Average Error: 14.4 → 0.4
Time: 3.4s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{1}{\frac{\frac{\left(x + 1\right) \cdot x}{1}}{0 - 1}}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{1}{\frac{\frac{\left(x + 1\right) \cdot x}{1}}{0 - 1}}
double f(double x) {
        double r37451 = 1.0;
        double r37452 = x;
        double r37453 = r37452 + r37451;
        double r37454 = r37451 / r37453;
        double r37455 = r37451 / r37452;
        double r37456 = r37454 - r37455;
        return r37456;
}
↓
double f(double x) {
        double r37457 = 1.0;
        double r37458 = x;
        double r37459 = 1.0;
        double r37460 = r37458 + r37459;
        double r37461 = r37460 * r37458;
        double r37462 = r37461 / r37459;
        double r37463 = 0.0;
        double r37464 = r37463 - r37459;
        double r37465 = r37462 / r37464;
        double r37466 = r37457 / r37465;
        return r37466;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.4

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  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 clear-num13.8

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

  7. Simplified0.4

    \[\leadsto \frac{1}{\color{blue}{\frac{\frac{\left(x + 1\right) \cdot x}{1}}{0 - 1}}}\]

  8. Final simplification0.4

    \[\leadsto \frac{1}{\frac{\frac{\left(x + 1\right) \cdot x}{1}}{0 - 1}}\]

Reproduce

herbie shell --seed 2020089 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))