Average Error: 14.6 → 0.1
Time: 13.1s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{1}{1 + x}}{-x} \cdot 1\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{1}{1 + x}}{-x} \cdot 1
double f(double x) {
        double r33778 = 1.0;
        double r33779 = x;
        double r33780 = r33779 + r33778;
        double r33781 = r33778 / r33780;
        double r33782 = r33778 / r33779;
        double r33783 = r33781 - r33782;
        return r33783;
}
↓
double f(double x) {
        double r33784 = 1.0;
        double r33785 = x;
        double r33786 = r33784 + r33785;
        double r33787 = r33784 / r33786;
        double r33788 = -r33785;
        double r33789 = r33787 / r33788;
        double r33790 = r33789 * r33784;
        return r33790;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.6

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

  3. Applied frac-sub14.1

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

  4. Simplified14.1

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

  5. Simplified14.1

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

  7. Applied frac-2neg14.1

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

  8. Simplified0.4

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

  9. Simplified0.4

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

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

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

  12. Applied times-frac0.4

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

  13. Simplified0.4

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

  14. Simplified0.1

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

  15. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))