Average Error: 14.3 → 0.1
Time: 15.9s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{\frac{-2 \cdot {1}^{4}}{1 + x}}{x - 1}}{1 \cdot 1 + \left(\left(-1\right) \cdot 1 + 1 \cdot 1\right)}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{\frac{-2 \cdot {1}^{4}}{1 + x}}{x - 1}}{1 \cdot 1 + \left(\left(-1\right) \cdot 1 + 1 \cdot 1\right)}
double f(double x) {
        double r101808 = 1.0;
        double r101809 = x;
        double r101810 = r101809 + r101808;
        double r101811 = r101808 / r101810;
        double r101812 = r101809 - r101808;
        double r101813 = r101808 / r101812;
        double r101814 = r101811 - r101813;
        return r101814;
}
↓
double f(double x) {
        double r101815 = -2.0;
        double r101816 = 1.0;
        double r101817 = 4.0;
        double r101818 = pow(r101816, r101817);
        double r101819 = r101815 * r101818;
        double r101820 = x;
        double r101821 = r101816 + r101820;
        double r101822 = r101819 / r101821;
        double r101823 = r101820 - r101816;
        double r101824 = r101822 / r101823;
        double r101825 = r101816 * r101816;
        double r101826 = -r101816;
        double r101827 = r101826 * r101816;
        double r101828 = r101827 + r101825;
        double r101829 = r101825 + r101828;
        double r101830 = r101824 / r101829;
        return r101830;
}

Error

Bits error versus x

Try it out

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--29.0

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

  4. Applied associate-/r/29.0

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

  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. Simplified0.3

    \[\leadsto \frac{1}{x \cdot x - 1 \cdot 1} \cdot \color{blue}{\left(\left(0 - 1\right) - 1\right)}\]
  9. Using strategy rm

  10. Applied flip3--0.3

    \[\leadsto \frac{1}{x \cdot x - 1 \cdot 1} \cdot \color{blue}{\frac{{\left(0 - 1\right)}^{3} - {1}^{3}}{\left(0 - 1\right) \cdot \left(0 - 1\right) + \left(1 \cdot 1 + \left(0 - 1\right) \cdot 1\right)}}\]

  11. Applied associate-*r/0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left({\left(0 - 1\right)}^{3} - {1}^{3}\right)}{\left(0 - 1\right) \cdot \left(0 - 1\right) + \left(1 \cdot 1 + \left(0 - 1\right) \cdot 1\right)}}\]

  12. Simplified0.1

    \[\leadsto \frac{\color{blue}{\frac{\frac{2 \cdot \left(-{1}^{4}\right)}{1 + x}}{x - 1}}}{\left(0 - 1\right) \cdot \left(0 - 1\right) + \left(1 \cdot 1 + \left(0 - 1\right) \cdot 1\right)}\]

  13. Final simplification0.1

    \[\leadsto \frac{\frac{\frac{-2 \cdot {1}^{4}}{1 + x}}{x - 1}}{1 \cdot 1 + \left(\left(-1\right) \cdot 1 + 1 \cdot 1\right)}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))