Average Error: 14.6 → 0.1
Time: 14.1s
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 r2544862 = 1.0;
        double r2544863 = x;
        double r2544864 = r2544863 + r2544862;
        double r2544865 = r2544862 / r2544864;
        double r2544866 = r2544862 / r2544863;
        double r2544867 = r2544865 - r2544866;
        return r2544867;
}
↓
double f(double x) {
        double r2544868 = -1.0;
        double r2544869 = x;
        double r2544870 = 1.0;
        double r2544871 = r2544869 + r2544870;
        double r2544872 = r2544868 / r2544871;
        double r2544873 = r2544872 / r2544869;
        return r2544873;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.6

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

  3. Applied frac-sub14.0

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

  4. Simplified0.3

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))