Average Error: 14.3 → 0.4
Time: 12.4s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\left(-2\right) \cdot \frac{1}{x \cdot x - 1 \cdot 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\left(-2\right) \cdot \frac{1}{x \cdot x - 1 \cdot 1}
double f(double x) {
        double r168094 = 1.0;
        double r168095 = x;
        double r168096 = r168095 + r168094;
        double r168097 = r168094 / r168096;
        double r168098 = r168095 - r168094;
        double r168099 = r168094 / r168098;
        double r168100 = r168097 - r168099;
        return r168100;
}
↓
double f(double x) {
        double r168101 = 2.0;
        double r168102 = -r168101;
        double r168103 = 1.0;
        double r168104 = x;
        double r168105 = r168104 * r168104;
        double r168106 = r168103 * r168103;
        double r168107 = r168105 - r168106;
        double r168108 = r168103 / r168107;
        double r168109 = r168102 * r168108;
        return r168109;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.3

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

  3. Applied flip--28.5

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

  4. Applied associate-/r/28.5

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

  5. Applied flip-+14.3

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

  6. Applied associate-/r/14.3

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

  7. Applied distribute-lft-out--13.7

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

  8. Taylor expanded around 0 0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))