Average Error: 14.7 → 0.1
Time: 10.8s
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 r2718829 = 1.0;
        double r2718830 = x;
        double r2718831 = r2718830 + r2718829;
        double r2718832 = r2718829 / r2718831;
        double r2718833 = r2718829 / r2718830;
        double r2718834 = r2718832 - r2718833;
        return r2718834;
}
↓
double f(double x) {
        double r2718835 = 1.0;
        double r2718836 = -r2718835;
        double r2718837 = x;
        double r2718838 = r2718835 + r2718837;
        double r2718839 = r2718836 / r2718838;
        double r2718840 = r2718839 / r2718837;
        return r2718840;
}

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. Taylor expanded around 0 0.3

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))