Average Error: 14.7 → 0.1
Time: 11.1s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{1 + x}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{1 + x}}{x}
double f(double x) {
        double r894861 = 1.0;
        double r894862 = x;
        double r894863 = r894862 + r894861;
        double r894864 = r894861 / r894863;
        double r894865 = r894861 / r894862;
        double r894866 = r894864 - r894865;
        return r894866;
}
↓
double f(double x) {
        double r894867 = -1.0;
        double r894868 = 1.0;
        double r894869 = x;
        double r894870 = r894868 + r894869;
        double r894871 = r894867 / r894870;
        double r894872 = r894871 / r894869;
        return r894872;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

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

  3. Applied frac-sub14.1

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

  4. Simplified14.1

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

  6. Applied associate-/r*14.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))