Average Error: 14.3 → 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 r2513675 = 1.0;
        double r2513676 = x;
        double r2513677 = r2513676 + r2513675;
        double r2513678 = r2513675 / r2513677;
        double r2513679 = r2513675 / r2513676;
        double r2513680 = r2513678 - r2513679;
        return r2513680;
}
↓
double f(double x) {
        double r2513681 = -1.0;
        double r2513682 = 1.0;
        double r2513683 = x;
        double r2513684 = r2513682 + r2513683;
        double r2513685 = r2513681 / r2513684;
        double r2513686 = r2513685 / r2513683;
        return r2513686;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.3

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

  3. Applied frac-sub13.7

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

  4. Simplified13.7

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

  6. Applied associate-/r*13.7

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

  7. Simplified0.1

    \[\leadsto \frac{\color{blue}{\frac{0 - 1}{1 + x}}}{x}\]

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))