Average Error: 14.5 → 0.1
Time: 14.9s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{x + 1}}{x}
double f(double x) {
        double r1875800 = 1.0;
        double r1875801 = x;
        double r1875802 = r1875801 + r1875800;
        double r1875803 = r1875800 / r1875802;
        double r1875804 = r1875800 / r1875801;
        double r1875805 = r1875803 - r1875804;
        return r1875805;
}
↓
double f(double x) {
        double r1875806 = -1.0;
        double r1875807 = x;
        double r1875808 = 1.0;
        double r1875809 = r1875807 + r1875808;
        double r1875810 = r1875806 / r1875809;
        double r1875811 = r1875810 / r1875807;
        return r1875811;
}

Error

Bits error versus x

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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

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

  5. Taylor expanded around 0 0.4

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

  7. Applied associate-/r*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))