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Derivation

1. Initial program 31.0

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

3. Applied flip--31.1

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

4. Applied simplify15.4

   \[\leadsto \frac{\frac{\color{blue}{\sin x \cdot \sin x}}{1 + \cos x}}{x \cdot x}\]
5. Using strategy rm

6. Applied *-un-lft-identity15.4

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

7. Applied times-frac15.2

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

8. Applied simplify0.2

   \[\leadsto \frac{1}{x} \cdot \color{blue}{\left(\tan \left(\frac{x}{2}\right) \cdot \frac{\sin x}{x}\right)}\]

Runtime

Time bar (total: 50.7s)Debug logProfile

herbie shell --seed 2018195 
(FPCore (x)
  :name "cos2 (problem 3.4.1)"
  (/ (- 1 (cos x)) (* x x)))