Average Error: 14.8 → 0.1
Time: 17.2s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1 \cdot 1}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1 \cdot 1}{x + 1}}{x}
double f(double x) {
        double r42335 = 1.0;
        double r42336 = x;
        double r42337 = r42336 + r42335;
        double r42338 = r42335 / r42337;
        double r42339 = r42335 / r42336;
        double r42340 = r42338 - r42339;
        return r42340;
}
↓
double f(double x) {
        double r42341 = 1.0;
        double r42342 = r42341 * r42341;
        double r42343 = -r42342;
        double r42344 = x;
        double r42345 = r42344 + r42341;
        double r42346 = r42343 / r42345;
        double r42347 = r42346 / r42344;
        return r42347;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

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

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019322 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))