Average Error: 14.8 → 0.1
Time: 17.2s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{\frac{x + 1}{1}}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{\frac{x + 1}{1}}}{x}
double f(double x) {
        double r44316 = 1.0;
        double r44317 = x;
        double r44318 = r44317 + r44316;
        double r44319 = r44316 / r44318;
        double r44320 = r44316 / r44317;
        double r44321 = r44319 - r44320;
        return r44321;
}
↓
double f(double x) {
        double r44322 = 1.0;
        double r44323 = -r44322;
        double r44324 = x;
        double r44325 = r44324 + r44322;
        double r44326 = r44325 / r44322;
        double r44327 = r44323 / r44326;
        double r44328 = r44327 / r44324;
        return r44328;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  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. Simplified14.1

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

  6. Applied associate-/r*14.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))