Error

Derivation

1. Initial program 31.1

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

3. Applied flip-- 31.2

   \[\leadsto \frac{\color{blue}{\frac{{1}^2 - {\left(\cos x\right)}^2}{1 + \cos x}}}{{x}^2}\]

4. Applied simplify 15.6

   \[\leadsto \frac{\frac{\color{blue}{{\left(\sin x\right)}^2}}{1 + \cos x}}{{x}^2}\]
5. Using strategy rm

6. Applied square-mult 15.6

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

7. Applied *-un-lft-identity 15.6

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

8. Applied square-mult 15.6

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

9. Applied times-frac 15.6

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

10. Applied times-frac 0.3

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

11. Applied simplify 0.3

    \[\leadsto \color{blue}{\frac{\sin x}{x}} \cdot \frac{\frac{\sin x}{1 + \cos x}}{x}\]
12. Removed slow pow expressions

Runtime

Time bar (total: 28.1s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(3283856077 3183919125 3399458751 396155847 3688194147 1862413033)'
(FPCore (x)
  :name "cos2 (problem 3.4.1)"
  (/ (- 1 (cos x)) (sqr x)))