Average Error: 14.4 → 0.1
Time: 13.4s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1 \cdot 1}{1 + x}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1 \cdot 1}{1 + x}}{x}
double f(double x) {
        double r36398 = 1.0;
        double r36399 = x;
        double r36400 = r36399 + r36398;
        double r36401 = r36398 / r36400;
        double r36402 = r36398 / r36399;
        double r36403 = r36401 - r36402;
        return r36403;
}
↓
double f(double x) {
        double r36404 = 1.0;
        double r36405 = r36404 * r36404;
        double r36406 = -r36405;
        double r36407 = x;
        double r36408 = r36404 + r36407;
        double r36409 = r36406 / r36408;
        double r36410 = r36409 / r36407;
        return r36410;
}

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-sub13.7

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

  4. Simplified0.4

    \[\leadsto \frac{\color{blue}{0 - 1 \cdot 1}}{\left(x + 1\right) \cdot x}\]
  5. Using strategy rm

  6. Applied associate-/r*0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))