Average Error: 14.3 → 0.1
Time: 12.6s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{-2}{x + 1}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{-2}{x + 1}}{x - 1}
double f(double x) {
        double r111578 = 1.0;
        double r111579 = x;
        double r111580 = r111579 + r111578;
        double r111581 = r111578 / r111580;
        double r111582 = r111579 - r111578;
        double r111583 = r111578 / r111582;
        double r111584 = r111581 - r111583;
        return r111584;
}
↓
double f(double x) {
        double r111585 = 2.0;
        double r111586 = -r111585;
        double r111587 = x;
        double r111588 = 1.0;
        double r111589 = r111587 + r111588;
        double r111590 = r111586 / r111589;
        double r111591 = r111587 - r111588;
        double r111592 = r111590 / r111591;
        return r111592;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.3

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

  3. Applied frac-sub13.7

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

  4. Taylor expanded around 0 0.4

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))