Average Error: 14.4 → 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 r3196670 = 1.0;
        double r3196671 = x;
        double r3196672 = r3196671 + r3196670;
        double r3196673 = r3196670 / r3196672;
        double r3196674 = r3196670 / r3196671;
        double r3196675 = r3196673 - r3196674;
        return r3196675;
}
↓
double f(double x) {
        double r3196676 = 1.0;
        double r3196677 = r3196676 * r3196676;
        double r3196678 = x;
        double r3196679 = r3196676 + r3196678;
        double r3196680 = r3196677 / r3196679;
        double r3196681 = -r3196678;
        double r3196682 = r3196680 / r3196681;
        return r3196682;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.4

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

  3. Applied frac-sub13.8

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

  4. Simplified13.8

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

  6. Applied frac-2neg13.8

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

  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 2019171 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))