Average Error: 14.3 → 0.1
Time: 13.2s
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 r38878 = 1.0;
        double r38879 = x;
        double r38880 = r38879 + r38878;
        double r38881 = r38878 / r38880;
        double r38882 = r38878 / r38879;
        double r38883 = r38881 - r38882;
        return r38883;
}
↓
double f(double x) {
        double r38884 = 1.0;
        double r38885 = -r38884;
        double r38886 = x;
        double r38887 = r38886 + r38884;
        double r38888 = r38887 / r38884;
        double r38889 = r38885 / r38888;
        double r38890 = r38889 / r38886;
        return r38890;
}

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-sub13.7

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

  4. Simplified13.7

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

  6. Applied associate-/r*13.7

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

  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 2019325 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))