Average Error: 14.3 → 0.1
Time: 13.3s
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 r33602 = 1.0;
        double r33603 = x;
        double r33604 = r33603 + r33602;
        double r33605 = r33602 / r33604;
        double r33606 = r33602 / r33603;
        double r33607 = r33605 - r33606;
        return r33607;
}
↓
double f(double x) {
        double r33608 = 1.0;
        double r33609 = r33608 * r33608;
        double r33610 = -r33609;
        double r33611 = x;
        double r33612 = r33608 + r33611;
        double r33613 = r33610 / r33612;
        double r33614 = r33613 / r33611;
        return r33614;
}

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. Simplified0.3

    \[\leadsto \frac{\color{blue}{0 - 1 \cdot 1}}{\left(x + 1\right) \cdot x}\]
  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 2019303 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))