Average Error: 14.7 → 0.1
Time: 13.5s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{\frac{x + 1}{1}}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{\frac{x + 1}{1}}}{x}
double f(double x) {
        double r56502 = 1.0;
        double r56503 = x;
        double r56504 = r56503 + r56502;
        double r56505 = r56502 / r56504;
        double r56506 = r56502 / r56503;
        double r56507 = r56505 - r56506;
        return r56507;
}
↓
double f(double x) {
        double r56508 = 1.0;
        double r56509 = -r56508;
        double r56510 = x;
        double r56511 = r56510 + r56508;
        double r56512 = r56511 / r56508;
        double r56513 = r56509 / r56512;
        double r56514 = r56513 / r56510;
        return r56514;
}

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. Simplified14.1

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

  6. Applied associate-/r*14.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))