Average Error: 14.4 → 0.1
Time: 13.3s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{1 + x}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{1 + x}}{x}
double f(double x) {
        double r2867420 = 1.0;
        double r2867421 = x;
        double r2867422 = r2867421 + r2867420;
        double r2867423 = r2867420 / r2867422;
        double r2867424 = r2867420 / r2867421;
        double r2867425 = r2867423 - r2867424;
        return r2867425;
}
↓
double f(double x) {
        double r2867426 = 1.0;
        double r2867427 = -r2867426;
        double r2867428 = x;
        double r2867429 = r2867426 + r2867428;
        double r2867430 = r2867427 / r2867429;
        double r2867431 = r2867430 / r2867428;
        return r2867431;
}

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. 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

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))