Average Error: 14.4 → 0.1
Time: 11.8s
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 r3317204 = 1.0;
        double r3317205 = x;
        double r3317206 = r3317205 + r3317204;
        double r3317207 = r3317204 / r3317206;
        double r3317208 = r3317204 / r3317205;
        double r3317209 = r3317207 - r3317208;
        return r3317209;
}
↓
double f(double x) {
        double r3317210 = 1.0;
        double r3317211 = -r3317210;
        double r3317212 = x;
        double r3317213 = r3317210 + r3317212;
        double r3317214 = r3317211 / r3317213;
        double r3317215 = r3317214 / r3317212;
        return r3317215;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.4

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

  3. Applied frac-sub13.7

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

  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 2019170 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))