Error

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Derivation

1. Initial program 0.0

   \[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]

2. Simplified0.0

   \[\leadsto \color{blue}{1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}}\]
3. Using strategy rm

4. Applied add-cube-cbrt0.0

   \[\leadsto 1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{2 - \frac{2}{1 + t}} \cdot \sqrt[3]{2 - \frac{2}{1 + t}}\right) \cdot \sqrt[3]{2 - \frac{2}{1 + t}}\right)}}\]

5. Applied associate-*r*0.0

   \[\leadsto 1 - \frac{1}{2 + \color{blue}{\left(\left(2 - \frac{2}{1 + t}\right) \cdot \left(\sqrt[3]{2 - \frac{2}{1 + t}} \cdot \sqrt[3]{2 - \frac{2}{1 + t}}\right)\right) \cdot \sqrt[3]{2 - \frac{2}{1 + t}}}}\]

6. Final simplification0.0

   \[\leadsto 1 - \frac{1}{\sqrt[3]{2 - \frac{2}{1 + t}} \cdot \left(\left(\sqrt[3]{2 - \frac{2}{1 + t}} \cdot \sqrt[3]{2 - \frac{2}{1 + t}}\right) \cdot \left(2 - \frac{2}{1 + t}\right)\right) + 2}\]

Reproduce

herbie shell --seed 2019005 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))

Details

Time bar (total: 16.3s)Debug log