Average Error: 14.7 → 0.1
Time: 15.3s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1 \cdot 1}{1 + x}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1 \cdot 1}{1 + x}}{x}
double f(double x) {
        double r35571 = 1.0;
        double r35572 = x;
        double r35573 = r35572 + r35571;
        double r35574 = r35571 / r35573;
        double r35575 = r35571 / r35572;
        double r35576 = r35574 - r35575;
        return r35576;
}
↓
double f(double x) {
        double r35577 = 1.0;
        double r35578 = r35577 * r35577;
        double r35579 = -r35578;
        double r35580 = x;
        double r35581 = r35577 + r35580;
        double r35582 = r35579 / r35581;
        double r35583 = r35582 / r35580;
        return r35583;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

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

  3. Applied frac-sub14.1

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

  4. Simplified0.4

    \[\leadsto \frac{\color{blue}{0 - 1 \cdot 1}}{\left(x + 1\right) \cdot x}\]
  5. Using strategy rm

  6. Applied associate-/r*0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))