Average Error: 14.3 → 0.1
Time: 14.0s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{x + 1}}{x}
double f(double x) {
        double r1800816 = 1.0;
        double r1800817 = x;
        double r1800818 = r1800817 + r1800816;
        double r1800819 = r1800816 / r1800818;
        double r1800820 = r1800816 / r1800817;
        double r1800821 = r1800819 - r1800820;
        return r1800821;
}
↓
double f(double x) {
        double r1800822 = -1.0;
        double r1800823 = x;
        double r1800824 = 1.0;
        double r1800825 = r1800823 + r1800824;
        double r1800826 = r1800822 / r1800825;
        double r1800827 = r1800826 / r1800823;
        return r1800827;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.3

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

  3. Applied frac-sub13.8

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

  4. Simplified0.4

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

  5. Simplified0.4

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

  7. Applied distribute-rgt1-in0.4

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

  8. Applied associate-/r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019130 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))