Error

Target

Derivation

1. Initial program 29.8

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

3. Applied flip--30.1

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

4. Applied simplify14.3

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

6. Applied *-un-lft-identity14.3

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

7. Applied *-un-lft-identity14.3

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

8. Applied times-frac14.3

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

9. Applied simplify14.3

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

10. Applied simplify0.5

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

12. Applied simplify0.5

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

Runtime

Time bar (total: 21.1s)Debug log

herbie shell --seed '#(633950927 2092594946 1442981 2827247922 2812758452 390991499)' 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 1

  :herbie-target
  (tan (/ x 2))

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