Average Error: 14.4 → 0.1
Time: 12.8s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{x}}{x + 1}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{x}}{x + 1}
double f(double x) {
        double r1467626 = 1.0;
        double r1467627 = x;
        double r1467628 = r1467627 + r1467626;
        double r1467629 = r1467626 / r1467628;
        double r1467630 = r1467626 / r1467627;
        double r1467631 = r1467629 - r1467630;
        return r1467631;
}
↓
double f(double x) {
        double r1467632 = -1.0;
        double r1467633 = x;
        double r1467634 = r1467632 / r1467633;
        double r1467635 = 1.0;
        double r1467636 = r1467633 + r1467635;
        double r1467637 = r1467634 / r1467636;
        return r1467637;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.4

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  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 *-un-lft-identity0.4

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

  8. Applied distribute-rgt-out0.4

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

  9. Applied associate-/r*0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019141 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))