Average Error: 14.8 → 0.1
Time: 4.0s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{\left(0 - 1\right) \cdot 1}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{\left(0 - 1\right) \cdot 1}{x + 1}}{x}
double f(double x) {
        double r36255 = 1.0;
        double r36256 = x;
        double r36257 = r36256 + r36255;
        double r36258 = r36255 / r36257;
        double r36259 = r36255 / r36256;
        double r36260 = r36258 - r36259;
        return r36260;
}
↓
double f(double x) {
        double r36261 = 0.0;
        double r36262 = 1.0;
        double r36263 = r36261 - r36262;
        double r36264 = r36263 * r36262;
        double r36265 = x;
        double r36266 = r36265 + r36262;
        double r36267 = r36264 / r36266;
        double r36268 = r36267 / r36265;
        return r36268;
}

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-sub14.0

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

  4. Simplified0.5

    \[\leadsto \frac{\color{blue}{\left(0 - 1\right) \cdot 1}}{\left(x + 1\right) \cdot x}\]
  5. Using strategy rm

  6. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{\left(0 - 1\right) \cdot 1}{x + 1}}{x}}\]

  7. Final simplification0.1

    \[\leadsto \frac{\frac{\left(0 - 1\right) \cdot 1}{x + 1}}{x}\]

Reproduce

herbie shell --seed 197574269 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))