Average Error: 14.8 → 0.1
Time: 11.1s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{1 \cdot 1}{-\left(x + 1\right)}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{1 \cdot 1}{-\left(x + 1\right)}}{x}
double f(double x) {
        double r4282247 = 1.0;
        double r4282248 = x;
        double r4282249 = r4282248 + r4282247;
        double r4282250 = r4282247 / r4282249;
        double r4282251 = r4282247 / r4282248;
        double r4282252 = r4282250 - r4282251;
        return r4282252;
}
↓
double f(double x) {
        double r4282253 = 1.0;
        double r4282254 = r4282253 * r4282253;
        double r4282255 = x;
        double r4282256 = r4282255 + r4282253;
        double r4282257 = -r4282256;
        double r4282258 = r4282254 / r4282257;
        double r4282259 = r4282258 / r4282255;
        return r4282259;
}

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. Using strategy rm

  6. Applied frac-2neg14.2

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

  7. Simplified0.4

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

  9. Applied distribute-lft-neg-in0.4

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

  10. Applied associate-/r*0.1

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

  11. Final simplification0.1

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

Reproduce

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