Average Error: 14.1 → 0.1
Time: 2.1s
Precision: binary64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{1}{1 + x} \cdot \left(1 \cdot -2\right)}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{1}{1 + x} \cdot \left(1 \cdot -2\right)}{x - 1}
(FPCore (x) :precision binary64 (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (/ (* (/ 1.0 (+ 1.0 x)) (* 1.0 -2.0)) (- x 1.0)))
double code(double x) {
	return ((double) ((1.0 / ((double) (x + 1.0))) - (1.0 / ((double) (x - 1.0)))));
}
↓
double code(double x) {
	return (((double) ((1.0 / ((double) (1.0 + x))) * ((double) (1.0 * -2.0)))) / ((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 14.1

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

  3. Applied frac-sub13.5

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

  4. Simplified0.3

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

  5. Simplified0.3

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

  7. Applied difference-of-squares0.3

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

  8. Applied associate-/r*0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020198 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))