Average Error: 14.2 → 0.1
Time: 2.5s
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 r28669 = 1.0;
        double r28670 = x;
        double r28671 = r28670 + r28669;
        double r28672 = r28669 / r28671;
        double r28673 = r28669 / r28670;
        double r28674 = r28672 - r28673;
        return r28674;
}
↓
double f(double x) {
        double r28675 = 1.0;
        double r28676 = x;
        double r28677 = r28676 + r28675;
        double r28678 = r28675 / r28677;
        double r28679 = 0.0;
        double r28680 = r28679 - r28675;
        double r28681 = r28680 / r28676;
        double r28682 = r28678 * r28681;
        return r28682;
}

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-sub13.6

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

  4. Simplified13.6

    \[\leadsto \frac{\color{blue}{1 \cdot \left(x - \left(x + 1\right)\right)}}{\left(x + 1\right) \cdot x}\]
  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 2019353 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))