Average Error: 14.1 → 0.1
Time: 12.6s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{1 \cdot 1}{x} \cdot \frac{-1}{x + 1}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{1 \cdot 1}{x} \cdot \frac{-1}{x + 1}
double f(double x) {
        double r30794 = 1.0;
        double r30795 = x;
        double r30796 = r30795 + r30794;
        double r30797 = r30794 / r30796;
        double r30798 = r30794 / r30795;
        double r30799 = r30797 - r30798;
        return r30799;
}
↓
double f(double x) {
        double r30800 = 1.0;
        double r30801 = r30800 * r30800;
        double r30802 = x;
        double r30803 = r30801 / r30802;
        double r30804 = -1.0;
        double r30805 = r30802 + r30800;
        double r30806 = r30804 / r30805;
        double r30807 = r30803 * r30806;
        return r30807;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.1

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

  3. Applied frac-sub13.5

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

  4. Simplified0.4

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

  6. Applied *-un-lft-identity0.4

    \[\leadsto \frac{\color{blue}{1 \cdot \left(0 - 1 \cdot 1\right)}}{\left(x + 1\right) \cdot x}\]

  7. Applied times-frac0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))