Average Error: 14.8 → 0.1
Time: 26.9s
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 r4573461 = 1.0;
        double r4573462 = x;
        double r4573463 = r4573462 + r4573461;
        double r4573464 = r4573461 / r4573463;
        double r4573465 = r4573462 - r4573461;
        double r4573466 = r4573461 / r4573465;
        double r4573467 = r4573464 - r4573466;
        return r4573467;
}
↓
double f(double x) {
        double r4573468 = 2.0;
        double r4573469 = -r4573468;
        double r4573470 = x;
        double r4573471 = 1.0;
        double r4573472 = r4573470 + r4573471;
        double r4573473 = r4573469 / r4573472;
        double r4573474 = r4573470 - r4573471;
        double r4573475 = r4573473 / r4573474;
        return r4573475;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

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

  3. Applied frac-sub14.1

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

  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 2019200 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))