Average Error: 14.5 → 0.1
Time: 3.4s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{1}{\frac{x + 1}{0 - 1}}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{1}{\frac{x + 1}{0 - 1}}}{x}
double f(double x) {
        double r99508 = 1.0;
        double r99509 = x;
        double r99510 = r99509 + r99508;
        double r99511 = r99508 / r99510;
        double r99512 = r99508 / r99509;
        double r99513 = r99511 - r99512;
        return r99513;
}
↓
double f(double x) {
        double r99514 = 1.0;
        double r99515 = x;
        double r99516 = r99515 + r99514;
        double r99517 = 0.0;
        double r99518 = r99517 - r99514;
        double r99519 = r99516 / r99518;
        double r99520 = r99514 / r99519;
        double r99521 = r99520 / r99515;
        return r99521;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

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

  3. Applied frac-sub13.8

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

  4. Simplified13.8

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

  6. Applied associate-/r*13.8

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019354 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))