Average Error: 14.3 → 0.1
Time: 13.6s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{\frac{x + 1}{1}}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{\frac{x + 1}{1}}}{x}
double f(double x) {
        double r22563 = 1.0;
        double r22564 = x;
        double r22565 = r22564 + r22563;
        double r22566 = r22563 / r22565;
        double r22567 = r22563 / r22564;
        double r22568 = r22566 - r22567;
        return r22568;
}
↓
double f(double x) {
        double r22569 = 1.0;
        double r22570 = -r22569;
        double r22571 = x;
        double r22572 = r22571 + r22569;
        double r22573 = r22572 / r22569;
        double r22574 = r22570 / r22573;
        double r22575 = r22574 / r22571;
        return r22575;
}

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. Simplified13.7

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

  6. Applied associate-/r*13.7

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

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