Error

Target

Derivation

1. Initial program 29.8

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

3. Applied flip-- 30.0

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

4. Applied simplify 14.3

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

6. Applied *-un-lft-identity 14.3

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

7. Applied *-un-lft-identity 14.3

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

8. Applied times-frac 14.2

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

9. Applied times-frac 0.5

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

10. Applied simplify 0.5

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

11. Applied simplify 0.5

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

Runtime

Time bar (total: 12.8s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1067773715 2765207660 218871639 3688798924 2755544087 2054563380)'
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 1

  :target
  (tan (/ x 2))

  (/ (- 1 (cos x)) (sin x)))