Average Error: 14.5 → 0.1
Time: 11.6s
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 r53928 = 1.0;
        double r53929 = x;
        double r53930 = r53929 + r53928;
        double r53931 = r53928 / r53930;
        double r53932 = r53928 / r53929;
        double r53933 = r53931 - r53932;
        return r53933;
}
↓
double f(double x) {
        double r53934 = 1.0;
        double r53935 = x;
        double r53936 = r53935 + r53934;
        double r53937 = -r53934;
        double r53938 = r53936 / r53937;
        double r53939 = r53934 / r53938;
        double r53940 = r53939 / r53935;
        return r53940;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

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

  3. Applied frac-sub13.9

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

  4. Simplified13.9

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

  6. Applied associate-/r*13.9

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

  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 2019209 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))