Average Error: 14.0 → 0.4
Time: 12.0s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{-1}{x + x \cdot x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{-1}{x + x \cdot x}
double f(double x) {
        double r2225644 = 1.0;
        double r2225645 = x;
        double r2225646 = r2225645 + r2225644;
        double r2225647 = r2225644 / r2225646;
        double r2225648 = r2225644 / r2225645;
        double r2225649 = r2225647 - r2225648;
        return r2225649;
}
↓
double f(double x) {
        double r2225650 = -1.0;
        double r2225651 = x;
        double r2225652 = r2225651 * r2225651;
        double r2225653 = r2225651 + r2225652;
        double r2225654 = r2225650 / r2225653;
        return r2225654;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.0

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

  3. Applied frac-sub13.4

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

  4. Simplified0.4

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

  6. Applied neg-mul-10.4

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

  7. Applied associate-/l*0.4

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

  8. Simplified0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019134 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))