Error

Derivation

1. Initial program 0.1

   \[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]

2. Simplified0.1

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

4. Applied *-un-lft-identity0.1

   \[\leadsto \frac{\color{blue}{1 \cdot (\left(\frac{t \cdot 2}{1 + t}\right) \cdot \left(\frac{t \cdot 2}{1 + t}\right) + 1)_*}}{(\left(\frac{t \cdot 2}{1 + t}\right) \cdot \left(\frac{t \cdot 2}{1 + t}\right) + 2)_*}\]

5. Applied associate-/l*0.1

   \[\leadsto \color{blue}{\frac{1}{\frac{(\left(\frac{t \cdot 2}{1 + t}\right) \cdot \left(\frac{t \cdot 2}{1 + t}\right) + 2)_*}{(\left(\frac{t \cdot 2}{1 + t}\right) \cdot \left(\frac{t \cdot 2}{1 + t}\right) + 1)_*}}}\]

6. Final simplification0.1

   \[\leadsto \frac{1}{\frac{(\left(\frac{2 \cdot t}{t + 1}\right) \cdot \left(\frac{2 \cdot t}{t + 1}\right) + 2)_*}{(\left(\frac{2 \cdot t}{t + 1}\right) \cdot \left(\frac{2 \cdot t}{t + 1}\right) + 1)_*}}\]

Reproduce

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

Details

Time bar (total: 43.3s)Debug log