Average Error: 14.7 → 0.1
Time: 18.2s
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 r3392355 = 1.0;
        double r3392356 = x;
        double r3392357 = r3392356 + r3392355;
        double r3392358 = r3392355 / r3392357;
        double r3392359 = r3392356 - r3392355;
        double r3392360 = r3392355 / r3392359;
        double r3392361 = r3392358 - r3392360;
        return r3392361;
}
↓
double f(double x) {
        double r3392362 = -2.0;
        double r3392363 = x;
        double r3392364 = 1.0;
        double r3392365 = r3392363 + r3392364;
        double r3392366 = r3392362 / r3392365;
        double r3392367 = r3392363 - r3392364;
        double r3392368 = r3392366 / r3392367;
        return r3392368;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

    \[\frac{1}{x + 1} - \frac{1}{x - 1}\]
  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 inf 0.3

    \[\leadsto \frac{\color{blue}{-2}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]
  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 2019129 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))