Average Error: 14.5 → 0.1
Time: 11.7s
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 r1148590 = 1.0;
        double r1148591 = x;
        double r1148592 = r1148591 + r1148590;
        double r1148593 = r1148590 / r1148592;
        double r1148594 = r1148590 / r1148591;
        double r1148595 = r1148593 - r1148594;
        return r1148595;
}
↓
double f(double x) {
        double r1148596 = -1.0;
        double r1148597 = 1.0;
        double r1148598 = x;
        double r1148599 = r1148597 + r1148598;
        double r1148600 = r1148596 / r1148599;
        double r1148601 = r1148600 / r1148598;
        return r1148601;
}

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. Simplified13.8

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

  6. Applied associate-/r*13.8

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019155 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))