Average Error: 14.5 → 0.1
Time: 16.5s
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 r1818288 = 1.0;
        double r1818289 = x;
        double r1818290 = r1818289 + r1818288;
        double r1818291 = r1818288 / r1818290;
        double r1818292 = r1818288 / r1818289;
        double r1818293 = r1818291 - r1818292;
        return r1818293;
}
↓
double f(double x) {
        double r1818294 = -1.0;
        double r1818295 = x;
        double r1818296 = 1.0;
        double r1818297 = r1818295 + r1818296;
        double r1818298 = r1818294 / r1818297;
        double r1818299 = r1818298 / r1818295;
        return r1818299;
}

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-sub13.9

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

  4. Simplified0.3

    \[\leadsto \frac{\color{blue}{-1}}{\left(x + 1\right) \cdot x}\]
  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 2019164 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))