Average Error: 14.7 → 0.1
Time: 23.3s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{1 + x}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{1 + x}}{x}
double f(double x) {
        double r3787334 = 1.0;
        double r3787335 = x;
        double r3787336 = r3787335 + r3787334;
        double r3787337 = r3787334 / r3787336;
        double r3787338 = r3787334 / r3787335;
        double r3787339 = r3787337 - r3787338;
        return r3787339;
}
↓
double f(double x) {
        double r3787340 = 1.0;
        double r3787341 = -r3787340;
        double r3787342 = x;
        double r3787343 = r3787340 + r3787342;
        double r3787344 = r3787341 / r3787343;
        double r3787345 = r3787344 / r3787342;
        return r3787345;
}

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. 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

    \[\leadsto \frac{\frac{-1}{1 + x}}{x}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))