Average Error: 14.5 → 0.1
Time: 15.4s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{x}}{x + 1}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{x}}{x + 1}
double f(double x) {
        double r2768949 = 1.0;
        double r2768950 = x;
        double r2768951 = r2768950 + r2768949;
        double r2768952 = r2768949 / r2768951;
        double r2768953 = r2768949 / r2768950;
        double r2768954 = r2768952 - r2768953;
        return r2768954;
}
↓
double f(double x) {
        double r2768955 = -1.0;
        double r2768956 = x;
        double r2768957 = r2768955 / r2768956;
        double r2768958 = 1.0;
        double r2768959 = r2768956 + r2768958;
        double r2768960 = r2768957 / r2768959;
        return r2768960;
}

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 *-commutative13.8

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

  7. Applied associate-/r*13.8

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

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