Average Error: 14.7 → 0.1
Time: 13.6s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{x + 1}}{x}
double f(double x) {
        double r2693468 = 1.0;
        double r2693469 = x;
        double r2693470 = r2693469 + r2693468;
        double r2693471 = r2693468 / r2693470;
        double r2693472 = r2693468 / r2693469;
        double r2693473 = r2693471 - r2693472;
        return r2693473;
}
↓
double f(double x) {
        double r2693474 = -1.0;
        double r2693475 = x;
        double r2693476 = 1.0;
        double r2693477 = r2693475 + r2693476;
        double r2693478 = r2693474 / r2693477;
        double r2693479 = r2693478 / r2693475;
        return r2693479;
}

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. Simplified0.4

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))