Average Error: 14.7 → 0.1
Time: 52.8s
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 r3488820 = 1.0;
        double r3488821 = x;
        double r3488822 = r3488821 + r3488820;
        double r3488823 = r3488820 / r3488822;
        double r3488824 = r3488821 - r3488820;
        double r3488825 = r3488820 / r3488824;
        double r3488826 = r3488823 - r3488825;
        return r3488826;
}
↓
double f(double x) {
        double r3488827 = -2.0;
        double r3488828 = x;
        double r3488829 = 1.0;
        double r3488830 = r3488828 + r3488829;
        double r3488831 = r3488827 / r3488830;
        double r3488832 = r3488828 - r3488829;
        double r3488833 = r3488831 / r3488832;
        return r3488833;
}

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 flip--29.6

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

  4. Applied associate-/r/29.6

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

  5. Applied flip-+14.8

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

  6. Applied associate-/r/14.7

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

  7. Applied distribute-lft-out--14.1

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

  8. Taylor expanded around -inf 0.4

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

  10. Applied difference-of-squares0.4

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

  11. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{1}{x + 1}}{x - 1}} \cdot -2\]
  12. Using strategy rm

  13. Applied associate-*l/0.1

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

  14. Simplified0.1

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

  15. Final simplification0.1

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

Reproduce

herbie shell --seed 2019143 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))