Average Error: 14.4 → 0.1
Time: 2.9s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{1}{\frac{x}{\sqrt[3]{0 - 1} \cdot \sqrt[3]{0 - 1}}}}{\frac{x + 1}{\sqrt[3]{0 - 1}}}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{1}{\frac{x}{\sqrt[3]{0 - 1} \cdot \sqrt[3]{0 - 1}}}}{\frac{x + 1}{\sqrt[3]{0 - 1}}}
double f(double x) {
        double r41563 = 1.0;
        double r41564 = x;
        double r41565 = r41564 + r41563;
        double r41566 = r41563 / r41565;
        double r41567 = r41563 / r41564;
        double r41568 = r41566 - r41567;
        return r41568;
}
↓
double f(double x) {
        double r41569 = 1.0;
        double r41570 = x;
        double r41571 = 0.0;
        double r41572 = r41571 - r41569;
        double r41573 = cbrt(r41572);
        double r41574 = r41573 * r41573;
        double r41575 = r41570 / r41574;
        double r41576 = r41569 / r41575;
        double r41577 = r41570 + r41569;
        double r41578 = r41577 / r41573;
        double r41579 = r41576 / r41578;
        return r41579;
}

Error

Bits error versus x

Try it out

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-sub13.7

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

  4. Simplified13.7

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

  6. Applied associate-/r*13.7

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

  7. Simplified0.1

    \[\leadsto \frac{\color{blue}{\frac{1}{\frac{x + 1}{0 - 1}}}}{x}\]
  8. Using strategy rm

  9. Applied div-inv0.1

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

  10. Applied associate-/l*0.4

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

  11. Simplified0.4

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

  13. Applied add-cube-cbrt0.4

    \[\leadsto \frac{1}{\frac{x \cdot \left(x + 1\right)}{\color{blue}{\left(\sqrt[3]{0 - 1} \cdot \sqrt[3]{0 - 1}\right) \cdot \sqrt[3]{0 - 1}}}}\]

  14. Applied times-frac0.4

    \[\leadsto \frac{1}{\color{blue}{\frac{x}{\sqrt[3]{0 - 1} \cdot \sqrt[3]{0 - 1}} \cdot \frac{x + 1}{\sqrt[3]{0 - 1}}}}\]

  15. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{1}{\frac{x}{\sqrt[3]{0 - 1} \cdot \sqrt[3]{0 - 1}}}}{\frac{x + 1}{\sqrt[3]{0 - 1}}}}\]

  16. Final simplification0.1

    \[\leadsto \frac{\frac{1}{\frac{x}{\sqrt[3]{0 - 1} \cdot \sqrt[3]{0 - 1}}}}{\frac{x + 1}{\sqrt[3]{0 - 1}}}\]

Reproduce

herbie shell --seed 2020057 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))