Average Error: 14.8 → 0.1
Time: 10.4s
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 r3290338 = 1.0;
        double r3290339 = x;
        double r3290340 = r3290339 + r3290338;
        double r3290341 = r3290338 / r3290340;
        double r3290342 = r3290338 / r3290339;
        double r3290343 = r3290341 - r3290342;
        return r3290343;
}
↓
double f(double x) {
        double r3290344 = 1.0;
        double r3290345 = -r3290344;
        double r3290346 = r3290344 * r3290345;
        double r3290347 = x;
        double r3290348 = r3290347 + r3290344;
        double r3290349 = r3290346 / r3290348;
        double r3290350 = r3290349 / r3290347;
        return r3290350;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  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. Taylor expanded around 0 0.4

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

  7. Applied associate-/r*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))