Average Error: 14.7 → 0.1
Time: 10.8s
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 r1164896 = 1.0;
        double r1164897 = x;
        double r1164898 = r1164897 + r1164896;
        double r1164899 = r1164896 / r1164898;
        double r1164900 = r1164896 / r1164897;
        double r1164901 = r1164899 - r1164900;
        return r1164901;
}
↓
double f(double x) {
        double r1164902 = -1.0;
        double r1164903 = x;
        double r1164904 = 1.0;
        double r1164905 = r1164903 + r1164904;
        double r1164906 = r1164902 / r1164905;
        double r1164907 = r1164906 / r1164903;
        return r1164907;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

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

  3. Applied frac-sub14.1

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

  4. Simplified14.1

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

  6. Applied associate-/r*14.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019153 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))