Average Error: 14.1 → 0.1
Time: 2.4s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{1}{x + 1} \cdot \frac{0 - 1}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{1}{x + 1} \cdot \frac{0 - 1}{x}
double f(double x) {
        double r27697 = 1.0;
        double r27698 = x;
        double r27699 = r27698 + r27697;
        double r27700 = r27697 / r27699;
        double r27701 = r27697 / r27698;
        double r27702 = r27700 - r27701;
        return r27702;
}
↓
double f(double x) {
        double r27703 = 1.0;
        double r27704 = x;
        double r27705 = r27704 + r27703;
        double r27706 = r27703 / r27705;
        double r27707 = 0.0;
        double r27708 = r27707 - r27703;
        double r27709 = r27708 / r27704;
        double r27710 = r27706 * r27709;
        return r27710;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.1

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

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

  6. Applied times-frac13.6

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

  7. Simplified0.1

    \[\leadsto \frac{1}{x + 1} \cdot \color{blue}{\frac{0 - 1}{x}}\]

  8. Final simplification0.1

    \[\leadsto \frac{1}{x + 1} \cdot \frac{0 - 1}{x}\]

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))