Average Error: 14.2 → 0.1
Time: 9.9s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{x + 1}}{x}
double f(double x) {
        double r944844 = 1.0;
        double r944845 = x;
        double r944846 = r944845 + r944844;
        double r944847 = r944844 / r944846;
        double r944848 = r944844 / r944845;
        double r944849 = r944847 - r944848;
        return r944849;
}
↓
double f(double x) {
        double r944850 = -1.0;
        double r944851 = x;
        double r944852 = 1.0;
        double r944853 = r944851 + r944852;
        double r944854 = r944850 / r944853;
        double r944855 = r944854 / r944851;
        return r944855;
}

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

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

  3. Applied frac-sub13.5

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

  4. Simplified13.5

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

  6. Applied associate-/r*13.5

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019151 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))