Average Error: 14.5 → 0.1
Time: 13.3s
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 r2702332 = 1.0;
        double r2702333 = x;
        double r2702334 = r2702333 + r2702332;
        double r2702335 = r2702332 / r2702334;
        double r2702336 = r2702332 / r2702333;
        double r2702337 = r2702335 - r2702336;
        return r2702337;
}
↓
double f(double x) {
        double r2702338 = -1.0;
        double r2702339 = x;
        double r2702340 = 1.0;
        double r2702341 = r2702339 + r2702340;
        double r2702342 = r2702338 / r2702341;
        double r2702343 = r2702342 / r2702339;
        return r2702343;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  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. Simplified0.4

    \[\leadsto \frac{\color{blue}{-1}}{\left(x + 1\right) \cdot x}\]
  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 2019158 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))