Average Error: 14.7 → 0.1
Time: 12.7s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{1 \cdot \left(-1\right)}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{1 \cdot \left(-1\right)}{x + 1}}{x}
double f(double x) {
        double r3041609 = 1.0;
        double r3041610 = x;
        double r3041611 = r3041610 + r3041609;
        double r3041612 = r3041609 / r3041611;
        double r3041613 = r3041609 / r3041610;
        double r3041614 = r3041612 - r3041613;
        return r3041614;
}
↓
double f(double x) {
        double r3041615 = 1.0;
        double r3041616 = -r3041615;
        double r3041617 = r3041615 * r3041616;
        double r3041618 = x;
        double r3041619 = r3041618 + r3041615;
        double r3041620 = r3041617 / r3041619;
        double r3041621 = r3041620 / r3041618;
        return r3041621;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  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. Simplified0.3

    \[\leadsto \frac{\color{blue}{1 \cdot \left(0 - 1\right)}}{\left(x + 1\right) \cdot x}\]
  5. Using strategy rm

  6. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{1 \cdot \left(0 - 1\right)}{x + 1}}{x}}\]

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))