Average Error: 14.2 → 0.1
Time: 6.7s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{x + 1}}{x}
double f(double x) {
        double r890162 = 1.0;
        double r890163 = x;
        double r890164 = r890163 + r890162;
        double r890165 = r890162 / r890164;
        double r890166 = r890162 / r890163;
        double r890167 = r890165 - r890166;
        return r890167;
}
↓
double f(double x) {
        double r890168 = -1.0;
        double r890169 = x;
        double r890170 = 1.0;
        double r890171 = r890169 + r890170;
        double r890172 = r890168 / r890171;
        double r890173 = r890172 / r890169;
        return r890173;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.2

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  2. Using strategy rm

  3. Applied frac-sub13.5

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

  4. Simplified13.5

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

  6. Applied associate-/r*13.5

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019156 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))