Error

Target

Derivation

1. Initial program 30.3

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

3. Applied flip-- 30.5

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

4. Applied simplify 14.8

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

6. Applied *-un-lft-identity 14.8

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

7. Applied *-un-lft-identity 14.8

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

8. Applied times-frac 14.8

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

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

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

Runtime

Total time: 26.0s Debug log

Please report a bug with the following info:

herbie --seed '#(3355518702 3082089176 1536034797 3965119955 3471441782 1219187475)'
(FPCore (x)
  :name "NMSE example 3.4"
  :herbie-expected 1

  :target
  (tan (/ x 2))

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