:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 4
Error41.8
Cost706
\[\begin{array}{l} \mathbf{if}\;x \leq -1.0247328982238428:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 1.0121555451085444:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 5
Error57.1
Cost64
\[1\]

Error

Derivation

  1. Initial program 14.5

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

  3. Applied frac-sub_binary64_452013.9

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

  4. Simplified0.5

    \[\leadsto \frac{\color{blue}{-2}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]

  5. Simplified0.5

    \[\leadsto \frac{-2}{\color{blue}{-1 + x \cdot x}}\]

  6. Simplified0.5

    \[\leadsto \color{blue}{\frac{-2}{-1 + x \cdot x}}\]

  7. Final simplification0.5

    \[\leadsto \frac{-2}{-1 + x \cdot x}\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))