Average Error: 14.4 → 0.1
Time: 28.9s
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 r58050 = 1.0;
        double r58051 = x;
        double r58052 = r58051 + r58050;
        double r58053 = r58050 / r58052;
        double r58054 = r58050 / r58051;
        double r58055 = r58053 - r58054;
        return r58055;
}
↓
double f(double x) {
        double r58056 = 1.0;
        double r58057 = x;
        double r58058 = r58057 + r58056;
        double r58059 = -r58056;
        double r58060 = r58058 / r58059;
        double r58061 = r58056 / r58060;
        double r58062 = r58061 / r58057;
        return r58062;
}

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. 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 2019199 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))