Average Error: 14.2 → 0.1
Time: 42.0s
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 r4816666 = 1.0;
        double r4816667 = x;
        double r4816668 = r4816667 + r4816666;
        double r4816669 = r4816666 / r4816668;
        double r4816670 = r4816667 - r4816666;
        double r4816671 = r4816666 / r4816670;
        double r4816672 = r4816669 - r4816671;
        return r4816672;
}
↓
double f(double x) {
        double r4816673 = -2.0;
        double r4816674 = x;
        double r4816675 = 1.0;
        double r4816676 = r4816674 + r4816675;
        double r4816677 = r4816673 / r4816676;
        double r4816678 = r4816674 - r4816675;
        double r4816679 = r4816677 / r4816678;
        return r4816679;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.2

    \[\frac{1}{x + 1} - \frac{1}{x - 1}\]
  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. Simplified13.7

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

  5. Taylor expanded around inf 0.4

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

  7. Applied associate-/r*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019144 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))