Average Error: 14.2 → 0.1
Time: 3.6s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[1 \cdot \frac{\frac{-2}{x + 1}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
1 \cdot \frac{\frac{-2}{x + 1}}{x - 1}
double f(double x) {
        double r90321 = 1.0;
        double r90322 = x;
        double r90323 = r90322 + r90321;
        double r90324 = r90321 / r90323;
        double r90325 = r90322 - r90321;
        double r90326 = r90321 / r90325;
        double r90327 = r90324 - r90326;
        return r90327;
}
↓
double f(double x) {
        double r90328 = 1.0;
        double r90329 = 2.0;
        double r90330 = -r90329;
        double r90331 = x;
        double r90332 = r90331 + r90328;
        double r90333 = r90330 / r90332;
        double r90334 = r90331 - r90328;
        double r90335 = r90333 / r90334;
        double r90336 = r90328 * r90335;
        return r90336;
}

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 flip--29.2

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

  4. Applied associate-/r/29.3

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

  5. Applied flip-+14.2

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

  6. Applied associate-/r/14.2

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

  7. Applied distribute-lft-out--13.6

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

  8. Taylor expanded around 0 0.4

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

  10. Applied div-inv0.4

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

  11. Applied associate-*l*0.4

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))