Average Error: 14.2 → 0.1
Time: 11.0s
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 r71754 = 1.0;
        double r71755 = x;
        double r71756 = r71755 + r71754;
        double r71757 = r71754 / r71756;
        double r71758 = r71755 - r71754;
        double r71759 = r71754 / r71758;
        double r71760 = r71757 - r71759;
        return r71760;
}
↓
double f(double x) {
        double r71761 = -2.0;
        double r71762 = 1.0;
        double r71763 = 4.0;
        double r71764 = pow(r71762, r71763);
        double r71765 = r71761 * r71764;
        double r71766 = x;
        double r71767 = r71762 + r71766;
        double r71768 = r71765 / r71767;
        double r71769 = r71766 - r71762;
        double r71770 = r71768 / r71769;
        double r71771 = r71762 * r71762;
        double r71772 = -r71762;
        double r71773 = r71772 * r71762;
        double r71774 = r71773 + r71771;
        double r71775 = r71771 + r71774;
        double r71776 = r71770 / r71775;
        return r71776;
}

Error

Bits error versus x

Try it out

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--29.4

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

  4. Applied associate-/r/29.4

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

  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/14.2

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

  7. Applied distribute-lft-out--13.7

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

  8. Simplified0.4

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

  10. Applied flip3--0.4

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

  11. Applied associate-*r/0.4

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

  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 2019325 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))