Average Error: 14.5 → 0.1
Time: 12.7s
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 r52991 = 1.0;
        double r52992 = x;
        double r52993 = r52992 + r52991;
        double r52994 = r52991 / r52993;
        double r52995 = r52991 / r52992;
        double r52996 = r52994 - r52995;
        return r52996;
}
↓
double f(double x) {
        double r52997 = 1.0;
        double r52998 = -r52997;
        double r52999 = x;
        double r53000 = r52999 + r52997;
        double r53001 = r52998 / r53000;
        double r53002 = r53001 / r52999;
        return r53002;
}

Error

Bits error versus x

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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-sub13.9

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

  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 2019209 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))