Average Error: 14.5 → 0.1
Time: 14.1s
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 r3374528 = 1.0;
        double r3374529 = x;
        double r3374530 = r3374529 + r3374528;
        double r3374531 = r3374528 / r3374530;
        double r3374532 = r3374528 / r3374529;
        double r3374533 = r3374531 - r3374532;
        return r3374533;
}
↓
double f(double x) {
        double r3374534 = 1.0;
        double r3374535 = -r3374534;
        double r3374536 = x;
        double r3374537 = r3374534 + r3374536;
        double r3374538 = r3374535 / r3374537;
        double r3374539 = r3374538 / r3374536;
        return r3374539;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

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

  3. Applied frac-sub13.9

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

  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 2019169 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))