Average Error: 14.3 → 0.1
Time: 3.7s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{\left(0 - 1\right) \cdot 1}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{\left(0 - 1\right) \cdot 1}{x + 1}}{x}
double f(double x) {
        double r40549 = 1.0;
        double r40550 = x;
        double r40551 = r40550 + r40549;
        double r40552 = r40549 / r40551;
        double r40553 = r40549 / r40550;
        double r40554 = r40552 - r40553;
        return r40554;
}
↓
double f(double x) {
        double r40555 = 0.0;
        double r40556 = 1.0;
        double r40557 = r40555 - r40556;
        double r40558 = r40557 * r40556;
        double r40559 = x;
        double r40560 = r40559 + r40556;
        double r40561 = r40558 / r40560;
        double r40562 = r40561 / r40559;
        return r40562;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.3

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

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

  6. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{\left(0 - 1\right) \cdot 1}{x + 1}}{x}}\]

  7. Final simplification0.1

    \[\leadsto \frac{\frac{\left(0 - 1\right) \cdot 1}{x + 1}}{x}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))