Average Error: 14.8 → 0.1
Time: 48.2s
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 r3018090 = 1.0;
        double r3018091 = x;
        double r3018092 = r3018091 + r3018090;
        double r3018093 = r3018090 / r3018092;
        double r3018094 = r3018090 / r3018091;
        double r3018095 = r3018093 - r3018094;
        return r3018095;
}
↓
double f(double x) {
        double r3018096 = 1.0;
        double r3018097 = -r3018096;
        double r3018098 = x;
        double r3018099 = r3018098 + r3018096;
        double r3018100 = r3018097 / r3018099;
        double r3018101 = r3018100 / r3018098;
        return r3018101;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  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. Taylor expanded around 0 0.4

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))