Average Error: 14.2 → 0.1
Time: 20.0s
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 r1066799 = 1.0;
        double r1066800 = x;
        double r1066801 = r1066800 + r1066799;
        double r1066802 = r1066799 / r1066801;
        double r1066803 = r1066799 / r1066800;
        double r1066804 = r1066802 - r1066803;
        return r1066804;
}
↓
double f(double x) {
        double r1066805 = -1.0;
        double r1066806 = x;
        double r1066807 = 1.0;
        double r1066808 = r1066806 + r1066807;
        double r1066809 = r1066805 / r1066808;
        double r1066810 = r1066809 / r1066806;
        return r1066810;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.2

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  2. Using strategy rm

  3. Applied frac-sub13.5

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

  4. Simplified0.4

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

  5. Simplified0.4

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

  7. Applied distribute-rgt1-in0.4

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

  8. Applied associate-/r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019151 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))