Average Error: 14.6 → 0.1
Time: 7.3s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{-1}{x + 1} \cdot \frac{1}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{-1}{x + 1} \cdot \frac{1}{x}
double f(double x) {
        double r840446 = 1.0;
        double r840447 = x;
        double r840448 = r840447 + r840446;
        double r840449 = r840446 / r840448;
        double r840450 = r840446 / r840447;
        double r840451 = r840449 - r840450;
        return r840451;
}
↓
double f(double x) {
        double r840452 = -1.0;
        double r840453 = x;
        double r840454 = 1.0;
        double r840455 = r840453 + r840454;
        double r840456 = r840452 / r840455;
        double r840457 = r840454 / r840453;
        double r840458 = r840456 * r840457;
        return r840458;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.6

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

  3. Applied frac-sub14.0

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

  4. Simplified14.0

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

  6. Applied associate-/r*14.0

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

  7. Simplified0.1

    \[\leadsto \frac{\color{blue}{\frac{-1}{x + 1}}}{x}\]
  8. Using strategy rm

  9. Applied div-inv0.1

    \[\leadsto \color{blue}{\frac{-1}{x + 1} \cdot \frac{1}{x}}\]

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019128 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))