Average Error: 14.9 → 0.1
Time: 5.9s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{1}{x + 1} \cdot \left(-1\right)}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{1}{x + 1} \cdot \left(-1\right)}{x}
double f(double x) {
        double r48752 = 1.0;
        double r48753 = x;
        double r48754 = r48753 + r48752;
        double r48755 = r48752 / r48754;
        double r48756 = r48752 / r48753;
        double r48757 = r48755 - r48756;
        return r48757;
}
↓
double f(double x) {
        double r48758 = 1.0;
        double r48759 = x;
        double r48760 = r48759 + r48758;
        double r48761 = r48758 / r48760;
        double r48762 = -r48758;
        double r48763 = r48761 * r48762;
        double r48764 = r48763 / r48759;
        return r48764;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.9

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  2. Using strategy rm

  3. Applied frac-sub14.2

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

  4. Simplified14.2

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

  6. Applied associate-/r*14.3

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))