Average Error: 14.2 → 0.4
Time: 3.1s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{1 \cdot \left(-2\right)}{x \cdot x - 1 \cdot 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{1 \cdot \left(-2\right)}{x \cdot x - 1 \cdot 1}
double f(double x) {
        double r97245 = 1.0;
        double r97246 = x;
        double r97247 = r97246 + r97245;
        double r97248 = r97245 / r97247;
        double r97249 = r97246 - r97245;
        double r97250 = r97245 / r97249;
        double r97251 = r97248 - r97250;
        return r97251;
}
↓
double f(double x) {
        double r97252 = 1.0;
        double r97253 = 2.0;
        double r97254 = -r97253;
        double r97255 = r97252 * r97254;
        double r97256 = x;
        double r97257 = r97256 * r97256;
        double r97258 = r97252 * r97252;
        double r97259 = r97257 - r97258;
        double r97260 = r97255 / r97259;
        return r97260;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.2

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

  3. Applied frac-sub13.6

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

  4. Simplified13.6

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

  5. Simplified13.6

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

  6. Taylor expanded around 0 0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))