Average Error: 14.7 → 0.1
Time: 3.3s
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 r36286 = 1.0;
        double r36287 = x;
        double r36288 = r36287 + r36286;
        double r36289 = r36286 / r36288;
        double r36290 = r36286 / r36287;
        double r36291 = r36289 - r36290;
        return r36291;
}
↓
double f(double x) {
        double r36292 = 1.0;
        double r36293 = x;
        double r36294 = r36293 + r36292;
        double r36295 = 0.0;
        double r36296 = r36295 - r36292;
        double r36297 = r36294 / r36296;
        double r36298 = r36292 / r36297;
        double r36299 = r36298 / r36293;
        return r36299;
}

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. 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

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020065 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))