Average Error: 14.3 → 0.1
Time: 11.1s
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 r2400573 = 1.0;
        double r2400574 = x;
        double r2400575 = r2400574 + r2400573;
        double r2400576 = r2400573 / r2400575;
        double r2400577 = r2400573 / r2400574;
        double r2400578 = r2400576 - r2400577;
        return r2400578;
}
↓
double f(double x) {
        double r2400579 = 1.0;
        double r2400580 = r2400579 * r2400579;
        double r2400581 = x;
        double r2400582 = r2400579 + r2400581;
        double r2400583 = r2400580 / r2400582;
        double r2400584 = -r2400581;
        double r2400585 = r2400583 / r2400584;
        return r2400585;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.3

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  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 frac-2neg13.7

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

  7. Simplified0.4

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

  9. Applied distribute-rgt-neg-in0.4

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

  10. Applied associate-/r*0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))