Average Error: 14.1 → 0.1
Time: 2.2s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{1}{x + 1} \cdot \frac{0 - 1}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{1}{x + 1} \cdot \frac{0 - 1}{x}
double f(double x) {
        double r33036 = 1.0;
        double r33037 = x;
        double r33038 = r33037 + r33036;
        double r33039 = r33036 / r33038;
        double r33040 = r33036 / r33037;
        double r33041 = r33039 - r33040;
        return r33041;
}
↓
double f(double x) {
        double r33042 = 1.0;
        double r33043 = x;
        double r33044 = r33043 + r33042;
        double r33045 = r33042 / r33044;
        double r33046 = 0.0;
        double r33047 = r33046 - r33042;
        double r33048 = r33047 / r33043;
        double r33049 = r33045 * r33048;
        return r33049;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.1

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  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. Simplified13.5

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

  6. Applied times-frac13.6

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

  7. Simplified0.1

    \[\leadsto \frac{1}{x + 1} \cdot \color{blue}{\frac{0 - 1}{x}}\]

  8. Final simplification0.1

    \[\leadsto \frac{1}{x + 1} \cdot \frac{0 - 1}{x}\]

Reproduce

herbie shell --seed 2019347 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))