Average Error: 14.4 → 0.1
Time: 12.6s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{x + 1}}{x}
double f(double x) {
        double r5886512 = 1.0;
        double r5886513 = x;
        double r5886514 = r5886513 + r5886512;
        double r5886515 = r5886512 / r5886514;
        double r5886516 = r5886512 / r5886513;
        double r5886517 = r5886515 - r5886516;
        return r5886517;
}
↓
double f(double x) {
        double r5886518 = 1.0;
        double r5886519 = -r5886518;
        double r5886520 = x;
        double r5886521 = r5886520 + r5886518;
        double r5886522 = r5886519 / r5886521;
        double r5886523 = r5886522 / r5886520;
        return r5886523;
}

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-sub13.7

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

  4. Taylor expanded around 0 0.4

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019173 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))