Average Error: 14.4 → 0.1
Time: 13.1s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1 \cdot 1}{1 + x}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1 \cdot 1}{1 + x}}{x}
double f(double x) {
        double r35414 = 1.0;
        double r35415 = x;
        double r35416 = r35415 + r35414;
        double r35417 = r35414 / r35416;
        double r35418 = r35414 / r35415;
        double r35419 = r35417 - r35418;
        return r35419;
}
↓
double f(double x) {
        double r35420 = 1.0;
        double r35421 = r35420 * r35420;
        double r35422 = -r35421;
        double r35423 = x;
        double r35424 = r35420 + r35423;
        double r35425 = r35422 / r35424;
        double r35426 = r35425 / r35423;
        return r35426;
}

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. Simplified0.4

    \[\leadsto \frac{\color{blue}{0 - 1 \cdot 1}}{\left(x + 1\right) \cdot x}\]
  5. Using strategy rm

  6. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{0 - 1 \cdot 1}{x + 1}}{x}}\]

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))