Average Error: 14.3 → 0.1
Time: 12.1s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{1}{\frac{x + 1}{-1}}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{1}{\frac{x + 1}{-1}}}{x}
double f(double x) {
        double r47815 = 1.0;
        double r47816 = x;
        double r47817 = r47816 + r47815;
        double r47818 = r47815 / r47817;
        double r47819 = r47815 / r47816;
        double r47820 = r47818 - r47819;
        return r47820;
}
↓
double f(double x) {
        double r47821 = 1.0;
        double r47822 = x;
        double r47823 = r47822 + r47821;
        double r47824 = -r47821;
        double r47825 = r47823 / r47824;
        double r47826 = r47821 / r47825;
        double r47827 = r47826 / r47822;
        return r47827;
}

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

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

  3. Applied frac-sub13.6

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

  4. Simplified13.6

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

  6. Applied associate-/r*13.6

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))