Average Error: 14.7 → 0.1
Time: 14.6s
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 r40293 = 1.0;
        double r40294 = x;
        double r40295 = r40294 + r40293;
        double r40296 = r40293 / r40295;
        double r40297 = r40293 / r40294;
        double r40298 = r40296 - r40297;
        return r40298;
}
↓
double f(double x) {
        double r40299 = 1.0;
        double r40300 = r40299 * r40299;
        double r40301 = -r40300;
        double r40302 = x;
        double r40303 = r40299 + r40302;
        double r40304 = r40301 / r40303;
        double r40305 = r40304 / r40302;
        return r40305;
}

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

    \[\leadsto \frac{\color{blue}{0 - 1 \cdot 1}}{\left(x + 1\right) \cdot x}\]
  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 2019323 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))