Average Error: 14.2 → 0.1
Time: 2.6s
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 r50965 = 1.0;
        double r50966 = x;
        double r50967 = r50966 + r50965;
        double r50968 = r50965 / r50967;
        double r50969 = r50965 / r50966;
        double r50970 = r50968 - r50969;
        return r50970;
}
↓
double f(double x) {
        double r50971 = 1.0;
        double r50972 = x;
        double r50973 = r50972 + r50971;
        double r50974 = r50971 / r50973;
        double r50975 = 0.0;
        double r50976 = r50975 - r50971;
        double r50977 = r50976 / r50972;
        double r50978 = r50974 * r50977;
        return r50978;
}

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-sub13.6

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

  4. Simplified13.6

    \[\leadsto \frac{\color{blue}{1 \cdot \left(x - \left(x + 1\right)\right)}}{\left(x + 1\right) \cdot x}\]
  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 2019353 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))