Average Error: 14.6 → 0.1
Time: 7.7s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{\left(-1\right) \cdot 1}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{\left(-1\right) \cdot 1}{x + 1}}{x}
double f(double x) {
        double r42825 = 1.0;
        double r42826 = x;
        double r42827 = r42826 + r42825;
        double r42828 = r42825 / r42827;
        double r42829 = r42825 / r42826;
        double r42830 = r42828 - r42829;
        return r42830;
}
↓
double f(double x) {
        double r42831 = 1.0;
        double r42832 = -r42831;
        double r42833 = r42832 * r42831;
        double r42834 = x;
        double r42835 = r42834 + r42831;
        double r42836 = r42833 / r42835;
        double r42837 = r42836 / r42834;
        return r42837;
}

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. Simplified0.4

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019351 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))