Average Error: 14.3 → 0.1
Time: 10.7s
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 r2475018 = 1.0;
        double r2475019 = x;
        double r2475020 = r2475019 + r2475018;
        double r2475021 = r2475018 / r2475020;
        double r2475022 = r2475018 / r2475019;
        double r2475023 = r2475021 - r2475022;
        return r2475023;
}
↓
double f(double x) {
        double r2475024 = -1.0;
        double r2475025 = 1.0;
        double r2475026 = x;
        double r2475027 = r2475025 + r2475026;
        double r2475028 = r2475024 / r2475027;
        double r2475029 = r2475028 / r2475026;
        return r2475029;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.3

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  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. Simplified13.7

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

  6. Applied associate-/r*13.7

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

  7. Simplified0.1

    \[\leadsto \frac{\color{blue}{\frac{0 - 1}{1 + x}}}{x}\]

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))