Average Error: 14.4 → 0.1
Time: 10.1min
Precision: binary64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{\left(-2 \cdot 1\right) \cdot 1}{x + 1}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{\left(-2 \cdot 1\right) \cdot 1}{x + 1}}{x - 1}
double code(double x) {
	return ((double) ((1.0 / ((double) (x + 1.0))) - (1.0 / ((double) (x - 1.0)))));
}
↓
double code(double x) {
	return ((((double) (((double) (-2.0 * 1.0)) * 1.0)) / ((double) (x + 1.0))) / ((double) (x - 1.0)));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.4

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

  3. Applied frac-sub13.8

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

  4. Simplified0.4

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

  5. Simplified0.4

    \[\leadsto \frac{\left(-2 \cdot 1\right) \cdot 1}{\color{blue}{x \cdot x - 1 \cdot 1}}\]
  6. Using strategy rm

  7. Applied difference-of-squares0.4

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

  8. Applied associate-/r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020181 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))